Guided by the TERC Investigations program, Brookwood’s Lower School math curriculum allows children to develop a true conceptual understanding of math.
“There is an emphasis on building conceptual understanding before requiring students to memorize facts,” says Head of Lower School Nancy Evans. “Through an explanation of process and a balance of understanding, we want students to understand why we are doing what we are doing and what it means.”
Nancy says there are six guiding principles of the curriculum:
According to Elise Koretz, Grade 2 teacher and one the of the division’s Math Leaders, “children use manipulatives to build concrete understanding of concepts and they develop multiple strategies for solving any given problem. Our curriculum meets the needs of each learner by allowing him or her to solve problems in ways that make sense to his or her understanding at any given time. The teacher then helps each student move to more sophisticated, efficient strategies as he or she is developmentally ready, continually moving from the concrete to the more abstract.”
In the well-sequenced program, children begin by focusing on counting and building a foundation for understanding the number system. Elise explains, “They have repeated practice hearing and using the counting sequence in many different contexts. They learn how to connect number names with the written numbers and with the quantities they represent. They count sets of objects and make equal sets, learning to count each object once and only once and to develop a system that allows them to keep track of what they have already counted. In the early grades, they develop visual images for quantities up to 10.”
From that spring board, young students move on to developing an understanding of addition and subtraction; work on collecting, sorting and interpreting data by conducting surveys, deciding how to record responses and count and make sense of the results; begin to understand length and linear measurement; build a foundation for algebraic thinking by identifying attributes of objects in a pattern so they can construct, describe, extend, and determine what comes next in repeating patterns; and engage in geometry work that builds on their knowledge of shapes in order to develop their spatial sense and deepen their understanding of two-dimensional and three-dimensional shapes.
The Math Leaders team, comprising one teacher from each grade, has proved a very effective divisional group, strengthening the Lower School team’s math instruction. The teachers meet regularly to discuss “the important work children are doing at each grade level and to share strategies that work well for reaching a variety of learners. We discuss benchmarks, looking at ways to teach a concept differently or additional resources that allow for extra practice. We discuss ways to support learners that need additional practice, as well as ways to extend learners,” Elise says.
Teachers may be leading the classroom but they also play another important role within the Investigations program. Nancy says, “The curriculum focuses on the teacher as a learner as well as the students as learners. The teachers are constantly learning about each child’s understanding along with the students learning the curriculum.”
Math Leaders Jeff Wilfahrt, Grade 1 teacher, and Moira Smith, Grade 3 teacher, attended the “Promoting Mathematical Discourse” conference in January. “We (teachers) are really conductors in mathematical discourse, carefully orchestrating the conversation by listening in on small group conversations, zeroing in on the salient point of the lesson, and choosing speakers whose strategies can guide other learners. We saw that this doesn’t always mean choosing the child with the correct strategy, but the one who can represent the direction in which we would like the conversation to go. The teacher’s role in mathematical discourse is not reactive, but proactive,” they say.
Moira adds that by third grade her students “have a wealth of mathematical tools in their toolbox. They are honing their own strategies and styles, while at the same time becoming more curious about what their classmates are doing and thinking. These qualities set the stage for mathematical discourse, where students share and question and consider and repeat and agree and DISagree. I feel deep satisfaction in watching my students engage in this rich dialogue. It’s a bit like being an active, orchestrative fly on the wall.”
Jeff concurs, saying his students bring a great deal of knowledge to the classroom. “Young students have a great deal of practical, mathematical skills based on the problem-solving they do every day and look for guidance on how to make their strategies more effective and reliable and how to convert their understanding to the language of mathematics. Although they don’t know the structure of a division problem, they know how to divide a whole into equal shares. That’s where the excitement – and the challenge – come into play when teaching math.”