Sealey's layered reference frame for Riemann sum and definite integral understanding¶

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Description¶

The article synthesizes Sealey's (2014) framework characterizing students' understanding of Riemann sums and the definite integral. "Sealey presents a reference frame for understanding the structure of the Riemann integral that distinguishes four layers: Product, Summation, Limitand Function." The layers correspond to the operations in calculating the integral, with the Product layer multiplying a rate f(xi) by a difference Δx. From her experimental research Sealey added a preliminary Orienting layer for visualizing the situation and recognizing quantities.

Design Implications¶

Context¶

Requirements¶

• The conceptualization of the product f(x)Δx is identified as the most complex part of the integral problem-solving process despite the simplicity of the operations

Constraints¶

Target Learners¶

• students learning the definite integral

Target Learning Goals¶

• understanding the structure of the Riemann integral

Claims¶

Related Elements¶

Examples¶

• Use sequences of problem-situations to progressively contextualize and develop mathematical comprehension of calculus concepts

Key Sources¶

• Burgos, M., Bueno, S., Pérez, O., & Godino, J. D. (2021). Onto-semiotic complexity of the Definite Integral. Implications for teaching and learning Calculus. REDIMAT – Journal of Research in Mathematics Education, 10(1), 4-40. https://doi.org/10.17583/redimat.2021.6778