A reflection on the use of artificial intelligence tools for the meaningful learning of mathematics

Govender · Pythagoras · 2024 · education · 10.4102/pythagoras.v45i1.831 · record Govender2024-a-reflection-on-the-use-of-artificial-intell
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. limitations is empty deliberately: the editorial discusses limitations of AI in education (over-reliance, a diminished teacher role, the digital divide, data privacy) but never states any limit of its own argument, scope or evidence base, so nothing here would satisfy the 'the paper's own limits' rule. Claim relations is empty deliberately: every reference to prior work appears as a bare parenthetical citation supporting a general assertion, with no sentence positioning this editorial for or against a named study. The piece reports no data and no systematic search, so 'review' is the nearest method term for a discursive editorial. Claim type is 'prediction' because the load-bearing claim is about what AI can and will do for mathematics learning if implemented in a particular way. 2026-08-14, 2026-08-15 and 2026-08-26 schema-0.3 passes: 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
artificial intelligence 4 fields · large language models 2 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.

artificial intelligence generative AI large language models meaningful learning personalisation AI systems continuously re-tune problem difficulty to the individual student's measured performance, holding each learner at a level of challenge that is neither too easy nor too hard, which is the route by which personalisation is claimed to produce deeper learning immediate machine feedback lets a learner detect and repair an error while the attempt is still active, so the correct concept is reinforced instead of the mistake being consolidated meaningful learning in mathematics ChatGPT artificial intelligence (AI) review

Legend

relation to other work	`claim_relations`	how this paper stands to another: agrees, contradicts, extends, qualifies
claim type	`claim_type`	the shape of the claim: existence, mechanism, method, critique, prediction, null
concept edge	`concept_edges`	an asserted relation between two concepts, with the sentence asserting it
concept	`concepts`	an idea the paper works with, quoted where the paper uses it
content tag	`content_tags`	a finding, definition, quantity, statistic or variable named in the paper
limitation	`limitations`	what the paper says its evidence cannot support
mechanism	`mechanisms`	how the reported effect is said to come about
method	`method`	how the paper produced its evidence
phenomenon	`phenomenon`	the effect or regularity under study
sense	`senses`	a 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/10.4102/pythagoras.v45i1.831. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 4 · claim_type 1 · concept_edges 2 · concepts 5 · content_tags 7 · limitations 4 · mechanisms 2 · 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 2 relations 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.

