tag:blogger.com,1999:blog-8127943952591736682016-02-04T15:08:58.565-05:00Drawing On MathPonderings of a high school math teacher.Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.comBlogger297125tag:blogger.com,1999:blog-812794395259173668.post-9003885015953765842016-01-17T14:43:00.000-05:002016-01-17T14:46:33.617-05:00Solving One Variable Equations<div class="separator" style="clear: both; text-align: left;">I teach ninth graders who arrive to high school without a solid foundation in all the prerequisite math skills. Sometimes I have to correct firmly held misconceptions - students are <i>sure</i> their teacher last year did it that way. Other times students are equally sure they've never seen a topic before. So when I teach a concept that students may have seen before I aim to be as clear as possible. Many teachers think that the best way to be clear is to provide very detailed step by step directions on how to complete a process. But my version of clear is providing the bare minimum information for students to be successful. After we <a href="http://drawingonmath.blogspot.com/2015/12/visual-equations.html">played with pennies</a>, I boiled that experience down to two pieces of information to solve one variable equations:</div><div class="separator" style="clear: both; text-align: left;"></div><ul><li>Combine like terms</li><li>Use opposite operations</li></ul><br /><div class="separator" style="clear: both; text-align: left;">As I continued, I recognized that students needed a bit more clarity on when to use opposite operations (they were continuing to subtract from the same expression twice) so I modified it to:</div><div class="separator" style="clear: both; text-align: left;"></div><ul><li>Combine like terms</li><li>Use opposite operations when terms are in different expressions</li></ul><br /><div class="separator" style="clear: both; text-align: left;">Now when I encounter a student who is stuck when solving an equation, I ask them "where are your like terms?" If they're in the same expression - combine. If they're in different expressions - combine using opposite operations. If they're inside parentheses or absolute value - uh oh, they're trapped! Then students can either choose a different pair of like terms or apply knowledge of the distributive property, definition of absolute value, etc. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Limiting my instructions to two items means students have a chance of remembering them. It means students learn to make choices: some kids like have the variable on the left side - go for it! Some kids want to combine all like terms within an expression first - awesome! Some kids don't think ahead and move terms back and forth across the equal sign several times - you're making progress! It's really important to me to value all my students ideas. Later in the unit I might stop a kid and say - you're moving all the numbers to the same expression as the variable, it's legal algebra but it's not the fastest way to get there. But at the beginning? Yes! That's a great idea! Well done recognizing like terms!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">When we get to inequalities - same rules and one additional note on how to shade. When we get to equations in more than one variable - same rules and a note that an expression is a valid answer. By giving students the bare necessities I'm making it easier to see the connections. It still takes an awful lot of practice and some students struggle at first with paralysis of choice - it really doesn't matter whether I combine the numbers or variables first?? - but it's important for them to start making some decisions as early as possible so they aren't entirely paralyzed when they reach trig identities and the only way to solve them is just trying a substitution to see what works.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://exploremtbos.wordpress.com/"><img border="0" height="178" src="http://3.bp.blogspot.com/-tt3dDdum85c/Vpvn2witFGI/AAAAAAAALhQ/72IsFHw1xeU/s320/MyFav.JPG" width="320" /></a></div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-77322970713302926982016-01-13T22:20:00.000-05:002016-01-13T22:20:17.386-05:00A Day in the Life, Teaching Math to Students with Disabilities<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-aVQFKoqQaEc/VpcPJGZfQcI/AAAAAAAALg0/j-JwKlLVg6s/s1600/2016-01-13%2B07.16.57.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="http://4.bp.blogspot.com/-aVQFKoqQaEc/VpcPJGZfQcI/AAAAAAAALg0/j-JwKlLVg6s/s200/2016-01-13%2B07.16.57.jpg" width="200" /></a></div>I arrived at my classroom at 7:12 on the dot this morning. That’s the official teacher start time. Sunrise was at 7:11 this morning and I firmly believe that I should not have to rise earlier than the sun so I'm obviously not one to arrive early for school. I smile to see the identity proofs still on the board that my students worked on after school yesterday. Turned on my computer and checked a few emails before the bell rang at 7:24. One of those emails was a request to meet first block today so I checked in with the Algebra team, discovered they were not quite ready to start and figured I could go find out exactly what this somewhat vague string of emails had been about. <br /><br />It turned out that there is a student in our alternative program which runs in the building who is really struggling with geometry. He has some substantial learning disabilities and the special education teacher working with him needed help figuring out how to modify the curriculum for him. We discussed his goals and history (he’s a junior who hasn’t passed the sophomore state test which he needs to graduate) and then I was able to make some recommendations. I shared the materials that I used with the contained math class (students with substantial learning disabilities where the state test was a major hurdle) as well as the materials that I used with my inclusion geometry classes (students with moderate learning disabilities). Dropbox for work files is really the best thing ever, I can send anyone an entire year’s worth of materials organized into units with the push of a button! However, an entire year’s worth of materials is overwhelming so I got her started with some specific tasks to do and ended with an invitation to email any time and an offer to meet again. I enjoy being at the point where I’ve been in a school long enough that teachers in another program know that I would be a useful resource for the particular problem they are facing. I was especially glad they called because the poor special ed teacher was trying to write all the lessons herself – way too much work!<br /><br />At 8:10 I make it back to the team meeting. They’ve been planning out the rest of our unit on linear functions. We were problem solving how to help students who are struggling with substituting values into equations (to fill in a table or find intercepts) and I suggested <a href="http://cheesemonkeysf.blogspot.com/2013/05/substitution-with-stars.html">Elizabeth’s star method</a>. We joked/bemoaned that students would end up with two digit numbers if x has a coefficient (2x where x=4 becomes 24) and another teacher said that she requires them to always substitute using parentheses. I had this moment of shock – I did that when we were studying function notation but somehow dropped the parentheses in the intervening months and forgot about them entirely. This is why team time is so great, we can bring something we’re struggling with in our own classroom, share ideas and get new ones or a reminder of something we’ve used in the past. Conversation about the unit wraps up around 8:40 when my co-teacher arrives and I take the opportunity to check in with her for a bit. Then I overhear another coworker mention his upcoming wedding – he got engaged over the summer without telling anyone! It’s January and we have classrooms with an adjoining door and talk every day and I somehow didn’t know this. So I demanded that story and we were all properly excited for him. <br /><br />8:55 the bell rings. First block is over. A special ed teacher on the algebra team asks me about one of my students on his case load. We discuss his behavior and disability and what to do about his low grades. He's showing some initiative coming after school lately so hopefully that's a trend which will continue! Second block there’s a class in my room (I have a set of iPads in there so they use my room rather than their own room down the hall) so I grab my bags and head down to the library. I pick up a form from the office on the way (professional day request so I can attend an NCTM resources committee meeting in February), make some copies and finish processing my email. At 9:30 I switch over to planning. At 9:55 I transition to grading. I love block scheduling because I can have a solid span of uninterrupted work time to get things done! Some students in my precalculus class know interval notation for domain and range while another group didn’t even fill in the domain and range questions at all. That should be interesting. The bell rings at 10:26 but I sacrifice a few minutes of my 25 minute lunch to finish the pile of assignments I’m grading.<br /><br />As I leave the library I see my principal talking to someone. I need his signature on that form I just picked up, what timing! Head up to lunch in the second floor faculty lunch. Yup, we still call it lunch even though it’s 10:30. One year I brought oatmeal every day but this year I’m pretending it’s a normal time to eat and have a sandwich. I feel bad for kids who have first lunch on one day but second lunch (at 12:00) on the other day of our alternating block. I can adjust to eating at 10:30 and then having a snack when I get home, but switching off would just be weird. Lunch time depends on the department, so kids in math class during third block have first lunch while kids in English class during third block have second lunch. I chat with a few other teachers in my department about students and parenting and puppies.<br /><br />Lunch ends and I scurry up the stairs and across the building to my classroom. Most of my students beat me there but I’ve finally got them trained in appropriate waiting behavior (today one kid was pretending to kick the door – that’s major progress since September when it wasn’t pretend). Students pick up their binders and I turn on the projector and pull up the slides. My coteacher greets students and reminds them to get their materials. This is my Algebra Support class, 13 students who are all behind in math upon arriving to high school. We start every class with a couple minutes of skill practice. Today they are given shaded ten frames: they have to write the fraction, simplify the fraction and convert to a decimal. I wasn’t sure if giving them all ten frames would make the decimals too easy but it wasn’t – it was a great opportunity for them to use their calculators and then recognize a pattern. We talked about place value and equivalent representations. This was a great intro to our lesson on slope. I put a few tables on the board and students determined the slope. Then a pair of points. Then a graph with two points. Then I am so confident that I’ve said “y-distance over x-distance” so many times that they’re masters of slope and ready to conquer anything! I set them free to do a scavenger hunt where there are 17 papers taped around the room. Students answer the question at the bottom of the sheet and then find the matching answer on the top of a new sheet, repeating until they’ve made a complete loop. Except they’re all stuck? Uh oh. First mistake: I said rate of change, pattern, y-distance over x-distance… pretty much every word except slope. And this activity only says slope. Second mistake: we didn’t address horizontal or vertical lines. My co-teacher and I move around the room prompting and prodding and having kids draw examples and calculate. I think the scavenger hunt would have been great if the bottom half of the paper just had tables, graphs and pairs of points. However, I used a premade thing and the phrasing of the questions threw off more kids than it helped. I should have looked at it more carefully and kept my population in mind – several of them are working on phonics with the reading teacher, the vocab has to wait until after they’ve had some more experience. Next time I’ll make it myself… Despite the challenges they got some work done and I’ll be more prepared tomorrow. <br /><br />Bell rings at 12:28 and one class leaves. My next class has 5 minutes to arrive. This one is the contained Algebra class. They all have a moderate learning disability in mathematics (and several other issues outside of mathematics but the math disability is a prereq for the course). We do the same lessons as in Algebra and Algebra Support but they all have the class every day (a few of my Algebra students don’t attend the support block) and there are only six of them so they get much more individual attention. As one kid comes into class he declares he wants to take Street Law. I explain how course selection works and we get into a discussion of the content of the class and if it’s a good idea to run from the cops. I’m silently appreciative for my Twitter feed, particularly the #educolor crew because while I emphasized that being respectful is important, we also talked about how important it is to know your rights. The students in that class come from a variety of ethnic backgrounds and with cognitive impairments they’re not going to come across as the most well educated bunch to the untrained eye (even though they’re amazingly smart kids! With really slow processing speeds). They’re definitely at risk for getting taken advantage of and assumed the worst of. Thanks tweeps for making sure that my message had more depth than “don’t do anything to get in trouble.”<br /><br />We run the same lesson with this class but I’m much more explicit about using the word slope throughout the intro. I also add in a slide on horizontal and vertical slopes. I am thrilled when a kid (the same one who was curled up on her desk on Monday because the stress of a new coteacher replacing the sub was overwhelming) asks, “But why??” when we discover that 5/0 makes the calculator say “error.” We compare 0/5=0 and 5/0=error by looking at 5*0=0 and 0*?=5. One student is positive he can find a number that will make the second equation true. “Is it 5?” What’s 0*5? “Zero.” That’s not 5! “Is it 0?” What’s 0*0? “Zero.” That’s not 5! “Is it 1?” (repeat conversation) “Is it 5?” (repeat conversation) “Is it 0?” (repeat conversation) … “I don’t know.” Me neither! There isn’t a number we know. The calculator can’t think of a number either, that’s why it says Error. The girl who asked “But why??” originally says, “ooh!” and I already feel like whatever I did wrong last block I made up for it with this discussion. At least some kids are leaving today feeling enriched. They still need help with the scavenger hunt but with two teachers for five kids? We manage just fine. During the scavenger hunt one of my precalculus students is hovering outside the door. I go out and he asks what the course webpage is. I tell him (cardonmath.com) and he tells me that he was searching for it and found some other stuff about me “Apparently you’re really important! I had no idea.” It was rather adorable. <br /><br />2:02 and school is over. One student from last block stays to do some make up work. I find him a packet that needs correcting. Several teachers stick their head into my room "Do we have a meeting today?" We always have meetings on Wednesdays but we got this afternoon off since we have a full professional development day on Friday. One of the teachers comes in to ask about adding a student to my contained class. He's a student I was concerned about earlier in the year (I was in his class covering an adoption leave in September) but he's just now reaching the point where he needs a lot of extra help. We'll look into amending his IEP. Two students from precalculus show up and announce that they’re going to work on their ferris wheels today. The Algebra student is confused and makes some awkwardly funny jokes and my precalculus students are awesome about being nice to him. Everyone gets some work done and finishes around 3:00. I realize that I never put attendance in. For the last several years I had the same coteacher and she always did attendance. I yell at my students for not knowing how to be ready for class when it’s January but I’m just as bad. I pack up and walk out the door at 3:12. <br /><br />That makes today exactly an eight hour day! I usually leave around 3:45 and always do some work at home on Sundays but I make really efficient use of my prep and am in an awesome district that gives me 90 minutes of prep a day plus my duty is common planning time so I have a manageable amount of work. Tomorrow I will teach three blocks (honors precalculus, algebra and contained algebra) with one prep and 25 minute lunch in the middle. Then back to today’s schedule, alternating ad infinitum (well, for 180 days).Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com2tag:blogger.com,1999:blog-812794395259173668.post-85471532008157489962016-01-03T12:20:00.003-05:002016-01-03T12:20:41.210-05:00January Blogging Initiative<div dir="ltr" style="line-height: 1.656; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt;"><span style="background-color: white; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I, Tina, resolve to blog in 2016 in order to open my classroom up and share my thoughts with other teachers. I hope to accomplish this goal by participating in the </span><a href="https://exploremtbos.wordpress.com/2016/01/03/kicking-off-the-2016-blogging-initiative/" style="text-decoration: none;"><span style="background-color: white; color: #1155cc; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">January Blogging Initiation</span></a><span style="background-color: white; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> hosted by</span><a href="https://exploremtbos.wordpress.com/" style="text-decoration: none;"><span style="background-color: white; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: white; color: #1155cc; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Explore MTBoS</span></a><span style="background-color: white; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">.</span></div><span id="docs-internal-guid-413e4dd1-0880-7dcd-32f0-b52074a1c3d9"><br /><span style="background-color: white; font-family: Arial; font-size: 14.6667px; vertical-align: baseline; white-space: pre-wrap;">You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!</span></span>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-69000198573767750152016-01-01T18:27:00.000-05:002016-01-02T20:20:25.324-05:00Solving Inequalities with Learning DisabilitesAre you tired of the reminder that I teach Algebra for kids who arrive in high school not quite ready for Algebra 1? Or that one class is mostly students with learning disabilities and the other class is a contained class where all students have a math disability? I'm reminding you again because context is so, so important. While grading this morning I got frustrated that my students are still struggling with reading inequality symbols and organizing their work. I got a lot of great responses from people about all sorts of issues students face with inequalities, but it wasn't until an elementary teacher chimed in that I got a useful reply to help my students read the symbols. And the only person who even broached my issue with kids who struggle with organizing was an intervention teacher. I love this community because I can ask for help and get it from so many places! Today I really needed to hear from some people who have students like mine. Next time I'll type the hashtag correctly (#swdmathchat, not #swdchat) and get even more help!<br /><br />Now on to an overview of the unit, followed by an overview of the test and where I plan to go from here.<br /><br />We started by matching number lines to basic inequalities (one variable, one number, one symbol). We did a <a href="https://www.dropbox.com/s/h0qobr2axlqx031/1a%20Basic%20Ineq%20Sort.pdf?dl=0">card sort</a> and they gallery walked to see the categories other pairs used. They shared the categories they saw and I recorded them. I had them hold up an example of a card that might fit the category (to check if everyone knew the vocab and if the category is well defined). We discussed what open and closed circled might mean and also reviewed what the symbols meant. Everyone recorded the information in the box. Then they set off to match inequality to graph.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-O98ueRLwC2I/Vob2qg79WAI/AAAAAAAALdY/mEJKxlgMkVY/s1600/ineq%2Bsort.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="311" src="http://4.bp.blogspot.com/-O98ueRLwC2I/Vob2qg79WAI/AAAAAAAALdY/mEJKxlgMkVY/s320/ineq%2Bsort.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">For one of my students who especially struggles with symbolic notation I color coded: I wrote the greater than (or equal) symbols in red and the less than (or equal) symbols in blue. I had him color code the symbol first, then check which number line would match. Interestingly, when I wrote the definitions next to the symbol I asked him what word to use - greater, bigger, larger...? He understood greater better than any of the other words. I'm not sure if it's because it's more similar to Spanish or more familiar because it's an academic word but I was glad I asked rather than assuming he'd prefer to use bigger!</div><div class="separator" style="clear: both; text-align: left;"><br /></div>In the past I've had plenty of students with misconceptions about inequality symbols, but this year I had students who had trouble identifying the symbols, even with the notes in front of them. Some of them will even turn their paper to copy the symbol, apparently ^ is easier for them to see and write than <. I haven't had any solutions for this until I asked today and Jen said:<br /><blockquote class="twitter-tweet" data-conversation="none" lang="en"><div dir="ltr" lang="en"><a href="https://twitter.com/crstn85">@crstn85</a> from elem perspective: give the bigger number "2 points" (dots), smaller num "1 point" (dot) connect 2 dots to 1 dot to make symbol</div>— Jen Hudak (@jenhudak4) <a href="https://twitter.com/jenhudak4/status/682986784716910593">January 1, 2016</a></blockquote>I'm interested to see if drawing the dots on the endpoints and vertex can help my kids see the difference between <, = and > better.<br /><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">After the card sort we did more practice with just matching. Then given basic inequalities (one variable, one number, one symbol) I had them graph on a number line. This was a nice change of pace since we'd just concluded our study of absolute value equations. They also needed it. This is really a many step process:</div><div class="separator" style="clear: both; text-align: left;"></div><ol><li>Identify end point</li><li>Determine if end point is shaded</li><li>Determine which direction to shade from the end point</li></ol>None of these steps are obvious for most of my students. We continued to practiced reading the inequality aloud, picking values to check and then shading as we moved into more complex inequalities.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-sGynT95RRAs/VocANIInAZI/AAAAAAAALdo/WDTyiDw70JI/s1600/Capture2.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="http://4.bp.blogspot.com/-sGynT95RRAs/VocANIInAZI/AAAAAAAALdo/WDTyiDw70JI/s400/Capture2.JPG" width="295" /></a></div> <a href="http://2.bp.blogspot.com/-zDgswb5jTK8/VocANOQndkI/AAAAAAAALds/Rg-TgqJDT3g/s1600/Capture.JPG" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" height="400" src="http://2.bp.blogspot.com/-zDgswb5jTK8/VocANOQndkI/AAAAAAAALds/Rg-TgqJDT3g/s400/Capture.JPG" width="365" /></a><br /><br />While students noticed that dividing by a negative caused the direction of the inequality to change (and why! Those are student sentences! After some prompting and discussion of course, but students said them!) I really wanted them to be checking their work so I continued to emphasize how inequalities are exactly the same as equations until the final steps.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-JLXrSH2CeNI/VocBVjt9e9I/AAAAAAAALd8/akLl7oNz9XQ/s1600/Capture3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="215" src="http://2.bp.blogspot.com/-JLXrSH2CeNI/VocBVjt9e9I/AAAAAAAALd8/akLl7oNz9XQ/s320/Capture3.JPG" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">I have no idea what the IL was, though it appears to be my handwriting?</td></tr></tbody></table>We practice, practice, practiced. We did a <a href="https://www.dropbox.com/s/obknzxs9jdb8v20/solve%20inequalities%20CME.doc?dl=0">packet based off a CME problem set</a> on the difference between an equation and an inequality. We did compound inequalities (basically double the practice) (check out my colleague's <a href="https://www.dropbox.com/s/npy34vy2ado94ze/movie%20ticket%20compound%20inequalities.pdf?dl=0">awesome intro</a> via movie ticket prices). We did absolute value inequalities (a little extra work followed by double the practice). Several students continued to ask me what the symbols meant. :( A student had an aha moment about open vs. closed circles on a review day! :) The fifteenth time is the charm? Then we took the test a month after starting this unit and it was not awesome.<br /><br />Common issues:<br /><div><ol><li>Equation solving mistakes (integer operation errors, combining unlike terms, not using opposite operations).</li><li>Terms jumping the inequality symbol (3=x and x=3 may be equivalent but 3<x and x<3 are not).</li><li>Forgetting to change the direction of the inequality symbol after dividing by a negative.</li><li>Shading in the wrong direction on the number line.</li><li>Surprisingly, they made very few new mistakes on compound inequalities and absolute value inequalities. Some kids forgot to change the direction of the symbol for the negative inequality when splitting the absolute value.</li></ol><div>Next steps:</div><div><ol><li>We need to address this. Mostly it has to do with sloppy work. Some kids will need individual intervention.</li><li>Easy individual intervention when we address 1.</li><li>I'm not at all worried about this. It's annoying and we'll talk about it but this is where the errors should be during this unit!</li><li>I'll show all these kids Jen's dots on the symbol idea and hope that helps. I do think the issue is entirely in translating < and > into words, once they have words they're generally okay.</li><li>Again, not at all worried. Normal mistakes that kids will understand when they get their test back.</li></ol><div>So <a href="https://www.dropbox.com/s/vghou4wd8cx5dnp/Connecting%20Equations%20and%20Inequalities.docx?dl=0">I made a sheet</a> of equations, inequalities and equations with both x and y (leading into our linear unit coming up next). Each section has four problems using the exact same numbers. I gave them the answers and the goal is to show all work exceedingly neatly. Then to compare and contrast equations with inequalities (it's the exact same process! Except that pesky dividing by a negative thing and the extra work of graphing).</div></div></div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com1tag:blogger.com,1999:blog-812794395259173668.post-26529545696936661452015-12-06T14:17:00.000-05:002015-12-06T14:17:42.542-05:00Scaling the Teaching Curve: Sharing SessionLast night, after a full day of doing math and talking about teaching, nearly everyone still had more to give! We gathered at St. Mark's lovely Choate House for dinner and a sharing session.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-vi8fXA-UuJ4/VmRn-eU4S1I/AAAAAAAAKeE/kDjsKrGPjOQ/s1600/pcmi%2Bgroup.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="166" src="http://1.bp.blogspot.com/-vi8fXA-UuJ4/VmRn-eU4S1I/AAAAAAAAKeE/kDjsKrGPjOQ/s320/pcmi%2Bgroup.jpg" width="320" /></a></div><br />The sharing session was like an Ignite without slides - there were ten presenters and they all went fast! Too fast for me to tweet in between introducing each of them. Instead I took notes and will share them with you now. Hopefully we will get links for everyone's materials soon if they aren't included here.<br /><br /><b>Nick L: Using Voice Memos for Student Feedback</b><br />After looking at a student assignment, Nick uses his phone to record comments in a voice memo as an mp4 file which he then emails to the student. A voice recording allows him to convey tone, seems more personalized and encourages him to highlight student successes in addition to areas for revision. His students have also taken to asking questions via voice memo which is easier than attempting to type math notation into an email.<br /><br /><b>Kate H: Jigsaw</b><br />Students sit in groups and the whole group solves one problem (but different groups solve different problems). Then the teacher gives explicit instruction on how to be a good teacher - not telling the answer or showing the strategy. Once they are ready to be helpful group members, students shuffle their groupings so that each table has one expert on each problem. They work through all the problems, with a different student playing the role of teacher for each problem.<br /><br /><b>Dan H: <a href="http://www.nytimes.com/2015/01/11/fashion/no-37-big-wedding-or-small.html?_r=0">36 Questions to Fall in Love</a> (with your students)</b><br />Do you have any students that you struggle to like? Do you ever have students who you struggle to like even by the end of the year? The NYTimes article is intended for romantic partners, but Dan discovered that it is a great way to get to know your students in a deeper way. He gave students 5 minutes of quiet writing time at the beginning of class, then 2 minutes to share with a neighbor. He shared his own answer to the question and then collected student responses to read later. By the end of the year he was truly sorry to see his students go!<br /><br /><b>Seth B: Team Based Learning</b><br />Seth's PreCalculus classes have students work in groups of four, groups that are assigned in September and they stay in for the entire year. He'd read research stating that social experiences help with retention and collaboration helps with understand so he thought he would hit both of those by doing group work. Students are assigned group pre-tests and group problem sets. Then anyone in the group can be called on to present to the class. They spend time explicitly talking about how to function in a group and students find their groove when they stay with the same people, to the point that they were aghast when he asked if they wanted to change groups mid-year. Students give each other a grade on how much they contributed to the problem set in an interesting way - each student has 100 points to allot to their three team members in any way they see fit. The most balanced groups collaborate on this aspect as well so each person gets a 34 once!<br /><br /><b>Karen B: Modeling in PreCalculus</b><br />Students do some sort of modeling project every week in this class. At the end of the year instead of an exam, students choose a modeling project. They present their final product to a panel of teachers.<br /><br /><b>Jennifer F: Activity Builder in Desmos</b><br />Jennifer started students on a polygraph then had them explore rational functions by building and describing them. She put two students at each computer which encouraged discussion.<br /><br /><b>Dianna S: Graphing Videos</b><br />With her class of students who are English language learners, who have learning disabilities, and who feed into her Algebra class from several schools, Dianna needs activities that are accessible. She started by showing students <a href="http://graphingstories.com/">http://graphingstories.com/</a> and then tasked each student with coming up with a unique context for a piecewise linear function (including a horizontal segment). For example, one group had a dog going down the stairs, stop to eat a treat, then continue down the stairs. Interestingly, another group used a student moving around a track - the video shows elliptical motion but the function is linear - a common misconception! To aid students in making quality projects she has each group conference with her after making a plan.<br /><br /><b>Wendy M: Problem Solving Elective</b><br />For juniors and seniors who aren't on the traditional track, Wendy's school offers a problem solving course. She uses the book Crossing the River with Dogs. It's filled with chapters on problem solving strategies and the problems don't necessarily require Algebra or Geometry background. She found her students felt really successful with the problems in this book which was not the case in their past math classes.<br /><br /><b>Heather K: Interview Grid</b><br />Students answer an open question (Always, Sometimes, Never or <a href="http://wodb.ca/">wodb.ca</a>) and record their answer. Then they interview two classmates before having another opportunity to answer the question (possibly changing their answer based on what they heard from other students). This strategy is adapted from an ELL strategy - Level 1 or 2 students would copy their partner's answer word for word while higher level students would paraphrase or summarize.