Couldn’t agree more Dan! The only critics I had to this post (http://leahkstewart.com/examseason/) were talking about the importance of exams and everyone must have X knowledge by age 16. My response; Who says that if everything was optional students wouldn’t choose it? Intellectual and personal development (towards the good individuals care about creating) is something humans seek out. I like to think we’re all here to help each other to that end. If someone stands up as a teacher by offering something they know will help others and no one is picking it up, that’s a call for self development, not to make your thing compulsory in order to have a full classroom. No teacher outside of the school system (and there are many) can do that or would want to do that because it would rob them of the joy of working only with the people who need their lessons the most.

I guess maybe some people actually don’t believe motivation matters. And, sure, there are math war type zealots with unrealistic ideas. But, addressing this crowd seems like a bit of a deflection. The best response to critics is to produce the goods.

Creating a conflict or headache aspirin is difficult to do well. So is “speaking clearly about mathematics” and assigning appropriate “spiraled practice sets”. Your examples are not particularly compelling for headache/aspirin nor are the usual textbook, purple math, etc. particularly compelling for “speaking clearly…”.

I was reading a book by Eric Jensen about cognitive neuroscience and it said that when emotions are tied to an event, that the memory is stored in the episodic memory. The episodic memories are much stronger and easier to recall. It makes sense to me that using motivation while learning would increase student’s retention, let alone their willingness to participate.

I kinda think that there are two components for classroom motivation: the motivation of the students and the motivation behind the concept or idea that the lesson is structured around.

I think what Dan’s trying to say is that if we can show rather than tell (borrowing from our English colleagues) the motivation for the lesson we can add a little bit of motivation for the students.

Obviously a teacher needs to have the skills to foster motivation and what not in the classroom in an interpersonal sense, but to add the extra structure of making sure the lessons are “motivated” properly you’re going to get even more mileage. And if you can make that motivation genuinely mathematical and not boring, even better.

I think what was great about these “Headache” pieces that you did was that you showed we can do that type of thing without a bunch of extra bells and whistles, and that there’s not much math content that you can’t do it with, even stuff that seems really dry.

I feel like the aspirin-headache setup was great for the first case or two. Then, the headaches were too close to pure math to have the same effect for me.

The thought I always circle back to is “what about an innate desire to solve problems?” I had it in school and have it today, and now I’m a non-math teacher who reads math teacher blogs at lunch and works out problems on scratch paper because my brain demands I resolve them.

And I believe that most very young children have a natural sense of inquisitiveness, and that people in general are pleased — on a deep, core, animal brain level — by resolution of problems and conflicts.

…so many people seem to not have that. Aspirin-headache feels like a great real-world tool, like an interim crutch that helps the kids without the “innate desire” tune in for today’s math lesson. But it feels like there’s a bigger picture that we’re just on the cusp of breaking through to.

That innate desire…where does it go between birth and adulthood? Can we foster it, or bring it back? Would our entire schools have to adjust their approach? Would we be better for it? Am I on a wild goose chase that’s too big and complicated to actually ever be solved? We’re so, so close, I think, maybe, or not.

Of the nay-sayers, some aren’t active teachers. I’m suspicious of those that talk about what motivates kids to do things, but don’t have to face the consequences of their theories. I was taught some very useful stuff at Teachers College, and some utter tripe too.

A couple of others have (deliberately?) confused boredom and motivation. In terms of Maths teaching the two concepts are only slightly related.

Student perceptions are also a dangerous topic in terms of how much motivation there is. I know students who think they are motivated to learn — they aren’t bored in class and they do some work — but for me as their teacher l don’t think they have the motivation required. They don’t listen carefully, they don’t do their homework properly and, most importantly, they don’t really commit to doing things properly.

Dan,
My browser is just fine. But after quoting people instead of engaging them to fill in any blanks in what they mean you head of with an imaginary scenario to paint their view as ridiculous. That is a classic straw-man argument.

Take the quote “Success in skill is self motivating”. Do you disagree with that statement? Is it true but ignoring that even more motivation is possible or required? Perhaps you agree with it but believe initial success requires some motivation from a different source.

