Teaching for Understanding: Why Using Multiple Representations is Essential for Math Learners.
A common belief held by many people is that math is difficult to learn. Nothing could be further from the truth. In fact, each of us is a mathematician, and all students have the ability to make substantial growth in math. It is true, perhaps, that math could be very difficult to learn if all it is to students is an exercise in tedious memorization. You see, math is about much more than learning algorithms and memorizing multiplication facts and formulas.
MATH IS ABOUT THINKING.
From infancy all children wonder about the world around them, seeking out answers to problems based on the information available to them at the time. To help students grow as math thinkers, teachers and parents must get past thinking that memorizing math facts is enough. To grow and excel in math, students must be challenged at the earliest ages - even before kindergarten - to think about math critically. One of the best ways to help students develop this critical thinking ability is to expose them to multiple representations of mathematical concepts while challenging them to create representations of their own.
What would this look like for students in a middle school classroom? Given that math is about thinking, we must accept that it is also about communicating our thinking - and about challenging our thinking and questioning our approaches to problems. Consider the importance of these concepts in this brief video from Dan Meyer, doctoral fellow at Stanford University.
Recently, 8th grade math students at MSW were challenged to use multiple representations to analyze a non-linear pattern of growth. Their teachers, Nikki Kelley and Denise Wolfe, wanted students to share their thinking as they examined one another's work.
Some examples of student work from the Gallery Walk:"Students had to use various representations (tables, graphs, equations, pictures) to analyze a non-linear pattern of growth. They had to make connections between the representations with the idea that given one they should be able to create the others. The teams worked together to create the posters. Then the teams went on a Gallery Walk to analyze the other teams' posters. First they had to give feedback on the patterns the other teams created and critique the work the other teams produced. Then they had to compare and contrast the work done by different class periods that had the same rule as them. Overall the students should have a deeper understanding of multiple representations for algebraic problems." ~ Nikki Kelley
One of the best indicators of a student's math understanding is his/her ability to explain their mathematical thinking. As you sit down with your children to review their homework each night, ask them to explain their strategies for tackling problems. You'll be surprised how much you know about math and about how impressive our students are!
What's Up at West?
- 11/26 - Winter Sports Pictures at 3:45pm
- 11/27 - Students return from Thanksgiving Break
- 11/29 - Coffee with Mr. Scruci (7:30-9am at Tim Horton's)
- 11/29 - 6th grade Strings w/LHS orchestra (7:30 pm at GMSW auditorium)
- 11/30 - Progress Reports Go Home
- 12/6 - PTO meeting (7pm in GMSW library)
