Differentiation is a way of teaching that addresses the diverse academic needs and learning styles of students. It requires teachers to continually assess their students and respond to their learning needs in order to plan lessons that will maximize student learning. Essentially, it provides students with equity of opportunity.
Differentiation involves planning and designing a set of interrelated activities for students to work on individually, in small groups, or as a whole class. It does not involve creating unrelated activities for students to work on individually. For example, a lesson that I taught recently in Geometry required students to classify and organize a number of different polygons. A number of my high achieving students could already complete this assignment without any support, so I gave them a challenge. Instead of creating a completely unrelated assignment for them to work on, I had them investigate the more obscure polygons and determine if certain properties applied to them. Then, I had them research the platonic solids and their unique relationship to regular polygons. This addressed the learning needs of the high achieving students without deviating too far from the theme of the lesson. In fact, the assignment enhanced their understanding of polygons.
Another area in mathematics that differentiation addresses the diverse academic needs and learning styles of students is in their approach to solving problems. Too often teachers demand that students solve a problem a particular way. This not only squelches creativity, but it establishes mathematical procedures as rote operations. Differentiating mathematics to allow students the freedom to solve problems the way with which they feel most comfortable personalizes the experience of mathematical thinking. The benefit of this type of differentiation is witnessed in the level of critical inquiry that follows. Instead of every student following the same approach, they bring a different perspective to the problem – their perspective. While at first, some students may value the perspectives of others, they soon begin to appreciate the merit and strength of each perspective, thereby adding to a more comprehensive understanding of the mathematical content.
Throughout the year, I administer a number of performance-based tasks. At first, students work through the task independently. This helps them develop their own thoughts and arrive at their own solution. Then, they partner with another student, share their ideas, and create a combined solution. If time permits, the pairs of students partner with another pair of students, share their ideas, and create a combined solution. While the students present only one combined solution per group in front of the class, they have had the opportunity to share their own ideas to a number of students and listen to other students’ ideas for solving the task. In one example, the students were given a simple linear programming task to solve. Most of the students were attempting to create and graph a system of inequalities to achieve the desired results. One student, however, chose to visually represent the problem by drawing all the components. His solution was simple, much simpler than the algebraic approach. At first, the other students tried dismissing the approach, but then they considered a new approach that combined the simplicity of the one student’s approach with the procedural fluency of the other’s algebraic approach. If I were to have had the students approach the problem the same way, the one student may have struggled with the approach, while the other students may have never taken the time to reconsider their own approaches.