<br /><br />Finally, a group of us shared about <a href="http://twittermathcamp.com/">twittermathcamp.com</a> and <a href="http://exploremtbos.wordpress.com/">ExploreMTBoS.wordpress.com</a><br /><br />Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-33226885833535183742015-12-01T20:28:00.000-05:002015-12-01T20:40:30.839-05:00Visual EquationsI introduce equations with a pan balance, cups and pennies (basically <a href="http://mrpiccmath.weebly.com/blog/what-the-x-how-i-teach-basic-linear-equations">Timon's lesson</a>, I've adapted slightly but apparently I've never blogged it). Most kids see the visual, draw a few models, internalize the concept and work with the variables. Some kids see the visual, draw a lot of models and I coach them on the transition to variables. One student I have this year needed to touch the model. So we spent a few classes going back and forth between drawing and counting out pennies. Then we got to equations with negatives and I stalled and gave him different problems until his model was really solid. Then the class was working on equations with no solution and infinite solutions and we had a great debate with a kid who thought the model was silly but then needed it to really understand no solution equations. We even modeled the distributive property with cups and pennies!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-19T2m9N4GrQ/Vl5GhzKEVbI/AAAAAAAAKdQ/IgnFl1p3KXg/s1600/2015-12-01%2B20.06.26.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-19T2m9N4GrQ/Vl5GhzKEVbI/AAAAAAAAKdQ/IgnFl1p3KXg/s320/2015-12-01%2B20.06.26.jpg" width="240" /></a></div><br />Finally, I was talking to a colleague about this pedagogical challenge and she mentioned hot/cold cubes. Today I grabbed a red and a black marker and we got started working through some equations with negative numbers. I was ready to pull out the red (hot) and blue (cold) cubes if we needed them but he got it! It was also interesting to see him get tired of drawing pennies and start writing the number instead. I didn't snap a photo of his work (plus marker on graph paper doesn't work well if you use both sides - it bleeds through!). It wasn't as neat as mine (plenty neat for his needs though), but I used the notation he used today. He also didn't rewrite things on every line, but this way makes it clearer for you what is happening and in what order.<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-E3YvXJ0wrt8/Vl5Ghq9J70I/AAAAAAAAKdI/a3Q-gKQhjCA/s1600/2015-12-01%2B20.07.03.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-E3YvXJ0wrt8/Vl5Ghq9J70I/AAAAAAAAKdI/a3Q-gKQhjCA/s320/2015-12-01%2B20.07.03.jpg" width="240" /></a><a href="http://2.bp.blogspot.com/-BeuQYqaiBeI/Vl5Gh5wh8lI/AAAAAAAAKdM/kq1-FIDyYX0/s1600/2015-12-01%2B20.06.52.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-BeuQYqaiBeI/Vl5Gh5wh8lI/AAAAAAAAKdM/kq1-FIDyYX0/s320/2015-12-01%2B20.06.52.jpg" width="240" /></a></div><br />Bonus 1: Integer problems are easier like this. At one point he had a pink 30 and two more pink pennies. It was obvious to him that made a pink 32 in a way that -30 - 2 = -32 is not obvious.<br /><br />Bonus 2: the rest of the class was working on inequalities, which I have them solve by solving the equation and then testing values on the number line (both to check their work and so they don't forget to switch the direction of the symbol when dividing by a negative, not to mention we use this strategy in Calculus!). If you use the method above of always getting positive cups/variable by adding (instead of dividing by the negative number of cups) your inequality symbol never changes on you! I was psyched when he did that automatically and realized I wouldn't have to tell him any random rule about the symbol changing. So today this student successfully solved inequalities along with the class!<br /><br />Teaching the contained math class is tough, but it's so exciting for me and my students when we find a strategy that works for them. I'm looking forward to a lot more color in this kid's strategy kit!<br /><br />Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-47881579564362318152015-12-01T06:00:00.000-05:002015-12-01T06:00:07.922-05:00TMC16 Speaker Proposals<div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">We are starting to gear up for TMC16, which will be at Augsburg College in Minneapolis, MN (map is</span><a href="https://www.google.com/maps/d/u/0/viewer?mid=zJhyUMFB1LXc.kpFzm_-MdJCA&hl=en" style="color: #1155cc;" target="_blank"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt; text-decoration: none;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt;">here</span></a><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">) from <span class="aBn" data-term="goog_382604678" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">July 16-19, 2016</span></span>. We are looking forward to a great event! Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.</span><u></u><u></u></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><br /></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (</span><a href="http://bit.ly/TMC16-1" style="color: #1155cc;" target="_blank"><span style="font-family: Calibri, sans-serif; font-size: 11pt;">http://bit.ly/TMC16-1</span></a><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">). It’s a GDoc for people to list their interests and someone who might be good to present that topic. The form is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!</span><u></u><u></u></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><br /></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">This conference is by teachers, for teachers. That means we need you to </span><a href="http://bit.ly/TMC16speaker" style="color: #1155cc;" target="_blank"><span style="font-family: Calibri, sans-serif; font-size: 11pt;">present</span></a><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">. Yes, you! </span><span style="font-family: Calibri, sans-serif; font-size: 11pt;">In the past everyone who submitted on time was accepted,</span><span style="font-family: Arial, sans-serif; font-size: 11pt;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt;">however, this year we cannot guarantee that everyone who submits a proposal will be accepted. We do know that we need 10-12 morning sessions (these sessions are held 3 consecutive mornings for 2 hours each morning) and 12 sessions at each afternoon slot (12 half hour sessions that will be on Saturday, July 16 and 48 one hour sessions that will be either <span class="aBn" data-term="goog_382604680" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">Saturday, July 16</span></span>, <span class="aBn" data-term="goog_382604681" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">Sunday, July 17</span></span>, or <span class="aBn" data-term="goog_382604682" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">Monday, July 18</span></span>). That means we are looking for somewhere around 70 sessions for TMC16.</span><u></u><u></u></div><div class="MsoNormal" style="background-color: white; color: #222222; font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><br /></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit</span><a href="https://docs.google.com/forms/d/1mTwTOBkahcCE9u0_h3JZqShkaIXpL2NgAia292kMdZ8/viewform?usp=send_form" style="color: #1155cc;" target="_blank"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt; text-decoration: none;"> </span></a><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">the form. </span><span style="font-family: Calibri, sans-serif; font-size: 11pt;">The description you submit now is the one that will go into the program, so make sure it is clear and enticing. Please make sure that people can tell the difference between your session and one that may be similar. For example, is your session an Intro to Desmos session or one for power users? This helps us build a better schedule and helps you pick the sessions that will be most helpful to you!</span><u></u><u></u></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><br /></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.</span><u></u><u></u></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><br /></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">The deadline for </span><a href="http://bit.ly/TMC16speaker" style="color: #1155cc;" target="_blank"><span style="font-family: Calibri, sans-serif; font-size: 11pt;">submitting your TMC Speaker Proposal</span></a><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;"> is </span><b><span style="font-family: Calibri, sans-serif; font-size: 11pt;"><span class="aBn" data-term="goog_382604683" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">January 18, 2016 at 11:59 pm</span></span> Eastern time</span></b><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on </span><span style="font-family: Calibri, sans-serif; font-size: 11pt;"><span class="aBn" data-term="goog_382604684" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">February 1st</span></span>.</span><u></u><u></u></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><br /></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">Thank you for your interest!</span><u></u><u></u></div><div style="background-color: white; color: #222222; font-family: 'Times New Roman', serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="color: black; font-family: Calibri, sans-serif; font-size: 11pt;">Team TMC – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Cortni Muir, Jami Packer, Megan Schmidt, Sam Shah, Christopher Smith, and Glenn Waddell</span></div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-74427708163762309572015-11-22T21:06:00.000-05:002015-11-22T21:06:37.043-05:00What's Coming Up Next?When <a href="https://twitter.com/trianglemancsd">Christopher Danielson</a> spoke this summer about <a href="https://christopherdanielson.wordpress.com/2015/07/26/find-what-you-love-do-more-of-that-tmc15/">finding what you love and doing more of that</a>, I wasn't really sure what my thing was. I mean, I love teaching and I made a commitment to spend more of my time in the classroom, which means presenting at fewer conferences this year and avoiding my department head whenever she talks about wanting to be done being department head (she only gets to teach two classes and spends the rest of the day in meetings - yuck!). But this fall I figured out what it is I love doing, and I must love it because I signed up to do it so many times things got a bit overwhelming for a while there.<br /><br />I love organizing.<br /><br />Not just my desk (which I do like to keep organized, my system incorporates three accordion file folders this year). Not just my file cabinet or computer files (which are both sorted by course and then by unit). But big things, like events. There was a week recently where I was working on the Explore/Blogging Initiative in December/January, a PCMI conference in December, two NCTM MTBoS booths in November and TMC in July. For anyone who had to interact with me that week, sorry you didn't get my full attention. And major kudos to Ashli for listening to me whine about how four things that were occurring in four different months all somehow needed my attention simultaneously and why do I do this to myself?! (I have the best best friend.) But secretly? I loved it. I love the spreadsheets and the mental decision trees, the excitement of things coming together. I love helping other people accomplish their vision. I love problem solving as we hit snags, and sometimes stumbling across even better ideas as we plan.<br /><br />So, what are these things that I'm organizing?<br /><br /><b><a href="https://exploremtbos.wordpress.com/2015/10/18/a-new-exploration/">Explore MTBoS Mentoring Program</a></b><br />There's just about a week left to sign up to mentor or be mentored! We want to spread the word about this community but sometimes large scale initiatives aren't the right mechanism. Sometimes people really need tailored help. Maybe they read blogs but don't know how to use Twitter. Maybe they are on Twitter but don't know how to connect to the 'right' people. Maybe they are comfortable lurking but not so sure when it's okay to jump in. In those cases the generic instructions aren't sufficient. If you feel comfortable blogging and tweeting with other math teachers, we really need your help as a mentor! If you want to get started blogging and tweeting with other math teachers, get yourself a mentor! Sign up (by clicking the title above or images below) by December 1st and we'll get you all paired up for a month of exploration in December.<br /><br /><a href="https://docs.google.com/forms/d/1KccudYPj_na6esscmNjmvBKXPeeZkL6JrbeOvj83pCM/viewform"><img alt="mentee" height="268" src="https://exploremtbos.files.wordpress.com/2015/10/mentee.png?w=400&h=336" width="320" /></a><a href="https://docs.google.com/forms/d/1mGmrdXK1hDM9wkJYokd-WzC9rEhFWkYdWPOoAYh1LLQ/viewform"><img alt="mentor" height="268" src="https://exploremtbos.files.wordpress.com/2015/10/mentor.png?w=400&h=336" width="320" /></a><br /><br /><a href="https://exploremtbos.wordpress.com/2015/10/18/a-new-exploration/"><b>Explore MTBoS Blogging Initiation</b></a><br />We hope you'll join us in making a new years resolution to blog more. To help you carry out that resolution we will be posting weekly prompts in two strands - one geared toward new bloggers and one geared toward seasoned bloggers. I'm excited for the plans we've worked up!<br /><br /><b><a href="https://exploremtbos.wordpress.com/booth-supplies/">MTBoS Booth at NCTM Regionals</a></b><br />You're probably thinking, hey Tina! December is pretty busy for most people, why would you want people exploring then? And I'll say, hey reader! Thanks for reading! We chose December because the NCTM regional conferences (plus a variety of state conferences) just finished up and we wanted all of the people we invited to check out the MTBoS to have a mentor.<br /><br />After we closed down the booth in Boston in April, <a href="https://twitter.com/j_lanier">Justin</a> and I took notes on what future organizers would need to know, split the supplies into a couple boxes and got ready to pass the torch. <a href="https://twitter.com/veganmathbeagle">Megan</a> was the first to try her hand at exhibiting. <a href="http://mathybeagle.com/2015/11/15/regional-reflection-releasing-my-grip/">She</a> and <a href="http://www.coast2coast.me/carl/2015/11/14/airport-thoughts-after-nctmregionals-mlps/">Carl</a> each wrote about that experience. <a href="https://twitter.com/robertkaplinsky">Robert</a>'s chance followed shortly after and his exhibition concluded just a couple days ago. The supplies are headed off to San Francisco but the conversations don't have to wait until the next conference - because that's the beauty of the MTBoS - conversation is available for your perusal and contribution 24/7.<br /><br /><b><a href="https://pcmi.ias.edu/files/PCMI%20Dec%20PD.pdf">PCMI December PD Weekend</a></b><br />This event has definitely been the most work to organize. It's new - so new that the website is still in development and I have yet to decide if it's a conference or professional development opportunity or whatever other phrase surfaces as I type yet another email trying to figure this thing out. No matter what we call it, it's gonna be awesome! It's too late to join this event, but there are two more planned (in Salt Lake City and Chicago) for this school year, and as long as I don't screw things up too badly this year the plan is to really ramp up next school year and offer a lot of mini-PCMI experiences all over the country. One of the benefits of organizing events is that I get to make sure my friends know about it - two of my colleagues from school and several twitter friends applied before we reached capacity. I sent approximately 15,000 emails in the past couple months preparing for this but I'm confident it's gonna be worth the effort I put in. I'm so excited for the chance to do math, talk about education, hang out with awesome people and spread the amazing culture of PCMI.<br /><br /><b><a href="http://www.twittermathcamp.com/">Twitter Math Camp</a></b><br />Speaker proposals will be open soon. We're looking at last year's survey results and thinking up new ideas and generally getting excited! Mostly I'm excited about how much sun there is in summer. I love New England but waking up in the dark and leaving school at sunset is really depressing. Thoughts of summer fun with all of you counteract that!<br /><br />So that's what I've been up to. What do you love? How have you been doing more of that?Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com2tag:blogger.com,1999:blog-812794395259173668.post-72467743766134107032015-11-15T14:04:00.000-05:002015-11-15T14:05:03.365-05:00Sine and Cosine Waves with Activity BuilderMy PreCalc students have been studying the graphs and equations of sine and cosine for a month (an interrupted month but a month nonetheless). Tuesday they will have one final day to review before their test on Thursday (we run an alternating day block schedule). Some students are completely ready. They can identify transformations, graph complex equations, and write equations from both graphs and descriptions. They can apply their knowledge to a novel context (we did a Ferris wheel project). Other students still have to think about what the graph of y=sin(x) looks like. This is the widest range of students I've ever had in an Honors PreCalculus course so I'm really appreciative that Desmos made the <a href="https://teacher.desmos.com/activitybuilder/">activity builder</a> just in time for this class! It's a great way for me to differentiate.