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My Grand Challenge for Mathematics Education

In the spirit of thinking big, the National Council of Teachers of Mathematics (NCTM) recently invited its members to suggest grand challenges for mathematics education.  The NCTM defined a grand challenge as ambitious but feasible, positively affecting many people, and capturing the public interest.

So, here’s my grand challenge for mathematics education.

Build and maintain a free, comprehensive, modular, and adaptable repository of learning materials for all secondary mathematics content.

The foundational resources in this repository would be a variety of free, modular texts covering all secondary mathematics topics.  The content could be packaged together as “textbooks” that cover typical courses, or sliced-and-diced to meet the particular curricular needs of individual states, districts, and schools.  The texts could be downloaded or printed for student/teacher use and would include a wide variety of exercises and problems.

The repository would also contain supplemental curricular materials like enlightening videos made by teachers and mathematicians, rich tasks, technology-based demonstrations and explorations, assessment items, and more.

A full-time staff of professional teachers, mathematicians, designers, and editors would be charged with managing the repository.  This would include creating the texts and curricular materials, curating and integrating freely available content, and advancing the project.

To be clear, my grand challenge is not build the textbook of the future.  This is certainly a worthy goal, and the forward-thinking work of people like Dan Meyer is helping us to define what a digital textbook could, and should, look like.

But my grand challenge is more modest:  create a high-quality, comprehensive, customizable, freely available alternative to the standard textbook model.  Of the many benefits such a project would have, three immediately come to mind.

Reduce Costs, Dependencies on Publishers

It is estimated that schools in the US spend between $8 and $15 billion every year on textbooks.  For a fraction of that cost, a modest team of teachers and mathematicians could build and maintain a repository to satisfy the textbook needs of the vast majority of mathematics learners and teachers nationwide.

The mathematics taught in schools doesn’t change much, yet new math textbooks are produced and purchased every year.  This is mostly due to superficial changes from textbook publishers and short-lived reform movements.  A high-quality, free alternative would not only reduce the costs of acquiring textbooks, but could also put pressure on the multi-billion-dollar professional development industry, which is deeply influenced by textbook publishers.

Create Opportunities for Teacher Leadership

In conversations about improving the educational environment, we often hear about elevating the profession of teaching.  This project would create many teacher-leadership positions at all levels of education.  Teachers would be working directly to create, curate, and maintain the content in the repository, and teachers would also work at local and state levels to select and customize materials from the repository to best serve the needs of their districts and schools.

Giving teachers an active leadership role in adopting and customizing curricular materials would have a positive impact on schools and districts, as well as on the profession as a whole.

Promote a Common Language Around Mathematics Education

One of the purported goals of the Common Core State Standards Initiative was to create a common language around mathematics teaching and learning.  But the CCSS movement has stalled, due in part to serious implementation problems and inflexible mandates.

The proposed repository could help promote a common language around mathematics through the widespread use of high quality texts, problems, tasks, and other common resources.  Students from all across the country could work on shared problem sets and projects, and teachers could engage in professional dialogue about common tasks, texts, and demonstrations.  Because the materials in the repository would be free and editable, states and districts would have full power to choose only those materials they wanted to use, and to adapt them as they saw fit.

There are many more potential benefits to this project, and I think it satisfies the NCTM’s criteria for a grand challenge:  it’s ambitious but feasible, and it would have great impact.

To see the NCTM’s original call for Grand Challenges in Mathematics Education, click here.  And Robert Talbert’s excellent response at the Chronicle of Higher Education is also worth reading.


  1. David Wees says:

    I really like this idea suggested by NCTM. Ask people to suggest some “grand challenges” and ideally, follow-up by attempting to work on a few of them.

    Your grand challenge, while not changing the model of textbook, I think still is an excellent starting place. If we have a carefully curated public repository of instructional materials, all aligned to the specific mathematical ideas, then it would be easier for individual teachers to collaborate across distances on the use of those materials, and it would likely end up being less expensive in terms of time and money than our current model.

    I think there are some attempts to start this kind of repository, but they are all over the place. Someone could easily spend a couple of years just gathering and collecting resources in one place. I know, for example, that the Smarter Balance Consortium is working on a repository, as are others.

    • MrHonner says:

      The idea is certainly not new. Lots of organizations [and companies] are trying to do something like this. But I think if an organization like the NCTM took the lead and stood behind it, they could put together a professional team, get federal agencies on board (DOE, NSF), and make it happen.

