Constructivism versus Cognitive Load Theory: In Search for an Effective Mathematics Teaching

Upu, Bustang · 2021 · education · 10.48550/arxiv.2108.04796 · record upu2021-constructivism-versus-cognitive-lo
tag layer · index · concepts · authors · עברית
Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. This is an argumentative essay with no new data, so method 'review' is the closest fit; the quoted method sentence is from the abstract's description of what the paper does. The only self-stated limitation is the single word 'limited' inside a results sentence, which is thin - the paper never discusses selection of the reviewed evidence or counter-evidence it omits. Extraction artefacts preserved verbatim: the ResearchGate cover page precedes the text, the target of the first relation reads 'Kirschner et al’s' without a closing period in the source, and 'Hmelo- Silver' carries a line-break hyphen plus space. The record's dual first-person voice ('we present' in the abstract, 'I argue' throughout) is a source inconsistency the facets cannot capture. 2026-08-14 schema-0.3 pass: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node.
This record’s own method is review, and the tags below follow from that. A review’s findings, quantities and statistics are things stated IN this paper, and some of them report results obtained elsewhere. No tag on this page names a different author. Measured across every review in this corpus, 81% of a review’s tags carry no citation at all — most of them are the review speaking. The corpus does not adjudicate the rest: read an unmarked tag as a claim this paper makes, not necessarily one it made first.
How to read this page. The article itself is not reproduced here — this paper is not cleared for redistribution, so what follows is the tag layer alone. The evidence sentences are withheld with the article. The table at the foot lists every tag the record carries; each row names the facet it belongs to, and the whose words column says whether the tag records the paper's own wording or the tagger's sentence about the paper. Every tag links to each other paper in the corpus carrying it. The machine-readable edition of the same thing is the TEI file beside this one, where the tags live in standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.
Other fields define these differently the same word, defined another way in another discipline
working memory 4 fields

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 5 concept tags on this paper, all 5 are grounded in a quoted sentence.
constructivism minimally guided instruction cognitive load theory scaffolding working memory Scaffolding lowers cognitive load by structuring the task so learners attend only to the parts relevant to the learning goals, which is why constructivist teaching does not overload working memory long-term memory intrinsic cognitive load extraneous cognitive load germane cognitive load constructivist theory review

Legend

relation to other workclaim_relationshow this paper stands to another: agrees, contradicts, extends, qualifies
claim typeclaim_typethe shape of the claim: existence, mechanism, method, critique, prediction, null
concept edgeconcept_edgesan asserted relation between two concepts, with the sentence asserting it
conceptconceptsan idea the paper works with, quoted where the paper uses it
content tagcontent_tagsa finding, definition, quantity, statistic or variable named in the paper
limitationlimitationswhat the paper says its evidence cannot support
mechanismmechanismshow the reported effect is said to come about
methodmethodhow the paper produced its evidence
phenomenonphenomenonthe effect or regularity under study
sensesensesa distinct use of a term, quoted where the paper fixes it

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at https://doi.org/10.48550/arxiv.2108.04796. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 2 · claim_type 1 · concept_edges 1 · concepts 5 · content_tags 16 · limitations 5 · mechanisms 1 · method 1 · phenomenon 1 · senses 3

Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 1 relation here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

This record holds no controls. A layer is empty when the tagger recorded nothing in it — which is not the same as the paper having nothing to record.