<br /><br />Last week while working on the Ferris wheel project when I had some students who had no idea how to write an equation given their more complicated graph, I sent them to <a href="https://twitter.com/rdkpickle">Rachel</a>'s activity builder <a href="https://teacher.desmos.com/activitybuilder/custom/5638429b4871f4bb4c189e9d">Curve Fitting w/ Sine and Cosine</a> that went back to the basics of equation writing. They wrote the equation for a graph with amplitude not equal to one, then I referred them back to their Ferris wheel to identify the amplitude and put it into their equation. It was great because it was self checking and students experienced some success working simpler problems when they were frustrated with the complex problem I'd posed.<br /><br />Tuesday I want to create a similar situation - so I built a couple different activities.<br /><br /><a href="https://desmos-lesson-uploads.s3.amazonaws.com/activitybuilder/fe0858c6bd47d95908146527153f19e4" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="100" src="https://desmos-lesson-uploads.s3.amazonaws.com/activitybuilder/fe0858c6bd47d95908146527153f19e4" /></a><a href="https://teacher.desmos.com/activitybuilder/custom/564641f218b60b39060d34f2">Graphing Basic Trig Equations</a><br />This starts all the way back with y=sin(x) so my students who are lost can start back at the beginning and practice the whole unit all over again. When we sketch a graph, students plot the important points and then fill in the curve. I recreated this activity on Desmos by having students drag points on a grid. Then they can check their work by un-hiding the curve.<br /><br /><br /><br /><a href="https://teacher.desmos.com/activitybuilder/custom/5648b3b0048c4823217efdeb">Sine and Cosine Graphs with Multiple Transformations</a><br />Students will describe, graph and write equations for functions with multiple transformations. This one is aligned with what will be on the test.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-19rSWyDYsZE/VkjNkLR0icI/AAAAAAAAKZs/pkUeNv81CDI/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="224" src="http://4.bp.blogspot.com/-19rSWyDYsZE/VkjNkLR0icI/AAAAAAAAKZs/pkUeNv81CDI/s320/Capture.JPG" width="320" /></a></div><br /><span id="goog_1002183922"></span>I would love feedback on these activities! (Especially if you can provide it before 7:24 am on Tuesday.) I'll let you know how they go after that.<br /><br />Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com2tag:blogger.com,1999:blog-812794395259173668.post-19699526365351349202015-11-13T18:23:00.001-05:002015-11-13T18:23:16.263-05:00Last BlockWe run an A/B day block schedule. Our kids who are behind in math get double block math. A few years ago I had some students who had math last block every day. Then last year I had a great schedule where I had one group last block A days and a different group last block B days. It meant that on the alternating days I saw them second or third block. And they're really different kids at different times. This year I have my contained math class last block every day. I was not excited when I saw that schedule, but it wasn't until today that I realized exactly why it's so hard - I have them after <i>every other class</i>.<br /><br />Reasons I've cited before:<br /><br /><ul><li>some kids medications are wearing off by the end of the day</li><li>some kids have expended all their energy focusing in other classes and don't have anything left for me </li><li>some kids (less my ninth graders) will leave school last block if they don't want to attend, but they're less likely to skip a class in the middle of the day</li></ul><div>These reasons are all true, but today I realized that the biggest issue is not about the time, it's about all the things that have happened between 7:30 and 12:30. </div><div><br /></div><div>One kid walked into my class and immediately put her head down. </div><div>One kid walked into my class and was talking rapidly in a high pitched voice. </div><div>One kid walked into my class and touched another student, I told him to stop and then he did it again on his way back to his seat. I sent the affronting student in the hall and asked the other student to not yell because I was going to take care of it. That student threw his paper and pencil on the ground and pulled his sweatshirt up over his head and hid inside it. </div><div>Two kids started class ready to complete the first task. </div><div><br /></div><div>Yes, I have a special group of kids. All the more reason for them not to have math after all their other classes. </div><div><br /></div><div>Because the girl who put her head down starts her day cheerful but her mood changes based on her interactions with peers. </div><div>Because when I asked the boy talking in a high pitch voice to stop he said he'd had a hard day but he'd try to stay in control.</div><div>Because when I talked to the student in the hall he told me that he was really mad. He didn't want to talk about it. He didn't think he could come into the class without getting in trouble.</div><div>Because the student who was sitting in his seat until that other kid tapped his neck? If he'd been having an okay day he would have joked with his friend, or yelled at him and then moved on. But he was out of patience for the day.</div><div>Because I don't have quite as much patience as I would have earlier in the day.</div><div>Because one of those two kids who started class ready fell asleep repeatedly during class. He apologized at the end of class explaining that he'd had physical training in JROTC. He also shuts down and falls asleep in stressful situations - and class today wasn't exactly calm.</div><div>One student had a good day today.</div><div><br /></div><div>Does every day start like this? Of course not. Usually only a couple of them start the class off already frustrated. But every single one of them has a substantial learning disability in math. Almost all of them have other challenges (that's typical for kids with substantial learning disabilities). Asking me to teach them math (a challenging task to begin with) after they have already faced the challenges of an entire day of navigating ninth grade is unfair.</div><div><br /></div><div>So next time someone (including me) complains about teaching last block, I'm going to remind them (myself) that it's not really that they're fidgety and ready to get out of there by the end of the day, it's because they've already faced all the challenges of the day. Because school is really hard for a lot of our students for many more reasons than we ever remember. Because we're not our best selves as teachers after a full day either. But the schedule is already set for the year, so we have to deal with what we've got and allow students to take a minute to let the rest of the day go before we jump on them demanding they get started with our class. Maybe our do now activity should be deep breathing. I might just try that on Monday. At the very least it would prepare me to bounce between all the different emotions and experiences of my students.</div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-80675057085358070182015-11-12T21:21:00.000-05:002015-11-12T21:21:02.815-05:00Bar Models in AlgebraAt <a href="http://www.atmne.net/">ATMNE</a> a couple weeks ago I attended Kate Marin's session "Bar Modeling: A Model for All" and remembered this sheet (below) I had used in years past which was perfect for our current unit of equations in one variable. I've seen bar modeling before but attending Kate's session reminded me of some important ideas. One is the banter that should be involved in solving any problem but particularly a problem in context. She modeled the back and forth between teacher and students of asking who the problem is about, what the problem is about and drawing a model as they tell her pieces of information. I gave students some of the banter questions in the handout and also did it with the class for the first problem. Kate also told us that the model doesn't replace the equation, the model is an aid in writing the equation. The equation is still part of the goal. However, there are many possible equations, encourage students to share as many as they can to validate everyone's way of seeing the problem (we used 72-48=3B, 3B+48=72, 72=3B+48, B+B+B+48=72...). And finally she reminded us that the final goal isn't a number, it's an answer in context, so the answer should be in a complete sentence. I modified my sheet to make it clear that every problem needs an equation and a sentence. My kids with large handwriting didn't have enough space to work but they could always draw the model and solve the equation on separate paper and record just the equation and sentence on the handout.<br /><br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="https://www.scribd.com/doc/289502128/Word-Problems-with-Bar-Models" style="text-decoration: underline;" title="View Word Problems with Bar Models on Scribd">Word Problems with Bar Models</a> by <a href="https://www.scribd.com/tina_cardone1" style="text-decoration: underline;" title="View tina_cardone1's profile on Scribd">tina_cardone1</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="0.7729220222793488" data-auto-height="false" frameborder="0" height="600" id="doc_41579" scrolling="no" src="https://www.scribd.com/embeds/289502128/content?start_page=1&view_mode=scroll&access_key=key-vJpn6zWbRdqosQp0ocyX&show_recommendations=true" width="100%"></iframe><br /><br />You might notice that none of the problems have a question. Last year some students noticed at one point, but this year no one even remarked on it! A couple times I had to encourage students to find all the missing information (the price of the sandwich as well as the fries or the amount spent on books rather than the amount left) but generally students want to fill in everything they can on their model.<br /><br />I did not require students to draw a model, but I refused to discuss an incorrect equation with them until they had a model. Kids would tell me "I don't know how to do fractions or percents" but when I told them to draw a bar, and then draw 4/5, they could do that without assistance. The percents took a bit more banter, one conversation went like this:<br /><blockquote class="tr_bq">What do you know?<br />"There's a 20% discount"<br />What does 20% mean?<br />"I told you I can't do percents."<br />What percent do you have if you have everything?<br />"100"<br />So what does 20% mean?<br />"20 out of 100. No way! I'm not drawing that!"<br />I agree, let's not.<br />"20, 40, 60, 80..." </blockquote>No joke, I said nothing leading and he started counting by 20 under his breath! He trailed off so I said yes! that! and he drew his bar model. Who can't do percents? Not this kid!<br /><br />I'm not going to tell you how long we spent on this because you'll think less of me or my students (who are in 9th grade) or both(!) but suffice it to say, there was a lot of struggle, most of it in the form of learned helplessness. When I stood over them and said "Draw a model. Read me the info. Write it down. Read it again. Label. And again." they did great. Then I'd walk away and come back and find an answer without a sentence. "What does that mean? What does x represent? Read the problem. Read it again. Write down exactly what you just said." Basically my job in this class is to refocus their attention on the task and refuse to do things for them while convincing them I believe they can do it. For other 9th grade classes this might be a breeze. For plenty of middle school classes too I'm sure. But if you have kids who need spaced repetition this isn't too painful of a way to mix in some fractions and percents while doing Algebra. It reinforced rules of solving equations that some of my students are still shaky on: 5x means five x's and we divide by five in 5x=80 because we need to split that 80 up among the 5 boxes. Oh! I'm so glad that finally clicked for you kid, missing half of the introduction to solving equations wasn't helpful but we got you there eventually!<br /><br />This is what happens when I see a kid working quietly and independently and don't go check on him:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-EqTWbbENtrY/VkVF5x16yFI/AAAAAAAAKYs/AZ58T1HzpQk/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="169" src="http://1.bp.blogspot.com/-EqTWbbENtrY/VkVF5x16yFI/AAAAAAAAKYs/AZ58T1HzpQk/s320/Capture.JPG" width="320" /></a></div><br />Didn't anyone teach you that math makes sense? There are -2 stickers? Where? There aren't even any gift bags in the equation. I'm sorry that you learned that math is a magical land where you put numbers and operations together to get a mystery number, I'll work on undoing that belief.<br />(I cut this problem from the sheet above because the bar model isn't super helpful nor is there a particularly interesting equation to write, so I cut it for some extra space to write on the other problems. Forgot to fix the numbering, sorry!)<br /><br />Interestingly though, this student did expect the problem he wrote to make sense. It looks like he solved it by saying 40 (collars) - 20 (left) = 20 (who knows what unit) but then realized this didn't make sense, so he fixed it. This is the only problem he wrote a sentence for, and the only one where his equation matches the context. I also love all the student problems that don't have questions!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-eWHzg18Cb5I/VkVGNS1eW2I/AAAAAAAAKY0/TTW2HgxTW0A/s1600/2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="165" src="http://3.bp.blogspot.com/-eWHzg18Cb5I/VkVGNS1eW2I/AAAAAAAAKY0/TTW2HgxTW0A/s320/2.jpg" width="320" /></a></div><br /><br />Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-55996635419587546442015-11-09T21:10:00.000-05:002015-11-09T21:10:38.370-05:00Update: Math Practice Standard PortfoliosIn August I had an idea that students could build a <a href="http://drawingonmath.blogspot.com/2015/08/math-practice-standard-portfolios.html">portfolio</a> of examples of the standards of mathematical practices. Our first quarter ended on Friday so I gave students the <a href="https://www.scribd.com/doc/276543173/Math-Practices-Portfolio2">second version</a> I drafted in August. I'd planned to do it earlier, but... it's been a busy quarter. So on the last day of the quarter I told students to clean their binders, choose four examples of good work and describe how they exhibit the math practices on <a href="https://www.scribd.com/doc/276543173/Math-Practices-Portfolio2">the sheet</a>.<br /><br />Note! If you tell ninth graders to "clean up" their binders they will hear "clean out" and recycle everything. Even if you have clear instructions on the board about what is okay to recycle and what they need to keep. Organize is a much better word. Lesson learned.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-25ubYatY62M/VkFBxBkRc4I/AAAAAAAAKWs/PXdUPtfqDxg/s1600/Capture.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="90" src="http://3.bp.blogspot.com/-25ubYatY62M/VkFBxBkRc4I/AAAAAAAAKWs/PXdUPtfqDxg/s400/Capture.JPG" width="400" /></a></div>I wanted to give students some examples of what to write. For PreCalc I gave them an example of evidence and I asked which practice it could apply to (multiple! Persevering and using tools are the two I was thinking of). Then I set them loose and they did well. Yay for honors juniors and seniors.<br /><br /><br /><a href="http://3.bp.blogspot.com/-Np6JqqtofIQ/VkFDoMQSpoI/AAAAAAAAKXA/UsN0fy6bxnI/s1600/Capture.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="202" src="http://3.bp.blogspot.com/-Np6JqqtofIQ/VkFDoMQSpoI/AAAAAAAAKXA/UsN0fy6bxnI/s400/Capture.JPG" width="400" /></a>For Algebra I gave them some more specific examples. They still struggled. I walked around reading specific quotes to them "I can discover patterns." - "Can you find a paper in your binder where you found a pattern?" or having them find a paper they were proud of and asking them which practice it applies to (by reading them one at a time). This was kind of painful so in my contained class for students with substantial learning disabilities I took it one step further and we did the whole thing as a class. I read the practice, I read the student friendly quotes, I told them to find an example in their binders of that particular thing. I checked with everyone that they filled in the title and evidence, repeat three more times. For this class I just picked four practices that I knew would be easy to find examples based on the work we had done this quarter so they didn't have as many options. Maybe if I provide some support at the end of second quarter they'll be able to use their exemplars from first semester to work more independently second semester? Seems possible!<br /><br />I ended up with some great reflection from my PreCalc students. Plus it was interesting to look back at all the work we had accomplished in all my classes and see what students chose as examples of their best work! I would definitely recommend trying this activity with all your classes. If I was doing this again I might try asking students to reflect a few times on what they had done in class that day before jumping directly to reflecting over the whole quarter. I meant to do this, but again with the busy quarter. Luckily there's still most of the year left!