Seeing Structure

This weekend I visited my parents and my mom asked if I could teach her how to crochet. I was happy to do so! Obviously teaching math and teaching crocheting aren't the same, but just as obviously I can't help but make connections.

My mom chose to learn how to make a hat I'd given her, a hat that happens to be a rather advanced project. Is it crazy that she is starting with the hardest project I've made in a decade of crocheting? Sure. But she has enough transferable skills from knitting that it's not insane. We started out knowing that it may not be a perfectly even final project, but it was interesting for us to work on and it's the thing she wants to make so she was motivated and willing to persevere! 

Before she could start the hat she needed to learn some basic skills. The pattern required chain, double crochet, slip stitch and front post double crochet. When I learned to crochet I was made to sit and chain for a long time (the most boring stitch, you just pull a loop through another loop). But for my mom it wasn't worth the time to learn to chain an even tension foundation row when the goal was a hat worked in the round. It would've been essential if the goal was an afghan worked in long rows but for a hat she never needs to make more than three chains in a row. After she felt comfortable with the chain, I didn't even teach her to single crochet, we went straight to the double crochet. No point when it wasn't in the pattern. After practicing those stitches a bit we jumped right into the pattern! When we hit a new stitch in the pattern we stopped to practice with some different yarn and then went back to the project. 

I translated the pattern for her. Being able to read "[dc in next dc, two fpdc in next fpdc, dc in next dc, fpdc in next fpdc] around" isn't important right now. Instead I read the pattern to her in unabbreviated form, and we worked together to figure out how the pattern should look so she didn't have to count out each part. But, I hadn't made this pattern in five years so I didn't remember exactly how it should look. We were crocheting by following the steps blindly rather than seeing the big picture. Since we didn't see the structure, she made a mistake and missed a stitch which might have been caught earlier if we knew what it was supposed to look like. I didn't understand the structure so I missed some mistakes until we were on the next round and we decided there wasn't enough time to start over. But she learned a lot trying the challenging hat and I left her with an easier one to make until I visit again which seems super easy in comparison! 

My school has been working with LDC and a big part of their structure is to show students what their final task will look like at the beginning of each unit. The teachers have found students to be more engaged in the units and understand the objectives better. I would love to see one of their units in detail. What my evaluator took away from this is "writing objectives as 'I can' statements engages students" which is a vast oversimplification. I understand that having a task or project (that beautiful and functional hat) as a goal makes the work seem more worthwhile. I'm not entirely sure how that looks in practice unless you have the ability to run a full PBL program. An interesting idea to ponder while crafting!

Parenting as a Teacher

I returned to Twitter to ask for blogging ideas again. I asked for a quick prompt that I could write after going to the theater Saturday night. I think David thought he was being funny because this is no simple question! But then I ended up writing it anyway Saturday night, into Sunday, after I published my much quicker post.

@crstn85 How has being a parent affected your teaching?

— David Petersen (@calcdave) May 29, 2016

The more I have thought about it the more I realize that this is the wrong question. The correct question is, how has being a teacher affected my parenting? I understand this is impossible to answer accurately since I wasn't a parent before I started teaching but it is much more accurate in terms of the direction of influence. My teaching has changed very little since doubling the size of my household - I've had a decade of experiences to shape how I interact with teenagers. That decade of experiences absolutely influences how I approach parenting.

What I let go, what I address immediately, what I return to later. These are all decisions that I've made a million times in my classroom and I've found a balance among them that works.

At school I have a support team built in, at home I built one up (my friends and other kids' parents are good, professionals are great).

I've taught students in foster care, parentified kids and other kids who have had to grow up faster than their peers. I've learned to recognize the difference between maturity and independence. It's still rather impossible to navigate successfully - all teenagers demand opportunities while simultaneously avoiding other responsibilities. Jordan likes to tell me that kids do [insert thing she did or wants to do]; sometimes I need the reminder, sometimes she's delusional.

I could tell you that watching her do homework made me realize something about the work I assign, but that's not true. Or that hearing the way she talks about her teachers makes me want to change, but that's not true either. I like knowing more about how the middle school structure works so I can relate better to my grade nine students' culture shock. I also like knowing the middle school math content so I can tell my students with confidence that they've seen something before. There are some small improvements in the other direction.

Adding one more kid to the long line of other kids I've watched grow up hasn't changed my teaching. But watching a long line of kids grow up absolutely prepared me to be a better parent for the one that I let into my home.

Feeling Appreciated

When’s the last time you acknowledged hard work by each of your students? When’s the last time someone acknowledged your hard work?

— Tina Cardone (@crstn85) March 19, 2014

I don't remember much about the PD now, two years later, but I know there was a list of strategies for leaders/managers. The conversation inspired this tweet. The only reason I remember it is because it's my pinned tweet. I know giving and receiving kudos is important and I need the regular reminder to acknowledge my students accomplishments individually. This idea, acknowledging hard work, is also an excellent answer to the question I posed recently about teacher retention.

I ended the day yesterday feeling like my head was spinning and I was totally overwhelmed. (Thanks to my friends who listened to me talk through everything!) Among other things I was conflicted because in the morning my administrator talked to me about maybe changing up my schedule next year to teach mostly Algebra 2 but the department head for special education talked to me both before and after that about being part of the language based disability program, as an Algebra 1 teacher. Where I end up will depend on who we hire for the open positions and I still don't like the feeling of uncertainty I'm left with. But I want to focus on the positive aspects - it's nice to feel wanted.

The reason admin wants to move me is so I can lead the Algebra 2 team toward a more investigative and student centered teaching model. He referenced my solid understanding of the standards, my years in the district and my work with the Algebra 1 team. When discussing with the special education consultant and department head which training to attend over the summer they acknowledged that I already know many of the strategies that will come up. It's nice to be in a position where people know what training I've already done. It was nice to have conversations about my strengths with people who have been in my classroom. It was nice to be recognized.

I can't do everything, and I really hope that my preferences are taken into account, but for now I'm going to focus on feeling appreciated while I wait to see what unfolds.

Color by Number with Polynomials

I started this blog when I was teaching geometry. We did a lot of drawing in that class, and also some coloring. But there aren't as many opportunities for coloring in algebra or precalculus. Yesterday and today we did a coloring activity in algebra 1. I thought it would be a bribe to get kids to do the work, no false belief that there was anything authentic about it. They didn't even care about the coloring and were happy to do the computations without bribery! The practice was a nice mix of skills and it was refreshing to have students focused even when it's finally getting warm out.

First, students multiplied two sets of polynomials. Then, they added or subtracted the products. Finally, they matched the sum or difference with a color. I thought students would multiply two, add/subtract and then take a break to color! I was proven wrong. Most students did all the multiplication first (some not even combining the like terms in their product until later), while some others worked each row but still saved the coloring for the end. Even for students who didn't want to color at all I still encouraged them to compare their answers to the bank as a good way to check their work - it's easy to make an error (mostly students were mixing up their multiplication and addition facts when they were going back and forth between the two so frequently) in these problems. I liked that there were several steps before students reached the polynomials in the answer bank so it was more like a check sum activity than a matching game.

