Students can apply procedural knowledge to solve integration problems but show limited understanding of basic integration concepts¶

Claim · All claims
Evidence · 1 study · theoretical r2 · q1
Currency · newest study 2021 · not yet checked against its sources · not reviewed by a person · recheck by 2026: baselines and conditions change

Subclaims¶

q1 i? As reported in the background of a theoretical analysis of the definite integral, Serhan's (2015) study of students' conceptual and procedural knowledge of the definite integral found, coinciding with Orton (1983), that procedural skill coexists with limited conceptual understanding. → 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

q1 · theoretical analysis, reporting another study's finding · i? · no effect size · theoretical · r2

Burgos et al. is an onto-semiotic analysis of the definite-integral concept and of a mathematical text, not an empirical study of students. Its background section reports this result secondhand, citing Serhan (2015), who investigated students' conceptual and procedural knowledge using Hiebert and Lefevre's (1986) cognitive framework and Tall and Vinner's (1981) concept image/definition notions, asking which knowledge dominates and how students handle negative areas.

"The results coincide with those of Orton (1983) in that students can use procedural knowledge and solve integration problems but have a limited understanding of the integration of basic concepts."

Discussion¶

Related Claims¶

• Strategy Instruction Needs Conditional Knowledge — the general claim this finding bears on, with the studies behind it

• Understanding Stewart's formal definition of the definite integral demands mobilizing a system of prior knowledge across a network of semiotic functions — related

• Onto-semiotic analysis of Starbird's intuitive integral presentation identifies five epistemic configurations of practices, objects and processes — related
• Abusive generalization processes in the intuitive presentation are a source of potential semiotic conflicts
• Declarative knowledge dominates students' GenAI concept maps; only 9 of 64 maps integrate declarative, procedural, and conditional knowledge — related
• A clinical interviewing study investigated students' understanding of elementary calculus through tasks on integration and limits — related