tag:blogger.com,1999:blog-812794395259173668Sat, 22 Nov 2014 16:09:45 +0000Teaching_PracticesGeometryPre-CalculusAlgebranixfosterTMCDrawing On MathPonderings of a high school math teacher.http://drawingonmath.blogspot.com/noreply@blogger.com (Tina C)Blogger236125tag:blogger.com,1999:blog-812794395259173668.post-7277881915626202435Sat, 22 Nov 2014 15:56:00 +00002014-11-22T11:08:54.618-05:00fosterAge vs. Birth Year (#tmwyk)Last night I was talking to my 13 year old foster daughter (she's been here for over 3 months! hard to believe!) and the conversation wound around to my college 80's themed dodgeball competition, which somehow transitioned to J asking what year her friend Katie was born if Katie is 30 now.<br /><br />You can figure that out.<br />J: I don't know<br />Well, how old was she in 2004?<br />J looks at me like this is an equally difficult question and she has no idea why I asked it.<br />It's 2014 now, how old was she in 2004?<br />J: Oh. She was... 20.<br />Okay, so how old was she in 1994?<br />J: She was 10... So she was born in 1984!<br /><br />Conversations about the 80's continue. Then J asks what year I was born (I'm 29), then answers her own question - 1983! I shake my head, "I'm one year younger than Katie." J realizes that I was born in 1985, and proceeds to share her thought process (which I don't remember word for word but I <b>love</b> that she already knows we're going to have this conversation and wants to share). We discuss how it seems like one year younger should mean subtract one from the birth year, but it actually means I was born one year more recently.<br /><br />Then J turns the conversation to how old she will be in the future.<br /><br />J: How old will I be in 2025?<br />You can figure that out.<br />J (pulls out a chair and sits): Let me think about this... In 2015 I'll be 14.<br />(Mentally I'm super excited that she's about to use the count by decades strategy I walked her through earlier)<br />J: In 2016 I'll be 15.<br />(Mentally I'm sad she didn't use the strategy but interested to see if she'll count all the way there. And keeping my mouth shut with a neutral/interested expression on my face.)<br />J: In 2017 I'll be 16.<br />(Her face lights up and I realize the alternate strategy at the same time she does.)<br />J: So in 2025 I'll be 24!<br />What did you just realize?<br />J: Since I was born in 2001 I can find my age by subtracting one from the year! So if I forget how old I am I can always ask someone what year it is.<br />People might think you have a concussion if you don't know what year it is.<br />J: Well if I forget what year it is I can always ask myself, "How old are you, J?" (we laugh because she asks this very expressively, sometimes 13 is a really fun age) ... In class today they were asking us about what life would be like in 2050. So I was wondering how old I would be and I figured out that subtract one thing.<br /><br />So then she wanted to know what year it would be when she turned 99. My first thought was year 3000, but as I was thinking that she was saying 99+1=100 so I realized that it would be 2100, not 3000. While I was realizing how much more sense that made, J was saying how it wouldn't really be 100, it would be 3000. I should have asked her how she got that, but I was doing too much thinking of my own so instead I went with, "You were born in 2001, how long from then is 3000?" She realized her mistake and then I shared that I'd done the same thing!<br /><br />Conversation turns to getting old and how long she wants to live and me telling her that 70 is not old enough to plan on being done living. I told her that the average lifespan is in the 70's and that average means middle - so lots of people live longer than that. That factoid didn't lead to her doing any more math, which was just fine with me.<br /><br />Things that make me happy about this entire interaction:<br />J asked all the questions.<br />When I took her down a path where I modeled a strategy, she figured it out and continued the strategy on her own.<br />She was thinking about math and patterns outside of her math class (during the morning, plus this conversation).<br />She wanted time to think, and told me as much.<br />She didn't just tell me the pattern (year - 1=age) she also told me why (I was born in 2001).http://drawingonmath.blogspot.com/2014/11/age-vs-birth-year-tmwyk.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-1643132014642919586Sat, 22 Nov 2014 02:28:00 +00002014-11-21T21:28:50.571-05:00AlgebraDistance GraphWe are working on slope in my Fundamentals of Algebra classes. In my Laying the Foundation/NMSI training last year the leader recommended using piecewise graphs as a natural way to compute slope repeatedly and to provide opportunities to compare slope. Today I did just that!<br /><br />I gave my algebra students the graph below, without a story or any questions to answer, and asked them what they noticed and wondered.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-VJ3NwVhOiKA/VG_xm8G692I/AAAAAAAAGLc/-3kHQ6-PDmk/s1600/2014-11-21%2B16.15.33.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-VJ3NwVhOiKA/VG_xm8G692I/AAAAAAAAGLc/-3kHQ6-PDmk/s1600/2014-11-21%2B16.15.33.jpg" height="271" width="320" /></a></div><br /><br />Here is a record of their noticings and wonderings pretty much verbatim<br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-VpGN2ujT5uc/VG_xvX9zy6I/AAAAAAAAGLk/OX4Q22arvlc/s1600/Capture3.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-VpGN2ujT5uc/VG_xvX9zy6I/AAAAAAAAGLk/OX4Q22arvlc/s1600/Capture3.JPG" height="232" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">My SMART board has been so spastic. It is now connecting<br />words even if I pick up the pen between them.</td></tr></tbody></table><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://4.bp.blogspot.com/-LdPh0mJEfTw/VG_xv7tJosI/AAAAAAAAGLw/2vw-BGELWao/s1600/Capture.JPG" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-left: auto; margin-right: auto; text-align: center;"><img border="0" src="http://4.bp.blogspot.com/-LdPh0mJEfTw/VG_xv7tJosI/AAAAAAAAGLw/2vw-BGELWao/s1600/Capture.JPG" height="190" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">A student added the 7 hours observation during our discussion later.</td></tr></tbody></table><br /><br />Once I had everything recorded, I asked them to be more specific. "Someone said 'It is increasing' what is 'it'?" I pushed them until they read the entire label on the y-axis. Then I asked, "What does that mean?" Someone would realized that the person is walking away from home. To drive the point home I pointed to the graph - "This isn't a mountain. They aren't necessarily walking uphill. The graph is telling you <b>distance from home</b>, not height." I continued to pull together their various noticings and wonderings until they had a complete picture. I was so impressed that when I asked one class about their "goes positive, then goes negative" observation they identified that as positive slope and negative slope! These Transitions to Algebra workbooks from EDC just might be working!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-bR7HDvSVU9Y/VG_xvseb9cI/AAAAAAAAGLo/qKDNSS1esz0/s1600/Capture2.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="http://2.bp.blogspot.com/--3zUsOrOrj0/VG_xv9jTlfI/AAAAAAAAGL0/cZiIDheu4YM/s1600/Capture4.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/--3zUsOrOrj0/VG_xv9jTlfI/AAAAAAAAGL0/cZiIDheu4YM/s1600/Capture4.JPG" height="157" width="320" /></a><a href="http://4.bp.blogspot.com/-bR7HDvSVU9Y/VG_xvseb9cI/AAAAAAAAGLo/qKDNSS1esz0/s1600/Capture2.JPG" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-bR7HDvSVU9Y/VG_xvseb9cI/AAAAAAAAGLo/qKDNSS1esz0/s1600/Capture2.JPG" height="171" width="320" /></a></div><br /><br />I shared that this type of graph is called piecewise in response to their wonderings (What are the letters? Why would it be non-linear? Can there be more than one slope?), and told them that their task would be to find the slope of each piece. Then I apologized for my failure to photocopy the blue grid lines and we filled in the distance table as a class. Except I skipped 6 hours so they would have to figure that out independently. Then I sent them on their way to complete the rest of the task.<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/247799596/Distance-Graph" style="text-decoration: underline;" title="View Distance Graph on Scribd">Distance Graph</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_57054" scrolling="no" src="https://www.scribd.com/embeds/247799596/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br /><br />I was so happy that they managed to figure out the story with little prompting and answer several of the questions on the handout before they even got the handout with the story and questions! They were eager to get to work on the handout when they did get it because they already understood the context. It was awesome.http://drawingonmath.blogspot.com/2014/11/distance-graph.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-3345527131516547942Tue, 18 Nov 2014 01:04:00 +00002014-11-17T20:04:44.447-05:00Unit Plans and RequestsI miss writing here. I really want to process how Algebra 1 is going because I'm putting so much work into that class (90 minutes every day and I'm not following a particular book). So far all I've managed are my short notes in my unit plans, but that's better than nothing. This month has been dedicated to writing the second edition of <a href="http://nixthetricks.com/">Nix the Tricks</a>, but it wouldn't hurt to take a break to write about something here. So, here's the deal. Below I'm going to embed my unit 2 plan for both Algebra 1 and PreCalc. Then I'm going to ask you what you want to know about. I took most of the Algebra 1 lessons from the MTBoS and PreCalc isn't much different from last year so nothing in particular jumps out at me as urgent to share - that means you get to pick!<br /><br />Browse away:<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/246925363/Unit-Plan-2-One-Variable-Equations-Inequalities" style="text-decoration: underline;" title="View Unit Plan 2 One Variable Equations/Inequalities on Scribd">Unit Plan 2 One Variable Equations/Inequalities</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_37167" scrolling="no" src="https://www.scribd.com/embeds/246925363/content?start_page=1&view_mode=scroll&access_key=key-fRvdzZXYq0W8fdI3lU1T&show_recommendations=true" width="100%"></iframe><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/246925392/Unit-Plan-2-Trig-Graphs" style="text-decoration: underline;" title="View Unit Plan 2 Trig Graphs on Scribd">Unit Plan 2 Trig Graphs</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_96158" scrolling="no" src="https://www.scribd.com/embeds/246925392/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />Now ask some questions! They don't have to be about a specific lesson in these plans, I'm happy to write about class structure (and how frustrating it is when that structure is ruined for my PreCalc class a million times in a row due to short days and field trips) or anything else you're wondering about. So comment! Please!http://drawingonmath.blogspot.com/2014/11/unit-plans-and-requests.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-8663885582191365409Fri, 07 Nov 2014 01:42:00 +00002014-11-06T20:42:53.153-05:00How to Not QuitMy district is under a lot of pressure. Test scores dropped at the high school. One elementary school was already labeled as level 4 (level 5 means state takeover). Half that elementary school was handed to a private charter (stories I hear are crazy - having half a school privatized sounds like a nightmare). On the other hand, the high school met the 3 year progress goals set by the state and the elementary school in question had a big improvement in test scores (pre-privatization). It's really easy to get caught up in the negative and the demands to work harder/smarter/magically better with kids who seem to have more issues every year. Grades were due for quarter one today so pressure has built to a maximum and many people were venting their frustrations. So we took the time during our team meeting to step back and made this list (among others):<br /><br />What practices can we employ to feel good about our job:<br />a. Avoid negative talk/people. Replace with positive affirmations.*<br />b. Leave work at work<br />c. Attend school events (reminds us of the big picture)<br />d. Have a passionate hobby (have something other than teaching)<br />e. Don’t sacrifice your philosophy for other peoples' goals<br />f. Sing and laugh ’til you cry because you wet your pants.**<br />g. Eat lunch with people who laugh, sing and improve your outlook.<br />h. Exercise, both your body and your mind.<br />i. Sleep, many hours, every night.<br /><br />*I shared the <a href="http://onegoodthingteach.wordpress.com/">One Good Thing</a> blog, and vowed to go back to daily posting.<br /><br />**We rephrased this bullet point many times, and laughed about all possible phrasings.<br /><br />What would you add to this list?http://drawingonmath.blogspot.com/2014/11/how-to-not-quit.htmlnoreply@blogger.com (Tina C)2tag:blogger.com,1999:blog-812794395259173668.post-1741815544056818170Wed, 05 Nov 2014 02:47:00 +00002014-11-04T21:48:09.962-05:00nixNovember GoalFirst, an announcement:<br /><br />Nix the Tricks is now available in French!<br /><br />The translation is titled Terminé les Trucs (you have no idea how much work it took to find a title that I was happy with, thanks for everyone who helped brainstorm). Caroline Arcand has been hard at work translating the finalized document. I learned a few new things - did you know the acronym for multiplying binomials is PIED in French instead of FOIL? Whether it's a foot or a fencing tool it's still a trick, so now those who speak French in math class can learn alternatives. The translation is available at the same <a href="http://nixthetricks.com/Download.html">download page</a> as the English version; share it with all your French friends!