In a piece I wrote earlier I talked about how Dweck’s and Duckworth’s respective theories of growth mindsets and grit were being exaggerated and misinterpreted, exhibiting the tendency to “overcorrect”.

I also referenced Dan Willingham’s famous quote: “Sometimes I think that we as teachers are so eager to get to the answers that we do not devote sufficient time to develop the questions.”

I admitted I hadn’t read the book and made accusations of people running with that quote and using computer graphics/animations as approaches to “engage” students. I was met with a comment criticizing me for misinterpreting what the person was doing based on a book I never read. Fair criticism, so I read the entire context of Willingham’s quote. Having put the quote in context, what he was talking about was in fact, putting topics “in context” for students, rather than teaching a topic with no connections whatsoever, in a “do this, do that, answer this, answer that” mode. (Traditionally taught math is often mischaracterized this way: as students being taught skills and facts “by rote” with no connections to how such procedures were arrived or what they mean.)

The school where I teach has recently subscribed to a service called Pear Deck, which allows teachers to construct presentations in which students can interact, by answering questions on their computer. What caught my eye was this particular promotion of a Pear Deck presentation. I tweeted something about the presentation. I was met with various replies such as:

“Some tedium part of the deal. Not all things worth learning can be presented as fun, games.”

“Love algebra, no interest in video games. Not wondering anything about Super Mario.”

“I’d rather try to calculate when two trains going different speeds are going to meet up.”

I also received this:

“We believe that you can’t teach students before they have a question.”

I’m not sure if the “we” refers to people at Pear Deck and that the person who tweeted it works for Pear Deck. But it’s evident that “they” are running with the Willingham quote.

Context is important, for sure. And while there’s nothing wrong with a video game or graphic approach, per se, it also is not the only way to engage students. Sometimes, just asking the question in an interesting manner is enough to stimulate curiosity. One method I have used is in warm-up questions before class begins. Some of the questions are based on what they may have learned the day before. We might have talked about the equation of a line in the form y = mx + b, let’s say. But a warm up question might then ask “What is the y-intercept (b) of the line y = 5x + b if it contains the point (2,3)?”Which was not discussed. In fact, it is the topic of the day’s lesson. Some students may be able to stretch and use prior knowledge to actually answer it, others may be stuck. But curiousity has been aroused: “What’s the answer? How do you do it?” And the day’s lesson begins.

Activities purported to be engaging, such as finding the relationship between maximum area for a given perimeter of a rectangle, using graphics technology tend to be distractions. They are distractions if the math necessary to solve it in a more straightforward manner is not provided. As such, it may be “engaging” but does not provide mathematical information that can actually be transferred in solving other problems. (For example, instead of trying combinations of widths and lengths, why not graph the parabola that describes area as a function of various lengths and widths with a constant perimeter, and find the maximum point? Such an approach is a link to preparing students for the optimization approach that they will eventually learn in calculus)

Robert Craigen, a math professor at University of Manitoba, wrote about this in an earlier post about this topic, and I reproduce his comments here for you to think about:

*“Or even more to the point, it may represent a perfectly fine instructional piece all by itself in isolation, but not contribute meaningfully to coverage of the curriculum for a given class. That is what is wrong with this stress on digressive activities of the sort I collect under the rubric “candy” above. In a piece we wrote some time ago, Barry and I made a point about the distinction between “main dish” and “side dish” instruction. Side dishes can indeed make the experience of classes interesting and engaging, but they may or may not actually represent progress toward the main dishes in the course, as laid out in the curriculum. The problem with these miscellaneous “bright ideas” for one-off lessons you find on the internet for free or offered by these mercenary educational software groups is that they tend to be side dishes. Too much of that and your students may not get to through the main dish, and all these sparkly bright ideas will turn out to be a poor idea in the big picture.”*

“Huzzah! I read the page with the quote and it confirmed what I thought about the quote before I had read it.”

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I’m sorry to poke fun. I just can’t engage with your ideas on a more serious level because I can’t

understandthem. I’m trying to read this sentence and I can’t even find the verb:“Also, engaging activities such as finding the relationship between maximum area for a given perimeter of a rectangle, using graphics technology and be distractions.”

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Sorry, there was a typo.

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“For example, instead of trying combinations of widths and lengths, why not graph the parabola that describes area as a function of various lengths and widths with a constant perimeter, and find the maximum point?”

But … that’s exactly what happens. Check screen #7 and the next.

You interpreted Willingham without reading it. You’re critiquing an activity without looking at it. C’mon.

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I have read WIllingham’s discussion about developing the question and also read more closely what you describe in your post. I was incorrectly lumping you in with the people who say ““We believe that you can’t teach students before they have a question” and I see that that’s not what you are saying in that post. I don’t believe that it is a bad thing for a teacher to ask a question as part of setting a context.

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Peace in our time!

Let’s pose well-developed questions and then help students answer them.

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You’re really saying the same thing, Barry. 😉

I don’t like analogies, but I’ll try this one out. Do you get kids to eat vegetables by pureeing them and sneaking them into brownies or by serving up recognizable vegetables, knowing that kids might not be thrilled to see them on their plates? I guess in theory they are the same thing–getting kids to eat vegetables–but in practice they are quite different. One is getting kids to eat dessert and one is, over time, getting kids to see vegetables as regular part of a balanced diet.

Intellectual work has it’s own rewards, but it’s often a delayed gratification situation.

And it might not look like I LOVE math. But it should look like I can DO math.

So, I think what I see Barry and others saying is that student engagement is better driven by helping students master the content and skills of math year after year, than by flashy tech and gimmicky set ups–that may or may not, ultimately, cover much content no matter how busy and excited the students appear to be in class. And that it is helping kids learn to do math–and not getting kids excited about math–that should be driving instructional planning.

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