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-ibV6rygGAzU/VkFNoXimT_I/AAAAAAAAKXU/AlqxoJFS9rU/s1600/IMG_7880.JPG" imageanchor="1"><img border="0" height="358" src="http://2.bp.blogspot.com/-ibV6rygGAzU/VkFNoXimT_I/AAAAAAAAKXU/AlqxoJFS9rU/s640/IMG_7880.JPG" width="640" /></a></div><span style="font-family: inherit;">The u<span style="text-align: center;">nit circle is a great example of precision! </span></span><span style="font-family: inherit; text-align: center;">Several students used their unit circle projects for repeated reasoning.</span><br /><span style="font-family: inherit; text-align: center;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-E3TH8bhiKKs/VkFNoeWWSlI/AAAAAAAAKXY/0BhwGY4bpfs/s1600/IMG_7883.JPG" imageanchor="1"><img border="0" height="217" src="http://4.bp.blogspot.com/-E3TH8bhiKKs/VkFNoeWWSlI/AAAAAAAAKXY/0BhwGY4bpfs/s640/IMG_7883.JPG" width="640" /></a></div><div>I had students submit the work sample but this student is correct, not all math practices are visible. Ditto for kids who used tools (like the calculator example above).</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-nRLjYPP9V9s/VkFNogDG1rI/AAAAAAAAKXc/lLSLQnzUqJU/s1600/IMG_7884.JPG" imageanchor="1"><img border="0" height="174" src="http://1.bp.blogspot.com/-nRLjYPP9V9s/VkFNogDG1rI/AAAAAAAAKXc/lLSLQnzUqJU/s640/IMG_7884.JPG" width="640" /></a></div><div>Perseverance and growth mindset!</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-04984nFZkYk/VkFNo-N__oI/AAAAAAAAKXg/0BF21FrmuTc/s1600/IMG_7885.JPG" imageanchor="1"><img border="0" height="202" src="http://4.bp.blogspot.com/-04984nFZkYk/VkFNo-N__oI/AAAAAAAAKXg/0BF21FrmuTc/s640/IMG_7885.JPG" width="640" /></a></div>This was pne of the few cases where I needed to read the sample work, this student's explanations got more precise and concise as she figured out which information was important to record.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-VevI6I6sKao/VkFNpItvjjI/AAAAAAAAKXw/s8PpB4ROKOQ/s1600/IMG_7886.JPG" imageanchor="1"><img border="0" height="422" src="http://3.bp.blogspot.com/-VevI6I6sKao/VkFNpItvjjI/AAAAAAAAKXw/s8PpB4ROKOQ/s640/IMG_7886.JPG" width="640" /></a></div><div class="separator" style="clear: both;">Using the same work sample for multiple practices was fine with me. In fact, I bet they could have found all four examples they needed this quarter in some projects!</div><div><br /></div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com1tag:blogger.com,1999:blog-812794395259173668.post-43143059301766606382015-11-01T08:00:00.000-05:002015-11-09T21:10:51.810-05:00Expressions with Absolute ValueA few weeks ago I gave a test that included a section on evaluating expressions (order of operations) and two of the problems had absolute value as part of the expression.<br /><br />I made an observation that many students were making a mistake in one problem that they weren't making in the next problem. So I tweeted about it.<br /><br /><blockquote class="twitter-tweet" lang="en"><div dir="ltr" lang="en">It's astounding how many kids are making this mistake (or -3) in #3 but doing #4 just fine. <a href="https://twitter.com/mpershan">@mpershan</a> <a href="https://twitter.com/hashtag/mathmistakes?src=hash">#mathmistakes</a> <a href="https://t.co/FEemgRRbcX">pic.twitter.com/FEemgRRbcX</a></div>— Tina Cardone (@crstn85) <a href="https://twitter.com/crstn85/status/656277709174104064">October 20, 2015</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><br /><br />And because my online math community is spectacular, I got some feedback.<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://twitter.com/crstn85/status/656277709174104064"><img border="0" height="304" src="http://3.bp.blogspot.com/--9E-RlJ9aJM/VjVpIqmoXPI/AAAAAAAAKSE/zgLbFMa8Wzc/s320/Capture.JPG" width="320" /></a></div><br />Inspired by this conversation, I did an experiment last Thursday. I gave students these two problems for a <a href="https://www.teachingchannel.org/videos/class-warm-up-routine">My Favorite No</a> (without talking to them about the test first). The results weren't good, but they weren't particularly consistent either. This is what happened:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-wJZ_wVNJ2ZY/VjVrAcSjw6I/AAAAAAAAKSQ/CfRChTa6Ve4/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="25" src="http://3.bp.blogspot.com/-wJZ_wVNJ2ZY/VjVrAcSjw6I/AAAAAAAAKSQ/CfRChTa6Ve4/s320/Capture.JPG" width="320" /></a></div><br />- 8 and + 3 (3 students)<br />+ 8 and + 3<br /><br />- 8 and *3<br /><div><br /></div>*(-8) and *3 (3 students)<br />*8 and *3<br />*8 and *(-3)<br /><br />Dropped the 8 entirely, *3<br />- 8 and dropped 3<br />Distributed (both)<br /><div><br /></div>+ 8 and incomplete<br />*(-8) and incomplete (3 students)<br />Incomplete, *3<br />both incomplete (2 students)<br /><div><br /></div>I picked someone who subtracted 8 and added 3 as my favorite no. We found the good things. We found the mistake. We talked about implied multiplication. We moved on.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-V_drCXrzgeo/VjVr0UnWyNI/AAAAAAAAKSY/Zlkjoc2PWY4/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="58" src="http://2.bp.blogspot.com/-V_drCXrzgeo/VjVr0UnWyNI/AAAAAAAAKSY/Zlkjoc2PWY4/s320/Capture.JPG" width="320" /></a></div>I repeated the experiment this Thursday and I only had one student add! A couple distributed (we spent the past week working on solving equations and some were with distribution) and a couple multiplied by negative two. I didn't have as many students participate this week (alternating day schedule means this Thursday was my 15 student support rather than my 20 student Algebra class, and a fire alarm during my contained class meant they didn't all do it) but despite completely flawed data I'm allowing myself to feel a sense of accomplishment. If I'm a good researcher I'll do this again in a few weeks to see if they retained it. Remind me?Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com1tag:blogger.com,1999:blog-812794395259173668.post-253601992400940192015-10-20T20:29:00.000-04:002015-10-21T21:08:54.367-04:00Co-Teaching and a Teaching Philosophy Challenge*There's a challenge at the end of this post to write your teaching philosophy in a few bullet points. Feel free to skip to there if you're not up for an emotional story.<br /><br />Five years ago I moved to Salem and started teaching Fundamentals of Geometry among other things. I had a co-teacher, Lori, and it was the first time I had a co-teacher full time rather than a special educator pulling kids out or pushing in to my class on a sporadic basis. It was great. Over the past five years we've learned from each other, learned together (taking many grad classes together), developed routines and even made the big decision to move down to ninth grade with the stipulation that we had to be placed together. That's what our course preference sheets say every year - "I'll take two double blocks, including the contained math class, as long as I get to teach with Tina/Lori."<br /><br />At the beginning of this year the head of special ed had a meeting for everyone who is co-teaching this year and we were mentioned as an ideal co-teaching pair. I never imagined I'd be wishing I had gotten to attend that meeting with someone else. The goal of the meeting was to get to know your co-teacher (which was silly for Lori and I) and to start planning out how you would work together in the classroom. We had that down too, but it should've been a chance for us to share ideas we'd come up with since our last meeting. Instead it was a chance for her to update me on her latest doctor appointment, yet another inconclusive test, and to decide if I wanted a sub for her next appointment (the first week of school). We knew something was wrong back in the spring but despite getting sicker over the summer none of her doctors could diagnose her with anything. It took a couple more weeks, but they finally found cancer, advanced stages of it. It took a while longer to decide on a treatment plan but she just submitted paperwork stating that she'll be out for a minimum of six months.<br /><br />Starting the year expecting her to be there and then a couple weeks in to find myself on my own with a substitute has been incredibly hard. There are so many things that we did together that I never realized. Tiny things like she put in attendance while I handed out papers. Bigger things like being able to step in and finish my sentence for me when allergies struck and I had a coughing fit. I forgot what it's like to have a stranger in my room. A stranger I didn't even do the silly getting to know you activity with. I'm working hard to not blame the sub for not being able to step directly into Lori's shoes without any transition required. But it's really frustrating when she tells the kids tricks or does the work for them. And then it's frustrating when I don't know what to tell her other than "Don't do that!" I've realized that it's no easy task to describe my teaching philosophy in a few easy to understand points. Even after being in my room for a few weeks the sub hasn't figured it all out, so I need to write them down and then find a way to clearly explain my goals to her.<br /><br />*Here's the challenge: Can you explain your teaching philosophy in a few bullet points without any teacher lingo?<br /><br />Here's my attempt:<br /><br /><b>All ideas have value. All people have value. </b><br />No put downs of any kind. Telling a kid "this is easy" dismisses their idea that the work is challenging. Ignoring someone's contribution and focusing on an alternative answer/strategy devalues the original person's thoughts. Yes, it's going to take me a really long time to go over this one problem, but it's totally worth it if every student feels like their contribution matters to me.<br /><br /><b>Math makes sense, it's not a bunch of random rules.</b><br />Please don't recite tricks at them. <i>Please.</i> My kids process things at different rates, if someone figures out a shortcut - congratulate them! But let other kids get there on their own time. Everyone gets a chance to experience the context or the long way before we move to the abstraction or the shortcut. Then they have some understanding to fall back on when they forget, because everyone (memory disability or not) forgets.<br /><br /><b>Students need to know how to do the work independently, so they need to practice independently. (Even my kids with severe learning disabilities can think all by themselves!)</b><br />That might mean walking away and letting them struggle. That might mean showing them how to use resources they have (notes, classmates) rather than telling them how to do something. That might mean coming up with another example to work out with them and then asking them to do the one on the assignment independently.<br /><br />How'd I do? Clear enough? What would you include?Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com7tag:blogger.com,1999:blog-812794395259173668.post-15959347751239757762015-09-20T12:42:00.001-04:002015-09-20T12:43:15.699-04:00Intro to RadiansIn the past I've introduced radians by having students measure angles of a circle graph with these <a href="http://www.proradian.net/">weird protractors</a> and compare that to arc length and degree measure until we finally tease out what these things are. It's never smooth and it doesn't result in any major insights. The minor insight comes from this lovely <a href="http://tube.geogebra.org/student/m59882">geogebra applet</a> and the understanding comes from continued practice using radians. So I reorganized this year and I'm much happier with how things went. All the notes I took during this lesson are at the bottom. I'm too lazy to give them to you page by page so they go with the correct paragraph, I'm confident in your ability to match things up.<br /><br />We'd just finished <a href="http://www.mathalicious.com/lessons/as-the-world-turns-hs">As the World Turns</a> which uses both linear and angular speed. So we compare linear and angular distance for some turns a figure skater makes. They want to know the radius, I tell them to just use <b>r</b>. They find a nice pattern - add one revolution and you add 360 degrees or 2πr. This pattern is not nearly so convoluted. We realize this makes sense.<br /><br />I tell a nice little story about the history of 360 and how it's nice but arbitrary and the radian measure is not! Then we watch the lovely <a href="http://tube.geogebra.org/student/m59882">geogebra applet</a>. It's still not obvious to them that it will take ~6.28 radii to get around but there are some aha moments when someone shares that idea. Someone asks what if the circle was a different size, I love these children! I change the size of the circle and it looks the same, a few more aha moments. We add this to our notes.<br /><br />Great, now we have a thing that doesn't seem totally crazy, we really just need to practice with it. But before we jump into graphing in standard position, why not solve a little puzzle? I start out facing East (note - that's the positive x-axis aka standard position) and I make a quarter turn to the left. If you start out facing East, what other moves could you make to end up in the same position? Hm, now I'm wondering if it would have been better to just tell them I end up facing North, then ask, how did that happen? Only benefit of my initial scenario is it sets counter-clockwise as the original direction. Either way, they come up with -3/4 turn pretty easily. We express both as radians. Then I ask for more, we eventually get around to making Ms. Cardone dizzy and see that lovely 2π pattern again. A student describes the pattern beautifully and I make a big deal of it and write it nice and big on its own slide. I kept using the word co-terminal enough times and it ended up in the nice generalization.<br /><br />Now we all practice drawing a few angles in standard position - start to the East/positive x-axis and turn in the direction that the quadrants are numbered. This is where I find out who was fully engaged in that class discussion we concluded just moments ago and who was nodding and smiling without taking any notes (mental or on paper). Once I'm sure that everyone can draw an angle and recognizes a fraction of π as a fraction of a half turn, then we're ready for our pi(e) eating contest!<br /><br />A while back I saw <a href="http://exit10a.blogspot.com/2014/04/pie-eating-contest.html">this post</a> (possibly linked by someone who was doing this activity with radians?). Having them start in standard position and then add the angles together meant they were labeling angles around the unit circle without even knowing it! I gave them the first quadrant angles with some extra π/6's so no one won too fast. Having them make the angles with the <a href="http://www.proradian.net/">radian protractors</a> means they're building their own <a href="http://www.megcraig.org/?p=995">wedges</a> a la Shireen and Meg, which we'll be able to cut out and use next class. They needed the practice adding fractions so most groups were still on their first round when the bell rang (five minutes early! Possibly because we were having an assembly during advisory block or maybe just because the bells were messed up on our first advisory day). That means this whole thing took about 75 minutes (I was half way through passing out quizzes when the bell went off unexpectedly so we didn't get to the final two slides below).<br /><br />Next class we'll build the first quadrant of the unit circle together (similar to <a href="http://drawingonmath.blogspot.com/2014/12/useful-tech.html">second photo here</a>) and then they'll work in pairs to extend it.<br /><br />My pi(e) eating contest <a href="https://www.scribd.com/doc/282179124/Pie-Eating-Contest">boards and radians measures</a>.<br /><br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="https://www.scribd.com/doc/282178986/Radian-Intro" style="text-decoration: underline;" title="View Radian Intro on Scribd">Radian Intro</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_93544" scrolling="no" src="https://www.scribd.com/embeds/282178986/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-30933462924465957062015-09-20T11:42:00.001-04:002015-09-20T11:42:54.976-04:00Team Teaching and a ClotheslineThe Algebra 1 team this year is entirely made up of teachers who taught Algebra 1 last year. In a department with turnover like ours this is no small feat. We also had an opportunity to work together this summer to design our first unit. (It's so nice to have the basic outline of my lessons complete when I'm scrambling to keep up with all the other start of year paperwork!) These factors combined make us all a little more willing to try some new things this school year. One of those things is team teaching. We all have a support block for a subset of our students that meets on the opposite day of the full class. Guidance did an amazing job scheduling- all of the support blocks meet on red day! Since these classes are smaller we can merge two into one classroom and teach together when two classes meet at the same time.