Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge:Why the conjunction is important for teachers

Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge:Why the conjunction is important for teachers Hurrell

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Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge:Why the conjunction is important for teachers 2021 Australian Journal of Teacher Education 10.14221/ajte.2021v46n2.4 hurrell2021-conceptual-knowledge-or-procedural hurrell2021-conceptual-knowledge-or-procedural.txt, the project's staged copy fbd2a85cf97d21a23a47d8e8ea93c21ec9514e7f open-access education

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them critique Quotation withheld because this record is not cleared for redistribution. conceptual and procedural knowledge in mathematics teaching Quotation withheld because this record is not cleared for redistribution. review review Quotation withheld because this record is not cleared for redistribution. mechanisms once procedures have been memorised and practised without understanding, students lose the motivation to look for their meaning, which is why a procedure-first sequence blocks the conceptual half of the iteration Quotation withheld because this record is not cleared for redistribution. mechanisms acquiring procedural knowledge reduces the load on working memory, and the freed capacity can then be spent on building conceptual knowledge Quotation withheld because this record is not cleared for redistribution. mechanisms a powerful earlier understanding (e.g. reading the equals sign as 'give me an answer') obtrudes into later learning and obfuscates the teaching that follows Quotation withheld because this record is not cleared for redistribution. The paper's claim that misunderstanding of the two knowledge forms is widespread among teachers rests on anecdote rather than on collected data. Quotation withheld because this record is not cleared for redistribution. The paper concedes that the concept-first iterative approach it endorses has little empirical evidence behind it. Quotation withheld because this record is not cleared for redistribution. The dichotomy the paper's title turns on is reported as having been declared fundamentally unsound, on the ground that procedures are conceptual in nature. what this limits: the conceptual/procedural split as a sound partition: the paper reports Kieran declaring the dichotomy fundamentally unsound because procedures are conceptual during elaboration Quotation withheld because this record is not cleared for redistribution. Treating the two knowledge forms as two ends of a continuum is called false; the paper holds that either can occupy different positions depending on the situation. what this limits: a placement of a task or a learner at one end of the conceptual/procedural continuum: the paper calls that positioning false, since either can occupy different places depending on the situation Quotation withheld because this record is not cleared for redistribution. Two cells of Star's own matrix have no worked exemplars - the paper reports that deep-procedural and shallow-conceptual knowledge are hard even to illustrate. Quotation withheld because this record is not cleared for redistribution. conceptual knowledge conceptual knowledge Quotation withheld because this record is not cleared for redistribution. procedural knowledge procedural knowledge Quotation withheld because this record is not cleared for redistribution. concept concept Quotation withheld because this record is not cleared for redistribution. Relational Knowledge Relational Knowledge Quotation withheld because this record is not cleared for redistribution. routine expertise routine expertise Quotation withheld because this record is not cleared for redistribution. adaptive expertise adaptive expertise Quotation withheld because this record is not cleared for redistribution. CRA CRA Quotation withheld because this record is not cleared for redistribution. CPA CPA Quotation withheld because this record is not cleared for redistribution. Declarative Declarative Quotation withheld because this record is not cleared for redistribution. Instrumental Instrumental Quotation withheld because this record is not cleared for redistribution. conceptual knowledge → procedural knowledge THE DISTINCTION ITSELF IS DECLARED UNSOUND, and no type can say that. Kieran (2013) 'declared the dichotomy between them to be fundamentally unsound'. 'distinct-from' asserts the two ARE distinct; there is no way to record a cited author denying that the boundary can be drawn - the same gap quine1951 sits in. Quotation withheld because this record is not cleared for redistribution. procedures → concepts THE CATEGORIES INTERPENETRATE RATHER THAN RELATE: 'Quotation withheld'. Not 'is-a', not 'part-of', not 'same-as' - a claim that membership is temporary and phase-dependent, which no edge type carries. Quotation withheld because this record is not cleared for redistribution. concept - a mental representation embodying the essential features of an object, situation or idea, whose function is to let phenomena be classified as belonging together or not Quotation withheld because this record is not cleared for redistribution. procedural knowledge - characterised by some researchers as the capacity to follow steps in sequence to reach a mathematical goal Quotation withheld because this record is not cleared for redistribution. the conceptual/procedural relation - bi-directional but NOT always symmetrical, with conceptual knowledge at times the stronger support Quotation withheld because this record is not cleared for redistribution. conceptual/procedural - a single distinction carrying eight different name pairs across eight traditions (Skemp's instrumental/relational, Tulving's episodic/semantic, Anderson's procedural/declarative...), which the paper asserts are the same division Quotation withheld because this record is not cleared for redistribution. deep - in Star's matrix a property that BOTH knowledge types can have, not a property of conceptual knowledge alone Quotation withheld because this record is not cleared for redistribution. adaptive expertise - both knowledge types deep