Bill & Melinda Gates Foundation

Focus on Teachers: What it Means to Teach Students to Think Mathematically

August 20, 2013

A fifth-year high school math teacher at East Jessamine High School in Kentucky, Michele Honeycutt readily admits that the Math Design Collaborative (MDC) “revolutionized” her teaching.

“I used to teach math the way I learned it:  I do the procedures and then the students mimic me,” Michele explains.  “The Math Collaborative taught me how to teach so that the kids make sense of the math concepts.  Instead of listening to me talk about math, my students learn the math concepts by figuring out the problems. I provide them with guidance as they need it.”

The Math Design Collaborative began through a partnership between the Shell Centre for Mathematical Education and the College Ready Team here at the Foundation.  MDC supports teachers in implementing the Common Core State Standards in their classrooms through instructional tools and learning materials for students.  Teachers involved in MDC use a series of challenges—termed formative assessment lessons (FALs)—to engage students in a “productive struggle” with a significant math question.

As Michele suggests, the MDC tools reverse the traditional, “I do, we do, you do” instructional model. Instead of the teacher opening the class with direct instruction, students start the lesson by working on an assessment task. Students work alone and in groups as the teacher provides feedback and asks questions to check their math understanding and correct misconceptions. Rather than having students memorize steps to find an answer, the teacher supports students in using math reasoning to solve problems.  It is through this “productive struggle” with MDC’s assessment tasks that students deepen their mathematical understanding, as well as build their procedural skills.  

 Assessments are arranged in such a way that even the students who are behind can start to figure the problem out. Their re-engagement carries over to the class in general and they can build on their success.

In conversations with our team, Michele notes that the biggest change in her classroom from MDC was “seeing students who had disengaged in class, because they had been absent or had stopped paying attention, begin to re-engage with math. Math builds on itself and if a student becomes too far behind, he often becomes confused and doesn’t know what to do to catch up.  The MDC formative assessments are arranged in such a way that even the students who are behind can start to figure the problem out. Their re-engagement carries over to the class in general and they can build on their success.” 

Michele has been involved in MDC for four years and has a number of stories about individual students whose math skill, interest and belief in themselves improved dramatically through their work with the MDC assessment tasks.  One story is particularly striking.  In Michele’s words:  “I had one student who had his head down for almost a semester; I think he had a D average for the class and I just wasn’t connecting with him. When we did our first MDC formative assessment task, the class became stuck on one part of the problem.  When I called them back together as a class to discuss the issue, this student picked his head up and explained to the entire class the math concept they were missing.  From then on, he started to engage with the formative assessment tasks.  He was able to work alone on the problems, he could ask me questions when he needed to and I could give him extensions to make the challenges even more difficult.  I realize now that before we did the formative assessments, I didn’t truly understand how skilled he was in math and how much he already knew.  And, he was able to turn his grade around and pass the class.”

You can take a look at the sample MDC math assessment tasks made publicly available by the Shell Centre here.  They are designed to be “dropped in” to any math curriculum so you can select and place them throughout the year as you see fit.

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