<br /><br />One day we team taught was our introduction to types of numbers. We wanted to preview some of the ideas with our support kids before having the whole class complete a types of numbers diagram. So we just gave them the card sort (the diagram that would make an appearance the following day is also included here).<br /><br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="https://www.scribd.com/doc/282171241/Types-of-Numbers-Sort" style="text-decoration: underline;" title="View Types of Numbers Sort on Scribd">Types of Numbers Sort</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_41994" scrolling="no" src="https://www.scribd.com/embeds/282171241/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />When we prepped over the summer we said we'd do a card sort. Everyone seemed clear on that (all four of us who were there over the summer had attended PD that included this structure together a few years back) so we didn't include specific instructions. The first block I did this with we were in my room and so used my slides. I instructed the students to work with their partner to group the cards however they wanted to and then come up with names for each of the categories. We circulated and then when students seemed done with that task the other teacher told one partner to stay at their desk to explain while the other partner circulated the room. When I do a gallery walk I have kids all walk around and the writing on the desk (in dry erase marker) is all the explanation they get, I liked this method!<br /><br />I then had kids share one category they saw (why is <b>one</b> so hard for ninth graders?) until we'd exhausted all the options. Then I had kids hold up an example of each category and ask for clarification if they didn't know what the category meant. During this part of the lesson it was nice to have another teacher around to check the numbers because I made the font too small for this on the cards!<br /><br />Next up was the clothesline. I read <a href="http://mr-stadel.blogspot.com/2015/08/clothesline.html">Andrew's post</a> on clotheslines after our team planning time this summer so I threw the link into the unit map in case other people wanted to try it. Instead, I got to run it and the other teachers figured it out as we went. Again, it was great having other teachers around because they asked good questions and shared insights that didn't occur to me. If you study the card sort carefully you'll notice that there are a few equivalent values (such as 3 and 9/3) so we got to talk about how those go on the exact same spot on the number line (covering the previous one). We had some good conversations about fractions greater than and less than one. We ran out of time to dig into sqrt(1/5) being greater than 1/5. But we did have a great conversation about 0.7 vs. .75 - the leading zero only on one was purposeful and did bring out a misconception in some students, determining the distance between them and even which one was greater was also challenging. These were great conversations to be having in relative isolation before we ended up stuck on these concepts in the midst of a bigger problem. Of course I don't hold any grand ideations that I have cured my students of all misunderstandings related to fractions and decimals at this point, but it was a great start!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-7p56_dgM9mQ/Vf7MdwLaaBI/AAAAAAAAKE4/Q-juR_v8HI8/s1600/2015-09-18%2B15.06.45.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://2.bp.blogspot.com/-7p56_dgM9mQ/Vf7MdwLaaBI/AAAAAAAAKE4/Q-juR_v8HI8/s320/2015-09-18%2B15.06.45.jpg" width="320" /></a></div><br />I have another support block in the afternoon. This time instead of team teaching we split the class and each ran a mini-lesson, then traded. Our first attempt at grouping kids didn't end well, but the idea was that smaller groups would be nice in the afternoon since we have quite a few who are bouncing off the walls by then. It also means that the other teacher (who is in his second year) only needs to prep for one mini-lesson and he gets to run it twice. We don't get the benefit of adding to each others lessons in real time, but we are discussing ahead of time what we want to make sure the other person focuses on with our students. It should be fun to see how things develop with these two methods of team teaching. I hypothesize that there will be some lessons that lend themselves more toward each. We may have lost our special education co-teachers during these blocks, but that doesn't mean we can't co-teach!<br /><br />Notes on running this activity:<br /><br /><ul><li>Color code your card sorts! The fan was on and apparently I didn't follow <a href="http://drawingonmath.blogspot.com/2015/04/color-coding.html">my own advice</a> last year so when they flew onto the floor they got all mixed up. There was some frantic sorting while the next class started the do now.</li><li>The folded index cards were great for sliding along the clothesline but you do lose a little not being able to see the equivalent values by clipping them below each other. </li><li>Write in marker, not in pen. Duh Tina.</li><li>The best spot we could find to hang the clothesline was toward one side of the room where there were pipes running up the wall on both sides. But the desks were too close to the line and kids were tempted to duck under the line to get to their spot. Possibly because I was standing behind the line. This resulted in cards flying off at least once per class. Move the desks away and model staying in front of the line (or at least enforce it - standing behind the line does make it significantly easier to point things out without blocking)</li></ul><br />Notes on team teaching:<br /><br /><ul><li>I learned the first day we team taught (before the one I just described) that meeting in my room makes the other teachers look toward me for supplies. Even when they had suggested the activity. The answer is now "no, we can't change my plan unless you're going to run it and have all the stuff" because running activities that aren't in my slides apparently causes me to stress. (This is not to say I don't deviate from my plans mid-class, but that I only deviate to things I know how to run and have all the stuff for; especially because running to the copier mid-class isn't an option when you teach solo).</li><li>If someone else is going to run things I need to be open to different ideas. </li><li>We need to be comfortable enough with each other and with students seeing us discussing to take <a href="http://www.shadowmathcon.com/elham-kazemi/">teacher time outs</a>. This will take a bit of relationship building with one of my team members who I haven't had as many opportunities to work with.</li><li>This seems different from co-teaching because my co-teachers haven't been super confident with their math. There's also a bit of "my students" vs. "their students" which may have more to do with how many names I've learned so far, I'll be interested to see how that develops over time. I'm really excited for the opportunity to get to know more students (teaching double blocks seriously limits the number of kids I get to interact with).</li></ul><br /><br />Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-84154544572492945202015-09-04T18:37:00.000-04:002015-09-04T18:37:37.943-04:00Cultural CompetencyWe had our first two days of professional development this year and I'm impressed to say I can't complain. Sure there was some stuff I've seen repeatedly (the same required powerpoint on the difference between an accommodation and a modification along with repeated reminders that 504's are legally binding) but the refresher didn't hurt and the new teachers needed to hear it. A new idea we are working on this year is building our cultural competency. The teacher handbook includes a couple relevant definitions:<br /><br /><b>Cultural competency:</b><br />The ability to interact effectively with people of different cultures and socio-economic backgrounds.<br /><br /><b>Access:</b><br />Ensuring that students have equal and equitable opportunities to take full advantage of their education, generally requiring schools to provide additional services or remove any actual or potential barriers that might prevent some students from equitable participation in certain courses or academic programs.<br /><br />I have to tell you this amazing news right now, immediately after that definition: Free breakfast and lunch for everyone! No activity fees for clubs or sports! It's so unbelievably wonderful! We have always given free and reduced lunch to anyone who qualifies. We have always waived fees for anyone who needed it. But to qualify, we needed to process forms. To know that someone has need, kids had to tell us. When everyone gets free lunch and no one pays fees there's no stigma; there's no barrier to access. When there's no excuse not to eat breakfast and lunch I can nag kids who are hungry and answer my question of "Did you eat breakfast/lunch?" in the negative without worrying that they didn't eat because there's no food at home and they somehow didn't qualify for free meals. Most of the schools in the district qualified for the food grant (the school had to have a certain percentage of students who are economically disadvantaged) and the school committee decided to waive the activity fees (despite the budget crunch) presumably because equity is that much of a priority this year. I'm so proud to work here right now!<br /><br />Okay, end side bar, back to reporting in order:<br /><br />"The professional development in this category will enhance the cultural competence of all high school staff, in order to increase staff and student relationships and improve the overall school culture. As a result, we hope to see a decrease in behavior problems."<br /><br /><a href="http://sites.bu.edu/miccr/" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img height="79" src="http://sites.bu.edu/miccr/files/2014/08/GCIIWeb.jpg" width="200" /></a><br />We are working with the Massachusetts Institute of College and Career Readiness as a Gateway City to achieve this. During five professional development sessions we will work on the following goals:<br /><br /><br /><br /><ul><li>Establish that racial, cultural and economic differences are real and that they make a difference in education outcomes.</li><li>Establish the need for a personal and professional journey toward greater awareness of how race, culture and economic difference impact educational outcomes.</li><li>Demonstrate that difficult topics can be discussed in an environment that is honest, safe and productive.</li><li>Understand what a "welcoming community" is and develop a vision of excellence for all students.</li></ul><div>We started with a comparison of Salem 20 years ago (when our principal was a student at the high school) and now. The statistics have changed dramatically. In 1995 the school was mostly white and middle class (I didn't write down the percentages). Now we are:</div><div><ul><li>60% Economically Disadvantaged</li><li>48% White</li><li>39% Latino</li><li>5% Black</li><li>~30% Special Education</li><li>70% High Needs (economically disadvantaged, special ed, English Language Learner or some combination of the three)</li><li>I don't have current ELL data, but I remember hearing something surprisingly small last year (maybe 13%?) because it only includes students who are currently enrolled in ELL classes. I think the number of students who don't speak English at home would be much more informative.</li></ul><div>Then we took a multiple choice test (standing to vote for our answer) that boiled down to predicting if we write up students categorized by ethnicity below, at or above their population percentage. I was disappointed to be accurate in my choice that we write up Latino and Black students far more often than White students (proportionally speaking) but I was heartened to see that a decent percentage of the staff was aware that this might be the case.</div></div><div><ul><li>68% of write ups and ~80% of suspensions are Latino students (39% of our population)</li><li>22% of write ups and ~20% of suspensions are White students (48% of our population)</li><li>7% of write ups (and some non-zero number of suspensions) are Black students (5% of our population)</li></ul><div>We discussed these statistics in our tables (which were strategically grouped to be a cross section of grade levels and departments) and then shared out some ideas. We also discussed a situation where a teacher made some broad assumptions (a student was frequently absent from school so the teacher was going to talk to the parents about the importance of education). As a staff we have a lot of learning to do (myself included!) but I think that most everyone is open to learning. It's really hard not to be when the person leading these discussions is so engaging and dynamic that it feels like I'm listening to spoken word poetry when she speaks!</div></div><div><br /></div><div>Notes: </div><div><ul><li>I'm struggling with the feeling that I want to defend our data. But I'm not going to. Are there reasons that might skew the data? Sure. Is that any excuse for how incredibly biased we appear to be? Absolutely not.</li><li>In one of the ELL presentations the presenter mentioned that the language (e.g. Formerly Limited English Proficient) is not very positive. I know about person-first language but I might not have done such a good job today. I'm learning, we'll get there.</li></ul></div><div><br /></div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com5tag:blogger.com,1999:blog-812794395259173668.post-22168499194986892962015-08-27T15:32:00.000-04:002015-08-27T15:32:20.360-04:00Math Practice Standard PortfoliosAt our <a href="http://drawingonmath.blogspot.com/2015/07/district-sbg-implementation.html">standards based grading implementation</a> meeting the teacher working with us from the charter school asked about how we wanted to include the <a href="http://www.corestandards.org/Math/Practice/">CCSSM Standards of Mathematical Practice</a>. At the time we weren't sure but I've done some more thinking:<br /><br />Last year I asked PreCalc kids to journal sometimes on which one they'd used that day. They referred to <a href="https://www.scribd.com/doc/112325868/Math-Practice-Posters">posters</a> I have in the back of the room to choose one. I never asked Algebra 1 kids to do the same, but they're fully capable of it.<br /><br />While I want to assess them, because they're important, I don't want to require every kid to use the same practice on a single assignment (because that's not the point). However, assessing students on whatever standard(s) they do use sounds like a logistical nightmare, especially since we aren't due to get an SBG friendly online grading system until second semester at the earliest.<br /><br />Instead, what if I made the kids keep track? Basically, a portfolio! Kids would get the sheet below early on in the year and I'd tell them that they will need to find four good examples in their work of how they used the mathematical practices each quarter. That makes sixteen examples, two per standard. I could check their binders mid-quarter and near the end of quarter (providing enough time for revisions before report cards) and give them one SMP score based on the quality of their examples and explanations.<br /><br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="https://www.scribd.com/doc/276245930/Math-Practices-Portfolio" style="text-decoration: underline;" title="View Math Practices Portfolio on Scribd">Math Practices Portfolio</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_18207" scrolling="no" src="https://www.scribd.com/embeds/276245930/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />Reviewing my student friendly phrases, I feel like the modeling standard should include something about interpreting in context. Do the rest seem sufficiently clear?<br /><br />I wanted to make this fit on a single sheet front and back but I also want them to write a decent explanation. Maybe we should do one example of each per semester? It would still be four per quarter but that way I could give them one sheet for each semester which means more room to write. And that way they can't leave all the seeing structure examples until fourth quarter when they may not have two good examples of it. A possible alternate handout:<br /><br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="https://www.scribd.com/doc/276543173/Math-Practices-Portfolio2" style="text-decoration: underline;" title="View Math Practices Portfolio2 on Scribd">Math Practices Portfolio2</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_7203" scrolling="no" src="https://www.scribd.com/embeds/276543173/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />Have you done this with your students? How did it work? I'm still not entirely clear on what the evidence should look like. How would you make the reflection meaningful? Can you edit the following invented student responses to make them better? I'm definitely going to need some quality examples make this a valuable venture.