Towards Coherence

By William McCallum

Last week, we had our first large-scale in-person event in quite a while, a training for new and returning facilitators in Baltimore, with over 110 facilitators and 13 employees attending. I gave a virtual welcome to four rooms of eager learners who had spent a day diving into our curriculum. It was a wonderful sight. We are anticipating big growth in our curriculum and professional learning this year, and seeing all those faces of people wanting to join us in our journey towards better student math learning made me think about where that journey is headed and what the next steps are.

A fundamental problem we see in the United States is incoherence in mathematics instructional systems. We have made some strides in that direction. Coherent standards led to coherence of agreement among states about the progression of concepts and procedures across grade levels. That laid the foundation for IM to develop a coherent curriculum. If the standards are a destination, the curriculum is a carefully designed day-by-day itinerary towards that destination. We also built professional learning, coherently aligned to the curriculum, to prepare teachers for the journey and help them along the way.

But there is so much more that is needed to ensure the existence of a complete, coherent instructional system. Assessments are often not aligned with the curriculum teachers are using, pushing them to spend class time on material that does not have any apparent purpose. Learning management systems, assessment systems, and digital curriculum platforms often don’t talk to each other, and, in many instances, either don’t promote or actively thwart good teaching practices. Planning time for teachers is often not sufficient for teachers to move beyond a day-to-day planning schedule. Procedures for teacher evaluation can be at odds with good instructional practice. And teachers, schools, and districts face a dizzying array of supplemental materials that offer solutions for students with disabilities, English learners, socio-emotional learning, culturally responsive pedagogy, and students with unfinished learning. Such resources often work at odds with the curriculum and prevent students from engaging in grade-level work with their peers.

The reasons for this incoherence are complex. Other countries solve the problem with more centralized control of the education system, but that’s not a realistic option in the United States. However, change can come from within as well as from above, and open educational resources can be a nucleus around which an aligned ecosystem can grow. We believe that IM K–12 Math™ and its associated professional learning is the first phase in the evolution of a larger set of coherent supports for school systems on their own journeys to improve student mathematics learning.

Right now we are thinking hard about our next steps after the completion of IM K–12 Math. I described a little bit of that thinking in my previous blog post, Taking the Long View, and soon I will be able to describe more. But whatever the next steps are, they will be guided by the need for a coherent instructional system, and the vision of a world where all learners know, use, and enjoy mathematics.


William McCallum
CEO & Co-Founder at Illustrative Mathematics

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.