Mathematical Representation and Schema-Based Instruction for Students with Learning Difficulties — TEI-tagged view
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. TITLE MISMATCH: the queue metadata gives the title as 'Mathematical Representation and Schema-Based Instruction for Students with Learning Difficulties', but the article text itself is titled 'Is Mathematical Representation of Problems an Evidence-Based Strategy for Students With Mathematics Difficulties?'. All facets follow the article text, not the metadata. Claim type is 'method' because the conclusion certifies an instructional strategy as an evidence-based practice; a case could be made for 'existence' (the effect is real), but the article's own result sentence is framed around the practice meeting evidence criteria. The 'replicates' relation is the paper's own word 'support the results of prior research' applied to a synthesis rather than a re-run study. The extraction duplicates one sentence ('When instructional strategies include opportunities for students to interact with the objects...') and scrambles the Table 1-3 numeric columns; no facet depends on those regions. The paper also reports that under the competing CEC (2014) standards none of the studies qualify, which is a methodological caveat about evidence standards rather than a limitation of this review's own design, so it was not recorded as a limitation. 2026-08-19 and 2026-08-25 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. Update, 15 September 2026: EXCEPTION, measured with the merge gate's own predicate (Paper.locate): 3 quote(s) on this record are not found as one exact string in the current staged text - content_tags.definitions[0].evidence, content_tags.findings[0].evidence, content_tags.statistics[1].evidence. The sentence above does not hold for them as written. Where a row records why - the quote is grounded in another copy of the paper, joins two passages with an ellipsis, or differs from the staged text by extraction noise - that note stays on the row.
3 quotes on this page break a word across a line. The PDF this text was extracted from hyphenated those words at the end of a printed line — adversar- ial, repre- sentations — and the extractor kept the hyphen and the space. The quotes keep them because a quote is reproduced exactly or it proves nothing: the break is the typesetter’s, not the author’s. A search of this page will not find the affected words.
This record’s own method is systematic-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.
2 quotes on this page were cut from a different copy of this article. This project holds two extractions of this paper: the plain text every other quote here is anchored in, and the publisher’s own HTML edition, which we are not licensed to republish. They are verbatim in the second and cannot be found in the first — not because the tagging is wrong, but because the extraction damaged the passage: a page number dropped into the middle of a number, a formula moved out of its sentence, a ligature where two letters belong. The record names the copy for each one. The quote is the paper’s; the extraction is not.
Full text not reproduced here. We could not establish a licence for this paper’s text, so we have chosen not to republish it. The tag layer is ours and is below; the article is at the source. Read the full paper at the source:
DOI 10.1177/0014402915625062 ·
source page.
Our tag layer for this paper
Priming analysis (Sivroni & Stark meta-disciplinary definition; cited to Sivroni et al. 2023)Three characteristics: A · association S · secondariness M · modulation
| P · prime | a primed mathematical schema/representation |
| T · target | a word problem to solve |
| B · baseline | problem-solving without schema priming |
| E · priming effect | improved problem-solving accuracy |
| A · association | congruent (positive) |
Cross-disciplinary analysiscontent-tags & facets: phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text
| phenomenon | mathematical problem representation instruction— “The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties.” |
| claim-type | method— “Results suggest that the representation of mathematical problems as a strategy is an evidence-based practice based on the criteria set by Gersten et al.” |
| method — evidence | — “The authors evaluated 25 experimental and quasiexperimental studies according to the Gersten et al. (2005) guidelines for group research studies.” |
| transfer | from cognitive psychology (cognitive load theory): schema-based instruction and mathematical representations grounded in cognitive-load theory, applied to teaching students with learning difficulties— “in the literature on cognitive load theory” | transfers[0] |
| builds-on | Gersten et al. (2005) evidence-based-practice criteria— “Results suggest that the representation of mathematical problems as a strategy is an evidence-based practice based on the criteria set by Gersten et al.” | claim_relations[0] |
| builds-on | Gersten et al. (2005) quality indicators for group research— “Therefore, our review evaluated the quality of the research and evidence base for representation of problems as a strategy for students with MD using criteria for group research proposed by Gersten et al. (2005).” | claim_relations[1] |
| replicates | Gersten, Beckmann et al. (2009); Gersten, Chard et al. (2009)— “Further, the findings that the weighted mean effect sizes of +0.62 for students with LD, +0.70 for students at risk for MD, and +0.95 for both students with LD and those at risk for MD support the results of prior research about the benefits of representations for students struggling in mathematics (Gersten, Beckmann et al., 2009; Gersten… | claim_relations[2] |
