I have a couple of questions about “Social Justice Math”

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I have a couple concerns regarding “Social Justice Math” that I don’t think I’ve seen addressed. (If they have been, please let me know.)

From what I’ve read SJM is billed as a way to bring real world problems into the classroom with a “justice” lens. Problems related to climate change, economic inequality, racial equity, etc., would be used in class as frameworks for learning different math concepts. (Read more on that here.) In fact, it sounds a lot like Project Based Learning but with a more refined list of suggested issues to study.

The first concern I have is that, like it or not, “Social Justice” is associated with the political left.

Do those advocating for SJM openly say this is a political slant on mathematics and embrace it as such? (Let’s call this “motivation A”.)

Or do they argue they’re talking about social justice (fairness to people in general, without the political connotation) and not Social Justice? (Let’s call this motivation B.”)

In the former case I’d have real concerns if I was conservative minded person and my child was in that class (or independently/liberal minded and concerned about one political viewpoint seeping into mathematics curriculum). In the latter case the perception will still almost certainly be taken as a leftward spin on math, again because “social justice” is attached to the political left.

The second concern I have is, what exactly is the “social justice” aspect of the math. Is it simply the selection of the topics chosen? Or is it in the conclusions that come from the students’ analysis? Will the teacher point out that social problems are complicated and that both the left and the right have something to say about their causes and solutions?

I can imagine a teacher trying to present these problems in an unbiased fashion and letting students arrive at a variety of remedies to the problems (motivation B folks). But I would bet money that many teachers implementing SJM will be pushing students to arrive at solutions from the political left (motivation A folks).

If they weren’t, then why call it “social justice” math? Why not call it “real world mathematics” or some other less politically charged title that still acknowledges you’ll be analyzing problems that humanity faces? (Again, this seems a lot like a political form of Project Based Learning.)

I fear “Social Justice Mathematics” is the title because they don’t want students to learn to take a dispassionate approach to the problems. They want students to take a certain, Social Justice approved, approach to analyzing the problems. If this is the case then I think we’d be right to push back against SJM, and if it isn’t the case then SJM will face a branding issue for the foreseeable future.

Are my concerns justified or am I way off base? I’d love to discuss it in the comments.

“Why do we need this?”

My students in precalculus class have asked a few different times over the last couple of weeks, “When will I need this?”. I encourage them to ask this question of their teachers, because the teacher should be able to answer it. But when it comes up in the middle of a lesson I don’t really have time to answer it fully, so here are my thoughts, in a thought out format.

  • The blunt answer is that this is an elective and no one is making you take this. And if someone is making you take it (your parents, for example) then I can’t help you. I wouldn’t be satisfied with this answer if I was you, but it is true.
  • We don’t know and you don’t know what you’ll end up doing, so it’s better to err on the side of a broad knowledge base in high school.
  • These are things you need to understand if you’re going to take more math. Why might you take more math?
    • You might want to study math
    • You might want to go into a math related field
    • You might want to go into a science related field where calculus, at a minimum, will likely be required
    • You might want to go into pre-med or pre-vet (or pre-law?), where you’ll likely have to pass a calculus class
    • That’s what this class is designed for. That’s it’s stated purpose. It’s to get you ready for calculus, regardless of the reason you might end up taking calculus.
  • I admit, math is also a gatekeeper. It’s a way to check your level of competence. I’m not making a statement about whether that is right or wrong, but it is true. See a great exploration of this idea in Bad Drawings here.
  • But more broadly, math is giving you a language to describe and understand that world. Sinusoidal behavior (which is what we’re studying now) is everywhere. Anything that works on circular motion or has periodic behavior can be described by sine or cosine waves.
  • It also helps you exercise your rational thinking and pattern finding muscles. We don’t always do a great job of helping you work the pattern finding muscles, but the reasoning muscles are exercised every day. When you solve a problem you are reasoning. You put together a chain of logical statements, either explicitly or implicitly, to arrive at a conclusion. And those statements aren’t the same for each person, which is a great thing. There’s often more than one logical way to arrive at the same conclusion. But this mindset, of taking on assumptions and arriving at logical conclusions based on those assumptions is a vital component of thinking critically. It’s how we persuade other people. It’s how we make progress. It’s how we call BS on people when they make claims or statements that don’t make sense.
  • Mathematics, and the different parts of mathematics, can be viewed as games of sorts. You are given some rules (axioms, theorems, etc.) and then you see what is true given those axioms. You see how far you can push the rules and how far you can get in the game. But they’re often better than an arbitrary game. Many times they have implications in reality (although this isn’t a necessary condition for interesting mathematics and is not necessarily where mathematicians spend all their time). And sometimes those implications aren’t seen at the time, but turn out to be useful later on in science. A mathematical truth is a truth about reality itself.

