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.

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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.

6 Reasons This is My Favorite Lesson

I want to share what might be the best lesson I’ve created and a few reasons why.

I actually wrote about this a couple years ago but since we’re doing it right now I thought it useful to reflect on and share it again.

This lesson came from the following problem I was struggling with:

I had spent a lot of time thinking about how to help students understand the connection between trig ratios on the unit circle and the graphs of trig functions on the Cartesian plane. Despite a couple activities and practice I was convinced, mainly through questioning, that they didn’t fully understand it.

My solution to this was to make a giant unit circle and cartesian plane and have students use them to work out problems. This would allow us to literally walk to specific angles and equivalent places on the cartesian plane. The hope was that this would help students solidify the connection between the two.

The details of how the activity works are in the original post and the materials are linked at the end of this post, so I want to emphasize the aspects of the lesson that really make it effective, in a convenient list.

Assessment

The activity is broken into two parts. The practice portion and the assessment portion. The assessment requires students, working in pairs, to come into the hallway and work through five problems (like these). This portion is vital for the following reasons.

Like any assessment, it helps me know what they know.

It makes students take the practice seriously. The assessment mirrors what the practice rounds were like. They take it seriously and practice until they’re confident.

Students work in pairs, sometimes disagree, and then must convince each other of their reasoning. Tremendous mathematical conversations come from this time.

It puts students in a position in which the teacher is there, but can’t help. This is true of assessments in general, but the format of this one means students must convince themselves and each other that their answer is “their final answer”.

No calculator. No notes.

On the assessment, and likewise on the practice, students cannot use a calculator, notes, their unit circle, or anything besides their brains and a whiteboard. This means students don’t have any crutches with which to rely on. These problems are not algorithmic. Each one is slightly different from the other ones. This means that the only way to be successful is to truly understand what is going on in the math.

Engagement

This is my third year doing this activity and every year there’s nearly full engagement. Now, this is precalc and while I wouldn’t say that all of these students want to be there, it is an elective. But it’s difficult for me to get this level of engagement from them.

This is, in part, because they know there’s a test coming after they’ve practiced. But I think it’s also because each problem sparks at least a little bit of curiosity. “How do we figure this out?” Initially many students don’t have a clue about how to approach something like sec(2pi/3) with only their brains and a whiteboard. But with a good understanding of trig they can figure it out.

And figuring it out is satisfying. Students are proud of themselves when they solve one of these problems correctly. I love seeing high fives in my classes, and this is one of those activities where they happen.

Embodied Cognition

I’ve written about embodied cognition before so I won’t go into too much detail, except to say that it’s incredibly valuable if you can incorporate it effectively. There is something fundamentally different from paper and pencil when you can stand there with a student inside of a unit circle and discuss these problems. It’s something that is hard to describe, but once you’ve tried it you clearly see the value.

Purposeful practice without a book assignment

A few weeks ago students initially learned how to do these problems via a lesson and practice problems. If that was effective, then I wouldn’t have needed to do this activity. What ends up happening in this activity is that students end up doing a bunch of practice problems, that I never assigned! I just tell them they can do as many practice rounds as they feel they need. Then they work until they have convinced themselves they’ve mastered it.

Partners

The test and practice require students to work in pairs. This is incredibly valuable as students are constantly conversing and helping each other understand. Once again, the knowledge that there’s an assessment plays into this, but who cares? From my observations students are rarely begrudgingly woking through these problems. They seem to enjoy them.

I probably see more learning and teaching happening between the students in this activity than any other lesson I do, for any class.


I understand that without seeing it happen it might be difficult for you to implement this. I’ve included some images below to give you an idea of the set up. Feel free to contact me with any questions you have. I’d encourage you to look for opportunities to use embodied cognition in your classes as I think it can be an incredibly useful teaching tool.

Here are the resources for doing the activity

Description Sheet

Possible Problem Bank

Practice Cards

Assessment Cards (Yeah, I’m not posting these on the web. I, shockingly, sometimes have students read my blog. But if you reach out to me I would be happy to email them to you and save you the time of making them.)

Assessment Rubric

X-axis “Tick Marks”

“Everything Springs from That”

I don’t listen to many political podcasts. In fact, only one. Dan Carlin’s show, Common Sense. In his latest podcast he interviews James Burke, a science historian, documentary creator, broadcaster and all around smart dude.

This episode flirted with politics, but was more focused on how technology affects society and how the rate of change often has unforeseen ripples. It’s a fascinating interview, but the best part for me comes at the end of the interview. Dan presents Mr. Burke with a hypothetical (which I’m paraphrasing).

Suppose the leaders of the country call you up and ask for your advice. What would you tell them in regards to the absolute most important thing to focus on in the future?

“I’d say put a massive amount of effort into the educational system. Everything springs from giving people the kind of education that allows them to think more clearly and express themselves more clearly. Everything springs from that.”

I’ve been thinking about education a lot lately. I recognize that might be like pointing out that a historian has been thinking about history a lot lately. But I’m talking about the big picture of how we educate our society. With the appointment of charter school evangelist Betsy Devos to the head of the Department of Education and recent moves by the Michigan congress to weaken the teaching profession and cut funding, I worry greatly about where we are headed.

The election of Donald Trump, the proliferation of fake news, the gravitation towards soundbites, the lack of empathy, and constant decrease in social capital mean that having a society that can’t think critically could be (already is?) disastrous. If there was any time in our history that we should be focused on education, it should be now.

We can’t have a society of mindless drones that will believe the headline and first two lines of any article that comes across their news feed. We can’t have a society that can’t take another person’s perspective. We can’t have a society that fears change. We can’t have a society that doesn’t understand the value of civil discourse.

An education system that’s working on all cylinders can help prevent this.

We should be focused on how to graduate great teachers. We should be focused on how to help teachers become great. We should be looking to other education models and schools that we want to emulate. We should be focused on making teaching a profession that our best and brightest want to pursue. We should be working to get away from standardized test scores as the sole measurement of a quality education.

As Mr. Burke mentions in the podcast, if we put as much energy and money into education as we did into the Apollo project it could have countless dividends for our society.

Order – How Mathematics is Life

Humans are in a constant pursuit of order. We try to develop schemas to help us deal with frequently occurring situations. We constantly look for patterns. We try to make our lives somewhat predictable.

The brain doesn’t like to think. Thinking is hard. So the brain naturally gravitates towards pattern finding.

This is mathematics.

Mathematicians look around the world for patterns. Looking for truth. They take things they know to be true, and build on them. Constantly growing the body of patterns we know to be true.

The difference between me noticing that whenever it’s cloudy out I’m a bit gloomy and that the derivative of a parabolic function is linear, is that the latter is true always. It’s a fact that exists regardless belief, mood, perspective, or measurement.


I wrote the idea for this post down months ago, but it seemed relevant as this week I embarked on teaching my algebra II class how to factor polynomials. Something that nobody does, with the exception of math teachers and their students. (And I mean that quite literally. I went to the twittersphere and came up empty.) My advice to students was similar to other seemingly obscure content we learn in mathematics.

Treat these problems like puzzles and look for the patterns.

Because pattern finding, curiosity, and creativity in problem solving are all skills that are valuable and can be improved with practice.

Nobody does a puzzle and while they’re doing it says, “This is never going to help me in my life.” I don’t claim to be an expert on the motivation of puzzlers, but I did puzzles just to figure them out. I enjoyed the mental exercise.

This is how I want my students to approach math problems. I want them to enjoy and appreciate the pursuit of solving the problem. I know that’s abstract and might be difficult for teenagers to grab onto, but I’m not sure of any other justification for some of the concepts we teach.

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