A Common Language for Math
STORY BY NATAKI MCCLAIN AND JENNIFER SPRAGUE // Photo by Kathy McPherson
This year, Middle School teachers prepared for a different type of math student to enter fifth grade: one who is steeped in Bridges, a curriculum that has allowed students in the Lower School (and soon the Preschool) to speak the same, comprehensive math language. This year’s fifth-graders are the first class with fluency in a comprehensive math language and a dynamic learning process that makes math accessible to all students, regardless of their learning style. The Bridges curriculum uses varied models of instruction that allows students to learn math in individualized ways — whether that’s through direct instruction, visual models, investigative games, group or individual work.
Now in its second year of implementation in the Lower School, Bridges has been instrumental in “bridging” the gap between students’ conceptual and concrete understanding of math. For teachers, the Bridges curriculum has allowed students and teachers across the Lower School to share a similar framework, learning goals and expectations for mathematics.
“We just finished a month-long investigation in Number Corner where students use objects and information to identify patterns, analyze data or gain insights into number relationships over time using tables and graphs,” explained third-grade teacher Jeff Burch. “During that time, students were introduced to new math vocabulary and context. This will help them when we dig deeply into geometry and start working with shapes and area because these will not be new terms. They will have the background knowledge gained through these concrete math experiences and be ready to apply them in context.
“Bridges has helped me to be a better teacher,” he said, “because I am learning to look for student thinking, not just the correct answer to a problem.”
We decided to implement the curricular connections made across Lower School math classes in the Middle School. Fifth-grade math teacher Fabrice Fortin helped lay the foundation by observing Bridges math classes with us at the Lower School last spring. We visited many classrooms, but mainly focused our efforts on fourth grade. After observing classes, interacting with students and teachers and meeting with us, Middle School and Lower School math teachers applied for and received a Durham Academy summer grant.
Work from the summer grant focused on ensuring a meaningful and seamless curricular transition as students shift from fourth- to fifth-grade mathematics. We reviewed every unit of the fourth-grade Bridges program, and had discussions about the important strategies being emphasized and how those strategies could continue in fifth grade. This work provided insight into the language and approaches fourth-graders have developed, and set expectations for what rising fifth-grade students would know.
Work Places, Problems and Investigations and Math Practices are key Bridges components that translate well to Middle School, particularly teachers’ ability to differentiate within a class and the flexibility to work with students collectively, independently or in small groups.
Work Places engages students in math lessons through the playing of games. Students might use a probability game to help master and practice basic subtraction facts, with one student focusing on mastering their facts while another student, who has already mastered them, gets some extra practice while also gaining valuable experiences with probability concepts. Problems and Investigations allows the entire class to share thinking and grapple with math tasks, facilitated by the teacher. Teachers also observe students’ habits and mindsets of learning and working during Math Practices. This time is critical as students are developing fluency and practicing strategies for problem solving.
To better connect to the Bridges program, we revised the scope and sequence of the fifth-grade curriculum, which concentrates on skill work with operations and different types of numbers (whole, fractions, decimals) and culminates with geometry and percent units. One major curricular shift in sequencing was a change from teaching all of the operations related to one type of number, to separating the operations with different types of numbers. We continue to build collaborative relationships and recognize the importance of a consistent and cohesive mathematics program, and we look forward to what this deeper partnership will bring.