I didn't have an electronic copy of this file, it was in my file cabinet. Obviously we can't give our kids anything without tweaking it so we scanned, used my co-worker's awesome pdf to word converter and edited to give kids more space to work. If it's yours, let me know!

Edit 6/30/2016: Figured out the original file was from Gina and is available for purchase here.

Retention (of Teachers)

I was part of a panel of interviewers today, as I have been for the past many years. We have a math department of fourteen teachers and every year we hire at least one new teacher. In fact, I just made a list, and we have hired at least two new teachers every year since I started. Six years in and there are only four teachers remaining in my department who were here when I started. It only took two years for me to be in the middle of the department in terms of seniority. But if you look at the reasons why people leave, they're retiring, getting married, having kids or getting a job closer to home. We certainly don't want to keep people from retiring or choosing how to raise their kids, but I know that if we had a better situation then people would be willing to make the longer commute and convince their spouse to move here rather than the other way around.

Our district has the lowest pay of all the surrounding districts. But despite crazy turnover we have an amazing department. Our contract is always expired or interim. But every teacher in my school loves their students. Our students bring with them a variety of challenges. But they are the most wonderful kids, appreciative of teachers who genuinely care for them. Our administration is stuck in meetings too often to sufficiently support teachers who need alternate options for students. But admin means well and have great ideas if not great implementation. The "but's" help, however it's not enough. Meaning well and having good intentions doesn't make up for challenges we face. What can we do to improve teacher retention?

Want to come work at my school next year and help me figure it out? Because we're hiring!

Retention

This post is about student's retention of content. I should write another post about our school's retention of teachers. 

At lunch the other day a geometry teacher told me that the current sophomores know that absolute value means distance from zero. This was very exciting news since solving absolute value equations was something those same kids consistently struggled with last year. Every time a student forgot how to solve an absolute value equation or inequality I asked them what absolute value meant and told them to draw that on a number line. Every time. It was so repetitive. We did an absolute value problem weekly as a warm up for months. I kept at it. Apparently, they learned it.

This sort of repetition works for a definition. A basic concept. Can we identify several of these building blocks in our courses? If so, we could build in repetition of these ideas (I'm thinking spiraled homework) and narrow our focus. If students can learn these they will experience greater success with higher level tasks. This is not to say that rote practice should come before application but to say that it would be helpful to have a short list of key ideas we can ask students to think back to during problem solving tasks.

Algebra 1:

• Solve equations by combining like terms, using opposite operations for opposite expressions.
• The solution to an inequality is a region.
• Absolute value means distance from zero.
• Lines are defined by a starting point plus the rate of change.
• Exponentials are defined by a starting point times the rate.
• An exponent tells you how many factors of the base (if you forget the rules, write out the expanded form)
• Multiply (and factor) polynomials using the distributive property.

Precalculus:

• Function transformations (adding shifts, multiplying stretches, negative reflects)
• Undefined values are formed by dividing by zero, even roots of negatives, and logs of zero or negatives.
• You always have multiple options when solving a problem, choose strategically (aka, child please, use the graphing calculator wisely!)

Can you phrase any of these better? Which would you de-emphasize? What would you add to the list? What are the building blocks of other courses?

Many Voices

I'm not the only one promising to stay in the classroom!

A few years back I did a great job updating the #matheme page, a name I came up with as a blend of math theme and meme. It includes posts related to certain themes. One theme was Teaching, Our Profession which include a few letters on why we're staying in the classroom.

This week has seen a few more updates!

"Some will love you, some will hate you, most won't remember your name in 5 years." And yet, #WhyIWontQuit #mtbos30 https://t.co/N1ppfK1Nce

— Rose Roberts (@MsRobertsRoom) May 24, 2016

Why I Don't Quit by @RPhillipsMath

Why I Don't Quit {A Letter of Non-Resignation} by @misscalcul8
"I can't fix the system but I can fix how my students experience the system."

Is This Where You Want to Be? by @DietzTeach

Did you write a letter that I missed? Will you write one now? Post it in the comments so I can include it on the #matheme page!

Status Update

Since I wrote that letter...

I haven't quit teaching. And I still have no intention of quitting.

The elementary school that was at Level 4 (marking the district as Level 4) made great strides that year. But the school committee had already given up on them before the test results came back and handed management of the school to a private charter. I don't know how they're doing now but it was a source of intense frustration that the teachers at that school worked incredibly hard in a terrible high pressure environment, showed growth, and still all had to reapply to their jobs.

The high school reached Level 1 status (top tier) this year. Want to know the one thing that I believe had the biggest impact? We started to only give the tests to students who are prepared for it. The state says that we must give the English and Math MCAS to all sophomores. But they don't specify what the requirements are to make a student a sophomore. So we changed our requirements - students have to pass Algebra 1 and English 1 in order to be coded in the system as grade 10. And then we showed growth. Maintaining Level 1 status will be no easy feat as we have to continue to show growth toward the target of 100% proficiency. While I love that Massachusetts only requires three tests for graduation (science in grade 9, math and English in grade 10) I don't love that students have to take a math test that's primarily on Algebra in tenth grade since most of our students are taking geometry. I would rather have an end of course test for both 9th and 10th than spend a month in geometry class reviewing 8th and 9th grade content.

Administration still has far too many tasks. While our deans used to be able to build relationships with students, establish boundaries and be available for consult when I needed backup, they are far too often in meetings. The same with our department heads. A lack of trust and respect permeates our school culture and I believe that this is based in the fact that we spend so much time planning/reacting and not enough time engaging. Everyone is aware that it's an issue, but we need a critical mass of adults to stand up and say that we need to stop building the pressure and start stepping back to decide on our priorities. My priorities are building up students who are decent human beings and problem solvers. I don't need quarterly benchmarks to see if students are making progress toward those priorities. I don't need extra things, I don't need more content, I don't need more pressure. I need space to collaborate with my colleagues. I need time with my students. I need respect.

Staying in the Classroom

"The system's broken. I'm out" is a powerful message

So is "the system's broken. I'm working to fix it"

We need letters of non-resignation

— Justin (@JustinAion) May 22, 2016

A few years ago there was a flurry of letters written by teachers who were quitting teaching in protest of the state of education. Followed by one teacher who responded that she was not going to quit. So I wrote my own letter, I Will Not Quit.

Blogging is awesome because I can go back and read about how I felt 3 years ago. The entire goal of this post is to say, read my old post and write your own. Tomorrow I'll share how things have changed since I wrote that letter.

Test Prep Blitz

I'm sure you've seen the videos of kids singing songs about rocking their bubble tests. I can't watch, they make my heart hurt. We did do some power poses one year but that's as close as we've gotten to that type of thing. I don't love what we do for test prep. I don't love high stakes tests. I really don't like benchmark tests. But there are a few cool aspects of what we do - try to focus on those when you read this post.

It's English MCAS day. The sophomores have to take a 3 hour state test this morning. With nearly 30% of our students on an IEP or a 504 we have a lot of special testing accommodations so we hold school on a three hour delay to free up all the staff. In the past the ninth, eleventh and twelfth graders got a day to sleep in, but this year we did something different for ninth graders. They came in to school at the regular time and the ninth grade teachers all taught a mini math lesson. And not just the math teachers! The English and Biology teachers reviewed linear equations. The History and Health teachers reviewed functions. The Algebra teachers reviewed inequalities. After rotating through all three stations students took their Algebra benchmark test.

