Learning through Teaching

I was in New Orleans a couple of weeks ago visiting a school using IM 6–8 Math and was inspired by the efforts the school was making to implement problem-based instruction. I saw teachers at different stages on a learning curve with the instructional routines in the curriculum and realized how important it was to have a learning curve, and not a learning cliff, for teachers to grow into this way of teaching. We have tried to achieve this in many ways in our curriculum.

First, simply having well-defined instructional routines helps. Routines can make it less daunting to change teaching practice. You can learn them one at a time, starting with the simpler ones, and the repetition of routines throughout the curriculum provides for gradual growth rather than a sudden leap. You can read more about our instructional routines here, here, and here.

Second, we designed our curriculum to have multiple supports for teachers at the activity, lesson, and unit level. These include narrative overviews of each unit, lesson, and activity, which describe their purpose and how they fit into a coherent progression with other units, lessons, and activities; launches for each activity with guidance on how to make sure students understand the problem they are being asked to work on without depriving them of the opportunity to tackle it on their own; anticipated misconceptions; and syntheses at both the activity and lesson level that provide guidance on how to crystalize the mathematical purpose. 

Third, and perhaps most importantly, we offer content-based professional learning that is tightly aligned with our curriculum. All of our professional learning materials are written in parallel with the writing of the curriculum itself, and are directly aimed at supporting teachers in seeing the coherent progression of mathematical content in our curriculum and in practicing the problem-based instruction that will help students see it as well. And, recognizing that different schools and districts have different needs and capacity, we continue to seek out new ways to meet those needs.

As I think back to that school in New Orleans I feel hope for the impact we can have, especially with traditionally underserved communities. Although I am proud of the curriculum we produced, that impact comes not from the curriculum alone but from the commitment of a community of teachers passionate about student learning. Our mission is to support that community in every way we can.


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William McCallum
Founder and President at | Website

Bill McCallum, founder of Illustrative Mathematics, is a University Distinguished Professor of Mathematics at the University of Arizona. He has worked in both mathematics research, in the area of number theory and arithmetical algebraic geometry, and mathematics education, writing textbooks and advising researchers and policy makers. He is a founding member of the Harvard Calculus Consortium and lead author of its college algebra and multivariable calculus texts. In 2009–2010 he was one of the lead writers for the Common Core State Standards in Mathematics. He holds a Ph. D. in Mathematics from Harvard University and a B.Sc. from the University of New South Wales.

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