I love Sandy’s metaphor of the waves of educational reform:
As a teacher of mathematics since the mid-seventies, I have seen a lot of “waves” of reform come and go. All promise increased student performance with the implementation of the latest bells and whistles…. The latest “wave” of reform is the Common Core State Standards.
I was lucky to have enjoyed a long ride on a good reform wave during my time in the classroom. I taught from an NSF-funded reform curriculum for seven of my nine years of teaching, and my attitudes about teaching and learning math were shaped by that experience.
The reform curriculum I used had rich problems and activities, and students usually worked in groups. Some students and parents struggled with the unfamiliar format of the textbook we were using, which didn’t have worked-out examples or answers to odd exercises in the back. But at the end of the three-year curriculum, my students could all graph and solve equations; and none of them thought of a word problem as scary, because they solved word problems every day. I would say that most of them had pretty good grounding in most of the Mathematical Practices featured in the Common Core, particularly in Practice #1: Make sense of problems and persevere in solving them.
In my last year of teaching, I had to switch from the reform program back to a traditional algebra book. I hated it. I was frustrated by the lack of thought given to the sequence of the material in the traditional book—it started with the most abstract concepts of algebraic properties; it focused on symbol manipulation; application problems were mostly confined to the last lesson of each chapter; and the first six chapters of the book didn’t include ANY graphing.
When I think back to that last year of teaching, I remember a student I’ll call “Jay.” He was a sophomore repeating algebra and failing it a second time. One day, tired of the boring lessons in the book, I used an activity called “a silent board game” that I had used when teaching from College Preparatory Mathematics Algebra 2. I wrote an incomplete function table for a secret function on the white board, and students came up and filled in missing entries in the table based on the patterns they observed. I left correct answers up and erased incorrect answers. (Note that “wrong” answers gave valuable clues, so there was no shame in being erased.) It’s a simple activity—no technology is required, and it can be easily adapted to move from linear and quadratic relationships in algebra 1 up to logarithms in algebra 2. And the silent part is brilliant, as it puts quiet and vocal students on equal footing.
Jay turned out to be a superstar silent board game player. He was the go-to guy for finding the underlying pattern, and I could see him standing taller as the games progressed. That activity made it clear to me that Jay had plenty of aptitude for algebra. In fact, he was unknowingly demonstrating proficiency in the Standard for Mathematical Practice #8: Look for and express regularity in repeated reasoning.
That day sticks in my mind because it encapsulated my frustration with the traditional algebra text. If I had taught solely from that dry text, I wouldn’t have seen Jay’s potential.
I wish I could say that Jay’s new confidence boosted him up to become a star math student. But sadly, we each struggled through that year, both of us saddled with a curriculum that was focused on isolated skills instead of the development of concepts, and that didn’t build in opportunities to strengthen students’ problem solving, sense making, observation of patterns, and modeling—areas emphasized in the new standards.
I left teaching after that, frustrated by the feeling that I was moving backwards instead of forward; no longer propelled by the wave of good reform, but being pulled down by an undertow focused on standardized testing and isolated skills.
Like Sandy, I hope that the latest wave of the Common Core, particularly the Standards for Mathematical Practice, propels teachers and students forward.