TY - JOUR

T1 - The number of different digits determines solution and verification of multiplication problems

AU - Sapir-Yogev, Smadar

AU - Kavé, Gitit

AU - Ashkenazi, Sarit

N1 - Publisher Copyright:
© 2023 American Psychological Association

PY - 2023/11/16

Y1 - 2023/11/16

N2 - The solution and verification of single-digit multiplication problems vary in speed and accuracy. The current study examines whether the number of different digits in a problem accounts for this variance. In Experiment 1, 41 participants solved all 2–9 multiplication problems. In Experiment 2, 43 participants verified these problems. In Experiment 3, 26 participants solved 10 problems that differed in shared-digit network (SDN) size and matched in problem size. In Experiment 4, 24 participants verified these matched sets. Results show faster and more accurate responses to problems that include fewer different digits relative to problems with more different digits, and faster and more accurate responses to problems whose SDN is small relative to problems whose SDN is large. We thus show that the number of different digits in a problem, including the operands and the solution, determines the speed and accuracy of its solution and verification. This parsimonious account also explains why responses to five and tie problems, which include fewer different digits relative to nonfive and nontie problems, are faster and more accurate than responses to other problems.

AB - The solution and verification of single-digit multiplication problems vary in speed and accuracy. The current study examines whether the number of different digits in a problem accounts for this variance. In Experiment 1, 41 participants solved all 2–9 multiplication problems. In Experiment 2, 43 participants verified these problems. In Experiment 3, 26 participants solved 10 problems that differed in shared-digit network (SDN) size and matched in problem size. In Experiment 4, 24 participants verified these matched sets. Results show faster and more accurate responses to problems that include fewer different digits relative to problems with more different digits, and faster and more accurate responses to problems whose SDN is small relative to problems whose SDN is large. We thus show that the number of different digits in a problem, including the operands and the solution, determines the speed and accuracy of its solution and verification. This parsimonious account also explains why responses to five and tie problems, which include fewer different digits relative to nonfive and nontie problems, are faster and more accurate than responses to other problems.

KW - arithmetic

KW - five effect

KW - mathematical knowledge

KW - multiplication table

KW - tie effect

UR - http://www.scopus.com/inward/record.url?scp=85183437101&partnerID=8YFLogxK

U2 - 10.1037/xlm0001310

DO - 10.1037/xlm0001310

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C2 - 37971818

SN - 0278-7393

JO - Journal of Experimental Psychology: Learning Memory and Cognition

JF - Journal of Experimental Psychology: Learning Memory and Cognition

ER -