<br /><br />Second, my goal:<br /><br />I'm setting a new <a href="http://nanowrimo.org/">NaNoWriMo</a> goal - 30 new tricks in 30 days. Luckily (or unluckily?) we already have that many tricks described in the <a href="https://docs.google.com/document/d/1DIzN3ylzI6kGiMbVt5LGIfPR5nGgCv4Elc0lUdBDqTE/edit">For Review google doc</a>. So my goal for the month is less about writing and more about formatting. Because of this I have a stretch goal - the <a href="https://docs.google.com/document/d/1OFgYDu7zKQvP6PmUBUiz7C5uRMSxW1XisfC0EQ498yg/edit#">Vocabulary google doc</a> is filled with great definitions - what if this was a glossary at the end of the book? My bet is that if someone filled in that document with terms in the book, as a community we could build some great definitions. If you are willing to be that someone, please leave a comment.<br /><br />So, please hold me accountable! Tweet me (<a href="https://twitter.com/crstn85">@crstn85</a>) occasionally this month to ask me whether I'm working on edit, typesetting or images that day, because I should be working on one of those every day to reach this goal!<br /><br />http://drawingonmath.blogspot.com/2014/11/november-goal.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-4339621160040598114Wed, 22 Oct 2014 00:46:00 +00002014-10-21T20:46:41.173-04:00AlgebraTeaching_PracticesNWMC Days 2-3 RecapThis is the <a href="http://drawingonmath.blogspot.com/2014/10/nwmc-day-1-recap.html">second post</a> reflecting on the <a href="http://www.northwestmathconf.org/nwmc2014/">Northwest Mathematics Conference</a> I attended in Portland, OR last weekend.<br /><br /><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><b>I See It: The Power of Visualization</b></div><div style="text-align: center;"><b>Marc Garneau, Chris Hunter</b></div><div style="text-align: center;"><b><br /></b></div><div style="text-align: left;"><a href="http://1.bp.blogspot.com/-4BaAbcqMRGA/VEbwPbnjkWI/AAAAAAAAGGE/drWiH6AfA0o/s1600/asd.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-4BaAbcqMRGA/VEbwPbnjkWI/AAAAAAAAGGE/drWiH6AfA0o/s1600/asd.jpg" height="320" width="240" /></a>This session started with a great exploration of divisibility using base 10 blocks. It isn’t strictly applicable to my grade level (high school) but was a good puzzle that I will try to keep in mind for all the crazy shortened schedule days in case one falls between units. Kids of all ages find divisibility rules fascinating because they seem like magic, I enjoy finding the math that make tricks work.<br /><br />I’m most excited about the introduction to radicals. The approach is to focus on the geometric interpretation of a square root – it’s the root (side length) of a square! Take your basic perfect square, say 16. What side length gives the square an area of 16? Four, so four is the square root of 16. Now, what side length gives the square an area of 18? Not a whole number, but that number is called the square root of 18. Maybe we could simplify that a bit? Dividing the 18 into four squares doesn’t really help but nine squares comes out nicely – each side of the small squares is the square root of two, thus the side of the square with area 18 is three square roots of 2. I’m still amazed and I’ve talked through this a few times since the presentation. I was not looking forward to the radicals unit this year, but I am now!</div><br />Finally, we looked at dynagraphs. I was just talking to my coworker today about comparing linear and exponential functions. I think this is a great way to see the relationship between input and output – especially since we spend so much time focused on comparing two outputs (many of us in attendance were momentarily confused when the linear graph with a slope not equal to one didn’t step along the way that x+3 does).<br /><br /><br /><div style="text-align: center;"><b>Now What? </b></div><div style="text-align: center;"><b>Danielle Maletta</b></div><br />The majority of this session was a refresher on things I’d heard at other PD, but those reminders are important because anything not immediately applicable gets lost in the shuffle. She spent some time talking about how to give low status kids a boost. One way was to explicitly mention all the skills needed for a task – we’ll need help organizing and recognizing patterns and … so kids can recognize at least one skill as something they’re good at. Related to that is a “How are you math smart?” poster that I’d love to have in my classroom.<br /><br />One task I loved was something Danielle calls a treasure hunt. She gives groups of students a pile of cards (equations, graphs, descriptions etc.) and gives them the first clue. Students work with their group to find all the cards that fit the clue and send one person up to the teacher with the clue and the cards. If they found all the solutions they get clue two, if not, they get sent back to their desks. I like this because students have to look at characteristics of your choosing (ex: Is 4 in the domain?) rather than matching by one or two aspects.<br /><br /><br /><div style="text-align: center;"><b>Creative Integration: CCSS Math Practices, Quality Activities, </b></div><div style="text-align: center;"><b>Excellent Questioning Techniques and Technology</b></div><div style="text-align: center;"><b>Tom Reardon</b></div><br /><a href="https://www.blogger.com/blogger.g?blogID=812794395259173668" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a>We started right off with a rich task:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.blogger.com/blogger.g?blogID=812794395259173668" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><blockquote class="tr_bq">In how many ways can you use only the digits of 8 and plus signs ( + ) to create an expression whose sum is 1000?</blockquote>I didn’t think it was a particularly rich task to start (a great sign - it was definitely low entry) but as we went through all sorts of patterns emerged. This is another problem that doesn’t fit particularly well in a particular spot in my curriculum, but this one is great for the last ten minutes of class when my students need something a little different.<br /><br />The painted cubes problem was also fascinating.<br /><blockquote class="tr_bq">A cube with dimensions n x n x n, that is built from unit cubes, is dipped into a can of paint. How many unit cubes will have paint on zero faces? one face? two faces? three faces?</blockquote>This one could fit more directly into my curriculum as there end up being four different patterns – a constant function, a linear, a quadratic and a cubic. It is approachable in Algebra 1 and if I use it during the quadratics unit it would reinforce the characteristics of each type of function.<br /><br /><br /><div style="text-align: center;"><b>Modeling Mathematics Using Problem Solving Tasks</b></div><div style="text-align: center;"><b>Andrew Stadel</b></div><div style="text-align: center;"><br /></div>It’s always a debate for me when I attend a conference – do I want to attend sessions on things I’m familiar with or try to learn about something totally new? This session was a bit of both. I’ve read about most of what Andrew does and I use his Estimation 180 weekly, but I haven’t done many 3 act tasks before. I appreciated the opportunity to play the role of student in this class. Andrew did a nice job of modeling the role of the teacher, but then stepping outside of that role to highlight some choices he made and answer “What if students…?” questions. Even if I don’t jump into 3 act tasks with both feet, I’ll definitely take away this idea: For a sequel/extension question, flip the math. If you gave radius and asked for circumference in the original question, give circumference and ask for radius. Doing the same process with bigger, different or ‘harder’ (fractions, decimals) numbers isn’t much more challenging. Nor is doing the same process in a new context. Instead, change the givens and solve for a new unknown in the same context.<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.blogger.com/blogger.g?blogID=812794395259173668" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div style="text-align: center;"><b>Better Than Engagement</b></div><div style="text-align: center;"><b>Dan Meyer</b></div><div style="text-align: center;"><br /></div>I took away two main ideas from Dan’s session:<br />•<span class="Apple-tab-span" style="white-space: pre;"> </span>Dial up the math slowly.<br />•<span class="Apple-tab-span" style="white-space: pre;"> </span>Create the need for notation and vocabulary.<br />We so often jump directly to the abstract and the precise. We need to specifically ask kids to estimate, to sketch, to predict. Then once they have a baseline, they’ll want to know if they are right. This allows us to dial up a notch and try some examples. Dan asked “If math is the aspirin, what is the headache?” The headache should be something tedious or repetitive or cumbersome (ex: so many examples they wish for a generalization). It’s the teacher’s job to create a headache, then offer strategies and vocabulary as aspirin. This process of exploring first and formalizing later is something I’m good at in geometry. I am still working to find explorations for some aspects of Algebra but I’m getting there – this conference certainly helped build my pool of resources!<br /><br /><br /><div style="text-align: center;"><b>Bringing Problem-Solving Into Your Math Classroom</b></div><div style="text-align: center;"><b>Fawn Nguyen</b></div><div style="text-align: center;"><br /></div>I had to join this session late as it overlapped with my own. I really would have loved to attend the whole thing. Two quotes struck me in particular. The first, “When you do a problem solving task, choose a good problem from a chapter other than the one you’re currently studying.” Fawn argues that problem solving tasks should not be on the exact same thing that students have been completing, otherwise it will be obvious how to solve them and students lose the experience of problem solving. I agree with this sentiment, but I am not sure how to sell my administration on it. They expect everything to match the objective, the objective to align with the standards and the standards to fit into the unit plan on the district website. As an intermediate step I can use problem solving tasks at the beginning of a unit – this way students don’t yet know what we are studying – and I can use problem solving tasks that bring together a variety of topics – students will know how to do the one aspect we are currently studying but they will need to use problem solving skills for the rest of the task. The second quote, “Not telling an answer is showing respect for students” reminds me that I need to return to my goal for students – “you are responsible for your own understanding.” When I first made this goal my intention was to get students to advocate for themselves when they were stuck. Now I realize this also means students need to be responsible for themselves and not take away someone else’s opportunity to understand. Collaborating is a good choice, but telling answers ruins the experience for the person who hasn’t had a chance to reason their way to an answer.<br /><div><br /></div><a href="https://www.blogger.com/blogger.g?blogID=812794395259173668" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a>http://drawingonmath.blogspot.com/2014/10/nwmc-days-2-3-recap.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-9164730670483406472Sat, 18 Oct 2014 17:06:00 +00002014-10-20T19:32:06.050-04:00AlgebraNWMC Day 1 Recap I attended the <a href="http://www.northwestmathconf.org/nwmc2014/">Northwest Mathematics Conference</a> in Portland, OR last weekend and it was amazing. I got to hang out with so many awesome people! It was a crazy mix of tweeps and PCMI reunion and people I've never spoken to who have heard of Nix the Tricks (something that never fails to astonish me). I had so much fun that it was totally worth the stress of prepping two days of sub plans and being exhausted and (super) behind for nearly a week.<br /><div style="text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-KJjMCfB2oiM/VEKa-5A7btI/AAAAAAAAF_Q/EA4LP30Q35o/s1600/2014-10-10%2B03.09.26.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-KJjMCfB2oiM/VEKa-5A7btI/AAAAAAAAF_Q/EA4LP30Q35o/s1600/2014-10-10%2B03.09.26.jpg" height="150" width="200" /></a> <a href="http://3.bp.blogspot.com/-Ly2A6ouOUrQ/VEKa_LCWztI/AAAAAAAAF_U/elUZYBD2Pus/s1600/2014-10-09%2B18.48.13-1.jpg" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-Ly2A6ouOUrQ/VEKa_LCWztI/AAAAAAAAF_U/elUZYBD2Pus/s1600/2014-10-09%2B18.48.13-1.jpg" height="150" width="200" /></a></div><div style="text-align: center;"><br /></div><br />Friday I finally felt a normal amount of behind, so I started going through my notes and writing them up. Portland State is very generous and they are offering two grad credits to anyone who attended all three days of the conference and writes about it. There were some specific prompts to write to and I learned that my writing voice for papers is different from my blogging voice. At least it feels different. NWMC was great but not so life changing that I sound different, apparently I just write differently when typing into Word than when I compose in Blogger.<br /><br />On Thursday I attended two workshops:<br /><br /><div align="center" class="MsoNormal" style="text-align: center;"><b>What makes algebra hard to learn?