Building Conceptual & Procedural Thinking in Math
Whenever I talk to parents about "math these days," everyone is quick to comment on how different it seems from when we were growing up. And honestly? That's not wrong. A lot has changed!
Technology and research have allowed our thinking around math instruction to evolve in meaningful ways. We know more about how the brain processes and retains information than ever before, including how children develop number sense and come to understand complex mathematical ideas — ideas that are crucial to becoming mathematically literate citizens in our world. In addition, today's kindergartners have iPads with more computing power than the first desktop computer my family brought home when I was in 4th grade. Improvements in technology have impacted every part of our lives, and our math classrooms are no exception.
Over the past few decades, our understanding of how children learn math — and how instruction shapes that learning — has grown by leaps and bounds. We now understand that modes of instruction that prioritize fast computation and abstract execution of algorithms, while important in a historical context, ultimately deny students opportunities to build genuine understanding and mathematical reasoning. Concrete modeling, representational thinking, and abstract reasoning are all important ways of making sense of mathematical ideas, and students strengthen neural pathways when instruction draws explicit attention to the connections among these approaches.
We also recognize the importance of developing both conceptual and procedural thinking in tandem, and we've built instructional tools and strategies that support this work. In the younger grades, we spend ample time strengthening students' early numeracy — counting, grouping, subitizing (recognizing small quantities without counting), unitizing (grouping and ungrouping into tens and ones), and combining and breaking apart quantities within 20. These foundational understandings support all future math learning, so they must be solid and strong.
In the upper grades, we make intentional choices about when and how we introduce new concepts and procedures to maximize student understanding and fluency. We allow students time to develop conceptual understanding before introducing traditional algorithms, which, while efficient to execute, can often obscure or even undermine place-value concepts. Because our goal is to develop flexible, fluent problem solvers, our instructional trajectory is focused on helping students make sense of new concepts and build purposefully on what they already know.
In the first two sessions of our three-part "Math After Dark" series, we have helped parents and caregivers understand more about the what, when, how, and why of math instruction in the Lower School at Brimmer:
- What is my student being taught in math class?
- When can I expect my student to be introduced to, or to reach proficiency in, different topics?
- How does my student engage in mathematical thinking in their classroom?
- Why are these instructional methods considered most effective for students?
We hope you'll consider joining our final session on Tuesday, April 14, which will highlight the learning progression and pedagogical underpinnings for developing fractions and decimals across the elementary grades. For more information, please register here. Recordings and resources from the first two Math After Dark sessions — one on Addition & Subtraction and one on Multiplication & Division — can be found here.
Our Lower School Math Mission Statement captures our philosophy and approach to math instruction in the Lower School:
The mathematics program at Brimmer in the Lower School supports students in making real-world connections and integrating mathematical thinking across content areas through the use of concrete models, cooperative learning, and explicit and differentiated instruction. Teachers facilitate a collaborative and inclusive learning culture that fosters a growth mindset, encourages flexible problem-solving, and enables students to take risks.
By purposefully developing students’ conceptual and procedural understandings, and by supporting students in making connections both within mathematics and across the broader curriculum, our Lower School math program prepares all of our learners to live up to Brimmer's mission of becoming "informed, engaged, and ethical citizens and leaders in our diverse world."
Brimmer and May School
69 Middlesex Road
Chestnut Hill, MA 02467
617-566-7462
Chestnut Hill, MA 02467
617-566-7462
As an inclusive private school community, Brimmer welcomes students who will increase the diversity of our school. We do not discriminate on the basis of race, religion, sex, gender, gender identity and expression, disability, sexual orientation, national origin, ancestry, or any other characteristic protected from discrimination under state or federal law, in the administration of our educational policies, admissions practices, financial aid decisions, and athletic and other school-administered programs.