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By Shannon Higa and Audra Carli
At Carey, our goal is to ensure that all students develop a strong foundation in number sense and problem solving. Research shows that strong mathematical thinking is not only built on accurate computation but on flexibility with numbers, critical thinking and articulation of process. Our new math program, Bridges Mathematics, helps us deliver a math approach that encourages inquiry, collaboration and the use of multiple strategies to solve problems. Students are supported in developing deep conceptual understanding so they can confidently apply their learning to new and complex problems.
A large focus of the Bridges Mathematics program is encouraging students to communicate their mathematical thinking and strategies. While many students come into a grade level knowing how to compute, we also spend significant time diving deeper to focus on computational fluency, flexibility of thinking, and creative problem solving. In all grades, students engage in whole-class conversations every day and individual thoughts and strategies are shared and valued. In this way, teachers are distributing knowledge not through lectures or teaching how to solve problems, but rather, through sharing mathematical authority with the students equally. In the upper grades, formal Math Forums are times when students hold their own independent conversations around different math strategies their classmates share and provide feedback on each others' thinking. In addition, on written math work, we always ask students to "show their thinking", which differs from "showing their work." In order to highlight individual strategies and to find efficient solutions, we want students to focus on mathematical flexibility and show how they make connections from one problem to another. Sometimes that thinking is with pictures, with connected equations, or through modeling.
A popular structure found in Bridges Mathematics is Work Places. In all grades, students spend 2-3 days a week engaging in these independent, partnered practice activities. During Work Places, students are given an opportunity to select a game or extension activity and to engage collaboratively. This is also the time when teachers provide differentiation by meeting with students 1:1, in small groups, playing Work Places with the students or administering oral assessments. In addition, Concept Quests and problem solving challenges are offered during Work Place time for students of all abilities. These low-floor/high-ceiling challenges are a great way to build onto foundational skills and to challenge the thinking of even our strongest mathematical thinkers and problem solvers.
While computational fluency is a priority of our math program at Carey, we do not explicitly teach or test students to memorize math facts because research has shown that teaching kids to think mathematically and develop their number sense is the only effective way to establish meaning. In literacy, reading fluency is not just a measure of the speed of words being read, but also a measure of comprehension. Similarly, computational fluency is not just about reciting solutions to memorized facts, but finding meaning and connections between facts. Memorization is void of meaning and strategy, and people (children and adults) have varying abilities to memorize. Rather, true mathematical fluency means that students have developed efficient, accurate, and flexible ways of learning. When we discuss math facts with our students, we discuss how to use our knowledge of one fact to another or how to make connections between what we know and what we are seeking to find. In the Ignite Talk, There IS a Difference, K-5 math educator Graham Fletcher breaks down the difference between memorization and from memory to show that strong fluency comes from flexibly using our memory of mathematical relationships to find new solutions.
It is our core belief that "all kids are math kids" and it is important that all students at Carey see themselves this way. Our goal is to empower our students in a positive community of mathematical learners so that learning math is a joyful undertaking. In the Bridges Mathematics program, students experience math in a very different way from what many of us remember. You won’t see timed tests, pages of repeated practice, or a focus on memorizing steps to get the right answer. Instead, students are learning to think flexibly, explore concepts deeply, and explain their reasoning, building true understanding and confidence. We’re pleased with how the Bridges Mathematics program has come to life in classrooms, and it’s been wonderful to see students so engaged and joyful about math in these first few months at Carey.
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