It's Math MCAS day. The sophomores have to take a 3 hour state test this morning. The ninth graders again came in to school at the regular time and the ninth grade teachers all taught a mini biology lesson. And not just the science teachers! The English teachers reviewed open response questions. The Algebra teachers reviewed reading graphs and tables. The History and Health teachers reviewed cell transport. Biology teachers reviewed ecology.  After rotating through all the stations students took their Biology benchmark test.

Here are all the cool things about this model:

• I didn't have to spend a block giving the benchmark test!!
• I got to meet students I don't have in class.
• We got to talk to all the teachers about what we're studying in math class. 
• I found out what kinds of things are in the biology standards.
• Our students saw that teachers know other subjects.

I love science, so it was great for me to be able to share my enthusiasm for another topic during the Bio Blitz. In class a few days after the Algebra Blitz one of my students connected a problem she was solving with one from the review lesson saying, "Oh yeah! Ms. [health teacher] taught me that!"

In order to make this work we had to use some of our team time. The ninth grade team meets regularly; instead of having hall duty we have team duty. We meet as a whole team once a week and we meet in content groups once or twice a week (depending how the alternating day schedule works out). So we spent some content group time developing the materials and then one whole team meeting prepping the other teachers for their lesson. I think this was one of my favorite uses of our common planning time this year.

Put on Your Oxygen Mask

Every time you fly, the flight attendant reminds you, "Put on your own oxygen mask before helping those around you." And for good reason, if cabin pressure drops significantly you have a matter of seconds before you pass out. You can't help your kids if you're unconscious.

My therapist told me tonight that this is an oft quoted piece of advice for parents. And we all know that teaching is a lot like parenting. (Since I'm parenting and teaching the same age group right now all advice is doubly useful!) I am not a good teacher or parent when I'm stressed, tired, distracted or otherwise not 100% on. So I have to figure out what my oxygen mask is, and prioritize it. Things that make me a more functional human also make me more patient of others imperfections (and my own!). Not to mention much more fun to be around.

In January I made a new years resolution to actively engage in more of the hobbies that bring me joy or calm. I made a schedule and told Handle to remind me every day at 5 pm. On Mondays I would do the crossword, on Tuesdays I would play the ukulele, on Wednesdays I would read and on Thursdays I would color. I don't think I've ever successfully completed this routine, despite five months of reminders. Sometimes I feel bad for checking off tasks that I didn't complete, but my ever wise therapist reframed things for me - these are reminders of things I like in case I need them. Sometimes on a Monday I'm vegged in front of the TV and I appreciate the reminder to do a crossword while watching. Other times I'm in the middle of a great book and I read four days in a row without needing any reminders. This month blogging has been my oxygen mask and I haven't had time for much else.

I recognize my need for time alone after a long day of people constantly demanding my attention. I know that I need eight hours of sleep, more than that during allergy season. I know I like walking, hiking and sometimes even jogging but it's also okay that I'm not exercising while my immune system is waging the annual war. It's good to have options for ways to replenish my energy and it's okay for me to focus on a particular one for a stretch of time.

As my ever wise friends say:
You do you.
Practice radical self care.

Put on your oxygen mask people, you can't hold your breath until summer.

Livejournal Throwback

Did you have a live journal? Ever do one of these? Oh the memories... Thanks Anne!

A- Age: 31
B- Biggest fear: loss of internet (hulu keeps stalling out this afternoon! so frustrating!)
C- Current time: 5:10 pm
D- Drink you last had: water
E- Every day starts with: snooze, then checking what I missed on Twitter while I was asleep!
F- Favorite song: Up On a Roof
G- Ghosts, are they real? Nope.
H- Hometown: Salem, MA
I- In love with: a clean desk
J- Jealous of: people with social lives and the energy for such things
K- killed someone?: why is this a question?
L- Last time you cried?: at the movies, pretty much every movie
M- Middle name: Gabrielle
N- Number of siblings: one
O- One wish: that my immune system would understand that pollen doesn't mean me any harm
P- Person you last called: friend/co-worker
Q- Question you’re always asked: can you help?
R- Reason to smile: the sun is out!
S- Song last sang: this is the song that never ends (my lunch bunch at school is the best)
T- Time you woke up: 6:20
U- Underwear color: tan
V- Vacation destination: All of my friends (I'm joining Anne wherever this is!)
W- Worst habit: saying yes to everything people ask me to help with (and then getting overwhelmed with work later!)
Y- Your favorite food: Pie!
X- X-Rays you’ve had: Teeth
Z- Zodiac sign: Aquarius

You should play too!

Questions During Tests

I remember a twitter conversation (or an in person one? probably twitter) way back when where Elizabeth shared that when students asked a question during a test she would say, "That's a great question!" and then walk away. This is exactly my take on how to respond. When students ask me, "Do I do this next?" I say, "Sounds good!" and walk away. Poker face whether or not their plan would lead to an accurate answer.

The goal of a test in my class is to discover what a student can accomplish independently.

This is not a perspective shared by everyone. This fact continues to astonish me, but I continue to encounter dissenting opinions.

• My colleague told me that students complain that I don't answer questions during tests.
• My ninth graders get mad at me when I don't answer their questions. 
• My students continue to ask questions during tests, despite the fact that I never answer them (unless they are totally unclear on the directions in which case I provide minimal clarification).

This leaves me wondering what other teachers in our local community do. I have to assume that the middle school teachers answer questions since all the ninth graders come in thinking that it's status quo. And I've learned this year that a lot of other teachers answer questions and even explain concepts during tests because I've had the unfortunate circumstance of having four different co-teachers this year in my inclusion Algebra 1 classes. My long time co-teacher was diagnosed with cancer in the fall and has been out the rest of the year (she's doing okay now and expects to be back next year! Modern medicine rocks). I had forgotten what it was like to build that relationship and to teach/train/convince another teacher of some of my teaching practices. I remember very clearly now, because I've had three new teachers in my room since then. It's been hard, really hard. And I've tried my best to be flexible to different teaching styles. But some things really bother me, including anything that will mess up the data that I'm trying to collect by giving a test or quiz. I try to ask nicely. I try to explain the goal of tests in my classroom. I do a fantastic job of modeling what I want. And yet, out of a genuine desire to help students, co-teachers continued to help students during tests. At this point it's almost the end of the year and I know Lori is coming back in the fall so I've given up. I try to put a purple pen in my co-teacher's hand as soon as I notice her helping and ask her to initial next to all the questions she helps kids on. It's a compromise I can deal with for the next 6 weeks.

What are your classroom pet peeves? Is there anything you can't stand more than, "It's your job to teach me!" during the middle of a test? Because I don't think there's anything that spikes my blood pressure as intensely as that situation.

Do, Check or Grade? Quizzes (and Tests)

I asked Twitter on Thursday what I should blog about. And that day they wanted to know what's worth holding kids accountable for and how to do it. I wrote about Homework, Classwork and Projects so far. I probably could be done there but I know there's some debate on whether quizzes are formative assessment and whether or not formative assessment should be graded. So I'm writing one more post in this series. I'll mention how I grade tests while I'm at it so we cover everything I grade.

