Understanding Stewart's formal definition of the definite integral demands mobilizing a system of prior knowledge across a network of semiotic functions¶
Claim · All claims
Evidence · 1 study · theoreticalr2·q2
Currency · newest study 2021 · not yet checked against its sources · not reviewed by a person · recheck by 2026: baselines and conditions change
Subclaims¶
Reading the evidence codes
q is the design tier, i the impact, n the sample, and the kind with its r
the rigour judged within that kind: what each code means.
This claim: no standardized effect is recorded in observations/ for it yet, so no benchmark reading is possible.
q2 i? The OSA analysis of Stewart's (2016) definition of the integral as the limit of Riemann sums shows the reader must relate many object types (functions, intervals, partitions, sample points) and recognize each one's role in the definition process. → 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 · r2
Onto-semiotic analysis (type d) of the general definition in Stewart's section 5.2, decomposed into elementary practices P0–P7 grouped into epistemic configurations EC1-DG and EC2-DG (Tables 6–7), identifying the objects and interpretation, representation and definition processes each practice puts at stake.
"The subject who reads and understands the definition of definite integral (Figure 5) must mobilize a system of prior knowledge, for which he/she needs to relate the different objects involved in the practices and recognizing the role that each one plays in the definition process."
Discussion¶
Related Claims¶
- Students can apply procedural knowledge to solve integration problems but show limited understanding of basic integration concepts — 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 — related
- A clinical interviewing study investigated students' understanding of elementary calculus through tasks on integration and limits — related
- Generative learning involves mentally reorganizing and integrating to-be-learned information with prior knowledge, enabling application to new situations — a broader claim this one bears on
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
stewart-definition-prior-knowledge-demands |
title |
Understanding Stewart's formal definition of the definite integral demands mobilizing a system of prior knowledge across a network of semiotic functions |
description |
Understanding Stewart's formal definition of the definite integral demands mobilizing a system of prior knowledge across a network of semiotic functions |
status |
review |
evidence_strength |
moderate |
newest_evidence |
2021 |
recheck_by |
2026 |
generated |
by process:wiki-ingest on 2026-09-26 |
trust |
unverified — no one has confirmed this page's content |
sources |
1 — burgos-2021 |
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