| sense | A LITERATURE GRADED AGAINST A PUBLISHED CHECKLIST, AND THE ATTRITION IS ITEMISED RATHER THAN SCORED. 25 studies reviewed; `Thirteen of the 25 studies provided strong evidence of rigorous research across the four categories of the essential QIs`; and `Only eight of the 13 studies that met the essential QIs provided evidence of meeting at least four desirable indicators to be classified as high quality.` **25 to 13 to 8**, with each drop attributable to a named criterion rather than to a composite score. That is the `tool must be checkable` principle applied to a whole field: external criteria, per-criterion grading, failures named— “Only eight of the 13 studies that met the essential QIs provided evidence of meeting at least four desirable indicators to be classified as high quality” | senses[0] |
| sense | AND THE MISSING INDICATORS ARE NAMED ONE BY ONE, WHICH IS WHAT MAKES THE REVIEW ACTIONABLE: one study `failed to provide sufficient information on teachers delivering the intervention`; of the eight high-quality studies `only five ... also documented that data collectors were blind to conditions`; only one `provided information on the quality of implementation`; and `None of the studies used excerpts from audio or videotape recordings to summarize the nature of the intervention` - a zero across all 25. A reviewer reading this knows exactly what the next study should add, which a quality SCORE would not have told them— “None of the studies used excerpts from audio or videotape recordings to summarize the nature of the intervention” | senses[1] |
| sense | THE VERDICT IS EXPLICITLY RELATIVE TO ITS CRITERIA: `Results suggest that the representation of mathematical problems as a strategy is an evidence-based practice based on the criteria set by Gersten et al.` The qualifier is inside the claim. `Evidence-based` is not asserted as a property of the practice but as the output of a named, published standard - so a reader who rejects the standard knows exactly what they are rejecting, and a different standard could give a different answer without either party being wrong about the studies— “Results suggest that the representation of mathematical problems as a strategy is an evidence-based practice based on the criteria set by Gersten et al” | senses[2] |
| control | a fixed 25th-percentile cutoff for at-risk status, with studies using a higher cutoff excluded and mixed samples required to disaggregate or be majority LD/at-risk — held — rules out that the pooled effect is diluted by studies counting higher-attaining children as at risk - the cutoff is fixed to the published convention rather than to what each study chose— “We excluded studies that used a cutoff higher than the 25th percentile to identify students at risk for MD.” | controls[0] |
| outcome (stated by the tagger, no quotation) | control — held | controls[0] |
| for which use | limitation — the strength of the review's conclusions: FUTURE RESEARCHERS [must] ADDRESS THE COMPONENTS THAT DID NOT MEET THE MINIMUM REQUIREMENTS OR WERE FREQUENTLY UNMET— “Although these findings are encouraging, it is important for future researchers to address the components that did not met the minimum requirements or were frequently unmet in this database.” | limitations[0] |
| for which use | limitation — any claim about representations specifically: THE MAJORITY OF STUDIES INCLUDED REPRESENTATIONS AS PART OF MULTICOMPONENT INTERVENTIONS, MAKING IT DIFFICULT TO DETERMINE THE INFLUENCE OF REPRESENTATIONS— “A caveat to the findings is that the majority of studies included representations as part of multicomponent interventions, making it difficult to determine the influence of representations per se.” | limitations[1] |
| for which use | limitation — any attribution of the outcome to a particular element: IT IS NOT CLEAR WHICH ELEMENT OR COMBINATION OF ELEMENTS WAS RELATED TO THE OUTCOME— “The specific elements in the interventions that included representations varied across studies, and it is not clear which element or combination of elements was related to the outcome.” | limitations[2] |
| for which use | limitation — any implementation guidance: THE CONDITIONS UNDER WHICH THE PRACTICE OF REPRESENTING PROBLEMS IS EFFECTIVE WAS ALSO NOT CLEAR— “The conditions under which the practice of representing problems is effective was also not clear.” | limitations[3] |
| replication | untested |
| limitation | some methodological quality components were unmet across the reviewed studies, to be addressed by future research— “Although these findings are encouraging, it is important for future researchers to address the components that did not met the minimum requirements or were frequently unmet in this database.” | limitations[0] |
| limitation | Representations were bundled into multicomponent interventions, so their independent contribution cannot be isolated.— “A caveat to the findings is that the majority of studies included representations as part of multicomponent interventions, making it difficult to determine the influence of representations per se.” | limitations[1] |
| limitation | Which intervention element drove the outcomes is unknown because elements varied across studies.— “The specific elements in the interventions that included representations varied across studies, and it is not clear which element or combination of elements was related to the outcome.” | limitations[2] |
| limitation | The conditions under which the practice works were not established.— “The conditions under which the practice of representing problems is effective was also not clear.” | limitations[3] |
Content tagscontent-observations: finding · quantity · variable · definition · key-term — grounded in the full text
| finding | Representation of problems as a strategy is an approach for improving the mathematics achievement of students with mathematics difficulties.— “for representations to be effective, teach- ers should provide high l... an approach for improving the mathematics achievement of students with MD is representation of problems as a strat- egy” [checked against the archived source, not this rendering] | content_tags.findings[0] |
