Should I Use My Calculator?: Mental versus Calculation Assisted Arithmetic
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.028 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".