The Power of Small Ideas

William McCallum, IM President

Big ideas are popular in mathematics education, and you can find many lists of big ideas on the web. Some are more thoughtful than others, and I can see how some might be useful for organizing a curriculum. But few of the ideas I see in these lists really get me excited, or really capture what I love about the subject. I am a big fan of small ideas; like intricate joints in a fine piece of carpentry, small ideas often evade the eye, but are crucial to the beauty and structural integrity of the finished product. I’d like to mention a few of my favorite small ideas.

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Designing Coherent Learning Experiences K-12

Kristin Gray, Director of K–5 Curriculum & Professional Learning

One challenge in curriculum design is considering all we know and believe to be true about math teaching and learning and translating that into realistic and actionable pieces for teachers and students. Our recent post about the K–5 curriculum focused around our belief that each and every student should be seen as a unique person with unique knowledge and needs. And while that post centered on elementary materials, to truly design around this belief we must look past K–5 to consider each student’s unique K–12 mathematical journey. A journey that, for most students, looks very different as they move from elementary to middle to high school.

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What is problem-based instruction?

By William McCallum

When I was a child, I used to get puzzle books out of the library. One of the puzzles was the twelve-coin problem, the most difficult of all coin weighing problems. My mother and I worked on it separately at the same time, and she solved it first. Some time later that evening she came into my room to find me in tears of frustration. Instead of helping me, she asked: “Do you want me to tell you the solution?” I said no and she left. I will never forget the joy when I finally figured it out.

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