The fact that we attach grades to mathematics does minimize some of this. It’s not a fun game to play if there are real consequences (in terms of grades) for not understanding the rules quickly enough. And I get that. But I reject the notion that we should throw the whole project out the window because what you’re learning on a Tuesday in precalculus might not help you navigate your grocery shopping trip.

Thinking, Fast and Slow (Part 3)

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The first two parts of this series were created using Adobe Spark Page. I found while creating this third part that most of what was in it was text, and that a more stable place to host it was probably my blog. Hence, here it is. I’d encourage you to check out Part 1 and Part 2, if only briefly, before reading this part. 


We see in the last few chapters of Part I of the book that System 1 is a story teller. This system helps you make a coherent narrative of the world. This, like most things, has positive and negative aspects. I think the shortcomings of this tendency are important to understand.

The first problem with System one is that it’s relatively easy to manipulate it, especially since so much of it happens automatically. Take the following example from the book. Read the two words below.

Bananas

Vomit

In the second or two it took you to read those words and immediately following reading them you had a reaction. Some of it was physical, like the hair on your arms probably stood, your sweat glands were activated, your heart rate went up a bit. But you also likely sketched out a story that involved bananas causing the vomit (or in some other way being connected to the vomit). You did this automatically as system one is attempting to fit the input into a coherent story.

This, like most things, has positive and negative repercussions. It means that we are likely to seek out and find information that fits with the story system one is telling us. “Sally is lazy.” “James is smart.” “Maria is a hard worker.” Once we’ve put these narratives in our mind, system one tries to find information that fits the narrative. And while system two should be the hero here, always evaluating the assumptions of system one, it turns out that system two is a bit lazy. It’s much easier for system two to just go with the narrative. It takes cognitive work to constantly be evaluating everything system one is telling you, so often times that work is avoided by system two.

The key here is that we are aware of the narratives and stories we have in our minds. We need to be on the look out for information that both confirms our narrative (to be sure it does in fact confirm the narrative and that we aren’t overlooking something) and negates the narrative (so that we can change the narrative in our minds to better represent reality).

One major theme of the associative machine is this: when there is some sort of external input to your brain you’re not consciously aware of what’s going on in your brain. When you see an object or hear a sound or experience a feeling, you’re flooded with ideas which in turn activates more ideas. Only a few will pop up in consciousness and this flood of ideas is largely out of your control.

What does this mean for teaching?

When we deal with students we have to remember that fact. Much of the time they (and we, whether we care to admit it or not) are at the mercy of system one. Actions that you take or that other students take in the classroom can set off chain reactions in a student’s brain. The result could be positive or negative. You can imagine starting a lesson with some sort of introduction that primes students for learning, giving them some ideas that ignite other ideas (you might call this engaging prior knowledge) or put them in a positive mood. The latter idea is from Eric Jensen and is also described in the book and that is that being in a good mood helps your brain be prepared to understanding new concepts. You could also imagine taking some action that results in an unwanted behavior. The key to dealing with these behaviors is figuring out what the underlying cause of the behavior is. What is triggering their associative machine to result in the behavior?

The last note I want to make here is that we need to help students understand what’s going on in their brain. Just as I encourage anyone reading this to try to keep a check on the automaticity of system one, we should find ways to help students do this as well. I think doing activities that encourage metacognition is a critical step in that direction, but that’s a topic for another day.


Image is “Thinking” by Lee Thatcher. The original work can be found here.

The Absurdity of One-to-One Initiatives

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As comes up every year, someone in our department suggested we go one-to-one. Of course, this sparked lively debate. So much so that do to the frequency of these debates and the cycle of outrage I invariably go through after each one, I’m motivated to write out the multitude of reasons that going one-to-one with textbooks is an absurd idea.

First, let’s talk about costs. A good textbook costs close to $100. Sometimes less, sometimes more, depending on how many you buy. If a kid has five classes, that means it’s going to cost roughly $500 dollars per student to go one-to-one textbooks. And it’s not just $500 one time. Of course not, because in a few years much of what’s inside the books will be dated. They will need to be updated and some of them will be so obsolete they’ll need to be replaced entirely. Do we want to go through the up front costs and then the future costs to update and replace them?

Second, let’s talk about letting teenagers carry around several hundred dollars in textbooks. Have you seen the average teenager’s bedroom? Of course not! There’s too much stuff on the horizontal surfaces (and maybe even the vertical surfaces) to actually see any substantial part of the room. Are we going to let kids, who can hardly get a dirty tissue to the trash can across the room, be responsible for hundreds of dollars worth of school property? I think this is a nightmare that no administrator or teacher wants to deal with.