My point is if you are going to engage with someone who disagrees with you and quote them, either respond to the quote with your argument or with questions for the author of the quote.

If you don’t their response can be simply that is not what I meant and everything in your piece after “… imagine it” is irrelevant to the discussion.

A worthwhile piece of writing on this would address the strongest argument posed against your position and not waste time on the weakest or imaginary scenarios.

If this issue is important please take the time to engage with the best of those who don’t agree with you. For those of us reading both sides it would be far more useful and interesting than just watching echo chambers producing words.

You could start by clearing up my questions on your opinion on the quote “Success in skill is self motivating”.

Regards,
Stan

Thank you for the “time at the microphone.” (And the Harel C framework, which I quite enjoyed.) I will perhaps try and use this time just to mention two items:

1. The post that you linked to is not actually a criticism of the headache/aspirin setup. Its predecessor-post served this purpose more directly:

https://mathwater.wordpress.com/2015/07/03/situating-need-in-the-world-vertical-integration-with-headaches-aspirin-ha/

The link that you have provided is to a couple of excerpts from the writing of Neil Postman, as clarified in the comments, along with the remark that:

“I do not mean to suggest that I agree with the writing [of Postman]; I only deposit the excerpts as a pre-existing example of the sickness-reliever / mathematics educator analogy that you can find linked to in more recent math-ed weblogs.”

2. I cannot say that I share in the criticisms espoused by the latter group(s) described: specifically, those believing motivation is “overblown.” I believe that motivation is crucial, and that teachers who describe students as “unmotivated” may (knowingly or not) mean: unmotivated to do the given [math] assignments. (Are these hypothetical teachers motivated to identify why their assignments are not responded to positively? How can teachers carry out such an investigation?)

As to whether the gamification approach (turning mathematical learning into puzzle-playing, as some others suggest) is fruitful: I would add that, even if achieved, the recreational, satisfactory component of engaging with puzzles must be tied back to the empowering sense of agency that comes with a better understanding of mathematics (and the coeval better understanding of their world).

MQ

Reasonable folks can and did argue that you did not produce the goods with the factoring lesson. The rational expression lesson is basically the same concept. Headache/aspirin doesn’t seem to be readily applicable with these prototypical “skill” lessons.

I thought the series was thought-provoking and enjoyed reading it. You picked excellent examples to prove the point you wanted to make (a point I disagree with, but still).

Math isn’t aspirin. You simply can’t convince all kids that they have a headache.

The trick, to me, is to get kids to think about math and engage with problems even if they don’t care. To do more than working procedures endlessly without thought–or worse, nothing at all. That’s a significant difference in aim, because teachers don’t have to rely on the students to achieve their goals.

Having taken many, many, math classes at various points in my career and early education, I have to say that the single greatest pain I’ve felt with math has been:
Math Teachers.

My firm belief is that the extensive study of math literally reconfigures your brains so that you are no longer capable of appreciating anybody else’ solutions, methods or modes of thought, and are, coincidentally, rendered incapable of clearly expressing your own.

Nearly every math professor I’ve had was impatient, arrogant, demeaning and condescending… Right up to the point that they graded my tests.
I have had no such problems with ANY of my other professors, and I have noticed PRECISELY the same behaviours from my own childrens’ teachers.

I see similar qualities in the participants of the MTT2k series of videos. Indeed, the videos demonstrate EXACTLY what I’ve learned to loathe about stepping into a mathematics class of any sort. Namely, there is a strange propensity to consider methods that are not yours to be “wrong”, regardless of the quality of results.

I love the subject. I can not STAND the “professionals” who teach it.

Note: Below this box into which I am typing is a series of checkboxes. The first two say the same thing. Why are there two of them?

Well I’d just like to point out that not everyone’s Maths teachers were even remotely like Brian’s.

For a start a non-patient Maths teacher is going to die early of stress. You are daily given to watch people do slowly and badly what you find easy. The very first lesson I learned about being a good teacher is the ability to wait for someone slow do something at their own pace.

I’ve also as a teacher learned many different ways of doing the same problem. (As a trick to keep me occupied while students do hard calculus problems, I often solve the same problems the easy way without calculus.) If anything it is students who want to focus on the “one right way”. It’s the teachers who try to get the students to think graphically, numerically and algebraically to solve the same problem.