So, yes, quizzes are formative assessments. And yes, I grade them. Why? Because if I have to grade things, why not quizzes? Yup, that's the full extent of my thought process here. Seriously though, I think more grades benefits students. More chances to demonstrate understanding and no one thing counts for too much of the total grade.

Honors PreCalculus:
I mentioned before that I announce quizzes ahead of time in this class and students can make an index card for homework. At the beginning of class (after taking questions) I project three questions and students work them out on a quarter sheet of scrap paper. We're pretty casual around here (easier for me and also makes assessments seem low stress). I use the orange pen method (except my pens are purple) to have students grade themselves right away.

Quizzes are on pure skills. I only ever quiz a single small topic at a time. In the unit on solving polynomials with complex roots I quiz on operations with complex numbers. Then a few classes later I quiz on solving quadratics. Quizzes happen immediately after learning a topic and they're bite size. I allow retakes. Most students do well on the quizzes and if they don't we both know exactly what they need to learn.

To contrast, tests are on several skills and include multi-part questions. They also can't use their index cards on the test (except for the conics unit when they can use their dichotomous key) but students who have been actively working all unit have learned the formulas by heart by then anyway. For that same unit on solving polynomials I had students complete more questions on complex numbers and quadratics, but also added questions on higher degree polynomials. They had to think conceptually about the number and types of roots, justifying their claims. They had to write their answers as solutions to an equation set equal to zero, rewrite an expression in factored form and state a function's intercepts. Tests are broken into 2-3 sections and students earn a separate grade for each section. Then if they want to retake to improve their grade they only retake one section at a time. The retakes are questions written on index cards that students complete on scrap paper. I've had students tell me that they really like the retakes because questions on an index card seem so informal and therefore low stress.

Algebra 1:
I used to do three question quizzes in Algebra but we're trying to do common assessments across the Algebra 1 teachers and the other teachers' idea of a quiz is more substantial and formal than mine. I would like to move toward some more frequent, smaller check ins, maybe I can ask the team for some exit tickets? But for now I'm working on being flexible! We frequently spend the first half of the block practicing and the second half of the block taking a quiz. This provides some serious motivation to focus on the classwork for the first half of class. But it also means we're not testing recall at all, they are quizzing on something they've been doing for the last 45 minutes. We allow students to use their flappers on tests and quizzes.

Tests work the same as in PreCalc.

General Quizzes Conclusions
Mastering math content requires both skills and application. The projects we do examine student's ability to apply skills, but there needs to be a point where we check for the skills. It's totally possible to check skill levels without giving pure skill assessments but it's easier for me and clearer for my students to give short quizzes on a very specific topic.

Do, Check or Grade? Projects

I asked Twitter on Thursday what I should blog about. And that day they wanted to know what's worth holding kids accountable for and how to do it. I wrote about Homework and Classwork so far. When I taught geometry I did a lot of projects that involved making posters and coloring. Now that I have PreCalc and Algebra 1 I do some color coding of graphs but no posters. Since I don't do anything big that feels like a project I call them graded assignments. There are some assignments we do in class that are important enough I want to grade them. So I kind of lied in my last post when I said I didn't grade classwork, but I defined my way out of that lie at the beginning of the post!

Honors PreCalculus:
We do one graded assignment per unit. Students have the opportunity to start in class and typically have to do some parts at home. Sometimes students work in groups but usually these are individual tasks. The difference between these and a test are that I will help them and they can work together even if it's not a group project. If it is a group project there are still individual components to be sure everyone contributed. Also, there tends to be an element of choice to make them more interesting to grade. Students get to choose a ferris wheel to model, an exponential context to analyze, a photo to match etc.

They are graded out of a random number of points, whatever fits the assignment best. I really hate rubrics, there are too many words and they feel too vague. I give students checklists and each item is worth 1-2 points. This post has all of the ones I did in 2012-2013, while I've modified the assignments a bit the list is mostly the same as this year. (I called these things investigations back then). I should really write up the rest of them, I am surprised I've never shared my version of the ferris wheel assignment!

Graded assignments count as 30% of their grade. They are due on a particular day and I collect all of them whether students are done or not. When I return them they're marked up with highlighters and students can resubmit a corrected version for an improved grade. They have until the end of the quarter to submit/resubmit and raise their grade. Math Practice Portfolios fall under this category too.

Algebra 1:
Things work the same way as precalc but ninth graders get less choice it appears. I hadn't really thought about that before, but I guess it's true. In Algebra I collect problems in context (like this distance one) and less contextual challenges like Henri's designs (students do get some choice in that one!). I'll have to make a nice list of these too. That's part of our end of the year goal as we write up our curriculum. Someday it'll be organized.

Since we're doing standards based grading these assignments are graded by topic. For the distance graph assignment this year I had students answer the questions and write equations for each segment. The questions are all about rate of change, so students earned a score out of 5 for that topic. Then they earned a separate score out of 5 for their equations. We also are allowing students to submit/resubmit assignments from any quarter since their grade is a cumulative average rather than a fresh start each quarter.

General Projects Conclusions
I want to grade some work where students have a chance to take as much time as they want and collaborate. I try to pick a comprehensive assignment for each unit, and also one that is interesting. Students need to be able to demonstrate their basic skills on quizzes, but they also need to apply those skills. I also think it's important to balance grades. Projects are low pressure assessments, students need the opportunity to demonstrate their understanding in that climate as well as high(er) pressure assessments like tests. I never want to grade a parent's ability to do math so students are given ample time to work on these assignments in class.

Do, Check or Grade? Classwork

I asked Twitter on Thursday what I should blog about. And that day they wanted to know what's worth holding kids accountable for and how to do it. I wrote about Homework yesterday. For the purposes of this post, classwork is any work that students do in class that isn't a quiz, test or project.

Honors PreCalculus: 
There's an opener. We chat about homework. Then I either project some problems or give students a handout. They do the problems. I circulate. We discuss when a critical mass has reached a predetermined point. Repeat. These are honors juniors and seniors. When they aren't doing the work I invite them to start. When they have their phones out I ask them to redirect their attention. When they still don't engage I roll my eyes (I think mentally only but no guarantees) and move on to whoever is asking me a question. I am ready to help anyone who wants it. I'm not up for fighting with 16-18 year olds to make them engage when they're having an off day. At the end of every class students reflect by responding to prompts in their journal. Every two weeks I collect their journals and students self assess on a classwork rubric on the back. Together the journal and classwork rubric count for 10% of their grade.

Algebra 1:
My Algebra class has students who work at vastly different paces. This makes my usual method of going over a section when everyone is done really challenging. My ninth graders don't sit and chat or work on something else quietly when they're done so I had taken to giving lengthy assignments and doing a limited amount of class discussion. My administrator/evaluator suggested timers and randomly choosing students to share. This routine allows me to continue giving the lengthy assignment, and then after a set time (7-10 minutes) calling the class together to go over just the very beginning problems. Then they get back to work, I reset the timer, and after a while we go over the next few problems. Students can continue working at their own pace, but I can pull everyone's attention back to some key ideas on problems they have all had the chance to work on.