<br /><br />"You can see I persevered in this problem because I tried three different equations before finding one that worked. I highlighted all three trials and boxed my final answer. My final equation is the one that makes sense because ____."<br /><br />"In this problem I made a table and a graph. I found the pattern in the table which helped me to identify the slope of my line. I labeled the y-distances in green and the x-distances in blue on the table and the graph. In the original problem that slope means ____."Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com4tag:blogger.com,1999:blog-812794395259173668.post-16940941485359843002015-08-21T14:18:00.003-04:002015-08-21T14:19:07.964-04:00Algebra, the first monthOur first unit in Algebra 1 is focusing on the <a href="http://drawingonmath.blogspot.com/2015/07/district-sbg-implementation.html">priority standards</a> of Number Sense and Evaluating Functions. Four of the seven of us who will be teaching the course had the opportunity to work together this summer to map out the unit. That's five math teachers and two special ed teachers - our double block classes changed this year from co-taught every day to co-taught every other day and the math teacher with a smaller group (a subset of the co-taught Algebra 1 class so kids will have the same teacher both days) on the opposite day for a support class. Our goal with the support class is to do some pre-teaching and work on foundational skills that we'll need for the full class. In the map below that's the grayed out B Days. To recap- some kids will have class 90 minutes every other day, they'll do the white rows. Some kids will have class 90 minutes every day, they'll do all the rows.<br /><br />It was fun to work with the team to find resources because we had plenty of time to share our ideas and search for new ones - they know about the MTBoS but none of them have jumped in (yet?). All the materials for the unit are in a <a href="https://www.dropbox.com/sh/k88wlregkdypfvt/AAAy3NdSH2TrS6ZkzMfzP1m2a?dl=0">dropbox folder</a>. I'm sure we'll stray from this map by the end of the first week, but I'm so excited to have something available to refer to!<br /><br /><a href="https://www.scribd.com/doc/275498237/Unit-1-MAP" title="View Unit 1 MAP on Scribd">Unit 1 MAP</a><br /><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_59555" scrolling="no" src="https://www.scribd.com/embeds/275498237/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />Vocab:<br />Mad Minute: It's not a race to do the whole sheet in a minute, it's a promise we'll only do this rote practice for two minutes, and it's as close as I ever get to pre-testing.<br /><br />Exit Ticket: We don't know how we're going to have to grade the support class, we think it will be pass/fail. If so, the exit ticket will be a problem or two related to what we worked on that class and will be something in the online gradebook to appease admin :)<br /><br /><a href="http://drawingonmath.blogspot.com/2013/08/geometry-curriculum.html">Flapper:</a> An index card summary: definitions/generalizations go on the front of the card, an example goes on the back. They're taped to cardstock so they <i>flap</i>.<br /><br />TIP chart: Three column vocab organizer. Term, Information, Picture.Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-86225294922920663992015-08-20T11:47:00.001-04:002015-08-20T11:47:22.457-04:00Summer ReadingJ, my rising eighth grader, has a summer reading assignment, as most kids do. I have a few stories to share about our summer reading experience. There's a <a href="http://talkingmathwithkids.com/">t</a><a href="http://talkingmathwithkids.com/">mwyk</a> story* at the end, don't miss it just because you're not excited to read about reading!<br /><div><br /></div><div>At the beginning of the summer J had no interest in reading, it's hard for her and she just wanted to be on summer break. I offered her some choices for our daily reading time including: finding fun articles/blog posts, <a href="http://amzn.to/1hsrSKy">What If</a> (from the creator of <a href="http://xkcd.com/">xkcd</a>) and Charlotte's Web. She chose me reading her Charlotte's Web (yay! She wants to spend time with me!). I made the novice mistake of introducing it as a kids book which then made her question if she could use it for summer reading. <i>Hey Tina, you know better than to tell your ninth graders that the worksheet is from a third grade math site, what matters is that it's interesting and appropriate. This applies to all things, even at home.</i> Anyway, we recovered from that. As we read I was thrilled to find Charlotte using great vocabulary and Wilbur modeling excellent questioning techniques to understand. It had me wondering if there's a mathematical equivalent to a story with one character advanced and another character trying to learn. The <a href="http://cmeproject.edc.org/">EDC</a> does great model conversations in their books, but what if we showed students an example of a new math technique and had them ask questions. Is this just another way to use notice and wonder?</div><div><br /></div><div>We eventually finished Charlotte's Web and J picked out a graphic novel to read next (from the <a href="http://amzn.to/1K8C45S">Lunch Ladies</a> series). The summer assignment, by the way, was to read two books and submit reviews online. Any type of book they want! The reading specialist even said that research shows independent reading books should be a bit below the child's current reading level - the goal is to practice with something that is comfortable. J picked a book that was definitely easy for her, but I learned! I didn't say anything about it being a kids book, instead I was thrilled she'd picked out a book herself. She read it independently and was even willing to read before our usual scheduled reading time. While she read her book, I read my own. I was confused about what was happening in my book and J scolded me for interrupting her. She finished the whole book and was so proud of herself!<br /><br /></div><div>*<a href="http://talkingmathwithkids.com/">TMWYK</a> paragraph here</div><div>J wondered aloud how many pages the book she had just finished (in such a short time!) was. But the book didn't have any page numbers. I asked her to take a guess and she didn't have any idea. There was a 100 page book on the table so I told her, "This book is 100 pages, how long do you think yours is?" She decided to use the book as a ruler! She held them up next to each other, then matched them up spine to spine and determined that her book was over 100 pages. I asked, "A lot longer? A little? One and a half times as long?" She decided on one and a quarter. So I asked what a quarter of 100 was. "Hey! No, you always trick me into talking about math." I laugh silently and think: we've been talking about math kiddo, and I'm not trying to trick you, but, yes, we are talking about math. I smile broadly and say, "You can do that... What a quarter?" She says twenty-five cents. "So what's a quarter of a hundred?" Twenty-five. Great. I was done with the conversation and was going to continue reading my book when I saw her pick up her hundred page 'ruler' again. I watched her line up the books, mark the spot with her finger, open the book to her measured out 100 pages, and start counting aloud. She wanted to know if she was right! I watched, impressed that she counted pages (I was thinking about how many sheets of paper, but that's not how you number the pages of a book) and when she got 22 as her result I was seriously impressed! </div><div><br /></div><div>Since then she read the other book (in that series) we'd gotten from the library without prompting. And then she asked to go to the library (wonderful surprise! Of course we'll go!). When we got there she grabbed all the other books in the series without hesitation. As we headed out of the library with our piles of books she was able to verbalize that she likes these books because she likes reading short stories. I think I have a Shel Silverstein book from my childhood, that might be my next suggestion...</div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com2tag:blogger.com,1999:blog-812794395259173668.post-43065247094899768012015-08-15T22:58:00.001-04:002015-08-16T12:56:28.390-04:00I Did That?About a year ago, the EDC ran a training for <a href="http://ecmi.edc.org/">eCMI</a> table leaders. These individuals would be returning home and attending online PD with their departments throughout the school year. The PD is problem sets provided by EDC, but since these are remote sites, the table leaders would manage the participants and report back to whoever was running the session from Boston. Since I've been a table leader at PCMI (the live, in person, 3 week intensive version of eCMI) they invited me to model for the group. This was a fascinating experience. We spent some time working some problems together and engaging in discussion. They were an easy group to manage. When we finished the demo I was asked to explain what I did - this was shockingly hard to do. I could spout back some tenets of the program (don't give answers, you don't need to know any formulas to solve the problems so don't teach) but had no idea what else to say. People started asking questions and my answers surprised me. Someone from the EDC asked how I dealt with one of the quieter participants. My first reaction was "like everyone else" but that obviously wasn't true. I realized that I'd made a choice to let her work independently. Then at some point I'd made a choice to check in. Then I prompted a conversation with her neighbors who had a different perspective. After sharing that (and a few reasons why plus an anecdote about a particularly independent table member I'd had previously) the participant in question responded. She shared that I'd managed her very well, especially because she does not usually enjoy group work, and she hadn't even noticed what I'd done until I explained it.<br /><br />It was this interaction in particular that struck me, and that continues to strike me (I've discussed this day with several people this summer so apparently it's really stuck with me). When teacher as facilitator works, it seems effortless for both the student and the teacher. Neither of us noticed that we were doing a particularly good job working together until someone else asked. (It might've been <a href="https://twitter.com/bowenkerins">Bowen</a> who facilitated this realization.) I've heard the claim that the only people who make more decisions per minute than teachers are air traffic controllers, but I've never considered how many of those decisions are subconscious. Or maybe more accurately, conscious but not noteworthy? Reflecting back on twenty minutes of teaching, I couldn't identify my best teacher moves. I can sometimes identify my worst ones, those moments where the class or the interaction is suddenly derailed. But most days I attribute successful classes to a good lesson plan, or students having a particularly good day. I never celebrate something I did during the time I was teaching. Do we even have the language to describe such things?<br /><br />I am curious how I can have more of these realizations. How can I reflect on this aspect of my teaching? And I'm also concerned. If I never consciously think about where I give my attention, how can I eliminate bias in my teaching? Short of demanding Bowen observe my classes and ask insightful questions, what can I do?<br /><br />Two possibilities come to mind:<br /><br /><ul><li>Someone makes a list of things to be aware of, I pick one to focus on for the day or for the week. This could make an awesome blogging series if others joined in.</li><li>I record video and convince people to ask me questions. I don't think I can post it publicly though. And how would I know which chunk to share so that there's something interesting? Maybe that's exactly the point - I choose the most boring ten minutes I can and then others convince me I was still doing something worthwhile (or should've been).</li></ul>This whole thing has me curious about teacher prep. Is this why people say that teacher prep is useless and you either can teach or you can't? It takes a trained eye to recognize key decisions, how do we train more eyes?Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com1tag:blogger.com,1999:blog-812794395259173668.post-76592728277433427202015-08-15T22:00:00.001-04:002015-08-15T22:00:35.918-04:00Now What?I spent one afternoon at <a href="http://www.twittermathcamp.com/">TMC</a> listening to <a href="https://twitter.com/pegcagle">Peg Cagle</a> and <a href="https://twitter.com/_levi_">Levi Patrick</a> talk about ways to grow as teachers without leaving the classroom. As <a href="http://drawingonmath.blogspot.com/2015/08/making-our-global-math-department-more.html">I mentioned before</a>, TMC brought to the forefront that I'm entering a new stage of my career, and I don't know what that means. Peg and Levi pointed out that there aren't pathways for growth in the US if you're a teacher. This isn't the case everywhere though. In China there are levels to achieve and (diverging) pathways to take as you grow as a teacher. They gave some examples - mentor, research, write a book, spend part of your schedule training pre-service teachers, other things I don't recall. At least in my district, there's no support to do anything beyond my regular teaching schedule. And the teacher leaders are the ones who sign up for committees - which I hate doing because they're typically run during school and remove me from my class. Because I don't want to stop teaching. I love teaching. But it no longer requires 100% of my energy and I want to do more.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/--3UKjbzCT6g/Vc_skL50W3I/AAAAAAAAJiQ/Z4ID6D9hAj0/s1600/tweets2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="69" src="http://4.bp.blogspot.com/--3UKjbzCT6g/Vc_skL50W3I/AAAAAAAAJiQ/Z4ID6D9hAj0/s320/tweets2.JPG" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-MOF738tT0mc/Vc_skKuGmHI/AAAAAAAAJiU/7XrlC-QRvqc/s1600/tweets1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="59" src="http://1.bp.blogspot.com/-MOF738tT0mc/Vc_skKuGmHI/AAAAAAAAJiU/7XrlC-QRvqc/s320/tweets1.JPG" width="320" /></a></div><br />So what are my options? I sign up each year to mentor new teachers, because sadly our department turnover is so high that we hire at least one math teacher every year. But this year we lucked out and hired only experienced teachers! They'll certainly need some support learning about our school, but they're much more established than teachers I've mentored in the past.<br /><br />I never had any intention of writing a book, but <a href="http://nixthetricks.com/">that happened</a>. I spoke at several conferences last year but working the conference circuit holds no appeal to me. I don't like to travel far just to spend a day somewhere. As appreciative as I am that so many people want to learn more, presenting to large groups isn't engaging in the way that teaching a class is. Finally, I hate missing school (if you're reading this you don't need me to tell you why).<br /><br />I see <a href="https://problemproblems.wordpress.com/2015/08/10/7-how-kids-might-think-about-different-types-of-equations/">Michael</a> and <a href="https://fivetwelvethirteen.wordpress.com/2015/08/10/what-inquiry-has-to-offer/">Dylan</a> digging into topics to explore them from multiple perspectives. This doesn't appeal to me, though I do enjoy scanning their writing to glean new information. I participated in a teacher cabinet advising the mayor last year, but I didn't find that we did anything impactful. So what's left?