Third, I’d ask you if the cost is worth the benefit. Sure, textbooks have lot’s of knowledge in them. Give students books corresponding to the subjects they’re learning allows them to easily and quickly look up information, helpful diagrams, maps, and other media, but don’t we have teachers for that? Teachers have much of this knowledge, and if they don’t, then they can look it up in their book and deliver it to the students. What’s the point of a teacher if all the information is easily available to the students? Sure, the best teachers might use the books in coordination with their teaching ability to create near sublime learning experiences, but this would surely only be the most motivated of teachers, not the norm.

Fourth, it would be a logistical nightmare. Suppose your high school has 1000 students. Then we are talking about THOUSANDS of textbooks to keep track of. Not just keep track of, but record those that go missing and those that are damaged. Then schools have to make determinations about how much the damages cost. Then who pays for it? The students? What if it’s an accident? What if the student can’t afford it? What if they get lost in a house fire? Who’s on the hook for the bill then? And who does this burden of tracking fall upon? The library? The administrators? The teachers? There’s no good options. And then, who fixes them? Do we offload this responsibility on the already short staffed library personnel? We’d probably have to hire somebody to spend part of their day repairing textbooks, so tack that on to the bottom line.

It seems clear that the costs of trying to put the these resources into the hands of each student almost certainly outweigh the benefits. But this fight will never die. Year after year we’ll continue to hear how we should “give students access to the tools they’ll be using when they leave us”. Given what I’ve outlined above, I can’t see the logic that results in this being a good idea.

Update: I should make something clear. This is purely satire. I am simply trying to make the argument that when it comes to discussions of 1 to 1 technology I think the problems that are brought up are often ones that we have solved in other contexts. This situation never came up in my department. And even if it had, I would never throw them under the bus like this publicly. Once again, this is purely satire.

We should always be learning something new

Last week I started auditing a class on Hapkido, which is a Korean martial art. A friend asked if I’d be interested in attending the once-a-week class with him and I said I would. Having never done any martial art at any time in my life (I don’t even think I’ve watched any of the Karate Kid movies in their entirety), I was nervous. However, partway through the class I realized that there is clear value in learning something completely new.

I want to list a few feelings I had, as I think they reminded me of what it’s like to be a learner, as an adult or a teenager.

  • I didn’t want to make any mistakes. When the instructor demonstrated something, I wanted to do it perfectly. This notion is ridiculous because, as the instructor also pointed out, it takes thousands of repetitions before something becomes muscle memory. For as much as I preach the importance of mistakes in learning, I was shocked at how somewhere in my guts I still didn’t want to make them.
  • I didn’t want the instructor to come by me. Or at least if he did I wanted to be working on my right side (which I thought I was better at). I was afraid he’d find something I was doing wrong. Which I consciously knew would not be bad as it would get corrected and then I’d improve.
  • I compared myself to the people around me, unconsciously ranking myself. Better than that person, worse than those two, etc.
  • Frustration. I’ve never been particularly coordinated and I was consistently frustrated at knowing in my mind what I wanted my body to do, but struggling to make my body do it.

I walked off the mat at the end of class and my mind was reeling.


“Now I know why students are apprehensive to ask questions.”

“Now I understand better why a student might get uncomfortable while I hover over them watching them work out a problem.”

“I have to constantly remind myself to embrace the difficulty. That’s where growth comes from, but it’s difficult to do in practice.”

“Having an instructor that recognized we were all learning was incredibly helpful. He created an atmosphere where mistakes were not viewed as setbacks, but part of the process.”


My main takeaway was that these are feelings I need to constantly grapple with. I need to try to put myself in situations in which I’m the learner, with relative frequency. It helps me better understand where my students are coming from and I think will ultimately help me become a better teacher.

Also, here’s one more thought that has popped in my head recently and probably doesn’t need an entire blog post, but fits with the theme in this one. I’m in my fifth year teaching precalculus, AP calculus, and algebra II and I can feel myself having less empathy with my students, with people learning the concepts for the first time. The first year I taught these courses I think I had a better understanding of their struggles as I was solidifying my understanding of the concepts prior to teaching them as well. I’m not entirely sure what this means for my teaching now, but I think awareness of it is important.

My Brain on Lesson Planning

Okay. I’ve a got a few minutes. Where is what I did last year? Ah, that’s right. We did that activity, with some direct instruction following. Seems like I didn’t quite the point across when I closed the lesson. Like the kids still struggled with parts of this on the quiz. Maybe I should change it. Maybe I should just start from scratch. Did I leave myself a note or anything?

