When calculators lie: A demonstration of uncritical calculator usage among college students and factors that improve performance
Autoři:
Mark LaCour aff001; Norma G. Cantú aff002; Tyler Davis aff001
Působiště autorů:
Department of Psychological Sciences, Texas Tech University, Lubbock, Texas, United States of America
aff001; Department of Psychology, University of Louisiana-Lafayette, Lafayette, Louisiana, United States of America
aff002
Vyšlo v časopise:
PLoS ONE 14(10)
Kategorie:
Research Article
doi:
https://doi.org/10.1371/journal.pone.0223736
Souhrn
Calculators are often unnecessary to solve routine problems, though they are convenient for offloading cognitively effortful processes. However, errors can arise if incorrect procedures are used or when users fail to monitor the output for keystroke mistakes. To investigate the conditions under which people’s attention are captured by errant calculator outputs (i.e., from incorrectly chosen procedures or keystroke errors), we programmed an onscreen calculator to “lie” by changing the answers displayed on certain problems. We measured suspicion by tracking whether users explicitly reported suspicion, overrode calculator “lies”, or re-checked their calculations after a “lie” was presented. In Study 1, we manipulated the concreteness of problem presentation and calculator delay between subjects to test how these affect suspicion towards “lies” (15% added to answers). We found that numeracy had no effect on whether people opted-in or out of using the calculator but did predict whether they would become suspicious. Very few people showed suspicion overall, however. For study 2, we increased the “lies” to 120% on certain answers and included questions with “conceptual lies” shown (e.g., a negative sign that should have been positive). We again found that numeracy had no effect on calculator usage, but, along with concrete formatting, did predict suspicion behavior. This was found regardless of “lie” type. For study 3, we reproduced these effects after offering students an incentive for good performance, which did raise their accuracy across the math problems overall but did not increase suspicion behavior. We conclude that framing problems within a concrete domain and being higher in numeracy increases the likelihood of spotting errant calculator outputs, regardless of incentive.
Klíčová slova:
Behavior – Cell phones – Cognition – Deception – Human learning – Reasoning – Undergraduates – Numeracy
Zdroje
1. Vilorio D. STEM 101: Intro to tomorrow’s jobs. Occupational Outlook Quarterly. 2014;58(1):2–12.
2. Reyna VF, Nelson WL, Han PK, Dieckmann NF. How numeracy influences risk comprehension and medical decision making. Psychological bulletin. 2009 Nov;135(6):943–73. doi: 10.1037/a0017327 19883143
3. Mulhern G, Wylie J. Changing levels of numeracy and other core mathematical skills among psychology undergraduates between 1992 and 2002. British Journal of Psychology. 2004 Aug 1;95(3):355–70.
4. LeFevre JA, Penner-Wilger M, Pyke AA, Shanahan T, Deslauriers WA. Putting two and two together: Declines in arithmetic fluency among young Canadian adults, 1993 to 2005. Carleton University Cognitive Science Technical Report. 2014.
5. Noser TC, Tanner JR, Shah S. Have basic mathematical skills grown obsolete in the computer age: assessing basic mathematical skills and forecasting performance in a business statistics course. Journal of College Teaching & Learning. 2008 Apr;5(4):1–6.
6. Rittle-Johnson B, Siegler RS, Alibali MW. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of educational psychology. 2001 Jun;93(2):346–62.
7. Schneider M, Rittle-Johnson B, Star JR. Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental psychology. 2011 Nov;47(6):1525–38. doi: 10.1037/a0024997 21823791
8. Porter MK, Masingila JO. Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics. 2000 Mar 29;42(2):165–77.
9. Polya G. How to solve it. 2-nd ed. Princeton University Press, Princeton. 1957.
10. Schoenfeld AH. Mathematical problem solving. Academic Press, Orlando, FL; 2014 Jun 28.
11. De Corte E, Somers R. Estimating the outcome of a task as a heuristic strategy in arithmetic problem-solving-a teaching experiment with 6th-graders. Human learning. 1982 Jan 1;1(2):105–21.