</b></div><div align="center" class="MsoNormal" style="text-align: center;"><b>Steve Rhine</b><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">This session was full of resources and links to even more resources! I look forward to thoroughly exploring the <a href="http://algebraicthinking.org/">AlgebraicThinking.org</a>website, especially their database of problems used in research. Upon return to my classroom I was pleased to discover some of the apps loaded on our school iPads are from Steve Rhine. Hearing him discuss the intentionality behind these programs makes me much more likely to use them with my students. One in particular is Point Plotter. I never would have understood the goal of this app if I just tried it – a common misconception students hold is that there are a limited number of points between two points on a line (ex: only lattice points count) – this app pushes students to find as many points as they can between two points. This addresses a misconception while simultaneously encouraging students to use the equation of the line and/or definition of slope to calculate points.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I am teaching Algebra 1 for the first time in five years and it’s been an eye (re)opening experience. I had forgotten how challenging it is to explain the basics; I wish I’d attended this session (as well as many others) during the summer so I wouldn’t have made some of the mistakes I already have with my students. Luckily it is still early in the year so I have time to address their misconceptions. One of those is the difference between an expression and an equation. As a mathematically proficient adult, it is quite obvious to me that equations and expressions are very different objects, but when I asked my students about it this week they struggled to differentiate between the two. We have all seen the mistakes where students try to ‘solve’ an expression using inverse operations – Steve Rhine shared that this can be due to students feeling “lack of closure” when their answer is an expression rather than a number as it has been for the rest of their mathematical experience.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Another place where students struggle is in understanding variables. The idea that a variable changes with different contexts but is constant within a context isn’t one I’d wrestled with, let alone helped students wrestle with. The x in problem three has no relation to the x in problem four, however, if problem five is 4x + 4 = 5x students must realize that the two x’s in that equation are the same. As a group we decided that a variable is an unknown <b>quantity </b>because that definition encompasses x=5 as well as x=y+3. Steve emphasized the importance of a variable representing a quantity and not an object. H can represent the height of Harry, but H doesn’t equal Harry. Instead we should refer to variables as containers. It worked out nicely that I had started equations with this <a href="http://mrpiccmath.weebly.com/blog/what-the-x-how-i-teach-basic-linear-equations">pennies lesson</a> because now I can refer to variables as cups of pennies – a mystery quantity.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Our final topic of the morning was graphing. Students struggle to understand the difference between discrete and continuous graphs. One suggestion was to ask students who connect discrete data points what the midpoint represents. For example, if they connect Sally’s height to Ted’s height, is the midpoint meaningful on that graph? Lastly, lines having constant slope is a big idea, but one that students don’t often wrestle with. If we only give students tables where the patterns jump out at them (ex: x values always increase by one) then they don’t get the opportunity to engage with the concept. We need to make sure to give students that challenge them to think and that bring out misconceptions so we can address them!<o:p></o:p><br /><br /><div align="center" class="MsoNormal" style="text-align: center;"><b>Fostering Algebraic Thinking and the CC Math Practices</b></div><div align="center" class="MsoNormal" style="text-align: center;"><b>Irving Lubliner<o:p></o:p></b></div><div align="center" class="MsoNormal" style="text-align: center;"><b><br /></b></div><div class="MsoNormal">I thought the last session was full of resources, and then I got to this one – we received a bound notebook of activities! I have yet to go through the entire thing and I can’t wait to have a chance to do so. Irving Lubliner mixed teaching practices with content throughout the workshop. He made his teaching moves explicit so we could reflect on those as much as the activities. When someone gives a wrong answer he finds the question that their response correctly answers, in other words, he finds something right about their solution. We practiced for a few responses and it was a fun challenge that reminded me of <a href="https://www.teachingchannel.org/videos/class-warm-up-routine">My Favorite No</a>, an activity I’ve used weekly. It would be great to infuse that spirit throughout the course. He used tickets as rewards for participation and great ideas. I am generally hesitant to give students extrinsic rewards but my school is using the PBIS model so I need to consider it. I appreciate that he rewarded bravery rather than only correct answers.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Just like my morning session, we spent time talking about expressions vs. equations. My notes say *Spend time on this!* so I had better do just that. One example in this session was about language precision – you can’t double an equation, you double each expression. When evaluating expressions he gave a great tip for getting students to remember to use the order of operations – look at the expression in chunks. This process will help students think about terms which is helpful for expressions with variables as well. Underline the expression until you see a + or -, then write “later.” Repeat until you reach the end. <u>200*2</u> + <u>(3+4)*5</u> – <u>3*6</u>. Next evaluate each term (in whatever order makes you happy). Then rewrite each subtraction as adding the opposite. Finally, evaluate the expression (in whatever order makes you happy). This method pushes students to think about the structure of the expression, and also allows them to use their number sense – if the expression has 15 and -15 use those opposites instead of going from left to right. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">We played with a great model for solving equations. I’ve never seen the utility of a function machine model until this one:<span style="text-align: center;"> </span></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-QoYDk_CAeZM/VEKbDTZKYsI/AAAAAAAAF_k/ZqPNhYwN5Ec/s1600/2014-10-18%2B12.27.40.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-QoYDk_CAeZM/VEKbDTZKYsI/AAAAAAAAF_k/ZqPNhYwN5Ec/s1600/2014-10-18%2B12.27.40.jpg" height="320" width="240" /></a></div> <a href="http://3.bp.blogspot.com/-VCHutie-sqE/VEKbDf6UKFI/AAAAAAAAF_g/YcN_Vmg0HXk/s1600/2014-10-18%2B12.42.25-1.jpg" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-VCHutie-sqE/VEKbDf6UKFI/AAAAAAAAF_g/YcN_Vmg0HXk/s1600/2014-10-18%2B12.42.25-1.jpg" height="162" width="320" /></a><br /><o:p></o:p><br /><br /><div class="MsoNormal">Earlier this year I tried to use a representation where we evaluated at a specific value of x to show the ‘forward’ steps, then worked back up to determine the ‘backward’ steps. This diagram is much more intuitive and shows the ‘socks and shoes principle’ clearly. During the session he showed an example with 7 or 8 steps, I wish that example had made it into the book – it made a very complicated equation seem easy. I will have to search for or recreate it since my students still need more practice solving equations.<o:p></o:p><br /><br />Update 10/20/2014: The internet is awesome. Someone from NWMC saw this post and sent it to Irv and he responded with the image I was wishing for!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-Gngg0iA9DQM/VEWbYNU97SI/AAAAAAAAGFk/3u155klKMao/s1600/Function%2BMachine.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-Gngg0iA9DQM/VEWbYNU97SI/AAAAAAAAGFk/3u155klKMao/s1600/Function%2BMachine.png" height="320" width="162" /></a></div><br /></div></div>http://drawingonmath.blogspot.com/2014/10/nwmc-day-1-recap.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-7300131909268901942Thu, 02 Oct 2014 19:00:00 +00002014-10-02T15:00:02.830-04:00Teaching_PracticesNotebooks and BindersApparently I have a lot to say after the first month of school! The last four posts have been about things that are going well. Today I'm trying to figure some stuff out that hasn't gotten as smoothly as we'd hoped.<br /><br /><a href="http://3.bp.blogspot.com/-yIzvr_tkS-c/VCtTNwn2GyI/AAAAAAAAF90/y7j5qVafgoM/s1600/2014-09-29%2B10.47.56.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-yIzvr_tkS-c/VCtTNwn2GyI/AAAAAAAAF90/y7j5qVafgoM/s1600/2014-09-29%2B10.47.56.jpg" height="320" width="240" /></a>In the past we've used a <a href="http://drawingonmath.blogspot.com/2012/08/binder-system.html">binder system</a> where students have sections to organize their papers and a specific <a href="http://drawingonmath.blogspot.com/2013/08/geometry-curriculum.html">system for notes</a> in their reference section but the rest of the classwork was disorganized and frequently ended up in the recycling bin. This year we wanted to keep the binders for organizing assignments and reference materials but add a spiral notebook for classwork. We came up with a plan to merge several routines into the notebook. Then we started...<br /><br />First, students struggled with the instructions "on the left hand page." So we drew a sample notebook on the board to model leaving it open and writing on the left hand side. Every time they are supposed to write a new heading in their notebook I add it to the model on the whiteboard. And sometimes I provide sentence frames (because IEP/ELL/9th grade).<br /><br />Second, students don't want to write with their notebook flat, they always fold it back. This sadly defeats the purpose of starting on the left hand page - if they write their goals on the left we can still stamp while they're writing on the next page. But if they fold it back the spot to stamp rapidly disappears.<br /><br />Finally, putting everything in the notebook means we have to look at the notebooks. We thought it would be convenient to have the stamps, quizzes and journals all in one place. However, we did not think about how annoying it is to get out the crates, open up their notebooks, find the correct page, and then finally be able to grade their work. I love the convenience for the kids of having everything in one place but I'm not finding it convenient for me.<br /><br />The things that are currently in the notebook:<br />Stamps (ideally I'd like to tally them at the end of the week)<br />Do Now (not graded)<br />Classwork (not graded)<br />Quiz (graded)<br />Journal (read and responded to)<br /><br />Last year:<br />Stamps were on small papers that got lost and not tallied<br />Do Now and Classwork were on lined paper that ended up in the recycling bin most days<br />Quizzes were on quarter sheets of scrap paper that got handed in, graded and then kids frequently lost them<br />Journals were on a full sheet that we collected on Fridays, read and responded to, handed back and then kids put them in the recycling bin (or in their binder, I should give some kids credit, but they never looked at them again either way)<br /><br />Thought that occurred to me just now:<br />Stamp chart and space for the journal on a half sheet. Days with quizzes they'd take the quiz on the back. Then I'd actually look at all the things regularly. And a half sheet is big enough to hole punch and put in their binder but small enough to fit on the corner of their desk. Plus if the reflection is attached to the quiz they might even look back at it? Real possibility here! I'll offer this suggestion to my co-teacher and brainstorm further.<br /><br />So I'm left with a question:<br />How do you use notebooks? Do you grade anything in them or have them do work in the notebook and hand in graded assignments separately?http://drawingonmath.blogspot.com/2014/10/notebooks-and-binders.htmlnoreply@blogger.com (Tina C)1tag:blogger.com,1999:blog-812794395259173668.post-3318268934025038213Wed, 01 Oct 2014 19:00:00 +00002014-10-01T15:00:00.162-04:00AlgebraNumber Sense, Logic, PerseveranceFour of my five blocks this year are dedicated to teaching Fundamentals of Algebra 1. It's a double block course so I have two classes. They are filled with students with IEP's (one class is all IEP's and the other is mixed but the kids turned out to be about the same level despite a technical difference in the labels on the courses) and so I get to work with my awesome co-teacher from the special education department (this is our fourth year teaching together!). Since we have so much time we knew we wanted to dedicate time to the essentials of number sense, logic and perseverance in addition to the core concepts of Algebra 1. Students in the fundamentals courses tend to struggle with being students, those are skills we wanted to teach. These students have frequently lost their curiosity, we wanted to re-awaken it. Students with disabilities need to learn how their brains work, we wanted to help them discover techniques that help them learn.<br /><div><br /></div><div><b>Do Nows:</b></div><div>Mondays: <a href="http://www.mathtalks.net/">Mental Math</a><br />Tuesdays: <a href="http://visualpatterns.org/">Visual Patterns</a><br />Wednesdays: <a href="http://matharguments180.blogspot.com/">Math Arguments</a> or <a href="http://wyrmath.wordpress.com/">Would You Rather?