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Finding balance
Does anyone have advice about how to reach a balance between application, conceptual understanding and procedural fluency?
Far too many of the teachers in the district are still solely focused on low level (DOK1) procedural fluency, but actually that is not what my question is about. We have a couple sites (secondary) that have moved to instruction that focuses on developing concepts through application problems (with the support of curriculum that does this for them) for the last several years. However, we are finding that students are not leaving the class fluent. They are unable to “do” skills they used to and the cumulative effect is really impacting our Pre-calculus and Calculus courses. The struggle is that it takes so long to develop concepts and struggle through good tasks that there is not time for practice. Every day we are on to a new learning target.
Here are some questions you could answer that might help me:
1. How much of your time is spent practicing math skills?
2. How have you narrowed the focus of what we need to teach in each course so that time can be spent on developing deep understanding.
3. Any ideas of how to incorporate skills practice without doing piles of worksheets.
And of course any other general thoughts would be appreciated.
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1 Reply
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Great questions and problems of practice here.
Have you explored the 5 mathematical proficiencies from the Adding It Up document from the National Research Council? Chapter 4 is a great read and helps to articulate what true mathematical proficiency consists of.
Many struggle with first moving from procedural fluency only (or what they believe it is – usually just rote memorization, not real fluency) to building other proficiencies in. Here at Make Math Moments, we believe that you build procedural fluency through conceptual understanding. We do this through problem based lessons. Striking the balance between all 5 proficiencies takes time and cannot be articulated through blanket statements like ___ minutes of this or ___ minutes of that.
Super complex problem of practice, but so worth exploring!
Can you help paint a picture of what this looks / sounds like in the classrooms you have described?
