On Twitter this week, someone sent out a link to this survey from the NCTM asking users to submit their ideas for “grand challenges” for mathematics education in the coming years. I forget the precise definition and parameters for a “grand challenge” and I can’t go back to the beginning of the survey now that I’ve completed it, but the gist is that a grand challenge should be “extremely difficult but doable”, should make a positive impact on a large group of mathematics students, and should be grounded in sound pedagogical research.
To that list of parameters, I added that the result of any grand challenge should include a set of free, open-source materials or freely-available research studies that anyone can obtain and use without having to subscribe to a journal, belong to a particular institution, or use a particular brand of published curricula. In other words, one of the grand challenges in math education would be to decouple mathematics teaching from proprietary publication and software platforms as well as ridiculously expensive journals, and make a transformative move toward being an open access discipline.
Here are the specific grand challenges I suggested:
- Create a complete open-source curriculum for high school and early college mathematics, from Algebra 1 through Calculus, consisting of print/PDF textbooks, instructional videos, computer-based manipulatives and applets, and assessment tools that are founded in constructivist pedagogy and focus on conceptual understanding and metacognitive skills in addition to content mastery. The curriculum should be implementable in a flipped learning course setup or in more traditional course designs. All materials are to be made freely available under a Creative Commons license on the web and through a central print repository for those without reliable web access.
- Create a complete set of statistically-validated concept inventories for all K–12 mathematics subject areas, similar to the Force Concept Inventory for physics, to serve as a standard assessment student mastery of underlying conceptual knowledge in these subject areas. The result should be a freely-available repository of concept inventories, refreshed frequently to avoid replication of tests and available upon demand through internet downloads.
- Using the concept inventories developed in Grand Challenge #2, replicate the study by Richard Hake at all levels of K–12 mathematics and in university courses at the calculus level and below, using at least 10,000 students in each study across a wide range of institutional, cultural, and economic backgrounds.
- Create an online repository for preprints in mathematics education, including work on the scholarship of teaching and learning applied to undergraduate mathematics education, similar to the arXiv. The repository should allow for free downloads of preprints; upvoting, downvoting, and comments; and contain video abstracts that can be freely shared and embedded.
You could summarize this list as follows: (1) decouple schools from publishing companies, (2) catch up with the physics education researchers, (3) see point #2, and (4) allow SoTL researchers in mathematics to get their work out to the public faster than is already done.
This discussion about the arXiv for math education has been had before and it’s clear that the arXiv is not interested in setting up a separate area for math education, even though there is already a separate area for physics education, so it’s time to roll our own, as it were. That is by far the easiest of the four challenges I have here.
What would you add to this?