</a><br />Thursdays: <a href="https://www.teachingchannel.org/videos/class-warm-up-routine">My Favorite No</a> (this is the only day where the do now is related to the week's topic of study)<br />Fridays: <a href="http://www.estimation180.com/">Estimation 180</a><br /><br />Some kids have already learned to tell the day of the week from the type of problem on the board. "I didn't know it's Friday! Woo!" And they know what's coming: "Are you going to pick your favorite wrong answer?" There's a balance of structure and variety. While each day focuses on a different skill, they all focus on the math practices which are an essential foundation for math class. When we do these problems they have to complete the task to the best of their ability individually. Then I take contributions from most if not all of the class (everyone's estimate, everyone's vote or everyone's prediction). Finally, students are asked to explain their answer. Even in the first month they've made great strides in respectful disagreement and sharing their reasoning.</div><div><br /></div><div><b>Puzzles</b></div><div>In past years my co-teacher and I have kept a pile of logic puzzles, connect the dots, find the hidden object and other similar sheets. When kids finish an assignment early or need a break (say, after taking a test) we offered them the choice of any of those pages. They promote attention to detail and perseverance among other things. This year we knew we'd have freshman who would need to develop these skills and also might need a break more frequently than our students have in the past. We managed to nab a table and a couple extra chairs to set up in one corner. We took all of our games and puzzles and pages of challenge problems and put them together on this table. Students are motivated by the idea of having time to do puzzles and get their work done efficiently. We also direct kids there for a break if they need one. They don't think of it as developing their logic skills, they think of it as a game to play!</div><div><br /></div><div><b>Stamps</b><br />Last year we gave kids <a href="http://drawingonmath.blogspot.com/2014/03/clarifying-expectations.html">stamp charts</a> to give them regular feedback on whether or not they were meeting the goals we set. This year we are having them write the goals in the margin of their notebooks and stamping there. I'm undecided if that's better or worse than the small charts which would get lost between papers. We started with just "ready, on task and off task" and now we're adding "on topic and off topic" to get them to work together. But it's hard to stamp their notebook unless they're still on the first page of the day. Things we're still figuring out...</div>http://drawingonmath.blogspot.com/2014/10/number-sense-logic-perseverance.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-4359248618614953824Tue, 30 Sep 2014 19:00:00 +00002014-09-30T15:00:02.314-04:00Teaching_PracticesLong Blocks, Low Tolerance for Stillness<div><div>I have some seriously antsy students. They are pencil tappers, foot jigglers, pen clickers, finger strummers... You name it and they will find a way to wiggle it and make noise. On <a href="https://onegoodthingteach.wordpress.com/2014/09/28/energy-surplus/">Friday afternoon</a> they were bursting with energy. They were supposed to be taking a test and everyone was squirming in their seats. Some successfully settled by taking a walk to the water fountain, others needed a stress ball to move without making noise and the final student needed to sit out in the hall to stay focused.</div></div><div><br /></div><div>I teach kids with ADHD. I teach kids with learning disabilities that make focusing for longer periods of time tiring. I also teach <b>kids</b>. I get bored sitting and listening without doing anything. Kids shouldn't have to sit still and be quiet. It's not natural or healthy. Here's how I help my kids balance learning with their inclination to wiggle.<br /><br /></div><div><b>Breaks:</b></div><div>A 90 minute block is a long time. My co-teacher and I happily allow students to use the bathroom or get some water during work time. The school has a rule of no passes during the first 10 minutes or the last 10 minutes of class which means they won't miss the do now or exit. Otherwise, we let students go whenever they ask. Luckily we haven't had any issue with students wondering the halls - the bathroom is close to our classroom but even that brief chance to stretch their legs is often enough to get blood flowing and refocus. Some kids are in the habit of asking to "go for a walk" which we do not allow. They are welcome to walk but they need a destination.<br /><br /><b>Fiddle Toys:</b></div><div><div>I tried telling students to strum their fingers rather than tap their pencils, but they were just as loud with that so we needed to find some alternatives. Stress balls are working great so far (I have a variety - plastic-y, cloth, cloth and fuzz combined - they are all squishable and quiet). If students struggle with these (some are tempted to throw them rather than keep them in their left hand while they write with their right hand) we will try sticking some velcro to the desks next. If you put the two pieces side by side the texture difference between the loops and hooks can be enough stimulation to quiet the busy mind.</div><div><br /></div></div><div><b>Balance of structure and flexibility:</b><br />At the beginning of every class students come in, get their binders from the crate, put their homework on their desk (assigned seats) and set up their notebook according to the goals on the board (ready, on task, off task go down the margin). Then they start the do now. A minute after the bell rings I walk around the room, check homework and stamp everyone's 'ready' if they have the goals written and have started the do now. This section is very structured so students know what to do when they arrive and can transition into math class.<br /><br />In the middle of class students can choose to work with other students or independently. They can stay at their assigned desk, join another person at their desk (this part of the room has desks positioned in rows to face the front) or move to one of the groups of desks. We frequently set up stations so they have to move from one group of desks to another. This part of class is self paced. When students finish the assigned task(s) they are allowed to take something from the puzzle table. We have decks of cards for playing integer war, jigsaw puzzles, math bingo and more. They help kids develop logic and perseverance but the kids think they're getting away with not doing math!<br /><br />At the end of class students return to their assigned desks to reflect. They have to respond to two questions - one about goals or more general things and one about a specific math concept from the day. Then they need to clean up their areas and return to their assigned desks at which point they receive their homework. </div><div><br /><div style="-webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;"></div><br /><div style="-webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;"><div style="margin: 0px;"><br /></div><div style="margin: 0px;">Some things are still works in progress but overall this flow is working for us, and more importantly, it's working for the kids. They are learning and the pen tapping isn't driving me insane!</div></div></div>http://drawingonmath.blogspot.com/2014/09/long-blocks-low-tolerance-for-stillness.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-156430099185021327Mon, 29 Sep 2014 19:00:00 +00002014-09-29T15:00:04.184-04:00Pre-CalculusTeaching_PracticesPreCalc Unit 1 & 2Just like I'm doing for <a href="http://drawingonmath.blogspot.com/2014/09/algebra-units-1-and-2.html">Algebra</a>, I'm making unit plans for PreCalculus as well. There are some substantial differences here though. I've taught PreCalc for the past two years and so I was one of the teachers who put the curriculum into Atlas (our district planning site). Plus, the other teachers teaching PreCalc are interested in collaborating! One of them taught the course with me last year and we were able to chat regularly about the course as we went last year. The other teacher is new to the district (but not to teaching) and is interested in both hearing our ideas and sharing her own. I started the first unit plan on my own and shared it with them. Then we discussed and collaborated on the rest of the first and the second. There are some small differences between our classes (which is good!) so this plan reflects what I did, but we're working to include things like common definitions for vocabulary and the same projects. I'm really excited to have a place to record all my thoughts (which, again, are in comments that don't show up on scribd) and have an easy reference for when I teach the course again. I always write lots of notes to myself all over the place but the motivation to fix something now that I won't need for a year is never sufficient. This document will let me scan plans and make edits before I print things next year. Plus it's easy to look back to see how long I spent on something if they bomb a test or forget a concept that we need again in a later unit.<br /><br />Note: I teach on an alternating day block schedule so 3 weeks = 7 days is not totally nonsensical. (My Algebra classes meet every day since they are students who are substantially behind in math.)<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="http://www.scribd.com/doc/241248745/Unit-Plan-1-Circles-Triangle-Trig" style="text-decoration: underline;" title="View Unit Plan 1 Circles, Triangle Trig on Scribd">Unit Plan 1 Circles, Triangle Trig</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_34652" scrolling="no" src="//www.scribd.com/embeds/241248745/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><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="http://www.scribd.com/doc/241249777/Unit-Plan-2-Graphing" style="text-decoration: underline;" title="View Unit Plan 2 Graphing on Scribd">Unit Plan 2 Graphing</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_3558" scrolling="no" src="//www.scribd.com/embeds/241249777/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe>http://drawingonmath.blogspot.com/2014/09/precalc-unit-1-2.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-2994153134692768733Sun, 28 Sep 2014 16:31:00 +00002014-09-28T12:31:20.050-04:00AlgebraTeaching_PracticesAlgebra Units 1 and 2One of my <a href="http://drawingonmath.blogspot.com/2014/08/goal-setting.html">goals</a> this year is to have more balanced units. I am trying to achieve this by making a unit plan ahead of time and updating it throughout the unit. My school uses Atlas to share curriculum so when I start each unit I can open that site to find the list of standards we are supposed to address in a certain time frame. I reviewed that list as well as the skill and vocabulary lists. Then I try to organize all the information, along with all the resources I have from my past years of teaching the course and the MTBoS. Somehow I failed to include an assignment that I graded in this unit, despite all that planning. Kids had a balanced experience of investigating, notes (on <a href="http://drawingonmath.blogspot.com/2013/08/geometry-curriculum.html">flappers</a>), practice and quizzing but I didn't grade anything but quizzes and the test. Hm... Goals for next unit! Here is what I ended up doing for my first unit of Algebra 1:<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="http://www.scribd.com/doc/241248721/Unit-Plan-1" style="text-decoration: underline;" title="View Unit Plan 1 on Scribd">Unit Plan 1</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_79121" scrolling="no" src="//www.scribd.com/embeds/241248721/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />The descriptions are brief since they reference materials I have elsewhere, but the next time I teach this course they will be sufficient to jog my memory. I have all my card sorts and stations neatly organized in coupon holders so the next time I teach this course it won't be nearly so much work! I'll also know what the kids need a bit better so there may be less cycling back. You'll notice I have a "Next year" note to self. I am also using the comment feature, but apparently Scribd doesn't display those.<br /><br />At the beginning of the unit my plan looks much messier:<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="http://www.scribd.com/doc/241249796/Unit-Plan-2-Alg" style="text-decoration: underline;" title="View Unit Plan 2 Alg on Scribd">Unit Plan 2 Alg</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_34819" scrolling="no" src="//www.scribd.com/embeds/241249796/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />I have some skills I need kids to develop and some activities I know I want to use. I'll build the rest in and figure out what the timing has to be as I go. I haven't taught Algebra 1 in 5 years (pre-MTBoS!) and so there's plenty of learning on the fly going on. Ideally I would develop these plans with my colleagues teaching the same course to kids who came from the same middle schools, but when I asked "What activities do you use for the next unit?" I got a lot of blank stares. Thank goodness for all of you! I would love ideas for teaching solving equations and inequalities.<br /><br />My other goal is to mix in review. I've been doing that by assigning 5 homework problems each night and at least one of them is a review problem. Since in unit 1 the review was still all from that unit I didn't think to record how I was doing that. For the next unit I want to choose the review topic for the week and include that in the unit outline.http://drawingonmath.blogspot.com/2014/09/algebra-units-1-and-2.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-3354778867737296042Tue, 23 Sep 2014 23:38:00 +00002014-09-23T19:38:36.366-04:00AlgebraCentral ParkI'm still learning about my Fundamentals of Algebra 1 students. Some tasks I offer (operations on integers) they speed through with impressive skill. Other tasks (distributing with variables) stop them cold. I thought that <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB4QFjAA&url=https%3A%2F%2Fteacher.desmos.com%2Fcentralpark%2F&ei=BL4gVOzxKaWN8QHj-ICwDw&usg=AFQjCNFbhVSHgb04pfu-8DYB2I2_JldwCw&sig2=kIb9hANNHlpllIiv80GQCQ&bvm=bv.75775273,d.cGU">Central Park</a> would be a fun (re)introduction to variables but I was mistaken. It was a serious struggle. (Note: I think this is a great activity that I was ill prepared to support my students in achieving.)