<br /><br />This summer I've had the opportunity to do some curriculum work (Paid time! Not taking away from class time! Amazing!) with other teachers in my department. One day our leader from the charter school pointed out how wonderful it was to be doing this work with people who all know the content. That day I was working with our department head (another leadership position I don't really want because right now it's all bureaucracy, with only two teaching blocks) and another teacher who has taught five sections of Algebra 1 for each of the past three years. The same thing happened this past week, there were four of us in the room and with four years of Algebra 1 classes, I might have been the one with the least experience with the course. I also don't want to do curriculum work all the time, but these sessions made me appreciate the expertise of my co-workers. It's so much easier to work with people when I can say, "We need a lesson for the scientific notation part of this standard" and everyone 1) knows what's reasonable to ask our students, 2) has an idea from what they've done in the past, 3) can quickly assess other resources we discover, 4) can take my half sentence and turn it into a lovely handout doing exactly what I want (well, that may have more to do with us getting along that I didn't need to finish my sentence), 5) checks for common misconceptions and discusses how to address them. This is the benefit of having teachers stay in the classroom: we mapped out a month of classes (including a new Algebra support block), made student friendly handouts for all those lessons and chose assessment questions for each of the skills in the unit, in twelve hours. Two half days and a full day and we have photocopy ready plans for a month. There are some parts of class that aren't mapped out (we'll probably all do different openers and closers) and every pacing guide is meant to be broken, but what a huge accomplishment! (Right now all the files are in different places, including the school network, but once they're organized I promise to share.) These occasions make me see how important it is to have ways to keep these teachers in the district, in the classroom, with the students who deserve a teacher who knows what they're doing.<br /><br />I still haven't answered the question of now what? Soon the answer will be "teach" because despite a decade of doing this, I still have a terrible time learning names. I never remember to make extra copies of the syllabus for Meet the Teacher Night. I always want to try something new, or have to try something new, because every group of students is different. There is one more thing that I want to consider, but I'm going to make it a separate post because it raises many important questions, beyond those of teacher professional paths. Stay tuned...<br /><br /><br />Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0tag:blogger.com,1999:blog-812794395259173668.post-42166675931477394172015-08-03T21:04:00.001-04:002015-08-03T22:57:20.864-04:00Making Our Global Math Department More GlobalI realized at the end of TMC15 that I hadn't gotten any new lesson ideas, because I hadn't gone to any sessions focused on content. As I mulled over that fact I realized it said a lot about where I am as a teacher. I'm not teaching any new preps this year. It will be my sixth year in the same school, ninth year teaching. If you allow me to count student teaching I've been in the classroom for a decade. I attended sessions that made connections, whether they be K to 12, ELL to math, teacher to leader, MTBoS to NCTM... I love teaching, new lesson ideas are always welcome and I can't wait to plan with my co-workers next week and get back to the classroom next month. But these things don't have to be my top priority at a conference because I'm comfortable in my role as educator, my top priority is helping others reach this point - and one way to do it is to expand the reach of our community.<br /><br />This spring I organized and worked at a <a href="http://drawingonmath.blogspot.com/2015/04/mtbos-booth.html">booth at NCTM</a>. Once again I didn't attend many content sessions, as I <a href="http://drawingonmath.blogspot.com/2015/04/nctm-boston-experience.html">mentioned before</a>. Engaging with people in our community and introducing new people to our plethora of resources was too much of a draw for me to want to leave. I realized that weekend exactly how hard our community is to describe. Sam did a nice job explaining the <a href="http://samjshah.com/2015/07/27/my-thoughts-about-the-evolution-of-the-mtbos-2015-edition/">Evolution of the MTBoS</a> in a recent post. It is precisely because we have so many voices that we are so hard to describe - but by the end of the conference I decided that Global Math Department is the best descriptor. People understand that a department is made up of different teachers with different voices, and if we describe ourselves as the ideal department - one that collaborates and celebrates together - then people have a better chance of beginning to understand who we are before they get scared away by newfangled technology like Twitter. When I get around to writing my letter to a newbie, that's how I will explain what we are. Maybe you have a better metaphor? Sam wants you to share it:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://twitter.com/samjshah/status/626991363536625664"><img border="0" height="211" src="http://3.bp.blogspot.com/-KPhAYAbNmy0/Vb_-5nEKWVI/AAAAAAAAJcw/7qtECq0_RJc/s320/Capture.JPG" width="320" /></a></div><br />Sam (and Julie and I) also want you to share some thoughts that will be specifically helpful with the new blogger initiation we'll be running in November. What are the <a href="https://docs.google.com/document/d/1u1Wh-_oBT4PklQsJCTPj1FtxA7_D6kUNqv7klL-Uu7M/edit">MTBoS FAQs</a>? What <a href="https://docs.google.com/document/d/1HWXOjH24rY01_m25jwUI6zZshzAXbNj-xcjotMUDsrk/edit">lingo is confusing</a>? What else should we <a href="https://docs.google.com/document/d/1-aviqegkbtgWFR6UiK-QPdcvi1nDJ7sYVQmxIjgv6sc/edit">think about</a>? It might help to peruse the <a href="http://exploremtbos.wordpress.com/">past iterations of this initiative</a> if you have no idea what I'm talking about.<br /><br />We are running the initiative in November because it will follow the NCTM regional conferences. If you're going to Nashville, Robert is helping to organize that group:<br /><br /><div class="stream-item-header" style="background-color: #f5f8fa; color: #292f33; font-family: Arial, sans-serif; font-size: 14px; line-height: 19.25px;"><a class="account-group js-account-group js-action-profile js-user-profile-link js-nav" data-user-id="745583288" href="https://twitter.com/robertkaplinsky" style="background: transparent; color: #8899a6; text-decoration: none;"><strong class="fullname js-action-profile-name show-popup-with-id" data-aria-label-part="" style="color: #292f33;">Robert Kaplinsky</strong> <span class="username js-action-profile-name" data-aria-label-part="" style="direction: ltr; font-size: 13px; unicode-bidi: embed;"><span style="color: #b1bbc3;">@</span>robertkaplinsky</span> </a><small class="time" style="color: #8899a6; font-size: 13px; margin-right: 5px;"> <a class="tweet-timestamp js-permalink js-nav js-tooltip" href="https://twitter.com/robertkaplinsky/status/628252851601420289" style="background: transparent; color: #8899a6; text-decoration: none;" title="9:45 PM - 3 Aug 2015"><span aria-hidden="true" class="_timestamp js-short-timestamp js-relative-timestamp" data-long-form="true" data-time-ms="1438622126000" data-time="1438622126">2h</span><span class="u-hiddenVisually" data-aria-label-part="last" style="border: 0px !important; clip: rect(1px 1px 1px 1px) !important; height: 1px !important; overflow: hidden !important; padding: 0px !important; position: absolute !important; width: 1px !important;">2 hours ago</span></a></small></div><div class="TweetTextSize TweetTextSize--16px js-tweet-text tweet-text" data-aria-label-part="0" lang="en" style="background-color: #f5f8fa; color: #292f33; font-family: Arial, sans-serif; font-size: 16px; line-height: 22px; white-space: pre-wrap; word-wrap: break-word;">Are going to <a class="twitter-atreply pretty-link js-nav" dir="ltr" href="https://twitter.com/NCTM" style="background: transparent; color: #8b1a1a; text-decoration: none;"><span style="color: #b97575;">@</span>NCTM</a> Nashville in Nov? Please fill out this form to help us figure out if we can run a <a class="twitter-hashtag pretty-link js-nav" data-query-source="hashtag_click" dir="ltr" href="https://twitter.com/hashtag/MTBoS?src=hash" style="background: transparent; color: #8b1a1a; text-decoration: none;"><span style="color: #b97575;">#</span>MTBoS</a> booth. <a class="twitter-timeline-link" data-expanded-url="https://docs.google.com/forms/d/1JLQE-pj_1kSE8GaheEOqs7ru62gsmgYI-wfRkmMjvRo/viewform" dir="ltr" href="https://t.co/5NMO4mMtNV" rel="nofollow" style="background: transparent; color: #8b1a1a; text-decoration: none;" target="_blank" title="https://docs.google.com/forms/d/1JLQE-pj_1kSE8GaheEOqs7ru62gsmgYI-wfRkmMjvRo/viewform"><span class="tco-ellipsis"></span><span class="invisible" style="font-size: 0px; line-height: 0;">https://</span><span class="js-display-url">docs.google.com/forms/d/1JLQE-</span><span class="invisible" style="font-size: 0px; line-height: 0;">pj_1kSE8GaheEOqs7ru62gsmgYI-wfRkmMjvRo/viewform</span><span class="tco-ellipsis"><span class="invisible" style="font-size: 0px; line-height: 0;"> </span>…</span></a></div><br />If you're going to Atlantic City or Minneapolis (or San Francisco, why not plan ahead!) and have any interest in running a booth, please comment here or <a href="http://twitter.com/crstn85">tweet at me</a> (I promise we did all the work last year, your role will be pure fun!). If you're not interested in organizing a booth but are presenting at any conference, please consider giving out some sort of info card. <a href="https://docs.google.com/document/d/1gN8sW0Ti_KH_Kw0E4UYQE5FiTrgekOVBi_o-ZwXrTmw/edit">This one</a>, modified from the NCTM version, might give you some ideas.<br /><br />Like Sam, one of the things that I love is this community. Will you help us share it?Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com1tag:blogger.com,1999:blog-812794395259173668.post-26420545191477866312015-07-17T15:22:00.000-04:002015-07-17T15:22:26.051-04:00District SBG ImplementationI am so excited!! The district decided to move to K-12 Standards Based Grading. They spent the past year researching, including consulting with Bob Marzano, Kim Marshall and Tom Guskey. The charter school in the district has been using SBG so the leadership team did site visits to learn more. This summer there were two 3 day workshops for teachers who are going to pilot the program to learn and begin the work. There is a three year plan unfolding. If you know anything about working in schools that serve high need populations, you might know just how flabbergasting this paragraph is. Teachers rarely see roll out of initiatives as intentional, most initiatives last a few months before the next one comes along. I thought I was going to have to spend the week holding my tongue and deciding what points were worth fighting for, instead I was floored by the level of preparation and I got to spend my time digging into the important questions. The work I got to do the past three days made so many connections - the work we have done building curriculum maps over the past two years led beautifully into our task this week of choosing priority standards and writing progressions. It's amazing. What a beautiful gift to get this summer to renew my faith in our ability to succeed as a district!<br /><br />I have to say, the work of unpacking the standards is something that's absolutely worth doing yourself. I was on the geometry team when we did our curriculum mapping so this was the first time I'd carefully analyzed the algebra standards. I followed the map, but I knew what we needed in Algebra 1 from teaching it five years ago and since I only taught below grade level kids this year the small shifts to push further in Algebra 1 compared to the previous Massachusetts standards didn't apply. But, since not everyone has the luxury of three days of curriculum work with their team, I'm happy to share what we came up with (below).<br /><br />Our year was already divided into units. We took all the units and found priority standards to fit those units. Then we distributed the remaining standards for Algebra 1 (according to Appendix A) as supporting standards for the priority standards. Once we had all of those mapped out we identified the skills students need to demonstrate to be proficient. The skills were divided into a "Score 3" and "Score 2." A two is partial understanding and a three is proficient. So we separated out the more complex skills and declared those as the requirement to earn a three.<br /><br />These are far from final, but I am amazed how much work we got done - the three mornings were spent on an introduction to the philosophy of SBG and some whole group discussion. Then we had the remainder of the morning and our afternoons to work in content teams. We were so productive since we had long stretches of uninterrupted time to wrap our heads around the ideas, get into a groove and maintain momentum. We had teams of grade 3 math, grades 4/5 math, Algebra, Biology and grade 9 English represented. Last week they had a few other teams. At the high school we are hoping to pilot SBG with the entire 9th grade team, at other schools they are looking at one subject per grade level. There are a lot of details on how to make this work with our existing grading software but I think we're up for the challenge. (Speaking of, if you know a program that does SBG and student information services well, I would be happy to pass that recommendation along to the district!)<br /><br />Without further ado:<br /><br /><a href="https://www.scribd.com/doc/271859747/Algebra-1-Priority-Map">Curriculum Map</a><br /><br />My<a href="https://www.scribd.com/doc/271859656/Grade-Scale"> poster for explaining the scoring</a> (that I think still aligns with the district understanding)<br /><br /><a href="https://www.scribd.com/doc/271859721/Math-Practice-Posters">Math Practices Posters</a><br /><br /><a href="https://www.scribd.com/doc/271859748/Algebra-I-Priority-Standards">Priority Standards and Proficiency Scales </a>(The blank pages help with double sided printing)<br /><br /><div><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="https://www.scribd.com/doc/271859748/Algebra-I-Priority-Standards" style="text-decoration: underline;" title="View Algebra I Priority Standards on Scribd">Algebra I Priority Standards</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_39647" scrolling="no" src="https://www.scribd.com/embeds/271859748/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /></div><div><br /></div>Tina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com2tag:blogger.com,1999:blog-812794395259173668.post-88200291671760430152015-07-13T17:00:00.000-04:002015-07-13T17:00:02.180-04:00TMC Morning SessionTwitter Math Camp is coming up soon! We just emailed people who listed our morning session as a first or second choice but it's not too late for you to decide to join us! (In person or virtually by following #TMC15 #equiv)<br /><br /><br /><div style="text-align: center;"><b>Comings and Goings: Building a Shared Understanding of </b></div><div style="text-align: center;"><b>Math Education </b><b>from Kinder through Calculus</b></div><br /><b>Session Description:</b><br /><br />Are you an elementary or middle school teacher who has wondered, “Why do my students need to know this?”<br /><br />Are you a middle or high school teacher who has wondered, “Didn’t they learn anything about this in earlier years?”<br /><br />In teaching it’s crucial to know both where our students are coming from and where they are going. But the people who teach young kids and older students often don’t even work in the same building. How can we help struggling high school students, and what matters most in the elementary years? In this session we’ll bring math teachers for students of all ages together to build deep knowledge about the math that our students are learning. <br /><br />In each day of this three-day session we’ll look at a different topic that cuts across the curriculum. Topics may include: proportional reasoning, the distributive property and area. Our goal is for every participant to leave this session with some new questions and serious food for thought. Come draw connections across grade levels, deepen your curricular understanding, better understand the CCSS, write great problems for students of all ages and be part of a one-of-a-kind conversation.<br /><br />Presenters:<br />Jennifer Bell<br />Tina Cardone<br />Brian Stockus<br />(Remote: Michael Pershan)<br /><br /><br /><b>Email:</b><br /><br />We are going to spend some time discussing the big idea of equivalence through the lenses of the distributive property and proportional reasoning. If you have a favorite resource (or three!) related to one of those topics we would encourage you to bring it along. (No need to make copies, a digital file that would be easy to edit would be ideal but any contribution is welcome.) We will be tweeting, working in google drive and using padlet during our session - if you have a device with you at TMC, please bring it to the session.<br /><br />Brian found a great article relevant to our goals: <a href="http://www.authenticeducation.org/bigideas/sample_units/math_samples/BigIdeas_NCSM_Spr05v7.pdf">http://www.authenticeducation.org/bigideas/sample_units/math_samples/BigIdeas_NCSM_Spr05v7.pdf </a><br /><br />Perhaps you can read it poolside before TMC, or on the plane or in the car (but not if you’re driving!) on the way to TMC.<br /><br />We look forward to learning with you all soon,<br />Jennifer Bell, Brian Bushart, Tina Cardone, Michael PershanTina Cardonehttps://plus.google.com/112203737799714958050noreply@blogger.com0