  2. Dan Meyer says:

    Lots of companies have attempted this (BetterLesson, for one) and even professional organizations (like AFT’s ShareMyLesson). But none has caught fire to the point that I find teachers referring to them in casual conversation (not even once, either one, in years) and no one in my social networks links to them except to criticize a lesson.

    Your thesis, as I read it, is that NCTM’s imprimatur, curation, and guidance will be the secret sauce to finally catalyze this lesson sharing idea. But I’m wondering if there’s a more fundamental issue – call it teacher autonomy, maybe – that prevents these lesson sharing sites from taking root.

    • MrHonner says:

      I don’t know anyone who uses lesson sharing sites, either. In fact, I doubt that very much of a lesson, whatever we think a lesson is, can be transferred outside the scope of a specific teacher/student/school configuration without substantial customization (or, personalization, if you will). This is where teacher autonomy comes in, I think.

      I don’t see “lessons” as being a part of the repository at all. The first goal is to provide a viable set of free mathematics texts (including problems and exercises) that can be used by any math teacher or student.

      The second goal is a collection of those resources which can successfully exist outside of lessons: things like flexible tasks (for example, your 3 Acts, and others), expert videos (like those of James Tanton), supplementary problems sets, and the like.

      Finally, there’d have to be a modest staff in place to maintain and create new materials, and help teachers and schools package and use the materials to best suit their needs.

      In some ways, what I’m proposing is a National Public Library for Teaching and Learning Mathematics (NPLTLM).

      • Dan Meyer says:

        Is the idea that “resources” would be used more than “lessons” because they’re more modular?

        I’m cynical, but only because my intuition has been proven wrong over and over again on the question of resource sharing by teachers.

        • MrHonner says:

          I think your cynicism regarding the modular resources is entirely valid. We both know there are tons of free, amazing resources out there that go unused by teachers and students who could greatly benefit from them.

          But the primary goal here is the production of viable, modular math textbooks. We know these are purchased every year (at great cost) and used widely (to varying extents), so there are potential adopters out there. Once they start using the texts, the rest of the resources come along for the ride, as the curators can package suggestions to go along with the texts that are produced.

          Cynicism regarding the production and widespread adoption of such texts is justified, too, but a Grand Challenge probably requires some amount of optimism.

  3. This was sort of similar to one of my proposed grand challenges as well (thanks for the link). I wonder if the “challenge” is not so much creating the repository as it is to catalyze its widespread use. I have no idea what that would take, but I think it would involve giving schools the ability to grant time and space to teachers to develop their own lessons with the materials in the repository — to say, if you use the materials in that repository then we’ll incentivize it by giving you more professional freedom.

    Cynically, I’m not sure a grand challenge like this will fly, because the money to make it happen would come from the Federal government which is probably flush with lobbyist from the textbook publishing world. But I will try to stay optimistic.

    • MrHonner says:

      I liked all your proposals, Robert, and mine is similar to your first one. I wanted to scale back a bit, by focusing first on textbook replication, and on high school curricula (where textbooks likely have the biggest impact on instruction). I also wanted to expand a bit on the benefits, beyond the obvious cost savings.

      I share your specific concerns about the politics involved, but it’s nice to be an optimist sometimes and think big!

  4. Dylan Kane says:

    Elizabeth Green wrote in her article last week on why Americans stink at math about how the Japanese have come to some level of consensus on which specific problems are best for students exploring a new concept — she used the example of 13 – 9 to explore different strategies for subtraction. I think a more modest, but more attainable and maybe more immediately useable goal would be a repository of tasks designed to introduce students to a new concept. NCTM could use its resources to test a wide variety of problems in a large number of classrooms, and “upvote” the problems teachers like best.

    • MrHonner says:

      I think it’s important to have a set of good problems and tasks for teaching and learning that everyone can use, and I definitely see that as part of the repository.

      But a task can only be effective when it fits the mathematical culture of the classroom, which is a product of both the teacher’s mathematical attitudes and those of the students. I think this is part of the “teacher autonomy” Dan mentioned earlier: teachers have certain mathematical prejudices and predilections, and this factors in to which tasks will be most effective for their classrooms.

      The key part of what you say, Dylan, is consensus. It’s not just that these tasks exist; the teachers seem to understand why they are useful and, thus, how to use them.

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