<br /><br />We started off great: "We get to use laptops today?" "No, that cart has iPads." "IIIPPPPAAADDSS!!"<br /><br />The estimation went pretty well. Students were a bit competitive but also helping each other out. One student got frustrated on the third one and I asked what would make it easier, then showed him how he could skip that step, no big deal.<br /><br />Then there was a question (what measurements would be useful). There were many answers that didn't make sense, but some students asked for clarification. No one stressed about that part.<br /><br />Next came some numbers. I was walking around the room rather than watching what happened at the teacher page so I didn't realize that most kids were guessing and checking. This is a valid strategy, they were using reasoning to increase or decrease the width. However, it meant that they were running straight toward a wall (writing an expression with a variable) rather than moving up a ramp that would get them over the wall (writing expressions with numbers). Kids' frustration levels built as they were guessing and checking successively more difficult problems and then they hit a breaking point when they couldn't figure out how to use variables (plural!) to represent all the situations. A good teacher would have re-gathered the entire class when most of them hit that point to have some conversation. I wasn't a very good teacher since I was focusing on being a good tutor (lame excuse- allergy season meant my ability to talk at whole class volume was limited). A couple students had the essentials and needed a small push. Many students were able to talk through a number situation with me and then (with a lot of prompting) generalize. Several students had already shut down and wouldn't talk to me or my co-teacher or anyone else.<br /><br />After class I realized: students weren't writing anything down. I had to ask students to open their notebooks so I could draw pictures and write in numbers and show how multiple calculations looked the same. Apparently students expect that if they are using iPads they are only using the iPads - no paper, pencil or calculator required. I talked to some people on twitter that night (thanks team) and came up with a follow up plan.<br /><br />We did spaces with lines between (partitions with no width). I walked around the room to check that every student had drawn a picture and labeled it. We did several with different numbers of spaces (clearly showing our work for each one - lots of repetition), then wrote an expression, then substituted into that expression several times. Spaces mastered. Next we did the same process for two spaces with varying size partitions. The only complaint I have about the original activity is how hard it is to see the partitions being divided by p+1. I wish it was easy to see something like half of each wall in each space. The two spaces situation is great because the partition is clearly split down the middle so you can either subtract then divide or divide both and then subtract (distribution of division over subtraction!). Finally we wrote an expression for the partition size and width of the lot varying. I learned that my students were able to complete the original process but they needed much more support than the original activity. Central Park is great and I would recommend using it. But if you teach kids who have struggled in math and/or aren't confident using variables, have some scaffolds in your back pocket ready to provide. And for goodness sake make them draw pictures and record their work!http://drawingonmath.blogspot.com/2014/09/central-park.htmlnoreply@blogger.com (Tina C)2tag:blogger.com,1999:blog-812794395259173668.post-3601182544827014820Tue, 23 Sep 2014 00:21:00 +00002014-09-22T20:21:03.756-04:00AlgebraPhone BatteryYesterday I read this awesome post by <a href="http://fivetwelvethirteen.wordpress.com/2014/09/21/number-talk-phone-battery/">Dylan Kane</a>. Today I posed the same question to my students.<br /><br />Before I get into the details I have to say - I'm so excited to have Algebra 1 classes this year. There are always so many great ideas for algebra and I haven't been able to use them in the past. I am currently teaching two double block courses of Fundamentals of Algebra 1. They are for students who arrive in high school below grade level in math. The majority of the students have an IEP and I co-teach with my awesome special ed partner (this is our fourth year teaching together which means we know each other well enough to finish each others sentences). So these kids need some number sense and problem solving foundations solidified as we work on mastering the concepts of Algebra 1. 90 minutes every day is a blessing (but I didn't realize exactly how much prep it would be - I haven't taught Algebra 1 in 5 years so I'm mostly starting from scratch). Enough background, on to today:<br /><br />We start each Monday with a mental math problem. Since most of my kids are allowed calculators even on state tests I'm modifying these to be "estimate first, then do a calculation on paper/calculator, then compare." I hope this will reinforce thinking while typing rather than blindly trusting the calculator.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-Bkka36-AFvw/VCC1j9LaJ1I/AAAAAAAAF84/7xNMZCulNAE/s1600/Capture2.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-Bkka36-AFvw/VCC1j9LaJ1I/AAAAAAAAF84/7xNMZCulNAE/s1600/Capture2.JPG" height="320" width="246" /></a></div> <a href="http://1.bp.blogspot.com/-NQ1P9nGENJs/VCC1j6QRmvI/AAAAAAAAF80/e7KdHXBiWjI/s1600/Capture.JPG" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://1.bp.blogspot.com/-NQ1P9nGENJs/VCC1j6QRmvI/AAAAAAAAF80/e7KdHXBiWjI/s1600/Capture.JPG" height="318" width="320" /></a><br /><br /><br />Just like Dylan, I got some kids who said 31 because there are two numbers so you must do something with just those numbers. I also had a student in each class who said the situation was preposterous and several who agreed. In the first class (red ink) I was able to describe the situation as checking your email every half hour. In the second class they took offense and couldn't move on so I changed it to "<b>the</b> phone battery" and then they were able to move forward. Another student made the point that it depends on a lot of things (and then sidetracked to ask if his battery life is effected by the fact the side of his phone broke off) so I acknowledged his excellent point and emphasized "what do you <b>expect</b>?"<br /><br />Listening to kids react to each other's estimates is really interesting. We're working on respectful disagreement. There were many noises when 0.50 went up but nothing specific. In the other class, however, when a student said 1% another student responded by saying "Percent?" With some prompting the students directed their questions at each other rather than at me and I got them to state that answers should be in terms of hours. They even questioned the next two responses to make them include units!<br /><br />The first class (red ink) had several strategies which you can see don't make much sense. The last one was the 7/3*93 and another student very intelligently asked "Where did the 7 come from?" When the student responded I took that opportunity to write "3 hours, 7% used" and then pose the question "What percent would be used after 6 hours?" The rest of that table was a combination of my posing questions and students offering suggestions.<br /><br />The second class (black ink) was unwilling to share any strategies. While I was wandering the room as they thought, I noticed a student who wrote "7% goes away after 3 hours" and so I asked him to share what he wrote. First he shared "I don't know the answer" but then he shared that other relationship (I'm fascinated that he knew enough to discover that relationship but lacked the confidence to even make a guess). I posed the 6 hours again and then this class headed off in a different direction. They came up with the multiplicative relationship right away (the other class was additive all the way down the table). One student decided it would be about 17 hours because 15 hours would be 56% (28% doubled) and 18 hours would be 112%. Another student - who I'd asked earlier in the class to face forward and stop talking (about the game tonight) - asked me “Can I respond to that?” Then he turned around and asked the other student if 112% was possible. My co-teacher and I still needed to run interference as they weren't listening so much as waiting their turn to talk, but it was exciting to see the beginning of dialogue. They figured out that student 1 chose 17 hours because he knew 112% was too high, but also that the doubling technique only works if you double both the hours and the percents. Then I asked the class to go back to their previous observation. We eventually got to “What times 7 equals 100?” After each kid told me a guess and how close their guess was, I asked “Can you get closer?” Soon I had students frantically typing into calculators and excitedly yelling out their next best solution. (Yes, I know that 9th graders should know to divide in this situation but we started with mental math and I wasn’t about to interrupt that enthusiasm.)<br /><br />I really enjoyed this problem. It led to some fascinating conversations on units, proportionality and reasoning. Not to mention all the practice we had with good math discussion skills!http://drawingonmath.blogspot.com/2014/09/phone-battery.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-5419974094599080583Mon, 01 Sep 2014 16:01:00 +00002014-09-01T12:01:35.975-04:00Teaching_PracticesTechnology FlowAt <a href="http://mathforum.org/pcmi/">PCMI</a> this summer we were discussing integrating student work into discussions and I realized I don't do this well. I also realized that I have a document camera that I almost never use - last year I used it to project my homework solutions in PreCalc daily and that one time I was being observed. That might be it. So I stopped to think, why? I am not one to use technology for technology's sake, but the document camera is a great tool and it's easier than having students come up to the board to rewrite their solution. It finally dawned on me that I don't use it because it is such a pain to switch from projecting the computer to projecting the doc camera and it messed up the alignment of the SMART board (the homework was first so it wasn't an issue). Plus, the problems were on the SMART board so once I switched to the doc camera we couldn't reference that information anymore.<br /><br />So, I'm not going to use the document camera and the SMART board because it interrupts the flow of class. I had to find a way to incorporate student work in another way. Next step: brainstorm.<br /><br />SMART board:<br />I already have it and know how to use it and it's already paid for.<br />I can make slides ahead, add new slides as I go and annotate everything.<br />I can export the annotated version to pdf (to share with students and coworkers)<br />Kids can write on the board.<br />The notebook software slows my computer way down (but they're updating it and adding RAM to the computer - it's 8 years old)<br /><br />Document camera:<br />Some teachers use just the doc camera but I like having my lesson plan queued up. I have the technology to have neatly typed things with cool graphics and I'm comfortable using it. Using just the doc camera seems like going backwards.<br /><br />iPad:<br />Someone wrote a grant and then left teaching for a district position, which means I get his class set of iPad minis and an AppleTV.<br />Use the iPad and powerpoint to have slides and annotate and include photos.<br />It should run faster than the notebook software. But if the network is down I lose the ability to annotate.<br />Doceri seems cool but it crashes when I want to export to pdf and it costs $$.<br />I don't want to make slides on the iPad, I want a full functioning computer for prepping. But I need to be able to add slides as I go. Turns out this isn't common (or even at all possible?).<br /><br />After a few weeks of struggling to find a system that will do all the things I want I'm mostly going back to my old standby. The people who wrote the grant didn't have a plan for how to use the AppleTVs, they're just as lost as I am. Who knew asking for the ability to both prep and change plans as I go was such an unusual request? Many people recommending using things other than slides but I really like projecting things that are meant to be projected (screen shaped), with the flow of class all lined up (I copy over all the essentials like the warm up and exit ticket format as well as any slides I didn't get to the previous class) but the ability to fill in (many slides have one problem and lots of work space or a note to self in tiny font) and adjust as I go (I can easily add slides - two clicks - when I need more space). The new addition is an iCloud photo stream. I can take photos of student work with my phone or iPad, but instead of worrying that students might see all my photos (not that I take inappropriate photos but my students are easily distracted and might want back stories), I can send them to the specific Math Class photo stream where only classroom photos reside. Bonus - if I get all the iPads hooked up to the same photo stream then I can snag any kid's photo (including screen shots) on days we use the iPads. Assuming the update and extra RAM help my computer out it should only take a few quick clicks to insert a photo into my slides and I don't have to deal with the board getting misaligned.