facettagfieldconf.whose words
claim_typecritique
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claim_typethe paper's words
phenomenonconstructivist instruction versus cognitive load in mathematics teaching
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phenomenonthe paper's words
methodreview
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also in: review
methodthe paper's words
mechanismsmechanisms
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
mechanisms[0]the tagger's words
limitationsThe author characterises the review of constructivist research as limited in scope.
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limitations[0]the tagger's words
limitationsThe empirical dispute rests on a prior question of naming: whether one label covers the other.
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what this limits: the claim that constructivist teaching is or is not effective: the author argues these approaches cannot be equated with minimally guided instruction, so the two sides of the dispute are not necessarily discussing the same class of teaching
limitations[1]1.0the tagger's words
limitationsThe contradicting result is about a different outcome from the one the original claim measured.
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what this limits: a comparison of direct instruction against constructivist approaches: the opposing finding concerns robust acquisition and maintenance of knowledge over time, which is not the outcome the efficacy claim was made about
limitations[2]1.0the tagger's words
limitationsThe theory on the other side of the argument rests on a stated assumption about cognitive architecture.
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what this limits: any prediction drawn from cognitive load theory here: it is based on the assumption that human cognitive architecture can process only a limited amount of information in working memory in a given time
limitations[3]1.0the tagger's words
limitationsThe paper argues from other people's studies rather than from evidence gathered for it.
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what this limits: the support offered here for constructivist approaches: the author discusses guidance and evidence drawn from published studies to argue these approaches cannot be categorised as minimally guided instruction, rather than reporting a new study
limitations[4]1.0the tagger's words
conceptsconstructivism
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concepts[0]the paper's words
conceptsminimally guided instruction
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concepts[1]the paper's words
conceptscognitive load theory
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concepts[2]the paper's words
conceptsscaffolding
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
also in: scaffolding
concepts[3]the paper's words
conceptsworking memory
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concepts[4]the paper's words
sensesconstructivism vs minimally guided instruction - THE IDENTIFICATION THE WHOLE DISPUTE TURNS ON: one side treats constructivist teaching as an instance of minimally guided instruction and attacks it on that basis, and this author denies the equation, so both sides can be right about different classes of teaching
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[0]1.0the tagger's words
sensesworking memory and long-term memory - TWO DEFINITIONS, BOTH ATTRIBUTED: the first is the memory used for all conscious activities and the only one that can be monitored, the second a large and relatively permanent store, and both are given on the authority of named authors rather than argued for here
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senses[1]1.0the tagger's words
sensesscaffolding - DEFINED BY CITATION: the process by which a teacher or more knowledgeable peer alters the learning task so the learner can accomplish what would otherwise be out of reach, attributed to a specific author and year rather than stipulated
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senses[2]1.0the tagger's words
claim_relationscontradicts → Kirschner, Sweller and Clark (2006)
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claim_relations[0]the tagger's words
claim_relationsbuilds-on → Hmelo-Silver, Duncan and Chinn (2007)
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claim_relations[1]the tagger's words
concept_edgesconstructivism —distinct-from→ minimally guided instruction
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strength of the relation: 1
concept_edges[0]the tagger's words
content_tagsThe paper argues that constructivist approaches allow flexible adaptation of guidance and so fit how cognitive structures are organised.
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content_tags.findings[0]the tagger's words
content_tagsIts concluding claim is that scaffolding is what makes constructivist approaches compatible with human cognitive architecture, because scaffolding reduces working memory load.
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content_tags.findings[1]the tagger's words
content_tagsConstructivist approaches such as problem-based and inquiry learning supply learners with scaffolding covering both how to do the task and why it should be done that way, so learners are not left to construct everything alone.
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content_tags.findings[2]the tagger's words
content_tagsReviewing the evidence, the paper concludes the claim that constructivist approaches do not work is not well supported and that evidence points the other way.
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content_tags.findings[3]the tagger's words
content_tagsConstructivism is a general theory of learning, while Realistic Mathematics Education is a theory of learning and instruction specific to mathematics.
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content_tags.findings[4]the tagger's words
content_tagsThe paper does not claim that constructivist approaches are better than other instructional guidance such as direct instruction.
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content_tags.findings[5]the tagger's words
content_tagsminimally guided instruction
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content_tags.definitions[0]the tagger's words
content_tagsscaffolding
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also in: scaffolding
content_tags.definitions[1]the tagger's words
content_tagsworking memory
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content_tags.definitions[2]the tagger's words
content_tagslong-term memory
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content_tags.definitions[3]the tagger's words
content_tagscognitive load theory
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content_tags.definitions[4]the tagger's words
content_tagsintrinsic cognitive load
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content_tags.definitions[5]the tagger's words
content_tagsextraneous cognitive load
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content_tags.definitions[6]the tagger's words
content_tagsgermane cognitive load
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content_tags.definitions[7]the tagger's words
content_tagsconstructivist theory
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content_tags.definitions[8]the tagger's words
content_tagsfive to nine items — Working memory capacity for not-previously-learned information, the limit the paper reasons from (attributed to Miller, 1994)
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content_tags.quantities[0]the tagger's words

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