facet	tag	field	conf.	whose words
claim_type	prediction Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_type`		the paper's words
phenomenon	AI tools in mathematics education Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`phenomenon`		the paper's words
method	review Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: review	`method`		the paper's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: AI systems continuously re-tune problem difficulty to the individual student's measured performance, holding each learner at a level of challenge that is neither too easy nor too hard, which is the route by which personalisation is claimed to produce deeper learning	`mechanisms[0]`		the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: immediate machine feedback lets a learner detect and repair an error while the attempt is still active, so the correct concept is reinforced instead of the mistake being consolidated	`mechanisms[1]`		the tagger's words
limitations	The subject is introduced by equating three different things - a field, a capability and a class of model - in the editorial's first sentence. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: any claim in this editorial about 'AI': the opening sentence treats artificial intelligence, generative AI and large language models as the same thing, so a claim about one is written as a claim about all three	`limitations[0]`	1.0	the tagger's words
limitations	The term the whole argument rests on is given only by what it exceeds, never by a criterion that would decide a case. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: a judgement that some AI-supported activity produced meaningful learning: the term is defined here as going beyond rote memorisation and mechanical application, which says what it is not	`limitations[1]`	1.0	the tagger's words
limitations	The editorial's own caveat is that the technology may displace the teacher rather than assist them. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: a recommendation to adopt these tools: the editorial names over-reliance as a concern that may lead to a diminished role for teachers, and states AI should complement rather than replace them	`limitations[2]`	1.0	the tagger's words
limitations	Access to the technology is named as a precondition for any of the claimed benefits. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the benefits claimed here for mathematics learning: they are conditional on equitable access to the technology, which the editorial states is essential for any positive impact	`limitations[3]`	1.0	the tagger's words
concepts	artificial intelligence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: artificial intelligence	`concepts[0]`		the paper's words
concepts	generative AI Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: generative AI	`concepts[1]`		the paper's words
concepts	large language models Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: large language models	`concepts[2]`		the paper's words
concepts	meaningful learning Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: meaningful learning	`concepts[3]`		the paper's words
concepts	personalisation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: personalisation	`concepts[4]`		the paper's words
senses	meaningful learning - DEFINED BY NEGATION: what it goes beyond (rote memorisation, mechanical application of algorithms) rather than by any property that would let a reader decide whether a given lesson achieved it Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[0]`	1.0	the tagger's words
senses	artificial intelligence - AS THREE NAMES FOR ONE THING: the editorial's opening sentence treats AI, generative AI and large language models as interchangeable, which is the conflation every later claim inherits Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[1]`	1.0	the tagger's words
senses	personalisation - AS THE PROPOSED MECHANISM: customised learning paths tailored to each student's strengths, weaknesses and pace, which is what the editorial means when it says AI supports meaningful learning Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[2]`	1.0	the tagger's words
claim_relations	qualifies → Grájeda et al. (2024) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: WHETHER THE TOOL BUILDS THE SKILL OR SUBSTITUTES FOR IT. 'HOWEVER, THERE ARE CONCERNS THAT OVER-RELIANCE ON AI TOOLS SUCH AS CHATGPT MIGHT UNDERMINE STUDENTS' ABILITY TO DEVELOP THEIR OWN PROBLEM-SOLVING SKILLS.' The same capability that makes the tool useful for a task is what removes the occasion to learn the task - and note that wang2024's students said this themselves, 22 of 48 unprompted, so it is reported here as a literature concern and there as a first-person one	`claim_relations[0]`	0.95	the tagger's words
claim_relations	builds-on → Grájeda et al. (2024) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: WHAT THE SAME SOURCE IS CITED FOR. Grájeda et al. supplies BOTH the list of effective-teaching components - which includes 'INCORPORATING TECHNOLOGY' - AND, two sentences later, the over-reliance concern. One citation carries the endorsement and the caution, and a reader following either citation alone gets half of what that source says	`claim_relations[1]`	0.9	the tagger's words
claim_relations	builds-on → How & Hung (2019) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: WHICH THREE THINGS ARE PUT IN ONE LIST. 'the integration of AI into education also raises Quotation withheld' - an empirical question, a distributional one and a normative one, joined by 'and' and answerable by entirely different kinds of evidence. The record's own limitation already notes access being named as a precondition for any claimed benefit	`claim_relations[2]`	0.9	the tagger's words
claim_relations	qualifies → Grájeda et al. (2024) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: WHETHER THE TOOL BUILDS THE SKILL OR SUBSTITUTES FOR IT. 'HOWEVER, THERE ARE CONCERNS THAT OVER-RELIANCE ON AI TOOLS SUCH AS CHATGPT MIGHT UNDERMINE STUDENTS' ABILITY TO DEVELOP THEIR OWN PROBLEM-SOLVING SKILLS.' The same capability that makes the tool useful for a task is what removes the occasion to learn the task - and note that wang2024's students said this themselves, 22 of 48 unprompted, so it is reported here as a literature concern and there as a first-person one	`claim_relations[3]`	0.95	the tagger's words
concept_edges	generative AI —same-as→ artificial intelligence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: generative AI · artificial intelligence	`concept_edges[0]`		the tagger's words
concept_edges	large language models —same-as→ artificial intelligence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: large language models · artificial intelligence	`concept_edges[1]`		the tagger's words
content_tags	The editorial holds that AI should complement rather than replace the teacher's role in facilitating meaningful learning. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[0]`		the tagger's words
content_tags	It argues that leaning too heavily on tools such as ChatGPT may stunt students' development of their own problem-solving skills. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[1]`		the tagger's words
content_tags	It warns that unequal access to AI tools risks widening rather than narrowing educational inequality. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[2]`		the tagger's words
content_tags	It identifies student data collection by AI platforms as an unresolved ethical and privacy problem for schools. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[3]`		the tagger's words
content_tags	meaningful learning in mathematics Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: meaningful learning in mathematics	`content_tags.definitions[0]`		the tagger's words
content_tags	ChatGPT Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: ChatGPT	`content_tags.definitions[1]`		the tagger's words
content_tags	artificial intelligence (AI) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: artificial intelligence (AI)	`content_tags.definitions[2]`		the tagger's words

Interpretive choices

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