Check Google doc for comments

Nothing. Good job me. I’ve got to do a better job of that. But sometimes it’s tough to find time. Yeah but it pays off and saves time eventually. Like it would be saving time right now. Okay. I get it. Anyway. I don’t have time to totally revamp it. How can I tweak this to make it work better? Maybe I’ll start with a more open ended question. I read that’s a more effective way to start a lesson then just with direct instruction. Okay. So what’s the question or task?

Goes on the Internet. Checks the MTBoS search engine. Writes down 4 ideas.

Well the first two are probably too much work/time. I might be able to tweak the third though. That would give students a chance to discuss some solving methods before we do the lesson. But I know Sam won’t participate. Man, what is his deal? What is my deal with him? Did I make him mad at some point? I need to talk to him and try improve that relationship. Maybe he’d be more willing to work with his peers. But, he’s doing fine in class so maybe I should just leave him alone. Ugh. I’ll sort that out tomorrow. Anyway. I think this will work. But it’s probably going to take longer than last year. Yeah it’s definitely going to take longer. I really only wanted to spend a day on this. But if they learn this better because I spent more time on it, will it pay off in the future? I don’t think so. It’s not really a topic that builds on itself. But shouldn’t we try to teach every topic really well? Even if it doesn’t get built on later? Maybe. Otherwise why am I teaching it? Well some students will get it and remember it, just fewer than if we spent more time. Okay. So let’s do it, we’ll reduce the assignment a couple of problems and carve out 5 or 10 minutes tomorrow to wrap up anything we don’t get to.

Phone rings

“Yes, I’ll send her down when she gets to class. Thanks. Bye”

She really needs to be in class today. I need to remember to make a copy of the notes for her. She won’t be able to make up the discussion we’ll be having but I guess there’s no way around that.

Glances at papers to grade next to the phone

Ugh. I guess those aren’t going to get done today. Maybe I can do those on my prep tomorrow. Dang. I need to finish that lesson. I think I’m ready to update the weekly plans. I need to make sure I can accommodate this for my autistic student. Did I write down those notes on him yesterday? Nope.

Writes down notes in observation document

Okay. I can make this work for him as well. I need to remember to go through this the morning before we do it.

Adds it to to-do list

Well that should be all set. Just need to look at my other two classes and do the same thing… I hope those don’t need revision. They probably do. I mean how can you assume that they’re in their best form? You’ve been teaching for 5 years. They may not be but they should be in good enough form. They’ll have to be because I don’t have time to rework either of them. Man I hope we have school tomorrow. If we don’t then I can just……..

What I wish I could tell my students

Here’s a list of few things I want to say to students, but am not quite sure how to do it. I’ve said of some of these in whole class contexts and variations of some to individuals. But I’ve noticed in my career that sometimes I notice things about students that are difficult to tell them directly. Maybe it’s the natural human aversion to confrontation, I’m not sure, but here’s the list:

  • You don’t have to go to a four year college if you have no idea what you want to do with your life.
  • If you don’t get into that school, your life is not over. You will get out of college what you put into it.
  • I understand that you’re a bright student. There’s no need to demonstrate that to me and your peers at every opportunity. In fact, you risk alienating some of your peers if you keep doing this.
  • Your ACT or SAT score does not define you, as important as it seems right now.
  • You’re in a controlling relationship. You deserve to be in a relationship in which you don’t feel like the thumb of power is constantly pressing on you.
  • I understand that you’re introverted. The ability to communicate well is an essential life skill. When someone says “hi” to you, you have be able to respond with, at minimum, “hi”.
  • Learning is not a competition, so when you get your quiz back, resist the urge to see how you “stack up” against your peers. (Okay, I’ve actually said this one.)
  • You can break the cycle of poverty in your family, but not unless you make some significant changes to your approach to life and the people in your life.
  • You’re addicted to your phone. Not in like a “haha, I’m trying to talk you so stop snap chatting” kind of way. More like a, “I’m really concerned about how this is going to negatively affect the rest of your life if you can’t get it under control” kind of way.
  • You’re in “regular” math class (as opposed to honors) but that doesn’t mean you can’t be an engineer, computer scientist, etc. In fact, I think you’d be a damn good one.
  • The pressure your parents are putting on you to perform is unnecessary and probably doing more harm than good. Work hard, but don’t cry over test scores, college applications, or an A-.

I’m sure I’ve forgotten some, but this is a pretty good list. Some of these are positive, but I struggle with how to explain them to students in a straightforward way. One that doesn’t sound preachy. I’m curious as to how other teachers approach situations like this with their students.