Tuesday, July 30, 2019

A Tool for Developing a "Curriculum Portfolio"

HOT TAKE: There is No “Magic” Math Curriculum
  • I don’t think that there is ever going to be one-perfect curriculum that works well for all teachers, students, and contexts. This is because teachers, students, and context are so diverse across the world, and math is so rich, that trying to say that there is one “best way” to articulate a math curriculum is folly. Maybe you get lucky, and find one curriculum that works for you, your kids, and your context. But even that can be hard! Teaching is hard!
  • I think one way to manage this is to instead develop a “curriculum portfolio” that you use. You’ll probably start with one curriculum (formal or otherwise) that you are OK with. Then you branch out and deliberately investigate and analyze other curricula, one by one, adding them to your portfolio. You take the things from each curriculum that you like, leave the things you don’t, and try to incorporate these desirable elements into your classroom and practice. There are countless curriculum you have to add to you portfolio. Naming just the national high school math curricula I know off the top of my head, you have CPM, IMP, CME, Exeter, and Illustrative. Then you have the countless thoughtful educators on the #MTBoS and beyond sharing their lessons, projects, units, materials, and reflections.
  • I recognize that some teachers are forced to adhere to a given curriculum with fidelity, which hampers their ability to make use of even the best/smallest parts of other curricula. While curricular coherence across years, schools, and districts is valuable, I think that restricting teacher curricular autonomy to this extent does more harm than good. But I guess that’s between you and your administrators? Good luck?
  • Given how many math curricula there are, and how complicated curricula can be, it is helpful to have an efficient and reflective process for analyzing and cataloging curricula, and organizing your curriculum portfolio. I’d like to share with you the process that I have developed this summer. This is just a snapshot of my current process, and with every portfolio addition, the process is refined further.
My Process for Analyzing Curriculum
  • It helps to have a general structure that you are connecting your analyses to. This is the “skeleton” of your current portfolio. This skeleton can be as extensive or sparse as you want. The more extensive it is, the less arduous your curriculum analysis is going to be. This is because you have a better idea of what you are looking for in the curriculum--what is relevant. That doesn’t mean more is better, though. You may not want or need to constrain your curriculum analysis so much in this way. You may be open to investing time and energy into questioning/challenging your existing portfolio. It depends on what you have time for and what you’re looking for.
    • For example, the curriculum skeleton I had when analyzing IMP (and that I generally have) was this: I follow the units as outlined in CPM Int 1, skipping over a couple that I have already identified for the sake of time. For these units I have a set of unit plans where I keep track of what I have done. I am pretty clear on what Big Ideas I want to cover in each unit, but am super flexible in what day to day lessons I use.
    • With this skeleton in place, I’m generally looking for:
      • Strong tasks and problems for a given topic
      • How they design for interleaving of topics, and mixed-spaced practice?
      • Understanding certain (challenging) topics of interest
        • These are a small handful of topics I’m particularly interested in, either because they’re going to be new for me, they continue to be challenging, or I’ve heard the curriculum does it well. The grain size depends on what’s interesting, but is generally unit level. For example, this year I analyzed IMP with an eye for Similarity, because I’m teaching it next year, didn’t love the one way I did it in the past, and heard that IMP did it well. Solving linear equations is always on the list. And I teach mostly 9th graders, so linear functions is usually up there, too.
        • Some things I will try to analyze in the curriculum is how the curriculum builds schema for those challenging topics. For example, how does a curriculum introduce solving equations? Do-undo tables? Algebra tiles? Make equivalent equations until you know what the variable is? Graphing?
  • At the same time, I also try to analyze curricula on a more general level. The goal is to advance what I know about curriculum, pedagogy, and math in general. These days, I’m usually looking for: 
    • The relative valuation of conceptual understanding, procedural fluency, and application, and how that’s realized.
    • How do they develop a course narrative (as communicated/summarized partially in a ToC)? How explicitly is it stated?
    • The unit narratives--how do they make a unit feel like it builds cohesively? Again, how explicit is it?
    • How do they differentiate through universal design? In particular, I’m interested in how they design for daily accessibility of the content.
    • Any great problems in general, whether they’re relevant to any math I’m teaching now or later
  • In order to help structure my curriculum analysis, I will have a document that essentially has space for all of these components:
    • Course Narrative (ToC and Problems)
      • Here is where I identify the sequence of big topics (basically unit topics, and maybe sub-units if they’re meaningfully distinct)
      • Here is also where I keep track of good curricular problems/tasks
    • Tracking Big Ideas
      • Here is where I have my pre-identified topics of interest beforehand, and populate it with notes and reflections as they come up. I try to organize and connect ideas within each problem as they go along
    • Other Cool Problems
      • Here is where I note any problems that seem generally cool in general, along with a link to the original, and enough of a description/picture to remind me what they are at a glance
    • Reflections on the curriculum
      • Here’s where I track and organize my thoughts on the bigger ideas of the curriculum. Again, I may just write down any relevant notes, but I try to connect and cohere it to the other relevant notes and ideas as they come up.
    • Reflections on teaching
      • Anyone who has taught alongside me knows that my reflections tend to get really “big” really fast, and so I’ll often be drawn down a reflective rabbit hole at a moment’s notice (whether or not it’s really the best time for that!) This frequent big picture reflection has felt super valuable here in my early stages of development as an educator. So I try to create space for this in my document as well, so that I can keep track of my reflections, and provide them with space to grow. Or if right then isn’t really the best time, at least leave myself a note that I may want to go back to it at some point.
      • This is actually how this very blog post came to be! I had just finished perusing IMP Years 1-3, during which I had organically developed the curriculum analysis document. I was then going to transition to analyzing some of Illustrative Math’s curriculum, and wanted to evaluate/reflect on how the structure of the document aided my process. Then this reflection kind of started, and the genre of “blog post” felt like a useful way to force myself to be thoughtful and clear. A lot of the topics that tend to come up in this section are fodder for blog posts/drafts.
You can see a blank template for my curriculum analysis here. You can see an example of me using this template to analyze IMP Years 1-3 here. This analysis of IMP represents ~10 hours of work. Feel free to leave comments on the documents if you want!

As always, I hope that this blog post was helpful for you--I know it really helped me to reflect and organize my thoughts around curriculum analysis and my own “Curriculum Portfolio.”

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