Rather than a focus on memorizing teacher-taught algorithms to arrive at correct answers, today’s math standards focus on computational fluency, conceptual understanding, and application (problem solving). So, how do we shift the focus from correct answers to mathematical understanding and application? How do we make mathematics meaningful for our students?
Consider the role of context to support sense-making. How is student learning impacted when we teach through a context?
The Power of Problems
Rather than manipulating numbers and symbols to get answers, word problems allows students to identify what those numbers and symbols mean. Rather than 3 + 5, we may be talking about 3 chocolate cookies and 5 peanut butter cookies on a plate? How many cookies? Students now see a situation that illustrates the operation of addition.
Rather than 3 x 1/2, we may be talking about making 3 batches of pancakes which each need 1/2 cup of sugar. How much sugar is needed? The problem situation illustrates the mathematics and helps students make sense of repeated addition or multiplication.
Word problems are a simple and effective way to bring meaning to equations. Beginning a lesson with a problem, rather than an equation helps students make sense of the equation and strengthens their problem-solving skills as they continually see the connections between situations and equations.
The Power of Stories
Another option for providing context to math lessons is the integration of children’s literature and mathematics. Beginning a lesson with a story, examining the situations in the story, and relating those situations to math skills and concepts is a powerful tool for helping students make sense of mathematics.
I Love Saturdays y domingos by Alma Flor Ada tells the story of a child’s fun days spent with two different sets of grandparents. So much math can be explored through the situations in the story whether it is about the various fish they spy at the seashore, the types of animals they see at the circus, the number of owls in Grandma’s owl collection, or the items that might be in the piñata. Students are immediately engaged by the story, then we design tasks inspired by the characters and events. Students explore the mathematics through the story context.
Even older students enjoy children’s literature and a simple read aloud can spur observations and discussions about a wealth of math concepts. Consider The Patchwork Path: A Quilt Map to Freedom by Bettye Stroud, the story of a young girl’s path to freedom on the underground railroad. Hannah’s Mama stitched a quilt and the patterns on its squares provide clues that Hannah and her Papa use to guide their path. The story is exciting and inspiring and includes images of the quilt squares. After honoring the book with discussions about the story, students might explore the quilt squares through a mathematical lens, looking for ways to describe the designs using what they know about attributes of shapes. Their understanding of two-dimensional shapes, angles, lines, and symmetry provides them with the words they need to describe the quilt squares.
Exploring math in context immediately engages students in lessons and allows them to make sense of the mathematics as they connect abstract ideas to the word problems or stories. It is a powerful tool for making math meaningful to all students.