While students are working I reinforce positive behaviors via stamp chart. The stamps they earn don't contribute to their grade but sometimes they can earn things. A.k.a. we bribe them in the spring when my co-teachers run out of patience. Last year kids could trade stamps for candy one co-teacher bought. This year I have a different co-teacher and she knew that the JROTC has access to a back basketball court they don't use during our blocks. The class works together to get enough points to earn "recess" during the second half of class one day. We bring in some sporting equipment (badminton, frisbee, basketball...) and everyone goes outside together. Bonus: playing together a nice opportunity to build relationships. Maybe we should start this in the fall next year but make it more challenging so it's something they earn every three weeks or so.

Algebra Support:
This is a pass/fail class where I don't grade anything. At the end of class I walk around and give students a score out of four points based on how much progress they've made. If the bell catches me off guard I have them hand in their work but still only give them a score based on how far they got.

Sometimes I will collect an activity that we only got half way through during class to check all of their answers. The next class I give it back for them to correct before they continue with the remainder of the assignment. This is purely feedback so they don't miss an important idea, it doesn't have any effect on the progress score.

They have the stamp charts too. Their class tally is separate from the Algebra 1 tally for the "recess" reward.

General Classwork Conclusions
I do not have time to grade classwork every day. Kids do it because I'm walking around and engaging with them about the assignment. There are some extrinsic motivators. I like to think kids do assignments because they are interested and want to learn. I know that for many kids this isn't enough but I think my genuine interest in their thinking helps. Plus some bribery! I want to be above bribery, but I think rewards for good behavior are okay, especially where this year the reward is time together.

Do, Check or Grade? Homework

I asked Twitter on Thursday what I should blog about. And that day they wanted to know what's worth holding kids accountable for and how to do it.

how to hold kids accountable for classwork without grading everything @crstn85

— Jennifer Abel (@abel_jennifer) May 12, 2016

@crstn85 benefits and drawbacks of firm assignment deadlines

— Justin (@JustinAion) May 12, 2016

@MrVaudrey @crstn85 also how to pick winning lottery numbers which is just as likely as the above happening.

— Meg Craig (@mathymeg07) May 12, 2016

So, I'm going to do a series of posts on my routines, today we will start with homework.

Honors PreCalculus Homework
I don't grade this, I check it.

In PreCalc I'm still doing a hybrid SBG model so attempting homework counts for 10% of their grade. I walk around the room with my clipboard while students are doing something else (the daily SET, an awesome opener stolen from Michael Fenton) and if students have work written next to each problem I put a check mark next to their name. If they are absent that day or were absent the previous class they can show me later for full credit. Otherwise they can show me later for half credit because we're about to go over it.

At the beginning of the year I was awesome about projecting worked out solutions to all the homework problems after the opener. I gave students the opportunity to ask questions but (especially since this is honors PreCalc) I limited the questions, they couldn't ask me to talk through all of them and needed to ask a specific question for me to talk about more than one of the same type. At some point I hit an assignment I didn't want to post solutions for and then got out of the habit. I should start again! But even without posted solutions we've followed the same routine.

I don't assign many questions most nights. I started off with 5 plus an SAT problem but it really varies depending on the topic - 10 matching vs. 3 polynomials to solve including complex roots. This still isn't a super speedy process, but I have 90 minute blocks every other day and I think it's worthwhile with this class where most kids do the assignments. On a quiz or test day the homework is to make an index card for the quiz or study for the test. The "going over the homework" portion of class gets replaced with the "asking questions before the assessment" portion of class.

Algebra 1 Homework
Right now we don't even do this.

I have half of my students every day for 90 minutes. I think this is plenty of time to learn and practice Algebra 1 material. Sometimes when my regular class is particularly unfocused I assign the remainder of the classwork for homework. The students who have me every day get to do that work (plus other assignments) in the support block.

We had a great plan though. One that I think will happen (more of, most of?) next year. Spiraled homework!

Over the summer the Algebra team got funding to meet for some paid curriculum work. One of our team members was going to be on adoption leave starting the first week of school so we used her need for sub plans as motivation to focus on planning the first unit in detail. Since we had class activities planned and assessments written we were free to spend our common planning time making homework. We chose skills each week that were review (this would be past units but for the first unit it was 8th grade), practice from the current unit (but a week delayed) and preview (skills that would be necessary for the next unit - for example, before we started solving equations we reviewed evaluating expressions).

I'd like to post answers online but not solutions. Students could ask questions any day but we'll dedicate some time for it on Fridays. That way we've made the suggestion that students do some work each day, but also allowed for them to be flexible in their scheduling and plan ahead for busy days by getting extra problems done. The only difficulty is that I don't have my full Algebra class every Friday (or every Monday for that matter). A two week schedule makes much more sense when you're on an alternating block but two weeks is a really long time for ninth graders to be independently practicing. We should provide time to discuss homework on Mondays too.

Since we are doing SBG in Algebra, homework isn't graded. We thought it would be good to check, for data gathering and some extrinsic motivation. One teacher made it a category in the online grading system that counts for 0% of their grade. I'd like to do that next year too. If it's not graded though, where is the motivation to do it? Last year we discovered that student retention was really low so this year we tried to build in opportunities to practice via Friday Review Days. Next year part of the Friday Review Days will be a skill quiz on one or more of the homework topics. Students could also use the homework as evidence that they're ready for a retake of another topic. This way, students who have mastered the skills on the homework and don't need the practice can demonstrate that on the quiz. No penalty for not doing the extra practice if it's unnecessary. Students who do need the practice will see the benefit of it as they improve their scores. I'm impatient to see what our new online gradebook can do as we haven't decided if these Friday quizzes would be additional assessments or retake assessments. I'd love a system where everything counts but the more recent assessment is weighted more. Fingers crossed this will be a possibility!

General Homework Conclusions
I do not have time to be grading homework every day. I think if you assign it you have to acknowledge it regularly. I only want to assign homework that is meaningful. In PreCalc it's extra practice of current material since we have a lot of content and not a lot of time. In Algebra it's skill practice since students arrive with varying levels of mastery and building fluency frees them up to focus on the new algebraic concepts. It's not a lottery winning plan, but it's an effective one.

Note: if I had to go back to teaching every day rather than on an alternating day block I'd strongly consider giving 2 day homework assignments. It allows flexibility for kids who have certain days they're really busy and means you don't have to spend class time going over homework every day.

Anxiety

It's hard to challenge a student without overwhelming them. It's especially hard to find that middle ground when students have anxiety.