AND applicable to unfamiliar situations; routine expertise is the same knowledge without the transfer Quotation withheld because this record is not cleared for redistribution. contradicts → the belief, held by the experienced teachers the author surveyed, that conceptual and procedural knowledge are mutually exclusive and that conceptual is always the more necessary note: The paper's target is a belief held by practitioners rather than a published claim, and it is quoted from the author's own observation of them. Quotation withheld because this record is not cleared for redistribution. conceptual knowledge —renamed-across-fields→ Relational Knowledge conceptual knowledge Relational Knowledge strength of the relation: 0.9 · note: An in-text renaming attributed to a named source: 'notably characterised by Skemp, 1978, as Relational…'. Quotation withheld because this record is not cleared for redistribution. conceptual knowledge —renamed-across-fields→ Declarative conceptual knowledge Declarative strength of the relation: 0.8 · about this quote: PAGE FURNITURE IS SPLICED INTO THE 'evidence' QUOTE - the journal's page footer and a page number, between the sentence and Table 1: 'Vol 46, 2, February 2021 60 Australian Journal of Teacher…'. The words on either side of it were never continuous on the page; read the quote with it deleted. · note: TABLE 1 IS THIS PROJECT'S THESIS WITH A TABLE. Eight research traditions across 1976-1984 - Skemp, Piaget, Gelman & Gallistel, Resnick, Tulving, Anderson, Van Lehn, Baroody - each name the SAME two categories differently, and the paper says so outright: 'regardless of the labels, the divisions regarding the types…'. The claim of sameness is the paper's, not the tagger's. Quotation withheld because this record is not cleared for redistribution. procedural knowledge —renamed-across-fields→ Instrumental procedural knowledge Instrumental strength of the relation: 0.8 · about this quote: PAGE FURNITURE IS SPLICED INTO THE 'evidence' QUOTE - the journal's page footer and a page number, between the sentence and Table 1: 'Vol 46, 2, February 2021 60 Australian Journal of Teacher…'. The words on either side of it were never continuous on the page; read the quote with it deleted. · note: TABLE 1 IS THIS PROJECT'S THESIS WITH A TABLE. Eight research traditions across 1976-1984 - Skemp, Piaget, Gelman & Gallistel, Resnick, Tulving, Anderson, Van Lehn, Baroody - each name the SAME two categories differently, and the paper says so outright: 'regardless of the labels, the divisions regarding the types…'. The claim of sameness is the paper's, not the tagger's. Quotation withheld because this record is not cleared for redistribution. CRA —same-as→ CPA CRA CPA strength of the relation: 0.9 · note: 'also referred to as' - one instructional sequence, two acronyms live in the same literature. Quotation withheld because this record is not cleared for redistribution. adaptive expertise —contrasted-with→ routine expertise adaptive expertise routine expertise differs in: whether the knowledge transfers to unfamiliar situations - routine expertise applies to familiar ones only · strength of the relation: 0.8 Quotation withheld because this record is not cleared for redistribution. Experienced primary and lower-secondary teachers believed that conceptual and procedural knowledge are mutually exclusive and that conceptual knowledge is always the more appropriate thing to teach. Quotation withheld because this record is not cleared for redistribution. Procedural and conceptual knowledge both matter and each strengthens the other. Quotation withheld because this record is not cleared for redistribution. Either procedural or conceptual knowledge can be shallow or deep. Quotation withheld because this record is not cleared for redistribution. The synthesis endorses teaching conceptual knowledge before procedural knowledge in most cases. Quotation withheld because this record is not cleared for redistribution. Students are likelier to develop conceptual knowledge if they begin with it and then move to procedural knowledge. Quotation withheld because this record is not cleared for redistribution. The empirical support for concept-first is that students taught conceptually and then procedurally outperform students taught procedurally and then conceptually. Quotation withheld because this record is not cleared for redistribution. Sequencing arithmetic problems to expose conceptual relationships was efficacious; in random order the effect was not seen. Quotation withheld because this record is not cleared for redistribution. The conceptual-procedural relationship is bi-directional but not always symmetrical: at times conceptual knowledge supports procedural knowledge more strongly than the reverse. Quotation withheld because this record is not cleared for redistribution. The paper's answer to its own title is that teachers need conceptual AND procedural knowledge, with the timing and placement left to the teacher's professional judgement. Quotation withheld because this record is not cleared for redistribution. Kieran (2013) declared the conceptual-procedural dichotomy fundamentally unsound. Quotation withheld because this record is not cleared for redistribution. concept concept Quotation withheld because this record is not cleared for redistribution. conceptual knowledge conceptual knowledge Quotation withheld because this record is not cleared for redistribution. procedure procedure Quotation withheld because this record is not cleared for redistribution. procedural knowledge procedural knowledge Quotation withheld because this record is not cleared for redistribution. routine expertise routine expertise Quotation withheld because this record is not cleared for redistribution. adaptive expertise adaptive expertise Quotation withheld because this record is not cleared for redistribution. cognitive interference cognitive interference Quotation withheld because this record is not cleared for redistribution. attitudinal interference attitudinal interference Quotation withheld because this record is not cleared for redistribution. iterative view iterative view Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.14221/ajte.2021v46n2.4.