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Insights In Action

Beyond Algorithms: Developing Mathematical Understanding with CTP Data

Porter-Gaud School

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Porter-Gaud School’s narrative begins with a deep truth—doesn’t most meaningful change start by asking hard questions? So the school started asking some hard questions about a pattern of lower school students performing at less-than-desired levels in the CTP Mathematics test, specifically number sense and procedural knowledge. Can students explain a concept or process to others in a manner that shows conceptual and procedural understanding? Do they understand why and how they got to their answers?

Is Porter-Gaud building math learners with flexible and deep mathematical understanding that will serve them well in the future?

The school began an exhaustive investigation to answer these questions. In addition to observing classrooms, evaluating teaching materials, and analyzing existing curriculum, they explored CTP performance data and identified relatively low content mastery among Grade 3 and 4 in Operations with Whole Numbers and in Operations with Fractions and Decimals, as well as in the process areas of Conceptual Understanding, Procedural Knowledge, and Problem Solving. Perhaps of greatest concern, they identified a similarly weak foundation in number theory when looking at PSAT results for Grade 10 and 11.

After discovering some alarming answers to their hard questions, the Porter-Gaud school immediately took action.

They implemented a variety of "number talks" and instructional rounds to improve number sense by deepening conceptual understanding that moves beyond algorithms to problem-solving. They also expanded their "math groups" program to include additional assessment tools in order to better differentiate instruction among students. The Porter-Gaud School has even begun a curriculum mapping initiative that asks all teachers to consider the essential knowledge and key skills that compose each unit of math instruction.

With ongoing guidance from Porter-Gaud's Lower School Math Specialist, Academic Dean, and Lower School Division Head, they have secured the leadership and support to ensure the consistent and meaningful execution of this action plan. The school has already begun to see a change in their math classrooms with more dynamic learning spaces where students verbalize their thinking processes, visualize math through alternative methods, and ultimately build a resilient base of conceptual understanding to support their future learning.

Commitment to excellence does indeed require one to ask the hard questions, marshal the information necessary to answer those questions, and act on the insights made possible by these analyses.

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