It’s true that I stop students doing things by a method that isn’t correct, even though the student thinks it is acceptable (most often “solving” by arithmetic methods). I also shun complicated techniques that are difficult to learn and easy to get wrong, which can annoy the more formula focused students. But a correct method that works is always OK.

So, actually, I call BS on Brian. It seems much more like a personal animus than an actual statement of truth. I’ve known people say how all PE teachers were bullies and idiots, and that’s not true either.

I have a critique from a different direction than the two you specify. I think a major reason students lose motivation is that we teach them procedures that seem arbitrary. Your focus recently has been how to get kids to realize the need for what they’re about to learn, which is great (thank you for exposing me to Harel). But then you seem basically fine with just lecture & notes, once the kids are hooked.

I know I could use better hooks, so again, I appreciate this summer series, but I’m mostly concerned that students (especially those with big gaps in prior knowledge) can only understand the conclusions of the lecture that follows but don’t really understand the concepts leading to those conclusions. Like a student who never realizes that a graph shows the locus of points that are solutions to an equation, but remembers the procedure for graphing from y=mx+b. In the last couple of years, your work seems not to have addressed this issue as much as I would have liked…or when it did, I felt it overloaded kids’ brains in a way I fear could lead them to the correct conclusion without the time, practice, and discussion needed to consolidate that conclusion and the *reasons* for it in their long-term memories. So although you know I think cognitive load theory is a good guide for instruction, I’m actually criticizing your recent work for being too much like traditional instruction, not for being too crazy or creative.

How do you get kids to understand that in 2x/5x, you can simplify the x’s, but in (2+x)/(5x), you can’t? And how do you structure a lesson that addresses that kind of thing without being dreadfully boring? Your recent approach would help me find a flashy hook to show kids they need to know when you can and can’t simplify the x, but how do you get them to stay tuned to a long debate about what it really means to simplify a fraction, especially when they have already given up on math meaning anything?

Finally, I just think you misinterpret cognitive load theory as saying that we should only show kids worked examples and drill problems. There’s no reason you couldn’t do a Schwartz/Harel-inspired hook and then use worked examples in the lecture & notes that follow. And the worked examples could demonstrate both correct examples and common mistakes, and could ask students to explain the mistakes conceptually. All of that would be consistent with cognitive load theory, and as far as I can tell, would also be consistent with you like to do. The one thing cognitive load theory tells you not to do, which has been a big revelation for me, is to lead kids through a sequence of discoveries without giving them time to consolidate each discovery in long-term memory before moving on to the next one. That’s what I was criticizing here and then here.

It turns out that the process of encoding something in long-term memory actually consumes working memory. So if a student makes a discovery (“Aha!”) and it’s bouncing around in their working memory, they can lose it the next minute unless we give their working memory a break from thinking about new things and give it a task that reprocesses that thought a few times until it gets encoded in long-term storage. It’s simply not true, despite what many teachers think, that we tend to remember the things we discovered for ourselves. Instead, as Daniel Willingham says, memory is the residue of thought, so we tend to remember whatever we spent the most time thinking about. If we spent most of our time thinking something wrong, and only a little bit of time realizing that it was a mistake, we might remember the misconception more strongly that the fact that it’s not right! So we have to be really careful that the moment of correct discovery is followed by a decrease in cognitive load, with appropriate repetition and rehearsal, so that the discovery actually gets remembered. Is that really objectionable?

Okay, that makes sense. I think we’re on the same page on the big issues, though we’d probably diverge again somewhat if we were to consider a specific lesson plan.

Sometimes I think that much of what teachers think is good for students is clouded by “_______ worked for me and look how good I turned out. So it should work for my students” Not recognizing that most of us who turned out to be math teachers were already either self motivated or teacher pleasers or parent pleasers and no matter what method we were exposed to, we likely would have succeeded.

And for the most part that probably could have worked with no pushback up until maybe 15 years ago. But the fact is that now students have more available to them in the way of information, entertainment, and savviness, that we cannot give them what they have always got and expect them to just take it.