Today was the first Friday where it really felt like summer was coming. We've had a lot of rain and some unseasonably cold temperatures. Continuing with the school routine felt normal, until this week. Today the whole building was squirrely. Seniors only have two weeks left so tensions are high for that group as they scramble to finish everything in time. The rest of the building has a full month and a half remaining so teachers are frustrated that students are shifting into summer mode while simultaneously we're all also looking forward to the weekend. I didn't teach before lunch today (my lunch is at 10:30) but half my colleagues were already at wits end by then. I survived the block after lunch but pretty quickly into the last block of the day I felt the tensions increasing. One student after another was asking to take a break. One student asked to take a second break immediately after taking his first break and that was my breaking point. Usually I praise this student for knowing when he needs to step away, but today he needed the opposite lecture - sometimes you have to push through. I told the class that no one really wanted to be here right now, and it was making me really grumpy too. But together, we were going to push through! The pep talk and a lot of prompting got us through a couple questions but then they'd all shut down and I was getting frustrated that no one would answer my question and everyone kept asking to leave despite my repeated statement that we needed to get through this first. Thankfully I stopped. And took a breath. And told them all to close their eyes and take a breath. A student remembered a breathing video we'd done before and asked to do that. I was so happy he remembered and suggested it!! We watched point of focus with the lights off. I allowed the silence to stretch out for a few more moments and then asked them to make the next question their point of focus. We got through it. Everyone finished the minimum goal I set for the day. Some students surpassed it. We all survived. And now it's the weekend! Send calming energy and videos or audio we can use when we all need a break because June 27th is a really long time to spend with students who aren't in math mode, especially ones with anxiety for whom the space between bored and overwhelmed can be really hard to find. 

Authentic Math

We all know the math in textbooks frequently doesn't feel authentic. Much like my painting post, the interesting math in this story isn't in the predictable computation parts. In this case the most interesting aspect was knowing what math needed to be done!

As you may know, TMC is offering the option for people to stay in dorm rooms this year. Coordinating this has been a daunting task. People have a variety of options including single or double, AC or no AC, and 2, 3 or 4 nights. Do you know how many categories that is? There's a combinatorics problem for you. Each of the room types costs a different amount, multiplied by the number of nights, plus a one time linens fee. The challenge of organizing this information, in a way that all of the members of the team could understand and easily reference is another mathematical task. Our spreadsheet is clearly labeled. You learn fast that when you have too much information that a table is the way to organize it. Do I ever give my kids too much information? Or not provide the table? Skills they need to learn... But still, we haven't done any exciting math. We've categorized and labeled and calculated a few linear functions. All things students can figure out or type in the calculator.

The challenge came when we found out that PayPal charges a fee. That fee is 2.9% plus $0.30. We don't have cash on hand to be able to cover the fee, so we needed to charge people for it. But what do we charge? The nicest numbers are for the non A/C dorm double room, that's $25/per person/night + $15 linen fee. So if someone is staying all four nights we need to pay the college $115. That means we need to get $115 after the fee. If you're reading this with your mathematical mind engaged, you may have realized that the amount we need to charge isn't just $115 + 2.9% of $115 + $0.30. This moment is where the interesting math is: this point of recognizing that percents are relative. The idea that not all operations are undone as easily as addition and subtraction. Once I had this realization the act of writing an equation wasn't particularly challenging, nor was solving for the inverse equation. I started with a specific example to check my work but rapidly generalized so I didn't have to repeat the process nine times (nine isn't the answer to the number of possible combinations, but it is the number of actual combinations, and therefore the number of invoice templates I created!) Applying a generalized function to each different category was somewhat annoying because I don't know how to tell google sheets to reference "the cell above" without having to retype the cell name each time (I could drag across to auto-fill for each row but I had four different rows for the four room types).

The authentic math I'd love to see more students working with is things like Would You Rather problems comparing 70% off to 40%, then 20% then 10% off. Anything that challenges their intuition and builds this understanding of relativity; of non-commutativity. Experimenting with inverses and learning just how much order matters. These are great opportunities to practice important skills (you'll calculate a percent four times in that one would you rather example!) while simultaneously pushing students to question their assumptions. In this case that assumption doesn't change much (we'd only be off by $0.10 in the example) but that adds up after 99 payments (in our case) or more!

Follow Up: Standards Based Grading

Our whole district is transitioning to standards based grading. I've been using a hybrid version (only SBG for tests and quizzes) for several years. This summer we had a workshop and the Algebra 1 team implemented the plan this year.

Our Process:
Each assignment was graded on a 0-5 scale.
We divided the year into 12 units plus the standards for mathematical practices (I used the portfolios). Assignments in a unit were averaged to earn a score for each topic.

Each topic was weighted equally when averaging to get a report card friendly grade for the course. This was a bit tricky because first quarter we only had three topics to average. Then second quarter we needed to carry over first quarter scores and add new ones. I'm hopeful this process will be less tedious with Aspen, the new grading system we'll be using next year.

SBG was useful for me:

• the grade was focused on topics rather than assignments
• I was sure to balance assessment types
• there was at least one quiz, test and graded assignment for each topic
• unlike last year when I would grade six assignments but never quiz on some topics!
• I could see overall how students were doing by unit, with a balanced assessment of their skills. 
• It was easier to see where to start with retakes. 
• told kids to start by correcting the graded assignment (they can get help on those) 
• then retake a test or quiz (they have to do those independently)

SBG was unclear for students and parents after the first quarter:

Kids were already transitioning from middle school where grades are not numeric (they get marked as below/at/above grade level for each class and then marked on content and citizenship and something else). All the rest of their classes this year were numeric and each quarter was a fresh start, but in Algebra each unit was a fresh start, but the only thing that went home or that most people looked at online was the average, a cumulative average. For example, some students did poorly first quarter, then retook things (hooray!). But then when they did poorly second quarter it wasn't as obvious because they were only looking at the average of the improved first quarter grades and the new grades. If students and parents and other teachers would look at the topic grades things would be much clearer, but since we were the only team doing this it wasn't well communicated.

Next year:

We need to make reporting clearer or be consistent with the rest of the school. Ideally we would have a standards based report card, but the rest of the school isn't there yet. We could print our own (category averages are pretty easy to print for each kid, I imagine this will still be true next year in Aspen) and mail them home. But that's still extra work. Or, we could make sure each unit aligns with a report card. If we won't finish a unit we won't put it on the report card until the next quarter, but this makes spiraling back hard. We would frequently split an assignment into two topics - if we were graphing a line using a table we might grade on evaluating functions and graphing lines. Both standards are necessary to graph a line using a table, so we graded each separately and continued adding grades to that first quarter unit (evaluating functions) throughout the year. Tricky to track!

Overall I think we (as a team of Algebra 1 teachers) did a better job thinking big picture. Our conversations focused more around "Does this student understand the material?" than "How many point would you make question one worth?" I look forward to working with the team to provide opportunities for retakes built into class time. Everyone can benefit from review and if we want retakes to be something everyone does then we need to give some time in class for them. We talked about Friday review days last year and implemented them sporadically this year. Spiraled homework plus Friday review days would be great goals to focus on moving forward.

Follow Up: Grading with Highlighters

Early this year I started grading using only two highlighters. (Apparently I never blogged about it but I did tweet it) I had a green highlighter for correct work and a pink highlighter for incorrect work.

Believe it or not I stuck with it the whole year!

The routine I ended up using:
If the whole problem was correct I either highlighted the answer (if it was short) or the question number (if it was a longer response) in green. I sometimes highlighted key words in green to draw attention to the vocabulary/reasoning I was looking for. If the whole problem was blank I highlighted the question number in pink. Otherwise I highlighted the first mistake pink.

Pro: It was easy for kids to see exactly what needed fixing. They copied down the line above the pink, fixed the pink part and then continued from there.

