Making Choice Real

As I’ve read some fun books about making the tasks we do in school more authentic/genuine/engaging, one common theme is student choice. Image

But …

How do we make choice consistently meaningful? There are a few projects I do already where choice is (fairly) meaningful. When we study data for our Exhibition, students get to choose one of the variables they are investigating (and their choices range from % of population in prison, to MCAS scores, to physicians/1000 people). That choice seems meaningful. Often I allow students to choose a method for solving; that also seems meaningful.

But when I imagine students working on the everyday tasks next year, I struggle to imagine how choice could work. Here are my concerns.

First, I’m banking heavily on students completing tasks in different ways and teaching each other those ways in order to meet a myriad of Algebra standards. How will students compare methods if everyone is doing different problems? Perhaps it’d be fine if a critical mass of students were doing each problem and then together had to come up with a variety of methods.

Second, how in the world do we make the choice meaningful? Say I do put out 4 different word problems — what’s the process for having students read all the problems and having them choose the one that would be most interesting/accessible for them?

Literally as I’m writing this, I’m thinking to myself, well, it seems I do have a plan …

1) Offer choice in topic when it makes sense (i.e. Exhibition).

2) Choice in method is a fundamental value and so will (almost?) always be assumed.

3) Choice in task is perhaps most meaningful for me when there are few enough choices that student-to-student teaching can happen and when the choices are quickly processed by students (so more visual or topical than verbal).


I do care (somewhat) about content …

This is just to say, that I do care about content. And that I definitely think students can learn challenging content. I just question why we chose certain specific content within mathematics to privilege and why so much math teaching privileges content over thinking, and requires students to learn a specific content skill at a specific moment in time.

But, that said, I hope our first Algebra unit next year will be Patterns (please, jk?) and that through it, we’ll do lots of content! I plan for students to study physical, visual, real world, and decontextualized linear patterns (content: slope, y-intercept, tables, graphing, substituting/evaluating, generalizing/writing equations, solving equations). I just plan that studying patterns through investigation will lead first to critical thinking and multiple representations as students figure out the patterns AND the content as students analyze and verify their thinking. Students will get to/through content their way, since with their thoughts about the patterns, they will largely be controlling where we go with some guidance from yours truly.

Then we’ll move on to more fun patterns … exponential, Squares?, Fibonacci?, Triangle numbers? Quadratics? … yes please?

“Students don’t know things!”

In conversations with anyone from members of the math department to random strangers in coffee shops (all of whom have opinions about teaching) to family members, people often bemoan to me the idea that, “students these days don’t know things.” The complainant will often follow this statement with a list of content that students don’t know – how to simplify radicals, where India is, how to identify a complete sentence, etc.

And you know what, it’s sometimes true. Some students don’t know how to simplify radicals* (unless they learned in middle school). But I am only worried by what students “don’t know” when I am trying to teach them to solve a specific type of problem in a historically-identified efficient way. When I give students a rich, low-threshold, high-ceiling task (which by design means there are multiple ways to enter the problem and that students can take their thinking far), I get to see what students know. They can enter the problem and move through the more challenging questions at their own pace/using their own method. They can compare their method with others, argue about and defend an answer, and find another way to answer the same question.

Basically, the problem isn’t about students not knowing things, it’s about me not asking the right questions often enough. And accessing prior knowledge doesn’t (have to) mean trying to remember the CMP book that teaches the topic you’re about to address or writing a contrived word problem about food to relate something to students’ lives. Accessing prior knowledge can mean offering up a really good question** and letting students pursue it any way that makes sense to them (and they will!). When I allow students to do that, I get to experience all the things students know. Then, I can work on connecting all those ways and building up students’ problem-solving toolboxes.


p.s. I painted a slightly idealized picture of low-threshold, high-ceiling tasks. But it’s mostly accurate.

* And who the hell cares?
**Eventually, hopefully, I’ll figure out how to tap into students’ questions.

Standardized Testing Hurts My Soul

For the fifth time this year (so the 11th day), I proctored the MCAS to various students for various subject areas.  Students who needed a wide-range of accommodations were paired with me in tiny or large rooms.  I am glad that I am a provider of consistent accommodations, silly faces throughout the exam, and healthy snacks and treats.


However, I am not glad that I need to watch children sit through a high-stakes, high-anxiety situation.  I try to teach strategies to help students cope with these types of feelings – because we all know these feelings don’t go away just because high school is over – but it still hurts my soul to watch students become upset over these exams.  I’ve watched as students use paperclips and pushpins to scratch and cut themselves, cry through the entire (3-hours) exam period, and even hold their breath until they passed out so they didn’t have to take the exam (oh, but we still made him).  While these behaviors are extreme and are not universal to all students, we need to stop and think about why do these things happen!

Not only do I watch my students take these exams, I am somewhat required to ensure that my little ones are ready to take (and pass) these exams.  Perhaps if students feel they are more “prepared” for the exam, they will not see the exam as pure torture.  I’ve noticed, in the past, when I stress obvious test-prep, the students tend to freak out more in the actual exam.  So that’s not very helpful.

