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Two teams that cancel: a didactic analysis of a teaching progression for signed numbers from Grade 5 to Grade 7 — arXiv:2611.02294

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02294
License (as archived): CC0-1.0
Archived: 2026-11-03T11:39:35.028Z
SHA-256 of the archived text: e01dee13a48dede3f14b14050bc600b14047f6b55da954073e8955da6a0874f6
Stable URL of this page: https://metraipolis.com/documento/dc_0cf60eff5cf4

How to cite

Two teams that cancel: a didactic analysis of a teaching progression for signed numbers from Grade 5 to Grade 7 — arXiv:2611.02294 — arXiv (en), https://arxiv.org/abs/2611.02294 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0cf60eff5cf4 (Metraipolis archive dc_0cf60eff5cf4, sha256 e01dee13a48dede3f14b14050bc600b14047f6b55da954073e8955da6a0874f6)

BibTeX

@misc{dc0cf60eff5cf4,
  title = {Two teams that cancel: a didactic analysis of a teaching progression for signed numbers from Grade 5 to Grade 7 — arXiv:2611.02294},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02294},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0cf60eff5cf4; sha256 e01dee13a48dede3f14b14050bc600b14047f6b55da954073e8955da6a0874f6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02294. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Signed numbers make learners revise what addition, subtraction and the minus sign meant for whole numbers. This paper presents the design rationale and a critical analysis of a three-level source progression for signed numbers (Grades 5-7, nominal ages 10-13), from which French-curriculum and International Baccalaureate chapters published at this https URL are assembled. One representation is presented first and taken up throughout: an integer is drawn as a collection of positive and negative units, a positive and a negative unit forming a zero pair that leaves nothing. An integer therefore has many drawings, which makes visible the construction of the integers as classes of pairs of natural numbers. The design hypothesis is that the gesture pupils perform with the units, inserting a zero in the form a + (-a), is shared by the subtraction of a negative number, by the worked examples that accompany the 2026 French programme, and by the derivation of the sign of a product of two negatives through distributivity; the progression does not model that product, it derives it from the zero pair, a derivation that holds only if distributivity is kept. The number line supports position, order and distance; contexts provide applications. The choices are related to the epistemological obstacles described by Glaeser, to studies of counter and number-line models, including a classroom comparison in which a path model gave better results than chips, immediately and five weeks later, and to the French and IB curricula. A block-level audit of the dated source documents found the representation absent from the first level, no exercise asking pupils to draw, and the decisive subtraction never drawn; the revisions made after the audit are recorded. No empirical evaluation is reported; hypotheses for one are stated.

Tema degli esploratori: storia e filosofia della scienza (elenco arXiv math.HO, nuovi lavori del giorno).
Categorie arXiv: History and Overview (math.HO).
Pagina del lavoro: https://arxiv.org/abs/2611.02294 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:06:07.164Z dalla pagina https://arxiv.org/list/math.HO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).