Advice on Differentiating Math Teaching

In this article in Teaching Children Mathematics, Katherine Gavin (a professor at the University of Connecticut) and Karen Moylan (a math consultant based in Connecticut) describe how they asked a group of primary-grade teachers what geometry concepts they taught. The kindergarten teachers said, “The names of shapes, such as square, circle, triangle, and rectangle.” The first-grade teachers said, “The names of shapes, such as square, circle, triangle, and rectangle.” And the second-grade teachers had the same goal, with cubes and spheres added to the list. All the teachers were surprised that students were getting basically the same material three years in a row. 

“[S]tudents are capable of so much more,” say Gavin and Moylan. “From our research, we have… found that students in kindergarten, first grade, and second grade can think, reason, and justify their thinking at much higher levels than is often expected of them.” But the challenge is teaching students with widely differing entering knowledge and skills – hence the need for skillful differentiation. Some suggestions:

• Select an appropriate task. “Make sure that what you differentiate is indeed worthy,” say Gavin and Moylan. “Teachers often take whatever task is at hand and think about how to offer different experiences to students when, in fact, some tasks may not require this effort.” Differentiation is most appropriate with material that is truly new to students – for example, moving kindergarten students from saying a triangle is a triangle because it looks like one to understanding that it has certain properties – it’s a closed shape with three sides and three vertices. 

• Increase expectations for all students. “Consider concepts that will require students to reach beyond their comfort level and stretch their minds,” say the authors. Classroom curriculum should be challenging for high-achieving students yet accessible to all students with appropriate help and scaffolding.

• Facilitate class discussions about the concepts. “The most exciting classes are those in which students may have some confusion and agree and disagree with one another as they try to understand the big ideas,” say Gavin and Moylan. “Such discussions not only support children in acting like mathematicians but also allow the teacher to gain insight into students’ misconceptions and ways of thinking through a problem.” In the middle of one of these all-class discussions, a student said, “I now disagree with myself!”

• Get all students communicating their thinking in writing, pictures, or diagrams. “In ways similar to the use of class discussion, evaluating individual student writing is a valuable asset for teachers in differentiating instruction,” say the authors. It gives a window into students’ thinking, especially their misconceptions. 

• Offer additional support. This might consist of the teacher dropping Hint cards on students’ desks when they are stuck, giving their thinking a little nudge by providing a definition, posing a question, or making a connection to prior learning. 

• Provide extended challenges. Gavin and Moylan suggest Think Beyond activity cards for students who enjoy extra challenges. These can be at a learning station or dropped with individual students during class.

• Use formative assessment to inform instruction. The authors suggest embedding open-ended Think Deeply questions within each lesson, helping students make sense of what’s being taught and guiding the teacher’s instructional decisions in real time. “These questions are developed as the heart and soul of the lesson,” say Gavin and Moylan, “and they focus on the essential mathematical concepts. They are also the springboard for differentiating the lesson.”

• Start small. “Choose one unit of instruction to concentrate on,” advise the authors. “You might work together with grade-level partners and a math curriculum specialist to differentiate a lesson. Try it out, and then reconvene to reflect and revise. Keep in mind that the second time around is always better. Class discussions and student writing will give you a clearer picture of students’ misconceptions and which student need more challenge.” 

“Seven Steps to High-End Learning” by Katherine Gavin and Karen Moylan in Teaching Children Mathematics, October 2012 (Vol. 19, #3, p. 184-192), http://www.nctm.org; the authors can be reached at kathy.gavin@uconn.edu and moylankg@mansfieldct.org.

From the Marshall Memo #457