A solid presentation, as always Dan.

Live deleting the textbook problems was a brilliant way to show the world that anybody can go through the process in a short time. I’ve found the same high value /effort ratio in doing this for students.

I wouldn’t be surprised if this became the opening activity for math department meetings this week.

Dan, can you address the practice of saying, “I can see many of you enjoyed this kind of thinking today. Here are some careers that employ the same kinds of thought processes.”

I like your dial metaphor and I agree that mathematics should be intuitive, and this often means postponing rigor in the short term.

This year I broke from tradition while teaching similar triangles and just had my students create their own definitions for similarity & congruence, based on sets of images I showed. We also spent extra time on angle theorems because there was a lot to observe, debate, justify, and name.

These were class discussions and I didn’t formalize anything for them – I let them refine as necessary, and only suggested improvements to their vocabulary where it made sense.

I have no real evidence, but the engagement they brought to the task of solving problems with similar triangles, and the ease with which they have adopted basic trigonometry indicate to me that it was time well spent. It was also fun (way more fun than a lecture!!)

Pure math isn’t boring. Sometimes I think students are relieved when they aren’t expected to apply everything to the “real world”, and can just work on the theoretical stuff.

I’ve found some of the best ways to start class is with the Which One Doesn’t Belong. Students are dying to share a thought that others may not have. It also has that low entry high ceiling aspect that we are always after. Example, most can pick out that one of the terms has a negative sign, while the rest are positive.

My one adventure into “deleting the textbook” that stands out to me is from last year, http://joyceh1.blogspot.com/2015/11/day-44-fal-day-2-fish-tale-revise-rugs.html, when I used the Fish Tale problem from yummy math:
http://www.yummymath.com/wp-content/uploads/fish-tale.pdf

When I think about it, all I did was leave the text of the story up and deleted the numbers. I think this year, I’ll delete the paragraph and the numbers… Ask for questions, notice, wondering, etc. Then ask what info they need to solve it (the dimensions), and then let them get after it.

One of my issues is getting them to show their work clearly so that when they do present before Act 3, that we can clearly see their thinking and follow it. I’m also trying to figure out how to have my EL and SPED students access these tasks easier.

So far, I can only think, in the fish tale, is a cloze sentence where they are suggested to use the pythagorean theorem with questions? This is a cloudy topic where I think we as teachers need more help with. How do we make these engaging situations and grade level topics more accessible for the students with less background knowledge?

Thanks for the great talk! I got a number of valuable insights for teaching maths out of it (plus some cool pointers for great presentations:)

As an aside, the starting question – how do we make maths engaging – is somewhat ill-posed in so far as there appear to me multiple different conditions well worth distinguishing. For example, from my experience making things engaging to primary school kids can be quite different to making things engaging for middle school or high school kids. Also (and sometimes related) the specific task of engaging kids in maths seems to depend at least to some extent on previous experience – kids that have had years of positive maths experience can probably stay reasonably engaged even with standard practice. On the other extreme are kids that have had no positive experience with maths for years. There may well be all kinds of other relevant variables here.

Also – and while I fully appreciate that you could not possibly adress all common approaches to life student engagement in your presentation and hence focused on three common approaches plus your own – let me just mention that there are a number of other approaches that appear promising (at least for some groups of students) too. I, for example, would like to highlight aesthetic considerations. Maths can be beautiful and many students can come to appreciate its beauty if teachers draw out the beauty in the maths and direct the student’s attention to it. Or gamification. So much of maths can be taught through games and a lot of students love games (and, of course, desmos has some fantastic maths activities/games!).

Great talk Dan. I have the dubious honor of being the one who sent that ill-informed tweet in an effort to make the meatball problem more relevant to students. I recall having a realization after watching your 3-Act approach to this problem –it was not about the relevance per se; it was (partly) about lowering the level of abstraction to get students to buy in and want to solve the problem. Just because a problem is ensconced in some sort of “real world” scenario does not in itself create that “headache-in-need-of-an-aspirin” scenario that you have talked about in the past. When I have lowered the abstraction ladder, students’ questions are more inquisitive and nearly everyone is engaged.

Thanks.

Lots of fantastic stuff in this talk — I loved everything that you did with the white rectangle, and your take on “real world” is so sharp. (I cracked up when you toyed with the picture takers.)

My sense from the talk was that you imagine the math dial being turned up within a lesson. Meaning, first we ask for questions, then for estimates, then we dive into the problem. This is in line with a lot of your Three Act work, I think, and I’ve seen it work well.

Thinking about my own teaching, I more often find it helpful to turn up the dial over several days. This lets me use these early bits of the math dial as formative assessment, and I have time to think carefully about what they know and what they’ll need before productively struggling with a problem.

So, for instance, I might ask kids some lower-dial questions about a prism (noticings? estimations? etc.) a few days before I ask them to solve a prism volume question.

We always want to turn up the dial a bit during the lesson, but I think that’s a delicate matter.

Dan wisely said conflict can help make discussion useful. Let me try to start some.

Common wisdom seems to say the solution to alienation ( we can use that word, right?) is found in presentation and rearrangement of the usual material. From the outside it looks like common wisdom could be the result of internalizing constraints imposed by the profession and the system. After all the material and the basic approach is the same, and still focused on the education system’s internal needs; standardized tests and preparation for the next academic level. Don’t get me wrong, 21st century entertainment values are likely an improvement all the way around, but they do not get at the heart of the problem.

We all need to learn how to use mathematics, almost none of us will ever do it Current school mathematics has virtually none of feel of real problems. This is not a question of their subject matter, it is their academic orientation inward toward number and arithmetic, nothing of real problems seen outside an academic stetting, they reflect no outside input.

This is not a question of vocabulary nomenclature, or subject matter. It is an inverted emphasis on numerical calculation. Formulation of the quantitative expression of the problem is the secret to real problem solving; this is not a question of algebra.

The current approach to school mathematics prepares students for a consumer role in an advanced society. To be productive participants they need be learning how to approach real problems.