By William McCallum
A few weeks ago, my wife and I took a 17-day rafting trip through the Grand Canyon. We descended through the layers of rock, from the 270 million year old Kaibab sedimentary layer of chert, dolomite, limestone, and sandstone all the way through to the 1.7 billion year old tortured metamorphic Vishnu Complex of gneiss, granite, and schist. What astonishing beauty was wrought by the slow erosion of wind and water and compression of deep geological forces.
I sometimes think that improvement in student mathematics learning proceeds on geological timescales. Maybe not on million-year time scales, but on time scales long enough that those engaged in the work have trouble seeing change. But change there is! As we at Illustrative Mathematics start a new year with a complete K–12 curriculum and the professional learning that supports it, I want to look back at some of the waypoints on our nation’s journey towards mathematics learning for all, and at the work still to be done.
I’ll start with the 1989 NCTM standards. This was a coming-together moment, when teachers stood up and made a bold move that launched an era of state standards writing. It was the first national attempt to describe a destination for the journey, the student outcomes we wanted to see. In the ensuing years, various curriculum initiatives mapped out ways to reach those outcomes. Just as the standards set the destination, a curriculum aligned to those standards is a day-to-day description of how to get there.
The next waypoint was the 2010 release of the Common Core State Standards in mathematics. The NCTM standards had led to state standards but by 2010 there was more work to do. The 50 different sets of state standards had wildly different topic placements, and not everybody wanted to follow their state standards anyway. For example, the grade where students started to add fractions varied from grade 2 to grade 7. So a curriculum had to be either only locally aligned, or incoherent as it tried to satisfy contradictory demands. With such variation in pathways came variation in opportunity, which inevitably led to inequity. In the interest of equity and large-scale improvement, state standards needed to be more aligned with each other.
Although there has been much brouhaha around the standards since then, the fact is that today a good 40 states have a highly similar scope and sequence. Which brings us to the current waypoint for Illustrative Mathematics. IM K–12 Math is a coherent curriculum aligned to the standards of most states. It’s easy to forget that coherence and alignment would not both have been simultaneously possible before the Common Core.
The NCTM standards, the Common Core, and now the arrival of coherent standards-aligned curricula such as IM K–12 Math—each of these was a waypoint on a journey. There are two points I’d like to make about this. The first is that we are indeed making progress along that journey. People love to complain about fads and pendulum swings in education, and there are indeed plenty of those. But the windstorms of politics and social media have not stopped us from moving forward.
The second point I want to make is that none of these waypoints, by themselves, changes much. Standards by themselves don’t do anything without a plan to reach them, that is, a curriculum. And a curriculum does nothing if it just sits on a shelf. These are slow hard steps in a long march. But they represent progress nonetheless; we are further along now than 10 years ago, and 10 years ago we were further along than we were 20 years before that.
What is the next waypoint? We at Illustrative Mathematics have been thinking hard about that. It has something to do with thinking beyond curriculum and moving into the classroom where that curriculum is being enacted. Educators have known for years that instructional practice, institutional support for teachers in their classrooms, and empowering families and communities to help with their students’ learning are crucial. Now we think we have a way forward to make progress on those fronts. We haven’t figured it all out yet, but we are committed to continuing the march towards a world where all learners know, use, and enjoy mathematics. Stay tuned for more details over the next few months.
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.