12. Pugalee DK. Writing, mathematics, and metacognition: Looking for connections through students' work in mathematical problem solving. School Science and Mathematics. 2001 May 1;101(5):236–45.
13. Pugalee DK. A comparison of verbal and written descriptions of students' problem solving processes. Educational Studies in Mathematics. 2004 Mar 20;55(1):27–47.
14. Lipkus IM, Samsa G, Rimer BK. General performance on a numeracy scale among highly educated samples. Medical decision making. 2001 Feb;21(1):37–44. doi: 10.1177/0272989X0102100105 11206945
15. Reys RE, Trafton PR, Reys B., Zawojewski J. Developing Computational Estimation Materials for the Middle Grades. Final Report No. NSF-8113601. Washington, DC: National Science Foundation. 1984.
16. Glasgow B, Reys BJ. The authority of the calculator in the minds of college students. School Science and Mathematics. 1998 Nov 1;98(7):383–8.
17. Wason PC, Shapiro D. Natural and contrived experience in a reasoning problem. The Quarterly Journal of Experimental Psychology. 1971 Feb 1;23(1):63–71.
18. Griggs RA, Cox JR. The elusive thematic‐materials effect in Wason's selection task. British Journal of Psychology. 1982 Aug 1;73(3):407–20.
19. Carraher TN, Carraher DW, Schliemann AD. Mathematics in the streets and in schools. British journal of developmental psychology. 1985 Mar 1;3(1):21–9.
20. Carraher TN, Carraher DW, Dias A. Written and Oral Mathematics. Journal for Research in Mathematics Education. 1987 Mar;18(2): 83–97.
21. Blessing SB, Ross BH. Content effects in problem categorization and problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition. 1996 May;22(3):792–810.
22. Koedinger KR, Nathan MJ. The real story behind story problems: Effects of representations on quantitative reasoning. The journal of the learning sciences. 2004 Apr 1;13(2):129–64.
23. Koedinger KR, Alibali MW, Nathan MJ. Trade‐Offs between grounded and abstract representations: Evidence from algebra problem Solving. Cognitive Science. 2008 Mar 1;32(2):366–97. doi: 10.1080/03640210701863933 21635340
24. Jurdak M, Shahin I. An ethnographic study of the computational strategies of a group of young street vendors in Beirut. Educational Studies in Mathematics. 1999 Oct 30;40(2):155–72.
25. Walsh MM, Anderson JR. The strategic nature of changing your mind. Cognitive psychology. 2009 May 31;58(3):416–40. doi: 10.1016/j.cogpsych.2008.09.003 19013562
26. Pyke AA, LeFevre JA. Calculator use need not undermine direct-access ability: The roles of retrieval, calculation, and calculator use in the acquisition of arithmetic facts. Journal of Educational Psychology. 2011 Aug;103(3):607–16.
27. Lipkus IM, Peters E. Understanding the role of numeracy in health: Proposed theoretical framework and practical insights. Health Education & Behavior. 2009 Dec;36(6):1065–81.
28. Mulhern G, Wylie J. Mathematical prerequisites for learning statistics in psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates. Psychology Learning & Teaching. 2006 Sep;5(2):119–32.
29. Fyfe ER, McNeil NM, Son JY, Goldstone RL. Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review. 2014 Mar 1;26(1):9–25.
30. Slavit D. The role of operation sense in transitions from arithmetic to algebraic thought. Educational studies in mathematics. 1998 Dec 1;37(3):251–74.
31. Dixon JA, Deets JK, Bangert A. The representations of the arithmetic operations include functional relationships. Memory & Cognition. 2001 Apr 1;29(3):462–77.
32. Prather R, Alibali MW. Children's acquisition of arithmetic principles: The role of experience. Journal of Cognition and Development. 2011 Jul 1;12(3):332–54.
33. Krueger LE, Hallford EW. Why 2+ 2 = 5 looks so wrong: On the odd-even rule in sum verification. Memory & Cognition. 1984 Mar 1;12(2):171–80.
