Mailbag: Acceleration, Inquiry, Structure, Chaos, Grading

From Jen:

I teach middle school math and every year I have a handful of students who seem genuinely ready to move faster than the rest of the class. They finish assignments quickly, rarely make errors, and often seem bored.

I’m torn about what to do next. I don’t want them sitting around disengaged or feeling held back. How do you think about supporting advanced students without creating a second curriculum to manage?

I definitely don’t have an answer to this at the individual teacher level. I’ll share something I’ve done that hasn’t worked very well, and a story from my school that I think illustrates why this problem is so challenging for teachers.

I’ve often had parents ask me if I can provide more challenging work for their kids. We’ll talk at parent-teacher conferences, come up with a plan, and I’ll put together some extension work to challenge the kid or teach them something new. The problem is, the student typically doesn’t do any of it. Some do, sure. But most of the time I feel like my effort was wasted. I’ll nag them, the parents will nag them, but nothing much happens.

Ok, here’s a quick story. A few years ago, my school had a modest acceleration program. We would offer students identified as gifted & talented the option to work through a bunch of math on Khan Academy over the summer after 8th grade and skip 9th grade math. This was restricted to students who were identified as gifted, which is a bit of an obtuse process. Gifted students are also not representative of our student body. They are, on average, more likely to be white and higher-income. In a typical year, we’d offer this option to around 5 kids, and around 2 kids would complete the work and accelerate. A reasonable person might say hey, only 2 of 5 kids are completing this work, it doesn’t seem like there’s much demand here for acceleration.

Then we got a new 8th grade teacher, who moved down from the high school level after his job was eliminated due to budget cuts. He started a really cool program. At the halfway point in the year, he uses standardized test scores and summative assessment scores to identify students who seem like they could handle acceleration. We have a twice-a-week extra-support math block, and he offers to schedule all of those students into the same section to work together on the acceleration program. If they finish it, they can skip 9th grade math.

I might have the exact numbers wrong, but it was something like 17 kids offered spots, 16 said yes, and 14 completed the work successfully. It was still through Khan Academy — twice a week for half a year isn’t much time to teach, so it’s more efficient to let kids work online. But they were all in the same room, with support from a teacher who can set intermediate deadlines, able to help each other out and benefit from the peer pressure to keep up with everyone else.

That’s an absolutely massive difference. We went from offering 5 kids acceleration with a 40% success rate to offering 17 kids acceleration with an 82% success rate.

The experience gave me a broad mental model for acceleration: students benefit from being in a cohort and are more likely to challenge themselves if they’re working with a group of peers. This isn’t very different from an “8th grade Algebra I” model where you offer something like this as a full-year math class. There are some boring logistical reasons why that isn’t a great fit for our school, but it’s very much in the spirit of what I’m describing.

You can also see here why the challenge work I offered before didn’t work very well: there was no community, no group of peers working through the same content. It was all piecemeal and individualized. There’s this idea that the ideal education meets a student where they are and lets them work at their own pace. I don’t think that’s true. Many students struggle to motivate themselves without a group of humans around them working with similar goals.

I don’t think individualized learning is totally useless. It’s a good fit for a very small group of students who are either very motivated or so far ahead that creating a cohort isn’t possible. Individualized learning also works for more kids if you put some systems in place to maximize motivation. But I don’t think that type of learning is ever going to scale to become a large part of the education system, and I think creating cohorts and community is a much more scalable solution.

Anyway, I didn’t really answer the question because I haven’t found a solution that works well at the classroom level. I think it’s important for teachers to understand these limitations. Putting challenge questions at the end of assignments or doing occasional extension activities or trying to create piecemeal work is fine if we have the bandwidth, but it’s not a large-scale solution. Classrooms are the best learning technology we have, and we can advocate for models that put students in classrooms with students who have similar goals, like my colleague did, while recognizing our own limitations.

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From Robert:

I am quite a new teacher of around 2 years of teaching experience in math. I always wonder how much direct instruction vs. inquiry-based learning I should do. Modern pedagogy often tells me to implement every topic by self-exploration, but sometimes I feel like that’s not the best way. What would you recommend to use in which context?

I’m going to be annoying and not give a direct answer. The main reason is that I find different teachers have very different definitions of direct instruction and inquiry-based learning, so it’s easy to end up talking past each other in conversations like this. Instead I’ll give a bunch of random pieces of advice that I find helpful in making decisions about teaching.

