Should I Use My Calculator?: Mental versus Calculation Assisted Arithmetic
Notice bibliographique
Résumé
Should I Use My Calculator?: Mental versus Calculator Assisted Arithmetic Wendy Ann Deslauriers (wadeslau@connect.carleton.ca) Clara John Gulli (cjgulli@connect.carleton.ca) Institute of Cognitive Science, Carleton University, Ottawa, ON, K1S 5B6, Canada Keywords: calculators; mathematics; mental arithmetic Introduction: Calculators and Mathematics Early studies investigating the influence of calculators on learning found that participants using calculators were faster and more accurate than their counterparts without calculators. Participants using calculators, however, showed no attitudinal improvements, and conceptual improvements were only evident for those already working at a higher computational level (for a review see Roberts, 1980). More recent studies have found that mental calculation is critical for recall of mathematical learning, and have supported the position that calculators may be more useful for students who already possess the cognitive processes necessary to retrieve answers, than for students with weak mathematical ability (Crutcher & Healy, 1989; McNamara, 1995). This study investigates the claim that calculators permit more rapid computations than mental arithmetic. calculators and other technological tools, yet, these studies often involved a control group that had been taught very differently from the experimental group. It could be the teaching, and not the actual usage of the calculator, that influences the mathematical performance and understanding of students. Since participants in the present study completed the same tasks under the same conditions, their performance should only have been affected by the use, or non-use, of the calculator. Thus, the inefficiency of calculator assisted arithmetic becomes apparent. Although technological tools may support mathematical conceptual exploration, and provide a feeling of security for students with math anxiety, they may not actually improve calculation fluency. One can begin mentally calculating the next problem while still writing down a previous response. This efficiency cannot occur while using a calculator, thus rendering mental calculation more rapid, as demonstrated by the results of the present work. Adult participants (n=15) completed a timed calculation test and responded to a questionnaire about their attitudes towards mathematics. Two subtests of the Kit of Factor- Reference Cognitive Tests (French, Ekstrom, & Price, 1963) were used to measure calculation fluency. Total problems correct across two pages of multi-digit addition, subtraction and multiplication problems were used as a measure of calculator assisted calculation fluency or mental calculation fluency depending whether the pages had been completed with or without a calculator. All participants completed both the calculator assisted and mental calculation fluency measures. Conditions and pages were counterbalanced. Participants completed significantly more problems when working without a calculator than when working with a calculator (43.5 vs. 36.1), t = 2.41, p < .05 (Figure 1). In contrast to previous findings, this study did not find a speed advantage for calculator assisted arithmetic. Nervousness towards mathematical activities did not significantly affect mental calculation fluency, F(3,11) = 1.90, p = .188, but did significantly influence calculator assisted calculation fluency, F(3,11) = 4.65, p < .05. Implications The exact impact of calculators on mathematical concept development remains unclear. The introduction of calculators into mathematics curricula has been perceived as changing the teaching of mathematics from routine procedures to thinking, reasoning and conceptual skills (Usiskin, 1999). Many studies have supported the use of Problems Correct Methods & Results Mental Calculation Calculator Assisted Calculation Addition Multiplication & Subtraction Figure 1: Comparison between mental and calculator assisted calculation fluency. References Crutcher, R. J., & Healy, A. F. (1989). Cognitive operations and the generation effect. JEP: Learning, Memory, and Cognition. 15, 669-675. French, J. W., Ekstrom, R. B., & Price, I. A. (1963). Kit of reference tests for cognitive factors. Princeton, NJ: ETS. McNamara, D. S. (1995). Effects of prior knowledge on the generation advantage: Calculators versus calculation to learn simple multiplication. Journal of Educational Psychology, 87, 307–318. Roberts, D. M. (1980). The impact of electronic calculators on educational performance. Rev. Ed. Res., 50, 71–98. Usiskin, Z. (Ed.) (1999). Groping and hoping for a consensus on calculator use [Special Issue]. Mathematics Education Dialogues, 2.
Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.
Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,006 | 0,028 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,001 | 0,001 |
| Bibliométrie | 0,001 | 0,001 |
| Études des sciences et des technologies | 0,001 | 0,004 |
| Communication savante | 0,004 | 0,005 |
| Science ouverte | 0,001 | 0,002 |
| Intégrité de la recherche | 0,002 | 0,002 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,009 | 0,002 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule source (Gemma direct ou Codex distillé), pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».