34. Krueger LE. Why 2× 2 = 5 looks so wrong: On the odd-even rule in product verification. Memory & Cognition. 1986 Mar 1;14(2):141–9.
35. Lemaire P, Reder L. What affects strategy selection in arithmetic? The example of parity and five effects on product verification. Memory & Cognition. 1999 Mar 1;27(2):364–82.
36. Fisher M, Goddu MK, Keil FC. Searching for explanations: How the Internet inflates estimates of internal knowledge. Journal of Experimental Psychology: General. 2015 Jun;144(3):674–87
37. Sparrow B, Liu J, Wegner DM. Google effects on memory: Cognitive consequences of having information at our fingertips. Science. 2011 Aug 5;333(6043):776–8. doi: 10.1126/science.1207745 21764755
38. Barr N, Pennycook G, Stolz JA, Fugelsang JA. The brain in your pocket: Evidence that Smartphones are used to supplant thinking. Computers in Human Behavior. 2015 Jul 31;48:473–80.
39. Henkel LA. Point-and-shoot memories: The influence of taking photos on memory for a museum tour. Psychological science. 2014 Feb;25(2):396–402. doi: 10.1177/0956797613504438 24311477
40. Ward AF, Duke K, Gneezy A, Bos MW. Brain drain: The mere presence of one’s own smartphone reduces available cognitive capacity. Journal of the Association for Consumer Research. 2017 Apr 1;2(2):140–54.
41. Risko EF, Dunn TL. Storing information in-the-world: Metacognition and cognitive offloading in a short-term memory task. Consciousness and cognition. 2015 Nov 1;36:61–74. doi: 10.1016/j.concog.2015.05.014 26092219
42. Ellington AJ. A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education. 2003 Nov 1:433–63.
43. Wilson WS, Naiman DQ. K-12 calculator usage and college grades. Educational Studies in Mathematics. 2004 May 1;56(1):119–22.
44. Boyle RW, Farreras IG. The effect of calculator use on college students’ mathematical performance. International Journal of Research in Education and Science. 2015 Jul 1;1(2):95–100.
45. Greer S, McCoy LP. A study of the effect of calculator use on computation skills of high school mathematics students. Studies in Teaching 2006 Research Digest. 2006 Dec.
46. Pyke A, LeFevre JA, Isaacs R. Why Do The Math? The Impact of Calculator Use on Participants' Actual and Perceived Retention of Arithmetic Facts. In Proceedings of the Cognitive Science Society 2008 Jan 1 (Vol. 30, No. 30).
47. Siegler RS, Lemaire P. Older and younger adults' strategy choices in multiplication: testing predictions of ASCM using the choice/no-choice method. Journal of experimental psychology: General. 1997 Mar;126(1):71–92.
Článek vyšel v časopise
PLOS One
2019 Číslo 10
- Tisícileté topoly, mokří psi, stárnoucí kočky a ospalé octomilky – „jednohubky“ z výzkumu 2024/41
- Jaké jsou aktuální trendy v léčbě karcinomu slinivky?
- Může hubnutí souviset s vyšším rizikem nádorových onemocnění?
- Menstruační krev má značný diagnostický potenciál, mimo jiné u diabetu
- Metamizol jako analgetikum první volby: kdy, pro koho, jak a proč?
Nejčtenější v tomto čísle
- Correction: Low dose naltrexone: Effects on medication in rheumatoid and seropositive arthritis. A nationwide register-based controlled quasi-experimental before-after study
- Combining CDK4/6 inhibitors ribociclib and palbociclib with cytotoxic agents does not enhance cytotoxicity
- Experimentally validated simulation of coronary stents considering different dogboning ratios and asymmetric stent positioning
- Prevalence of pectus excavatum (PE), pectus carinatum (PC), tracheal hypoplasia, thoracic spine deformities and lateral heart displacement in thoracic radiographs of screw-tailed brachycephalic dogs
Zvyšte si kvalifikaci online z pohodlí domova
Všechny kurzy