<br /><br />This was a stressful process. I want things to work smoothly for me and also have the ability to share what I'm doing (did I mention we have 4 new math teachers? My mentee last year really appreciated my filled in notes so I want to offer the same to this year's newbies). I hope this works because I don't want to have to worry about how I'm presenting, worrying about what I'm presenting is more than enough!http://drawingonmath.blogspot.com/2014/09/technology-flow.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-1627082477170314672Sun, 24 Aug 2014 20:08:00 +00002014-08-24T17:53:29.016-04:00Teaching_PracticesGoal SettingMy brain is still in summer mode but I've managed a few moments of clarity where I've reflected on my summer experiences and past years to make a plan for this year. I've come up with four goals, two that I am setting for students and two that I am setting for myself.<br /><br /><span style="font-size: x-large;">Student goals:</span><br /><br /><span style="font-size: large;">Develop (or strengthen) a growth mindset</span><br /><br /><b>Catch phrase:</b> YET<br /><br /><b>Message:</b> You can learn everything I ask of you (and more!) if you do the work. You don't need to be told how to do every step, you are capable of thinking.<br /><br /><b>Monitoring:</b> I am required to give four interim assessments throughout the year as predictors for the state test. Along with each of those I will have students complete a growth mindset survey.<br />Question: How do I convince students to answer with their true belief rather than what they think I want to hear (it's specifically named a survey not quiz and is ungraded, right now I have a question for name but I'm not attached to including it)<br />Hope: Taking a growth mindset survey before taking a test that they aren't necessarily prepared for might encourage students to see difficult problems on the test as challenges to look forward to accomplishing.<br /><br />I have a (draft?) of my <a href="https://docs.google.com/forms/d/169GoIeQVLSQCaKNL2M4O9O9oj_lo4293LVHc-Lh-fdE/edit">survey as a google form</a> and figured out how to get the <a href="https://docs.google.com/spreadsheets/d/1_JY0DQ3w_MpJte7xrioD19kWEZki1qYLbxKsVtCdq9A/edit?usp=sharing">spreadsheet</a> to score it for me! Make a copy of <a href="https://docs.google.com/forms/d/169GoIeQVLSQCaKNL2M4O9O9oj_lo4293LVHc-Lh-fdE/edit">the form</a> to save to your own drive. I don't think the spreadsheet and form will be linked if you copy both of them so don't do anything with my spreadsheet yet. You'll need some data to see how this works, so take the survey. Then go back to your editable form and select "view responses." Insert a new sheet in this spreadsheet and then copy the first two rows of my sheet 2 into your sheet 2. It should score your responses automatically. Once kids fill out the form their responses will be in the first sheet only. To score them, highlight cells A-Q in row 2 of sheet 2 and use the autofill dragging feature (drag the square in the right corner of selected cells down until you've highlighted as many rows as were filled in sheet 1). If that's totally unclear leave a comment or send me a tweet (@crstn85) and I'll try to help you figure this out. I wish forms were as easy to share as other things!<br /><br /><span style="font-size: large;">Responsibility</span><br /><b><br /></b><b>Catch phrase:</b> You are responsible for your own understanding.<br /><br /><b>Message:</b> We provide resources to help you learn. It's important that you figure out how you learn (this is especially important since I teach many students with learning disabilities). Use group space and alone time wisely. Find your math s<a href="http://kellyoshea.wordpress.com/2013/07/20/physics-soul-mates/">oul mate(s)</a> and use them wisely. Take the initiative (to ask a question, to do extra practice, to take a break).<br /><br /><b>Monitoring:</b> In my Algebra 1 classes I will use a modified form of the <a href="http://drawingonmath.blogspot.com/2014/03/clarifying-expectations.html">stamp charts</a> we used last year. (I'll share my new notebook setup once we've tested it and determined if there are major bugs.) The chart hits on many of the elements of responsibility and will communicate both to the students and the teachers what areas of weakness are. Perhaps in my PreCalc class I will use <a href="http://samjshah.com/2011/07/12/participation-quizzes/">participation quizzes</a>.<br /><br /><br /><span style="font-size: x-large;">Teacher Goals:</span><br /><br /><span style="font-size: large;">Build in review</span><br /><br />After attend Kathryn's <a href="http://iisanumber.blogspot.com/2014/07/twitter-math-camp-2014-jenks-ok.html">Math Maintenance</a> session at TMC14 I realized that I need structure in order to successfully build in review. If it's not a routine then it never happens. I'm taking her Math Maintenance routine and using it for homework. Each night there will be several problems on the topic from that day. In addition, there will be one problem on the review topic of the week and one problem that is sort of <a href="http://samjshah.com/2012/06/01/algebra-bootcamp-in-calculus/">bootcamp</a> for an upcoming topic. I love the idea of taking an open response question and spreading it across the week. It's also an easy place to put multiple choice practice (state test, SAT etc.). As an added incentive, I'll count the week's worth of review problems as sufficient to retake a test/quiz on that topic. In discussing this with my new colleague he mentioned that teachers at his previous school put problems that many students had struggled with on a recent assessment on the homework. I love this idea!<br /><br /><span style="font-size: large;">Balanced Units</span><br /><br />There are some units that include many skills that are easy to separate, those units see many quizzes. There are other units where I've found great tasks, lots of great tasks, and I want to do all of them. Part way through second semester last year I realized that my gradebook was becoming very uneven and I decided that I needed to be planning more medium picture. I have the big picture of which units happen in what order, and I plan the day to day, but I wasn't taking time to look at the unit to see if it was balanced in investigation vs. practice vs. assessment. This year I'm going to decide on skills and tasks <b>before</b> I start each unit. I will make a document with this list to go into the unit folder and then write comments there after completing any lesson that went particularly well or poorly and at the end of the unit. Ideally I will get my colleagues to comment on these documents as well so we can have a comprehensive unit overview to refer to next year. (Idea for the shared doc that people reflect in comes from a <a href="http://mathforum.org/pcmi/hstp/sum2014/wg/high/abstract.high.html">PCMI presentation</a>.)<br /><br />I'd love for the monitoring on my teacher goals to come from you. Ask me sometime to share my progress?<br /><br />What are your goals for the school year?<br /><br />http://drawingonmath.blogspot.com/2014/08/goal-setting.htmlnoreply@blogger.com (Tina C)2tag:blogger.com,1999:blog-812794395259173668.post-4372977729307007837Tue, 05 Aug 2014 16:52:00 +00002014-08-05T12:52:00.626-04:00nixTMC: Nix the TricksI got to give a presentation on <a href="http://nixthetricks.com/">Nix the Tricks</a> for the first time at <a href="http://twittermathcamp.com/">Twitter Math Camp</a>. I was pleased how well attended the session was and feel the need to apologize to all those people for being my "first period class." Thank you for your enthusiasm, patience, understanding and feedback. Second period is going to go much better but I'm hopeful that the guinea pigs still gained something from the experience.<br /><div><br /></div><div>We started the session with groups discussing the following problems:</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-A2zgtVBykOE/U95ro-vdKAI/AAAAAAAAFxA/mTG1lp24LXo/s1600/examples.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-A2zgtVBykOE/U95ro-vdKAI/AAAAAAAAFxA/mTG1lp24LXo/s1600/examples.PNG" height="319" width="320" /></a></div><div><br /></div><div>They didn't know it at the time, but these were all problems that I chose from <a href="http://mathmistakes.org/">Math Mistakes</a> with Michael's assistance because we felt the mistakes students made were a consequence of tricks they had learned. Here's a place where I need your help - I would love to have lots of examples of how students solve these problems. Having a single mistake to hold up and say, "I hypothesize this kid made this mistake for this reason." and then conclude, "Therefore no one should use tricks ever." is not good logic. But having a pile of mistakes that correlate to a variety of tricks? That would be more convincing. (I should also read those articles that I saved on research about understanding, as that's even better logic. Time has been at a real premium the past few months...) Feel free to <a href="http://www.scribd.com/doc/235750491/Nix-the-Tricks">check out the slides</a> which match problem to mistake to trick. (Next time I plan to include more info on how to nix the tricks, not just why tricks are bad.)</div><div><br /></div><div>We then got into some great conversations about long division, the multiple methods for teaching it and the necessity for teaching the standard algorithm in preparation for polynomial division. I love listening to people talk about areas of math I don't teach and seeing how it relates to what I know. I guess I'm not the only one:<br /><br /><img border="0" src="http://1.bp.blogspot.com/-2AK-fWNze80/U95x21qiMkI/AAAAAAAAFxM/1zC2qI5drJ0/s1600/notes.jpg" height="320" width="255" /> <img border="0" src="http://2.bp.blogspot.com/-IQ1XwrGOlco/U95x_zssVbI/AAAAAAAAFxU/_hf4oSz32hc/s1600/notes2.jpg" height="320" width="256" /></div><br /><div>These conversations are the aspect of Nix the Tricks that I've loved the most. People coming together to think deeply about how to teach something students find challenging. Because people don't invent tricks for things kids can do easily; tricks are in place because someone thought the understanding was too hard (for the kids or to teach). I'm wondering how to get that conversation going in a room full of teachers who don't know each other and who teach different things. There were many participants interested in this conversation but not everyone. To differentiate I could have each group pick one of the 8 problems from the beginning and decide how they would teach a lesson around that problem for understanding? But I'll have already talked about the related mistakes and tricks and how to avoid them. Although that sounds ambitious for an hour, perhaps I'll only have skimmed how to avoid them and it would make sense for people to dig deeper...<br /><br />I leave you with some questions:<br />1) Can you give one, some or all of the 8 questions above to one, some or all of your kids (at home or in school) and then share their mistakes with me? I'll even give you <a href="https://docs.google.com/forms/d/1bX_t4zdw6VsN-fcwHLZZjgmb73wfd4COKyhcMFipjLw/viewform">a form</a> to make it easy to share out. Also, if you know of anyone who already has this type of data I'd love to see it!<br /><br />2) I don't want a Nix the Tricks presentation to be about me telling people how to teach, but instead to get people thinking and interested in engaging on the site. How can I get teachers to talk to each other in small groups about nixing tricks? Is this the best way to get people interested in having continued conversation on the topic?</div>http://drawingonmath.blogspot.com/2014/08/tmc-nix-tricks.htmlnoreply@blogger.com (Tina C)1tag:blogger.com,1999:blog-812794395259173668.post-7263079205965696903Mon, 04 Aug 2014 15:45:00 +00002014-08-04T11:45:00.440-04:00Pre-CalculusTMC: PreCalc SessionI was lucky enough to spend my mornings at <a href="http://www.twittermathcamp.com/">Twitter Math Camp</a> facilitating the PreCalculus session with <a href="http://mrdardy.wordpress.com/">Jim Doherty</a>. We had a wonderful crew of teachers who were all eager to jump in and share and work together to create some awesome tasks.<br /><br />Each day Jim and I planned some sort of opening activity. We folded conics on patty paper, identified creatures using a dichotomous key (and discussed how dichotomous keys apply in PreCalc) and did a rational card sort. All three activities are <a href="http://twittermathcamp.pbworks.com/w/page/82580905/2014%20Pre-Calculus%20Morning%20Session">on the wiki</a>.<br /><br />We started the discussion by sharing the topics in our courses as everyone's interpretation of PreCalc is different, plus we had a few participants from outside the US who have an entirely different scope and sequence. Once we had a set of topics we considered what essential skills we'd like students to focus on in Algebra 2, and what essential PreCalc skills are necessary for Calculus.<br /><br /><a href="https://docs.google.com/document/d/1bftRfK6_wKlw_qf07vEY_BSsCAcy4k5V1vRNTJY0bvw/edit">Our Brainstorm</a><br /><br />The three highlighted phrases are the three topics we focused on. We split into groups to tackle the tasks. I know my group had some excellent insights and a lot of enthusiasm. It was wonderful to have three days to think about a single topic. I rarely have time for such depth on my own, but to have it with a group of teachers who were equally passionate about students making connections and understanding was amazing. We had the time to try things that didn't work (deriving the equation of an ellipse from the geometric definition is tedious and not a good use of kids time in our cases) and explore ideas that we weren't sure about. We didn't finish what we had hoped to, but we made progress and I think the energy of this conversation will carry me through to continue tinkering with it. Everything we did accomplish is posted on the wiki.