Activities and Coherent Curriculum

One theme I heard several times at CMC-South was the idea that building curriculum by cobbling together activities will not effectively serve students. Matt Larson addressed it in his talk on NCTM’s Principles to Actions publication, and from the tweets it seemed like Illustrative Math hit on a similar idea in their talk on their emerging course blueprints. I’ve also heard the phrase “CRAP” — Curriculum Resourced and Acquired from Pinterest. This theme was one I heard when I was getting certified to teach — a warning against being an “activity planner”, and prioritizing how cool and awesome activities are over their instructional value.

Principles to Actions addresses the same point in its chapter on curriculum. It names as an unproductive belief, “The availability of open-source mathematics curricula means that every teacher should design his or her own curriculum and textbook.” This is contrasted with the productive belief, “Open-source curricula are resources to be examined collaboratively and used to support the established learning progressions of a coherent and effective mathematics program” (72).

So there seems to be significant pushback against what I do to build my curriculum. I think everyone here offers a valid point about the dangers of planning lessons based on activities, but I’d like to offer a defense. First, a few more quotes from the Principles to Actions chapter on curriculum:

“In light of the sheer quantity of mathematics that could be addressed in any grade or course, it is important to make careful choices about what specific mathematics to include” (73).

“[W]hen teachers recognize the importance of developing students’ proficiency with the mathematical practices, they can more effectively select and implement appropriate tasks that emphasize mathematical thinking throughout the pre-K-12 years. Instructional materials and tasks selected by schools have a significant influence on what students learn and how they learn it (Stein, Remillard, and Smith 2007). Consequently, teachers need high-quality professional development to maximize the effectiveness of these materials, since even the best textbooks and resources can be misinterpreted or misused” (74).

“Structuring units — and lessons within the units — around broad mathematical themes or approaches, rather than lists of specific skills, creates a coherence the provides students with the foundational knowledge for more robust and meaningful learning of mathematics” (74).

I don’t have a coherent curriculum at my school, and I don’t have access to high-quality professional development. Instead, I have bits and pieces of great curriculum scoured and collected from the best resources around. I outlined over here how I’ve been planning lessons this semester, from a variety of resources but leaning heavily on Illustrative Mathematics, Geoff Krall’s curriculum maps, and Desmos.

The quality of my instruction has absolutely suffered at times because activities don’t sequence well with each other, and there are missing pieces in the middle. But I think the benefits far outweigh the costs. These resources meet the criteria in Principles to Actions. They promote the use of the mathematical practices, they focus on big ideas rather than lists of specific skills, and they often come with detailed how-tos in the form of blog posts to help me use them effectively.

Most importantly, many of these resources take approaches I wouldn’t have thought of, approaches that aren’t present in a traditional curriculum. Conic cards gave me a great new way to connect representations of conic sections. Match My Parabola pushed my understanding of the leading coefficient in a quadratic. This Darius Washington free throw task provided both an interesting application of probability and created a need for making some tough decisions about which data was most important.

When I’m doing this right, I’m not searching the internet for resources at 9pm as I plan the next day’s lesson. Instead, I collect the best ideas I can find before the unit starts, and as I work my way through the activities, I build an understanding of what it means for my students to engage with the mathematical practices through that content.

But a set of cool rigorous activities don’t make a curriculum. The instruction — the little bits of explanation, questioning, examples, and more that stitch these activities together — is planned backwards, built to make sure students have the knowledge they need to be successful doing worthwhile math. The key part here is that the starting point — the worthwhile math — comes from this patchwork of activities that set a much more useful bar than any canned curriculum I’ve seen.

And resources to make that instruction better are around too. Little ideas like Sam’s domain and range meter, Kate’s trickery summing arithmetic sequences, and Bob’s ESP to illustrate composite functions. And if I need something a little more comprehensive than a quick intro activity, I dig into someone else’s virtual filing cabinet — I’m especially a fan of Meg Craig’s work.

None of this stuff is in any textbook, and it makes a huge difference for students. I’m sure there are great textbooks out there that do great things as well. But teaching a curriculum based largely on a collection of tasks and activities has worked well for me, and I believe it makes me a much better teacher much faster than a prescribed curriculum. The process of finding a diverse set of worthwhile tasks for students, building my instruction backwards from those goals, and filling in the gaps is how I want to keep teaching.

8 thoughts on “Activities and Coherent Curriculum

  1. howardat58

    But at some point it is a good idea to look at the math “topics” involved in the activities, and make sure that there is a sensible order there, with nothing missing that is really “important”. Then you have your curriculum. Then you can file it away!

    1. dkane47 Post author

      Good point — one thing I didn’t mention here is how I pick and sequence the topics. Sequencing I’m still figuring out, but I have the general framework from past years’ curriculum here. It’s just a question of figuring out what we mean when we say “polynomials” or “function transformations”.

  2. Brett Gilland

    A thought experiment: The MTBoS consolidates many best practices into a coherent curriculum as some sort of collaborative project. (I will honestly be surprised if this doesn’t happen in the next 5-10 years). It includes many of the great activities and ideas you list above, along with others similarly wonderful that we don’t need to address here. It is built from Dan Meyer’s conception of a 21st century textbook that utilizes the full range of digital potential. It includes given notes about effective techniques, as well as a collaborative space for teachers to share about best practices for the lesson. Would using an ad hoc curriculum still make one a better teacher faster than using this uber-curriculum?

    I guess what I am pushing back against here is the idea that bespoke curriculum development necessarily causes superior gains in teaching. Given the textbook options that are likely available to you, it is almost certainly better now. But this seems to be a contingent fact, not an a priori one. It also de-emphasizes the need for real high quality curriculum, by suggesting that best practice is not to adopt, but to generate. And if we want good teaching to spread beyond the dedicated but relatively tiny minority, this isn’t a viable path forward.

    In short, the only basis I know of for selecting a textbook is whether it makes it easier for noobs to be a better teacher sooner. Right now, that leaves a tiny number of options. That needs to be remedied, not accepted as natural.

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  5. annablinstein

    I think that I thought very similarly to you until I started teaching using a coherent textbook this year in one of my classes (from CME’s Integrated series). I’ve always cobbled together and created my own curriculum, just as you have been doing, but having a good textbook showed me how beneficial it is… instead of the time I would normally use to plan and sequence and fill in the many gaps and inconsistencies, I had time to really look at student work, give much more detailed and thoughtful feedback, and put the kind of time into designing projects and assessments that I would have never had under the old system. There are still plenty of opportunities to supplement with extra activities, but the core of the course is much more coherent and tight. Anyway, just two cents from someone who used to swear by curriculum creation 🙂

    1. dkane47 Post author

      Thanks, Anna. I’m sure you’re right — I was hoping to be able to get CME this year but it didn’t work out. Having that coherent core — and all the little subtle things that I’m sure I wouldn’t appreciate until afterwards — is something I hope to get the chance to do, and hopefully won’t be too stubbornly stuck in my activity-chasing ways to take advantage of.


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