There are lots of ways to do direct instruction badly. The most common are:

• Lecturing for long periods without asking students questions to keep them actively thinking.

• Not providing enough practice because the whole class is spent giving explanations and examples. This is often compensated for with homework, but a significant chunk of practice should also be happening in class with teacher support.

• Not checking for understanding and adjusting based on those checks for understanding.

There are lots of ways to do inquiry badly. The most common are:

• Never explaining things to students even when they struggle to figure things out themselves.

• Observing that some students are successfully figuring things out and ignoring the fact that other students aren’t, so inquiry only works for a subset of students but you convince yourself it’s working because of some successes.

• Spending so much time on inquiry that students don’t practice or apply that learning in different ways.

Number one, avoid those traps.

Number two, I think in education we often focus too much on how we introduce an idea or concept to students. This matters, we should care about how we introduce new content. But in my experience, much more important is what students do with that knowledge. Are students practicing? How is that practice going? Once students are solid with the basic skills, are they applying their learning in different ways?

Number three is to develop different tools to introduce new content. Here are three I use. One is brief explanations, followed immediately by a chance to practice and apply that learning. Two is to study a model or worked-out example together as a class, asking questions about it and thinking about why it works. Three is to ask a sequence of connected questions that build gradually from what students know to what I want them to learn.

Each of these is useful in different situations. Each is active — students are answering questions, solving problems, and figuring things out. Each of these is also used by both successful inquiry-based teachers and successful direct-instruction-based teachers.

This is an example of why I don’t think it’s helpful to pick sides or label different types of teaching. Develop a broad array of teaching strategies. Get students thinking. Check for understanding to make sure they’ve learned. Practice. Repeat.

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From Nina:

What do you think of this take: One challenge in teaching is the balance between structure and chaos. You need to lead students along a structured, well defined path and provide them some ready-to-use tools (along with schemes, algorithms and so on) BUT then you also must disrupt their certainty from time to tome, throw in challenges, open up for wild ideas. It's a big challenge.

I think I agree. In math teaching I see two broad goals. One is to help students gain the basic skills we’re charged with teaching: fact fluency, arithmetic, percentages, basic geometry, solving equations, etc. This isn’t easy! Lots of students leave school without that knowledge. That area is where I think research in cognitive science and education has the potential to help us teach well and secure a reasonable standard of success for the vast majority of students. While our education system often falls short there, I can imagine a future where the teaching profession takes its job more seriously and we reach some pretty broad success with those basics.

The second big goal is helping students to apply that knowledge in lots of different ways. To solve problems in unfamiliar contexts, to figure out puzzles, to problem-solve, and more. This goal is also really important to me, and I don’t know that we’ll ever find a formula for success for it. That’s fine. Learning is a bit mysterious and we’ll probably never figure out all of its secrets. It’s important to aim to do both well. Take the core, well-defined path seriously and make sure students aren’t being left behind, and also challenge students and show them some glimpses of what else is out there.

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Also from Nina:

You rarely discuss grading (well, I have not read all of your past posts). What is your stance? Is grading a useful tool in teaching, or rather counterproductive, or a necessary evil? Or something else? How do you handle it?

Grading isn’t very interesting to me in part because my school has a standardized grading system. Everyone has the same gradebook setup, with set percentages for practice and participation, quizzes, and tests. I think this is good. It’s incredibly hard for students to keep track of a different grading system for every class they take.

Our system is pretty traditional. I won’t get into the nitty gritty details because I just don’t find that they matter very much. I’ve used some “innovative” standards-based grading systems at multiple different schools. I’ve found more complex grading systems to be a ton of work and to not really make a huge difference. They’re also often confusing for families, which can sideline parents and make it harder for them to advocate for their kids.

I don’t think the grading system I use now is perfect, but I also don’t think it’s worth the effort to try and tweak it. Messing with grading systems is a ton of work, and I would rather put that energy into other parts of my teaching. I don’t emphasize grades a ton. I grade things, because if I didn’t students would get the message that my class is less important than their other classes. But I don’t use grades as a major carrot or stick in motivating students. I try to make sure my expectations are clear, to grade fairly and accurately, to make sure every student has a path to success, but also to get grading out of the way and focus on learning.