In the future, I may be judged on the scores my students earn on these exams.  At the moment, there is just a dark cloud that rests over me that grows for each student who does not pass.  And a bit of guilt that on the first try some of my students don’t successfully jump over this hurdle and that they need to sit through this painful experience again.  And sometimes again.  I try to tell myself that my value as a teacher cannot be measured through pass rates or growth percentiles, but you know, many people think and tell me otherwise.


I talk with students, parents, administrators, other teachers, and outside partners about our next steps for preparing for the next round of retests.  When I talk with students, I stress that I have several back-up plans for them in case they do not pass the last rounds of retests.  And I do!  And they see that!  So they can relax about potentially not receiving a high school diploma but instead focus on asking questions about topics they don’t understand and help each other by reviewing their open-response write-ups.

When I interact with liberal educators, and the topic roles around to high-stakes exams, there is always a group that suggests we encourage students to boycott the exam like other groups have.  I would love for a system that use portfolios – rather than a single exam – to determine if a student holds a sufficient amount of knowledge/skills to move on.  Can we get there through boycotting?  What will I lose (I mean, other than my job) if I talk to children about it?

Part of me wants to continue to ride the train of good curriculum that pushes critical thinking will help students prepare for exams like the MCAS.  Part of me wants to incorporate more Do Nows/Exit Tickets/Periodic Multiple-Choice Questions into the usual curriculum to assist in assessing mastery of the standards I created (from a variety of sources) and for test prep.  I need to think deeper about how this may be implemented.

Who knows, as I think about it more, I may try to stage a revolt against the whole system.



Eric the Sheep


This week, the last week of instruction, my classes are completing portfolio and working on the Eric the Sheep problem.


I’m really enjoying another opportunity to run my class how I want to run it next year (all the time!). We started by brainstorming problem-solving methods. Then I asked if anyone knew anything about sheep shearing and showed an illustrative youtube video. I’m not sure how legit a use of technology that was, but it definitely helped hook students into the problem. We are 3 days away from the last day of classes and while a few students complained about doing work, zero (zero!) asked why they had to do this problem/what it had to do with real life. I think because it’s such a rich task (not because 100% of my students will one day be shearers/barbers). Here’s what students WERE saying …

“Ms. Langer, I need a way to figure out the answer without using chips!”
“We tried that rule too, like that exact rule, but it didn’t work for the first question, and any rule you make for a pattern has to work all the time.”
“She can’t watch this video; she’s vegetarian!”
“Why do you guys like goats and sheep so much!?”
“It’s not 18; it’s 16. Look!” (Actually, “it” was 17 … ;))
“You take all the time you need …” (A student who accurately answered the last step, which we had sloppily answered. Whoops/great!)
“I don’t want to draw 50 circles!”
“Wait, I didn’t understand what you just said about why I am wrong; can you say it again?”

AND I get to practice better discussions. Awesome. I tried to follow some of my discussion checklist for the discussion.  I had two goals: comparing representations of the pattern and generalizing. I had looked at the students’ work and had a trajectory/few ideas I wanted to surface (Why do you round up after dividing? What’s the connection between the groups who divided by 3 and the group that subtracted 3 repeatedly?). I didn’t choose a student to lead the discussion because that’s not a practice in my class this year, but I did have students present and they ended up taking over the conversation from me whenever I tried to direct things too much (sweetness).  Some questions I was left with included …

– How to deal with everyone writing up their math work but not everyone presenting. It seems much more authentic to write up your work neatly so that you are prepared to share your thinking with others (as opposed to writing it up b/c the teacher told you). And indeed, we did some really good talking and looking at each others’ work. But, I had everyone write up their thinking, and only some of the groups presented (some groups’ ideas overlapped/were incredibly similar). How did the students feel who wrote up their work but didn’t present, only participated in the discussion? (I guess I should ask them!) Would it work to have a norm of everyone writes up their math work so they’re ready to present/participate in discussion; not everyone will always “present,” but everyone will always participate?

– I HAVE TO worry less about content. I think worry less philosophically, but in the moment of class, I keep wanting to steer the discussion towards the generalized rule. I wanted to interrupt students who were inaccurately explaining why you round up. But really, the students were handling the discussion fine (and asking genuine questions), and I just needed to chill out!

Overall, super excited for next year, lots of problem-based learning, more discussions, more time on rich tasks, and less worry about content.


Discussion Checklist

I started to get my thoughts down for the aforementioned rubric. It came out as a checklist.  Here’s what I have so far.

Before the discussion, the teacher/students should:


During/After the discussion, the teachers/students should …


What do you think?

I’m most excited about the planning stages, where the teacher has to really explicitly decide the purpose of the discussion. This could change based on what the students do, but having a clear purpose and recognizing the nuances between generalizing, versus comparing, versus giving feedback, etc. will help me make the discussions more focused and therefore (hopefully) more accessible and engaging.