by Susan Ogilvie, Middle School Co-Director for Curriculum & Instruction, MYP Math Teacher, and 7th Grade Homeroom Teacher
“What does effective mathematics instruction look like?” It’s a question we have been leaning into at Mackintosh Academy since the spring of 2017 when the faculty read Jo Boaler’s Mathematical Mindsets. Under the guidance of our math consultant, the middle school math faculty piloted a few different programs that were identified to align with our International Baccalaureate (IB) curriculum and Mack Boulder’s approaches to learning and teaching. We were searching for a program that aligned with our desire for inquiry and investigation, deep conceptual understanding, and the development of a culture of problem-solvers. Ultimately, our Middle School chose to work with the Open Up Resources’ Illustrative Math (IM) curriculum. The faculty felt that this curriculum provided the most clear alignment with our goals. Our math consultant and further coaching has given the faculty guidance to incorporate Mackintosh Academy Boulder culture and approach the IB objectives with the novelty that activates memory retention in the brain and the confidence that makes lifelong mathematicians.
As an integral part of the Open Up IM curriculum, an important tool for each middle school math teacher to wield is the Five Practices for Orchestrating Productive Mathematics Discussion. Smith and Stein (2011) delineated the five practices of anticipating, monitoring, selecting, sequencing, and connecting as a powerful teaching structure for problem-based learning in math. Teachers anticipate student answers in their instructional planning and monitor the students as they work through conceptually rich problems. Then, teachers select and sequence student explanations of their solution process in order to make connections to previous learning and build new understanding. Students learn by doing and learn from others through a series of events carefully orchestrated by the teacher. As a class, they synthesize the information together and create new understandings that are recorded through notes, summaries, and application to new problems. The middle school teacher is the facilitator of this practice, acting as the DJ of an intricate dance between middle schooler’s connections with wisdom math (the math they know) and new understandings.
But, wait…hold up…have you ever been to a middle school dance?
Can you remember what it was like? Middle school dances were filled with awkward maneuvers, cringey outfits, and music to which most of us would rather not admit we listened. The experience of putting the 5 Practices into action over the past two years in math class has been a little like living through a series of middle school dances:
- This one was a little cringey.
- This one was awesome.
- This one got awkward because three people wore the same outfit.
- This one was awesome.
As faculty, we cherish all the lessons, even if they weren’t “awesome” dances. Some days, students weren’t quite sure of the right answer (it got a little cringey), or three groups had the same problem-solving method (everyone came dressed the same). Did our students stop learning or did the curriculum fail? No! As middle school faculty we consider, “What did they learn in addition to math that day?”
In cringe-worthy dances with the 5 Practices, our students have an opportunity to “practice failing well”, one of our IB Approaches to Learning (ATLs). The students consider what didn’t go well, just as real problem solvers do in our communities every day. The students also know they have a chance to re-work the problem in order to get it right or understand the problem better. This revision approach builds resilience and grit in our students with faculty support to normalize failure as a part of learning and understanding.
The dances where everyone dresses the same with the 5 Practices offer the faculty a chance to dig deeper with students and find an alternative “outfit” or approach to solving a problem. “What’s another way you could have solved this?” builds the students’ skills as multi-dimensional problem solvers as students are asked to consider alternate ways of thinking.
And some days, the 5 Practices dance is everything it is imagined to be. As a teacher, it’s like the book coming alive in your classroom. It happened just the other day, and I didn’t even expect it! Students were assigned a problem from our curriculum and grouped randomly as is a common practice in thinking classrooms. As I monitored, a multitude of methods for solving the problem became apparent and I became ebullient that the dance that day was indeed happening. Students discussed reasoning their way to a solution, used proportional relationships they studied last year and equations from the previous unit. Finally, I grouped up two students I saw using the same method of setting equations equal to each other. A few years of mathematical knowledge and the ability to “reason abstractly and quantitatively” (Mathematical Practice 2) came alive as the students presented their processes and solutions to an entirely new and novel situation.
Risking failure and considering alternatives are the kinds of skills students will need to face problems that we can’t even imagine will face us as a society and them as individuals in the future. We give them intentionally-sized opportunities to work on those skills every day, in addition to giving them rich mathematical problems with which to wrestle. The dance they do with mathematics in middle school at Mack readies them for future success in mathematics at all levels.
P.S. > You can read more about the entire process of our math program adoption here under “An Impressive Snapshot of our Math Curriculum Improvement” red button.