One of the most interesting and useful effects of keeping a blog or journal, I find, is that once I take the time to develop and articulate an idea, I start seeing it everywhere. Such is the case with my Big M, little m post from early this month. Because so many readers expressed interest and enthusiasm for the idea of making learning matter, I wanted to share a few resources I’ve collected about that since my original post.
First, on mattering from a research and instructional design perspective:
A reading in one of my courses pointed me to a pedagogical standard called the necessity principle, which states that content should be presented to students in a way that establishes an intellectual need for it (Harel & Tall, 1991). This, in turn, reminded me of a favorite article of mine that describes a framework for learning task design. The two design principles in the framework are purpose, stating that tasks should feel purposeful from the students’ perspective, and utility, stating that task should establish why the mathematics involved is useful (Ainley, Pratt, & Hansen, 2006). Necessity, purpose, and utility all feel intimately connected to the question, Why does it matter? I’ll include the full references at the end of this post in case anyone is interested in reading more. Interestingly, although the principle and framework from the articles have been used in some later research, they haven’t been used as much as I expected given that the ideas resonate so strongly with me. Perhaps I have found an interesting niche where there is room for a new scholar such as myself to make a contribution.
Next, mattering from a practitioner perspective:
My original Big M, little m post focused on how attention to why big ideas matter could make for a more connected and coherent school experience for students. As I reflected further on this issue, however, I realized that mattering has also been discussed at some length in relation to engagement. In particular, I was reminded of prolific mathematics education blogger Dan Meyer’s recurring theme of creating headaches for students for which mathematics is the aspirin. I first heard him speak about this at the Ontario Association of Mathematics Educators conference in 2015 and for a time followed his blog post related to this theme. I have since not followed it as closely for a variety of reasons — one in particular being my interest in elementary education and his focus on secondary education. Still, he gives some wonderful examples that the partitioners reading this might find useful and interesting. Give that Dan Meyer is now the Chief Academic Officer at Desmos, I may start following his work again to see how he uses technology to create new kinds of (productive!) headaches for kids.
Lastly, on mattering from a writer’s perspective:
One of the aspects of my coursework that I’m finding particularly valuable is my professors’ dual attention to helping us find footing in the academic literature and to helping us become better academic writers. In the reference list below, I’m including two books I’ve been reading, at the suggestion of professors, that each include super useful frameworks for structuring writing and research in ways that will convince your readers that your ideas matter. Graff and Birkenstein (2010) advocate consistently asking yourself, “So what? Who cares?” about your own and other writers’ points. It is rather annoying to continually have to articulate an answer to this, but it is an excellent exercise in making sure you get to a point that someone other than you will care about. Booth and colleagues (2016) provide a more structured way to get to the point, for when self-queries of “So what? Who cares?” come up empty. They suggest filling in three blanks: I am studying [blank] because I want to [blank] so that [blank]. For example:
I am studying how technology impacts mathematics teaching and learning because I want to understand how technology can be used to make mathematics engaging and meaningful for students so that fewer students leave school believing that mathematics is useless, meaningless, or, worst of all, not for them. Often, when I get bogged down in the small details of my research or writing, I lose track of the big picture. The third blank in Booth and colleagues’ framework is useful for remembering why I do this work.
I hope you find these resources useful! If you have more that you’d like to pass along, feel free to tell me in the comments!
Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23-38.
Booth, W. C., Colomb, G. G., Williams, J. M., Bizup, J., & Fitzgerald, W.P. (2016). The Craft of Research, 4th edition. Chicago: University of Chicago Press.
Graff, G., & Birkenstein, C. (2010). They say, I say: Moves that matter in academic writing, 2nd Edition. New York: W.W. Norton & Company.
Harel, G., & Tall, D. (1991). The general, the abstract, and the generic in advanced mathematics. For the learning of mathematics, 11(1), 38-42.
3 thoughts on “More on Mattering”
I’m sure that for many kinds of writing the sentence frame, “I am studying [blank] because I want to [blank] so that [blank]” is useful. But I’m not sure it works in all cases. There’s a lot of things that I “study” that are not really useful at all — or, at least, I don’t study them because they are or might be useful. I study them because they’re interesting or beautiful. Which translates back to an issue with Harel & Tall and Ainley, Pratt, & Hansen: Must everything we ask students to study be useful? How about fun? Or interesting? Or beautiful? By reducing education to pure instrumentality, aren’t we losing something important?
Right. I agree with that. The book that frame is from is all about writing research proposals and articles, so explaining why is it useful is a way for interesting your readers, getting funding, and do forth. But it doesn’t always work for your own interest. Or maybe, it isn’t always necessary for your own interest. The authors talk about how the first and second blanks are enough for you, mostly. You have your own reasons, and they might be simply “I just want to know!” And that’s great.
As to whether everything a student studies has to be useful, I think it depends on how you define utility. I don’t think everything has to be useful in a day-to-day life kind of way. That mindset only leads to contrived problems. But I do think it should be framed as being useful for figuring something out — even if that something has no real impact on anything but curiosity. This is what Dan Meyer means about creating headaches for which mathematics is the aspirin. Curiosity can be stimulated just as well with purely mathematical problems, for example, than with problem-based scenarios.
I just went back and read the big M little m post — and it occurs to me that since, as you say, little m mathematics is about thinking, one of the reasons mathematics outside of school is perhaps more appealing than Mathematics in school is because it involves thinking. And thinking is its own reward — it doesn’t need an instrumental payoff (though it often has one, at least if one is thinking well).