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It is common instructional practice to introduce foundational concepts such as refraction and lenses in optics instruction beginning with a diagram and an equation, often followed by demonstrations, problem sets, and experiments. This common instructional approach is consistent with how experts understand these phenomena, with mathematical relationships deeply integrated with conceptual understanding and thus the formulas are indecipherable from the core concepts. However, many students do not see the interwoven nature of the mathematics and concepts, and instead see our pivotal mathematical relationships, such as Snell’s Law or the Lensmaker’s Equation, as black boxes that provide an answer or a formula to be memorized, but not understood. These issues are only enhanced for students exhibiting math-anxiety. In this paper, we present an approach for presenting optics concepts in a way that promotes a student’s marriage of conceptual and mathematical knowledge by re-sequencing often used instructional activities. By placing conceptual understanding in the foreground, we can provide students with a rich set of experiences around the phenomena first and then layer formal mathematics ideas on afterwards. In this way, the mathematics become a validation tool for student’s conceptual knowledge. We provide general guidelines for the adoption of this instructional approach, followed by more detailed examples of how this instructional method could be implemented for two foundational optics phenomena: Snell’s Law and the Lensmaker’s Equation.
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