Onto-semiotic analysis of Starbird's intuitive integral presentation identifies five epistemic configurations of practices, objects and processes¶

Claim · All claims
Evidence · 1 study · theoretical r3 · q2
Currency · newest study 2021 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? The microscopic OSA analysis of Starbird's car-distance problem decomposes the intuitive Riemann integral meaning into five epistemic configurations (constant velocity, piecewise constant, variable velocity, space as function of time, integral as limit of sums), each with identifiable objects and processes. → Burgos 2021

Evidence¶

Burgos 2021¶

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

q2 · i? · theoretical · r3

Textual analysis (type d/e) of Starbird's (2006) presentation in section 4, using OSA tools. The authors analyze five configurations (EC1–EC5) via Tables 1–5, identifying languages, concepts, propositions, procedures, arguments and processes such as "Particularization", "Generalization" and "Algorithmization" in each.

"For the analysis, we break the process down into units (epistemic configurations), and in each one we identify the elementary mathematical practices that compose them."

Discussion¶

Related Claims¶

• Abusive generalization processes in the intuitive presentation are a source of potential semiotic conflicts — related
• Students can apply procedural knowledge to solve integration problems but show limited understanding of basic integration concepts — related
• Understanding Stewart's formal definition of the definite integral demands mobilizing a system of prior knowledge across a network of semiotic functions — related