<br /><br /><a href="http://twittermathcamp.pbworks.com/w/page/82580905/2014%20Pre-Calculus%20Morning%20Session">The Wiki</a><br /><br />If you have any questions on how people intended to use the materials linked please ask, we want the information to be useful for everyone whether they were present or not. Greg did a nice job of <a href="http://mathiex.blogspot.com/2014/07/tmc-2014-entry-3-development.html">recapping our presentations</a>.<br /><br />I can't wait to try out the trig and conic tasks (my course doesn't include vectors). I'll try to remember to share my experiences and adaptations, I hope you will too!http://drawingonmath.blogspot.com/2014/08/tmc-precalc-session.htmlnoreply@blogger.com (Tina C)2tag:blogger.com,1999:blog-812794395259173668.post-694839035735095997Sun, 03 Aug 2014 15:23:00 +00002014-11-22T11:09:45.910-05:00fosterTeaching_PracticesTMWYK: Productive StruggleA couple days ago a tweet rolled by on my feed that I wanted to respond to, that is really important to respond to, but was too big for me to begin communicating in tweet sized bits.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-LRdNyiu1z6U/U95JfF0-g9I/AAAAAAAAFww/BOG286PSYQk/s1600/productive+struggle.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-LRdNyiu1z6U/U95JfF0-g9I/AAAAAAAAFww/BOG286PSYQk/s1600/productive+struggle.PNG" height="156" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>But then yesterday I was hanging out with a seventh grader (my soon to be foster placement) and I did some things that supported her productive struggle that connect to the classroom.<br /><br />We were checking out the shelf of puzzles and games trying to decide what to do when she spotted the Rubiks cube. She'd never seen one before and picked it up. I told her to mix it up and suggested spinning in more than one direction (explicit instruction on how this thing works). She asked if I'd solved it and I confessed that I only knew how to completely solve it by following instructions (acknowledgement that this is a challenging task). This was plenty to pique her interest. Once I saw her eyes switch to focus mode I stepped away, said "I'll let you play" and picked up my yarn. While I watched her puzzle I realized that crocheting is an excellent equivalent to <a href="http://sarcasymptote.wordpress.com/2011/05/04/ukulele-dayz/">Greg's Ukulele</a>, I could watch her without her feeling the pressure of being watched because I was also doing something. She could talk to me but I didn't feel the need to constantly engage her in conversation because my hands were busy. She did talk while she puzzled; she said "This is hard!" every couple minutes for 15 minutes. Nothing else, and her eyes quickly returned to focus on the puzzle. And this is the hardest part for a teacher - how do you respond? It's tempting to jump in and provide help. But she didn't want help, she was expressing her thought process "My brain is working right now and I'm surprised how much my brain is working while spinning cubes!" I sometimes smiled, sometimes said "Yes." and other times said "Yup! But it looks like you're making progress." (growth mindset is helpful here). After 15 minutes she looked up and said "Wouldn't it be crazy if someone just did [mimed rapid spinning of the parts] and solved it?" To which I responded "There are people who can do that! They've worked really hard and learned how to solve it quickly. Have you ever seen a video of that?" She grabbed her phone and I wondered if seeing someone successfully complete the task would be motivating or frustrating, then I realized there must be "how to" videos online and I didn't want her to ruin the experience by stumbling upon one of those. I told her to search "Rubiks Cube Competition" so that they wouldn't appear in her search. The look of intense focus reappeared as she watched a video. She expressed shock, "15 seconds! It was too fast for me to even see what he did!" She watched a few more, then sat back in awe. I explained that some people could look at the cube, see the positions of all the blocks and then figure out in their head how to solve it, but that they had to practice a lot to get there. This prompted another 15 minutes of playing. At some point I gave her the hint of focusing on just one color to start with (strategy of looking at a simpler case) and she would occasionally share how many blue pieces she had grouped together. After another 15 minutes she put it down and said she was done. I went over and showed her a technique - thinking back I wish I'd asked if she wanted to know before telling (but 30 minutes of restraint was all I could handle!) - I showed her how to move some pieces out of the way to get a block in without messing up the current progress. She was impressed and excited and spent another few minutes trying to replicate the technique before deciding she was really done. And I let her be done.<br /><br />So how does this apply to my classroom?<br />I pose a problem and provide a bit of information.<br />Then I step back and let kids explore.<br />I'm available so they can ask for help, but not hovering.<br />I use growth mindset language as much as possible (the focus is the process not the answer).<br />I value kids ideas and questions.<br />I provide assistance when they are stuck: if a kid is just struggling (no longer productively) or has quit they need a teacher. The tricky part is deciding exactly what kind of assistance you can provide so the kid can continue working.<br /><br />The last thing I did, letting her stop, is really hard to do in a classroom. There's a goal for today and a pacing guide and all those outside pressures that make it challenging to let kids proceed at their own pace. One thing my co-teacher and I are planning to do is provide a puzzle table where kids can go if they need a break from the class activity. I also let kids go to the bathroom or get a drink of water whenever they want. Knowing yourself well enough to know when you need to step away and clear your head is an essential skill. In the classroom, I'd ask a kid to re-engage after a short break, but that's also the difference between working on a task carefully chosen for your students and picking up a Rubik's cube!<br /><br /><blockquote class="tr_bq">Wondering what the TMWYK in the title stands for? That would be <a href="http://talkingmathwithkids.com/">Talking Math With Your Kids</a>, the awesome idea, blog and book of Christopher Danielson.</blockquote>http://drawingonmath.blogspot.com/2014/08/tmwyk-productive-struggle.htmlnoreply@blogger.com (Tina C)2tag:blogger.com,1999:blog-812794395259173668.post-7050486623597353811Sun, 13 Jul 2014 23:44:00 +00002014-07-13T19:50:32.698-04:00Pre-CalculusParametric FunctionsIt's summer! I can't wait to share all the awesome things I've been up to at <a href="http://mathforum.org/pcmi/">PCMI</a>, but first I'm going back to my final unit in PreCalculus which I never got a chance to share. Last year we did an exploration of polar functions but ran out of time to look into parametrics. This year when I asked the calculus teacher what her preference was she said to focus on parametric instead. I chatted with several people on twitter, someone (<a href="https://twitter.com/dandersod">@dandersod</a> I believe) showed me how to graph parametrics on <a href="http://desmos.com/calculator">Desmos</a> and my colleague* shared her awesome materials with me. Put it all together and I got this:<br /><br />Kids finish a test and the instructions on the board say:<br />1. Pick up the assignment papers<br />2. Sign out an iPad<br />3. Work silently (other people are testing!)<br /><br />On the desks where I've spread out the assignment papers I write <b>Introduction</b> above the first page (in dry erase marker because I have dry erase desks) and <b>Choose One</b> above the remaining three pages. Most students finish the introduction (about half an hour) so I assign as homework completing that page and making a first attempt at the other assignment. The following class we discuss the intro, why parametrics exist and then they spend the rest of the period working on the context they chose. I like projects where there are similar options because students can still have conversations (they all have to graph and calculate) but each of them has to do their own work.<br /><br /><a href="http://www.scribd.com/doc/233723036/Parametric-Intro" style="font-family: Helvetica, Arial, sans-serif; font-size: 14px;" title="View Parametric Intro on Scribd">Parametric Intro</a><br /><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_14652" scrolling="no" src="//www.scribd.com/embeds/233723036/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />It was important to begin graphing by hand so students had an understanding of how parametrics work. Some students were concerned that the t value wasn't showing up on the graph and tried to include it in some rather creative ways. I've edited the instructions slightly (should've thought to post the original to ask for feedback on the adjustments...) so hopefully that will be a less prevalent error. Other students picked strange values for the second set of equations, ah radians. Two thoughts: 1) I'm glad I was able to incorporate a trig function since we hadn't used them much since first semester 2) I love graphing utilities - I was able to say, "Okay, you're not really sure what this graph was supposed to look like, that's fine. Graph it on Desmos and see what happens!" My box of helpful hints on how to type things into Desmos wasn't as visible in the first version, many kids skipped those steps. They were also unclear on what to type exactly as written and what to substitute with other information. Turns out (-4+3t, 1+2t) graphs just as well as f(t)=-4+3t, g(t)=1+2t and (f(t), g(t)), but I like the way we found to use Desmos as it shows that each value of t gives an (x,y) coordinate a bit clearer.<br /><br />Choose One:<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="http://www.scribd.com/doc/233723034/Parametric-Context" style="text-decoration: underline;" title="View Parametric Context on Scribd">Parametric Context</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_30590" scrolling="no" src="//www.scribd.com/embeds/233723034/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />These activities are designed to be done on Desmos as well. Some students didn't appreciate when I wouldn't help them with technical issues until they got out the intro sheet and put it side by side with their iPad. But, they were able to correct their own issues that way so it was worth the eye rolling. They also struggled with graphing the obstacle/hoop. In response to those questions I asked them, "Where is the obstacle/hoop?" And continued asking variations on that question until they told me "At x=__" At which point I responded, "So type x=__ on the next line." Then I pointed to the next line of instructions (how to restrict the range) and walked away.<br /><br />Great things:<br />These context based questions require students to continuously switch among equations, graph and description. They have to know what t represents and what it means to land as well as solve quadratics and estimate values on a graph.<br />A student asked me if the equation took gravity into account. What an awesome question! I was proud that I remembered my physics to point out the -16t^2 (this is feet based physics, I remember 9.8 for meters even more clearly).<br />In my opinion this assignment shows why parametrics are useful - you can know horizontal distance, vertical distance and time using one set of equations. I failed to successfully convince my students that this was amazing. They obediently wrote that down and that the parameter allows them to restrict the function. But neither of these facts were impressive to them. Thoughts on how to convince students that parametrics are useful and different?<br /><br />*Colleague O'Malley - I've yet to convince her to jump into our awesome online math community but she does recognize its power and occasionally asks me to ask twitter questions on her behalf. She found the equations and contexts in McDougal Littell Algebra 2 and then wrote up projects for TI. I only had to modify a bit so we could use Desmos. She very generously allowed me to share with all of you!http://drawingonmath.blogspot.com/2014/07/parametric-functions.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-858735764348561290Wed, 04 Jun 2014 22:14:00 +00002014-06-04T19:01:42.673-04:00Trigonometry UpdatesWhen I went to <a href="http://drawingonmath.blogspot.com/2014/05/the-same-people.html">meet with the consultants</a> I brought them materials from my trigonometry unit. they provided me with a variety of suggestions and we had a good conversation. Now that I've taught the unit I have some thoughts on what worked and what didn't.<br><br><b>Suggestion:</b><br>Make a template for kids to fill out for every trig problem they do.<br><b>Reality:</b><br>It was really useful, but I neglected to consider how big kid handwriting in dry erase marker is.<br><b>Conclusion:</b><br>Remake the template so it only has the triangle to label, ratios and cues to solve and check.<br><br>Version I used this year (print on paper, slide into a plastic sheet protector, instant dry erase template!)<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="http://www.scribd.com/doc/228198452/Trig-Template" style="text-decoration: underline;" title="View Trig Template on Scribd">Trig Template</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_13957" scrolling="no" src="//www.scribd.com/embeds/228198452/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br><br>Possible improvement<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="http://www.scribd.com/doc/228199513/Trig-Template-Update" style="text-decoration: underline;" title="View Trig Template Update on Scribd">Trig Template Update</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_69138" scrolling="no" src="//www.scribd.com/embeds/228199513/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br><br><b>Suggestion:</b><br>Have kids write out all the ratios, then pick the one that's easiest to solve.