| not machine-vouched | finding — declared-ellipsis - An elided quote: the dots ('...') mark where words were left out, and the first part stops mid-word ('high l...'). The quote keeps two line-break hyphens from the web page we fetched ('teach- ers', 'strat- egy'); the text we tag against prints those words whole. The second part also leaves out one word without marking it: the paper has 'An effective approach', the quote 'an approach'. | content_tags.findings[0] |
| finding | Use of visual representations yielded an effect size of 0.46 for teachers and students.— “an effect size of 0.46 for teacher and student use of visual representations” | content_tags.findings[1] |
| quantity | 0.46 effect size — effect size for teacher and student use of visual representations— “an effect size of 0.46 for teacher and student use of visual representations” | content_tags.quantities[0] |
| variable | mathematics achievement (dependent)— “improving the mathematics achievement of students with MD” | content_tags.variables[1] |
| definition | representation— “Representations refer to any configuration of char - acters, images, or concrete objects that symbolizes an abstract idea (Goldin & Kaput, 1996)” [UNVERIFIED AGAINST THE STAGED TEXT] | content_tags.definitions[0] |
| evidence status note | definition — marked quote-not-in-current-staged-text - today's merge gate would REFUSE this quote: Paper.locate() does not find it in the current staged text. | content_tags.definitions[0] |
| not machine-vouched | definition — not-in-our-copy - The quote is in the original page we fetched for this paper ('fulltext.html'), but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside. This body carries no measurable character damage at all. | content_tags.definitions[0] |
| definition | learning disabilities— “Students with learning disabilities (LD) and those at risk for mathematics difficulties (MD)” | content_tags.definitions[2] |
| definition | mathematics difficulties— “Students with learning disabilities (LD) and those at risk for mathematics difficulties (MD)” | content_tags.definitions[3] |
| key-terms | mathematics, students, representation, schema, instruction, learning, disabilities, interventions, achievement |
Conceptsterms this paper carries, each with the sentence it was cut from — the layer that joins one paper to another. Terms with no quote yet are on
CONCEPTS.html.
| concept | quality indicators — not defined in this paper's own words; AN EXTERNAL, PUBLISHED CHECKLIST used to grade a literature - Gersten et al.'s (2005) criteria, split into ESSENTIAL and DESIRABLE, so a study can pass the floor and still fail to be high quality— “The focus of our review was to evaluate the body of research on representation of problems as a strategy for students with MD by applying the quality indicators and standards for evidence-based practices proposed by Gersten et al” | concepts[7] |
| concept | evidence-based practices — not defined in this paper's own words; the verdict the whole exercise is aimed at, and the paper's point is that it is a CONCLUSION FROM STATED CRITERIA rather than a summary judgement - the standards are named, published and someone else's— “The focus of our review was to evaluate the body of research on representation of problems as a strategy for students with MD by applying the quality indicators and standards for evidence-based practices proposed by Gersten et al” | concepts[8] |
| concept | representation — not defined in this paper's own words; the intervention under review - representing a word problem diagrammatically before solving it - and the object whose evidence base is being graded— “Results suggest that the representation of mathematical problems as a strategy is an evidence-based practice based on the criteria set by Gersten et al” | concepts[9] |
Statistics — cross-field join keysfield-invariant statistical terms, used in their statistical sense (gated on a number / symbol / test). A p-value or a standard deviation means the SAME thing in physics, biology, psychology and sociology — so these are the strongest cross-field join keys. Grounded verbatim.
| confidence-interval CI | — “A practice is deemed evidence based if there are at least two highquality or four acceptable-quality studies supporting the practice and the weighted effect size with a 95% confidence interval is significantly greater than zero; a practice is considered promising when at least two highquality or four” | content_tags.statistics[0] |
| evidence status note | confidence-interval — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[0] |
| correlation r | as written: correlated— “representations (focus on relevant data and relations in the problem) are more meaning- ful, and their use is positively correlated with successful problem-solving performance (Hegarty & Kozhevnikov, 1999).” [checked against the archived source, not this rendering] | content_tags.statistics[1] |
| not machine-vouched | correlation — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside. | content_tags.statistics[1] |
| effect-size d | as written: effect sizes | content_tags.statistics[2] |
| evidence status note | effect-size — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[2] |
| mean μ | as written: group means | content_tags.statistics[3] |
| evidence status note | mean — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[3] |
| sample-size n/N | as written: sample sizes | content_tags.statistics[4] |
| evidence status note | sample-size — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[4] |
| standard-deviation SD/σ | as written: standard deviations | content_tags.statistics[5] |
| evidence status note | standard-deviation — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[5] |
| standard-error SE | as written: Standard Errors Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[6] |
| evidence status note | standard-error — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[6] |
| statistical-significance | as written: significantly Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[7] |
| evidence status note | statistical-significance — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[7] |
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.