Back in March, the National Council of Teachers of Mathematics put out a call for Grand Challenges in Mathematics Education.

A Grand Challenge is supposed to spur the field by providing a focus for research. NCTM came up with the following criteria for a Grand Challenge in math education:

So I ask you to help the brainstorm. What are the complex yet solvable problems we face in mathematics education that can have a great impact on people’s lives?

Add your thoughts in the comments below or through Twitter (@tchmathculture). Use the hashtag #NCTMGrandChallenge.

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I’m talking out of my elbow here, but I’m inclined to think that we need to rethink the relationship between research and practice. Here I’m influenced by your social media presence, the stuff Bill Penuel does in Boulder, Jack Schneider’s

From the Ivory Tower to the Schoolhouse, the potential online forums that might be developed for teacher-teacher conversations about teaching…How about this as a grand challenge: attempts to influence k-12 practice with knowledge generated outside of school contexts has often been frustrating for all involved. A grand challenge is to search for viable alternate models for the creation and dissemination of knowledge about teaching and learning math, and then to promote successful models.

Eh? How did I do?

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Great ideas! That sounds like a call to develop deeper connections, but what questions should we pursue in this vein?

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I think the research questions we will ask and assign importance to will change when there are deeper connections between k-12 teachers and researchers (and when we conceive of positions that fill the gap between those two poles). Do we even know how to ask the questions that are most important for our field?

More concretely, I’m willing to sign up for Max’s research program. That would be most helpful for my teaching.

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It seems like you’re looking for a way to generate new knowledge about teaching and learning from within the school context.

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I read this when you first posed the question and I’ve been thinking about it all weekend.

It sort of sounds like an attempt to pose questions like the Millennium Problems in mathematics, but it is much harder with social science to know when you are “done” with something.

In any case, I came up with two ideas of what I thought might be well-defined problems:

1.) Come up with a set protocol for detecting dyscalculia. Dyslexia is well known enough that elementary school teachers can often catch it and refer students, but I know of nothing similar for dyscalculia.

EXTRA CREDIT: Make headway on remediation for dyscalculia students; are there things that work for them specifically that give them a chance in mathematics class? EXTRA EXTRA CREDIT: Include other mental conditions like synesthesia that can affect mathematics use.

2.) Come up with a grand index of world mathematics practices. Which countries have which particular sequencing in curriculum? Which ones do which particular practices?

I’d like a focus on more than just the usual Japan/Finland/China/Singapore group. Some other countries are doing very interesting things (if perhaps low GDP, being behind to begin with, etc makes it invisible). If we are talking grand projects, I’d want to be able to see what’s going on in any country in the world, pull up videos, textbook samples, standards, etc. What’s going on with Estonia’s embrace of computer-based mathematics? How does Australia incorporate statistics so much more thoroughly than the US?

I’d also like honesty with these things on outside practices within a country. Any mention of “these practices cause these stats to happen” is incomplete without some mention about (say) how a large chunk of the student population does after-school math practice, or how a particular chunk is excluded from testing, or how not everyone in a particular country even goes to secondary school.

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Is this conversation hypothetical, or do you intend on sending something?

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Better measures of learning, doing and understanding mathematics than standardized tests that are acceptable to accountability mavens.

Some kind of agreement as to the purposes of school mathematics.

How to effectively support teachers in professional growth: what are some underlying principles. (Michael’s continual call for constructive teacher conversations seems like a good starting point.)

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I agree with Michael. I was told recently that the time between a practice being researched (like, say, the 5 Practices for Orchestrating Productive Math discussion) to seeing it being implemented widespreadedly in classrooms, is 10 years. A grand challenge could be figuring out how to shorten that time to 5 or 2 or 1 years.

Another grand challenge could be to extend the kind of work that went into CGI to high school Algebra, Geometry, Probability, Statistics, and Calculus concepts, so that teachers teaching, say, right-triangle trig, or similarity proofs, or solving quadratic equations, or standard deviation, had a map of learning progressions in that space and ideas about kids’ informal intuitions and misconceptions, multiple representations that connected to various aspects of a fully operational mathematical understanding, and then linkages among those multiple representations. Related to this, I’d like to see more work on creating rich sets, well-annotated sets of student work on simple, almost universal tasks (and less work on creating rich tasks — so I’d rather see how a bunch of kids made sense of and solved a problem that could be found in any unit on quadratic equations, than a lesson plan for a really awesome task that involves kids doing super-fun investigations with quadratic motion).

Finally, I’d like to see more work that builds on stuff like the NCEE report: http://www.ncee.org/college-and-work-ready/. As John Golden said, agreement on the goals of school mathematics, which could, in turn, inform better assessment design. Could we have a fairly comprehensive and nuanced view of what mathematics people regularly do, need to do, should do, how they do it, and how they got that way? Curricula that supported learning to do the math people actually do, plus the math they enjoy and appreciate, would be so joyful to teach!

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Oh, I forgot one. There’s a huge gap out there about the efficacy of various approaches to “teaching problem solving” and whether that should even be a thing, even though that’s a major critique of whole families of instruction and curriculum (that they don’t teach problem solving). A grand challenge could be to develop a more complete set of “mathematical practices” or “mathematical habits of mind” or “critical mathematical reasoning skills” or what-have-you, that shows how these things develop from novice to expert — do they transfer across domains? how do they change in individuals over time? in groups over time? what is the relation to content knowledge? etc.

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I would like to see research which produces something definitive, or as close as you can get, on the following complex of questions:

In learning mathematics, what, if anything, should children know by heart? and Assuming that it is useful for them to know things by heart, what things? (The times tables, on up to … algebraic identities? The first 25 primes? …) and Again, assuming that knowing certain things by heart is useful what are the best ways to achieve this, and at what level in their mathematical development?

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