Con: I had one student who was red/green colorblind. She asked her friends to tell her which was which until mid-year when she told me she was colorblind and I went back over hers with pen after that. Next year I will have to ask up front if anyone is colorblind.

Pro: I wrote less. All those helpful notes seem like such a good idea, but they take up a lot of time and the students didn't have to do the thinking to figure out their mistake. Kids can always ask a neighbor who got it right or ask me if they can't figure out their mistake. I did occasionally write something with either a nearby pen or the highlighter since I got thin ones.

Con: I bought a lot of highlighters and only used the pink and green ones. I didn't need a lot, none of them have run out, but I wanted a set in my desk at school, a set in my grading bag and a set at home.

Pro: The kids like it. A student made up a test after school and asked me to grade it. I grabbed whatever pen was in front of me and he said, "No! You have to use the highlighters!"

Notebooks!

I wasn't a notebook person until recently. I used scrap paper for the occasional to do list but mostly my system was electronic. At conferences I liked to have a notebook and everyone else seemed so excited about their notebooks that I figured I'd try it out. Staples has this lovely one - cardboard front and back, I want to say it's made of recycled materials but I'm not positive that's true. 

 My favorite part of this notebook is that it has three types of paper - lined, blank and graph. They are in two sections. I used the front half for miscellaneous stuff including these fun math problems! However, it's starting to fill up and people were talking about Arc Notebooks on twitter so I thought I'd check out my other options.

These notebooks are cool! You can pull pages out and pop them back in as needed. That means that I can reorganize. One part that is frustrating about my current notebook is that there are a bunch of lined pages followed by a bunch of blank pages followed by a bunch of graph paper. Sometimes I want graph paper next to my lined paper. 

So I picked up a set. A couple dividers/folders and a to do list pad. No more scrap paper to do lists that I worry about losing. They didn't have any graph paper at Staples but I might order some. I also plan to go back and use the coupon I got while checking out to get a hole punch (there's a portable one rather than that $40 one) and an elastic band. I thought the band was unnecessary but then I realized that I couldn't put a pen in the spiral if there was no spiral, so the band will hold my global math department pen!

 The accessories pop right into place!

The best part? It's nice and small and folds completely back. The notebook I currently have has a giant spiral on it as well as a thick cover so I'm excited for a version that will tuck into a bag more easily. And since it's refillable I don't have to worry about having a lot of paper in it at any given time so there's no need to get a bigger one - take out the stuff that I don't need (old to do lists) and add more paper as needed!

Saturday Morning Math 2

Alternate title: The Purpose of a Teacher

So, as promised, as soon as I hit publish yesterday I got started doing some math. I worked for a bit and wrote down much more than I normally would knowing that I would be sharing my work today. But then I hit a point where I didn't really know what to do next. And so I started reading blogs. And then went to run errands, ended up seeing a movie with a friend and staying out late working on a website she needed help with. This morning I thought about looking at the problem again but there were lots of other things to do so I didn't. And this is exactly why learning math with a teacher or a study group is better for me than working solo. I'm not stuck, there are lots of options to try, but I have no idea what might end up being interesting. And I'm not sufficiently invested in the problem to want to put time into experimenting. So, here's where you come in. If you're going into this problem as blind as I am, then share what you've tried and what you're curious about. If you have a good idea about how this problem works, provide a helpful nudge in an interesting direction. Without further ado, here's my work from yesterday.

Saturday Morning Math

When you're a student (k-12, college or grad school) you do math all the time. As a teacher I do math regularly, but rarely math that's new or surprising. This week I challenged my problem solving muscles to create a set of rational functions that would have different limits, nice intercepts, and a balance of holes and asymptotes. But that's still not the same as diving into a new problem, remembering what it's like to be a student and feeling a sense of accomplishment when I make a discovery. A few times we've tried to create problem solving groups. Rachel posted about a problem we played with individually and then discussed. Carl ran #probchat where people solved a problem live on twitter. I've done a variety of google hangouts including Saturday Morning Math, which was tough because of time differences and variability of schedules and a PCMI eTable which is always fun but super concentrated - every day for three weeks in July. I don't have a good solution, but I miss doing math and Justin posted a problem this week so this morning I'm going to be a Saturday math gang of one!

If you want to play first, now's your chance! I'm hitting publish now to go play. Then I'll share what I learned tomorrow.

Curriculum

I teach ninth grade. The middle school is looking at picking a new curriculum for the accelerated eighth grade program and they asked us to look at it. Hooray for vertical alignment!

They are looking at Eureka Math which looks pretty good as far as curriculum goes. The lessons are broken into chunks with approximate times in parentheses next to each chunk. The sight of those times made one of my coworkers have a strong negative reaction. You can tell what kinds of administrators teachers have had based on how they react to something like that. I pushed back, saying that the time estimates are useful so long as admin doesn't come in saying, "It's day 3 and we're twelve minutes into the period, why aren't you doing ___?" Another coworker, who has only taught at our school with rather hands off administrators, laughed at that idea. He didn't think anyone could actually be that crazy. His perspective is refreshing!

When evaluating the curriculum I was looking for resources, not a script. The website provides sample discussions which is helpful, especially for someone new to a course (teacher turnover at the middle school is appalling). It provides maps, activities, scaffolds and extensions. It provides assessments that are not so realistic but there are useful bits to them. The site provides a lot of things on which to base a coherent course. I think that's really important to have.

We, on the other hand, have nothing. Well, that's not entirely fair - we have textbooks and teachers guides to go with them, but we don't use them. I'd already taught three years of algebra before starting to teach it here and so I had a well developed understanding of course progressions and had amassed a variety of activities. The other teachers on my team have done the same. Over the past few years we've spent many a professional development taking our mishmash of materials and building something that admin can see and new teachers can access without needing to jump between dropbox, google drive and the school network folder!

Curriculum is something I have a hard time forming an opinion on. I don't take well to being told I'm getting pulled from my classroom to write a unit with the latest consultant (I can think of four groups I've written with in my six years here). But I also spent half an hour retyping an activity this week because I didn't like the phrasing of some parts or the examples in one section. Is it my job to write curriculum? No. Do I trust anyone else to do it? Not really. I understand that with a five : two ratio of teaching : prep time I don't have time to grade, prepare materials (copy, cut, sort...), communicate with all of the community members and write lessons from scratch. I know the solution is a solid curriculum where I have resources to pull from and need only modify for my students with unique needs. My dropbox folders are close to reaching that point with unit plans filled with notes from last year and lots of files. But the first year of each class isn't nearly the same as the third. Which will always be true. But a curriculum that can point out common misconceptions and has little boxes reminding students to apply something from an old unit so they don't forget that skill would be nice to start out with. Maybe we'll get there someday, so the new teachers can jump right into the hard work of picking out the best student work to have the class examine, rather than googling "exponent rules discovery" hoping for a decent activity the night before they need to teach it.

Mathematics Teacher Article (1)

The new issue of Mathematics Teacher is out from NCTM. A while back I decided that as long as I pay so much for membership I should at least read some articles! I've been tweeting about them but apparently not using a hashtag so they're hard to find. So hard to find that Dan didn't realize there were any! Maybe we could start using #MTNCTM? For this week though, I'll blog my responses. Go #MTBoS30! 