<br><b>Reality:</b><br>It takes forever for them to fill in six ratios. All my students struggled with understanding opposite vs. adjacent at the beginning (even when I had them place a finger over the angle in question) and switching between the two angles was rough.<br><b>Conclusion:</b><br>Undecided. I wanted to believe that with more practice the ratios would come faster but with the number of interruptions we've had lately it hasn't happened yet for many kids. I do want to do all six a few times and have kids notice that sin/cos all have the same denominator (hypotenuse doesn't depend on angle), that sin(A)=cos(B) and that tan(A) is the reciprocal of tan(B). After that discussion I'm not sure it's worth the time. There's value in looking at the information given, looking at the possible equations and choosing which one to set up and solve. I may give kids the option to do that in the future.<br><br><b>Suggestion:</b><br>Have kids solve for all three side lengths using trig, then hand the paper to a partner to check using the Pythagorean Theorem. Kids won't want to check their own work but they'll happily check each others.<br><b>Reality:</b><br>Kids don't finish at the same time. Waiting and interrupting are both bad options.<br><b>Conclusion:</b><br>Some kids wanted to check their own work, which was great. Other kids I directed toward any student who wasn't working (not necessarily their partner), this gave kids who were frustrated with the spacial or algebraic demands a chance to do some computations. A few kids I checked for them. I like checking with the Pythagorean Theorem because we get to talk about equal vs. close. Next time I'll start with kids checking their own work and if anyone is resistant I'll offer the other options.<br><br>Having a three day weekend and state testing during the middle of our unit on trig was a problem. There were a lot of interruptions and with a block schedule they only have me every other day to start. It was hard to build any sort of automaticity. Such is life.<br><br>I also updated the <a href="http://www.scribd.com/doc/228198177/Trig-Intro-GeoGebra-2014">trig intro investigation</a>. That went well. (<a href="http://drawingonmath.blogspot.com/2012/06/trig-intro-applet.html">Original post</a> has more detail.)http://drawingonmath.blogspot.com/2014/06/trigonometry-updates.htmlnoreply@blogger.com (Tina C)3tag:blogger.com,1999:blog-812794395259173668.post-2687684518689248744Sat, 24 May 2014 01:27:00 +00002014-05-23T21:27:39.082-04:00Students Who Are BehindStudents who are behind are a big problem at my school. Next year we will have more levels of algebra 1 than I can count. Seriously - it's after 9 pm on a Friday so keeping track requires more brain power than I have; counting levels of a course shouldn't require brain power. We have a tracking problem, but we also have a money problem. Kids who would be placed in specialized schools in most districts are kept in house because it's cheaper. When people talk about mixed level classes I think how wonderful that sounds. But the reality is that we are teaching kids with significant learning differences and kids who are years behind. I don't know what the right thing to do is. Some days I complain that it's torture to make certain kids take the state test. Other days I complain that no one bothered to teach math to our autistic kids (who are fully capable of learning math). I know these are conflicting arguments. I don't know who should be deciding which kids get which placement and what they should learn in each placement. The school committee decided that every 9th grader should be taking algebra 1. No matter what. So I taught those kids who hadn't done math "algebra 1" but that had to look different than the mainstream algebra 1 courses. To start addressing this issue my department head shared an excerpt from <a href="http://www.amazon.com/gp/product/1416618686/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=1416618686&linkCode=as2&tag=nixthetri-20&linkId=FGVATMP2FIFS55HG">Learning in the Fast Lane</a>. <a href="http://www.ascd.org/publications/books/114026/chapters/Acceleration@_Jump-Starting_Students_Who_Are_Behind.aspx">Chapter 1</a> is free to read online. This one is going on my ever growing list of things to look at 'later.' Whenever that may be.<br /><div><br /></div><div>Today marks 30 days in a row of posting. Expect a drop in frequency around here shortly. Still a few more things to share this weekend before I get lost in end of school stuff. June tends to simultaneously fly and drag...</div>http://drawingonmath.blogspot.com/2014/05/students-who-are-behind.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-4280031468557166782Thu, 22 May 2014 20:39:00 +00002014-05-22T16:39:11.978-04:00Human Knot ReasoningYesterday was our last advisory of the year. We had advisory once or twice a month for an hour. We started this schedule in June of last year and it's had some pluses and minuses. At the beginning of the period I had students reflect on their year - in general, in school and in advisory. I'll probably read and post about them sometime this weekend. Then we played games including pictionary, charades and at the end of the block, the human knot.<br /><br />There was some interesting reasoning occurring as they worked to untangle themselves in the human knot.<br /><b><br /></b><div><b>There's an odd number of hands!</b></div><div>They were making a joke when someone couldn't find a hand to grab onto. Love math jokes!</div><div><br /></div><div><b>At the end the order will go: me, then A, then B, then C. </b><br />This was at the very beginning where everyone was in a complete tangle. She was tracing the path and envisioning the end result. Which also helped her consider the consequence of moving - since every time she moved she had to drag A, B and C along behind her.<br /><br /><b>Is it always solvable?</b><br /><div>I shared a few examples of results I've seen - one circle, two separate loops, interlocking loops - I wonder what their definition of solvable is. Sadly the bell rang before they were able to untangle and see what kind of result they would have. It was a really tough knot because they were working together and listening to kids outside the knot who had a clearer perspective and it was still slow progress.<br /><br /></div>I got a few photos and another student took a video that will be fun to share at our first advisory next year (they're sophomores now so we get to spend two more years together). Maybe next year we'll solve a knot with everyone participating!</div>http://drawingonmath.blogspot.com/2014/05/human-knot-reasoning.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-3400902975275139598Wed, 21 May 2014 21:39:00 +00002014-05-21T17:39:34.784-04:00Simplifying Looking BackPart of today's department meeting was getting together with our content groups to reflect on the year. Last year we made curriculum maps for Algebra and Geometry and this year we tried to stick to them, to varying degrees of success. We wanted to decide what units to move, which to shorten and which to lengthen. We'd been having this conversation throughout the year but today was the day to hash out the details. Hashing out details that included first quarter is difficult to do. Luckily I've developed a system where I save my smartboard files for each class in a public google drive folder with the date. The goal is for kids to have a place to check if they're absent or forget to write down the homework or need help with their homework. But it worked great today when we needed to figure out how long we'd spent on each unit.<div><br /></div><div>All of my g<a href="https://drive.google.com/folderview?id=0B98A9F2SC_jpTHhYUC1UOUZrUEE">eometry notes</a> for the year, in order, in one place.</div><div><br /></div><div>I sent an email to the high school tech person after I found out about <a href="http://googleblog.blogspot.com/2014/05/previewing-new-classroom.html">Classrooms</a> because I want in, and more than that, I want us to switch over to google apps for education because it would be soo much easier than what we currently have. We use FirstClass for email and last month got an email telling us that we wouldn't be able to email anyone outside of our domain for a while. There was a spam issue they couldn't solve. Teachers are starting to use Drive and expect kids to submit assignments online, but kids don't have email addresses through the school and don't have google accounts. I have to wonder if the district used google apps, would the students look back at their google drive as they studied for finals? That could be a cool assignment that I can technically do because my drive is public... Some of my classes are small enough that each kid would get a month to summarize. I'm going to ponder this idea further...</div>http://drawingonmath.blogspot.com/2014/05/simplifying-looking-back.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-31404850987658838Tue, 20 May 2014 22:31:00 +00002014-05-20T18:31:31.566-04:00GLBT HealthRecently there was a Sexual Health Grant meeting at my school, I wasn't able to attend because I had another meeting, but they sent a survey ahead of time and asked us to respond. I was invited as the former Gay Straight Alliance advisor. We have since broadened the definition of the club to build interest (unsuccessfully). Currently the GSA is under a larger umbrella of Friends of Rachel and is focusing on GLBT issues as well as other forms of community outreach. Even with that branching out I have 3 consistent members and two of them are seniors. Many students participate in events like the Day of Silence that occur during school hours, but few kids are staying after school for the club.<br /><br />We have a generally open and accepting environment at the school and I get the sense that most students don't need a GSA as a safe space as they are able to be out at school. I also know that NAGLY (a local group for gay and lesbian youth that meets outside of school) is well attended. But I would still like to have a functional club that works on some of the issues presented in the questionnaire as well as other awareness campaigns. While things are better for the GLBT community than they have been in recent history, things still aren't good. The rates of suicide and depression in GLBT teens are scary and most don't feel like they have an adult they can talk to.<br /><br />Some questions in the survey:<br /><br /><b>Do you have a comprehensive and clearly focused school anti-bullying policy, with training for students and staff?</b><br />We worked on that last year, but I'm not sure that new teachers or freshman got any training. This needs to be ongoing.<br /><b><br /></b><b>Are there protections for gay lesbian, bisexual and transgender students and staff from harassment?</b><br />We are lucky enough to have a conflict resolution person on staff along with a slew of counselors and administrators and a police officer who works with the school. When harassment is reported it is taken seriously. However, I'm not sure how often it is reported. Are kids hiding their comments from teachers? Are teachers aware of the derogatory terms used against LGBT students? How often do you here students say "That's so gay!"?<br /><br /><b>Is there a plan for education that meets the needs of students who are diverse in terms of ethnicity, language, gender expression and sexual orientation?</b><br />Our health teachers are pretty aware and supportive, but I don't know the curriculum precisely. We'd talked about having a GSA meeting where we bring in a nurse to answer any questions students might have but wouldn't be comfortable asking in health class. But that hasn't happened (yet?).<br /><br /><b>Does your district have partnerships with youth-friendly community organizations that provide sexual health services including LGBT supportive services?</b><br />Yup! NAGLY is awesome and all the guidance counselors and nurses at the very least know about it and refer kids. They also send some representatives to our annual health fair.<br /><br /><b>Does your district have safe space policies in place that support: LGBT youth?</b><br />One thing my club did accomplish was making Expect Respect stickers for every classroom and office door. I don't know about policies though.<br /><br /><b>Is there administrative support for addressing the health and psychological needs of LGBT youth?</b><br />Yes?<br /><br /><b>Is there community support for addressing the health and psychological needs of LGBT youth?</b><br />Yes. We are lucky that Salem is a very diverse town. After the witch trials were declared the terrible thing that they were, the city became a mecca for Wiccans. And then all sorts of eclectic people. Combined with the diversity inherent in a seaport and we have a funky city that's accepting of everyone. We even have a pride parade which I think is unusual for such a small city.<br /><br /><b>Are district staff comfortable and willing to address the health and psychological needs of LGBT youth?</b><br />I'd say willing but uninformed. Recently a teacher asked me how to help a transgendered kid who is thinking about dropping out of school as he transitions. I just remembered we had a really great training for the staff at a school I worked at before, I should email the school to get their contact info.<br /><br />How does your school address the physical and emotional health and wellness of GLBT students? Any ideas on events the GSA should have or how to improve student involvement?http://drawingonmath.blogspot.com/2014/05/glbt-health.htmlnoreply@blogger.com (Tina C)0