First up I chose Teaching Mathematics and Language to English Learners

This paragraph struck me:

"Incorporating short writing activities in the classroom is one way to boost language practice opportunities. Having your students explain their steps in complete written sentences using sequencing words (such as first, next, then, finally) can help reinforce vocabulary and content understanding while also providing EL students with a chance to do some thinking about a particular problem before discussing it aloud in class."

Last week my co-teacher was working with a student in study skills (study hall plus to fit the time on learning law in MA) and so she knew that the ELL class was working on comparisons. Then this week we were doing exponents including powers of two and so wrote sentences including "half as big as" and "twice as big as." Our student in the same ELL class was able to jump right in and my co-teacher made the connection. It would be great if we were able to communicate better between courses - when they were doing comparisons they could do some mathematical comparisons to support our content. And if we knew what vocab they were working on in ELL class we could incorporate it when possible. Sequencing words don't seem like academic language I would make sure to teach but they're definitely useful words that students need to know for academic success. New goal: make a point to stop by an ELL class during a prep block next week. even glancing around at their word wall (which I assume is more impressive than mine!) would be a helpful first step.

Fundraising

Many of my students have low socio-economic status. We have enough students who qualify for free or reduced price lunch that the school qualified for a grant which provides free breakfast and lunch to all students! The breakfast is grab and go in the main entrance. Lunch is the same as usual but when everyone gets free lunch there's no stigma or barrier if students lose their ID cards or don't have the reduced price. It's a great program and better-fed students is always a great thing to have in the classroom. Plus sometimes I get a bonus string cheese or cereal if kids don't want all of their breakfast. But that wasn't what I wanted to tell you about today...

The music department does a fundraiser where a wholesale mattress company comes to the school and offers great prices on mattresses. A few years ago I had just moved from a one bedroom apartment to a two bedroom condo so I took advantage of the event and bought a great mattress. But it's a great mattress, so I didn't need to replace it two years ago when they did the fundraiser again, and I still don't need to replace it this time around. My co-worker and I asked one of the students if they make any money off it. She shared that other towns make something like $8,000 each time they run it, but Salem has made around $8,000 total. In other towns people can afford to replace their mattresses frequently (which is apparently recommended? I think I had my childhood mattress from when I first moved into a 'big kid bed' all the way through ... well, forever, it's still there as a guest bed) but in Salem people aren't upgrading or replacing mattresses on a regular basis. The majority of the money raised was from a local inn that needed to replace all of their mattresses. How great that a local company supported the school music department! But, this makes me realize (again), that the schools that need to fund raise the most are the ones where parents and community members don't have the disposable income to spend. I doubt that people from neighboring cities are interested in supporting our schools, and people in our city generally don't have the money to support the schools. Where does that leave us?

Having a great school isn't all about having money, but it sure helps when the music department can buy new instruments or uniforms, and can afford to travel to competitions. Because when our band and color guard do get to compete, they win. Our students work incredibly hard to become excellent musicians and deserve the chance to show off their accomplishments. I wish they didn't have to work so hard to raise the money necessary to do so.

Reading and Repetition

Today I had my algebra support block (we run an alternating day block schedule so I see my algebra class every other day for 90 minutes, but half of my algebra class sees me every day for 90 minutes because they also have this support class) and my contained algebra class (they all see me every day for 90 minutes).

Sometimes during the support block we work out of the EDC's Transition to Algebra, which I love. They do a great job of starting with numeric examples and making the patterns very clear. However, they are filled with language. The page is chock full of information (I understand that they are consumable workbooks so they squished lots of information on the page to reduce cost). The problems and hints are conversational, not to mention the actual student conversations mixed in. Sounds great, right? Here's something you probably don't know about my classes - I have many students with substantial language based learning disabilities and a couple students new to learning English (I like the phrase emerging bilinguals except what if English is the student's third language like it is for one of mine?). So this much language is really challenging. However, especially this semester since I'm working with a co-teacher who was in English classes last year, I've taken on the responsibility of supporting their language acquisition while teaching the math.

Monday in support we began exponents in the TTA book. To start, we assigned parts and read out one of the student conversations. I was so pleased how many students wanted to read! It's a huge testament to how much they trust their classmates when students who struggle with reading are willing to read in front of the class. We read it, talked about it, read it again and then made a connection between the reading and their own work. As we discussed I took notes on the things my students said, but then they asked me where to write it down (no spare space on the page, remember?). But, everything we'd written down was in the conversation! So we pulled out the highlighters and kids read the conversation yet again to highlight the key observation we'd made. It's always surprising to me how challenging this is for them. I was always a strong reader and I just cannot imagine going through high school trying to learn content when it's a challenge to locate a key phrase that we've just discussed. Activities like these remind me to slow down, recognize the difficulty and continue pointing out (not to mention recognizing for myself) strategies as we read.

I don't remember who said it, but it's really stuck with me how in math, conciseness is valued. In an essay you read the main idea in the first paragraph, you read more detail and many repetitions of that main idea in the following paragraphs and a recap of the main idea and details in the conclusion. In math we make a definition as dense as possible and that's it. A problem set may contain many repetitions but the language is brief and requires many read throughs. Since hearing that I realized this is exactly what makes a math text book so hard to read and have focused on convincing students that math requires reading many times.

Today we worked on another page in the TTA book. It was all about powers of two. In one question students figured out that if the exponent decreases by one then the value would be divided by two. In the next question students needed to decide what half of 2^50 would look like. All around the room students wrote 2^25. But children! We just talked about that! And then I realized that 1) it's far from intuitive, that's why they included more questions in the book to solidify this idea and 2) the language changed. I went back and we made the connection that "double" and "multiply by two" are the same thing. So then we figured out that "halve" and "divide by two" are the same thing. Then we tried some simpler cases. Then a couple kids changed their hypothesis but most students were far from convinced. Then I wrote out what 2^50 and 2^49 look like. Then I had some more students explain. Then a student was stuck and I had him "phone a friend" and they were silly about it. One friend wasn't helpful. Another friend said "Call me!" The student put him on "speaker phone" to be able to talk and write at the same time. The friend got annoyed how many times he had to repeat himself and my co-teacher said "Now you know what we feel like!" But it was worth the time - first because it's important to play together, and second because hearing something that many times makes it stick! The next question asked students to find half of 2^100 and I was ready to have a debate on that solution but they all got that it was 2^99 on their own!

It's hard to be patient and say something a million times. I already get it. By the time I get to my contained class where everyone has a math disability in addition to other challenges, I've already spent the last 90 minutes explaining this thing. But students need to hear, see and say things many times for it to stick. I need to get them talking to each other as much as I can because I might pull my hair out if I have to repeat something over and over and over, but no matter how many times I've already explained something, hearing a kid explain it to their partner always results in me directing a genuine beaming smile towards the pair followed up with a hear felt "thank you! well done!" after the conversation ends. I love how I can hear myself in student conversations. Instead of telling an answer or even listing a series of steps, they've picked up the questioning and explaining. It's awesome. Sometimes the end of the year is hard, but the hardest part is giving up my wonderfully trained students who are willing to read to the class and take the time to make sure their partner could do the next problem on their own.