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      The Relationship Between Problem Size and Fixation Patterns During Addition, Subtraction, Multiplication, and Division


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          Eye-tracking methods have only rarely been used to examine the online cognitive processing that occurs during mental arithmetic on simple arithmetic problems, that is, addition and multiplication problems with single-digit operands (e.g., operands 2 through 9; 2 + 3, 6 x 8) and the inverse subtraction and division problems (e.g., 5 – 3; 48 ÷ 6). Participants (N = 109) solved arithmetic problems from one of the four operations while their eye movements were recorded. We found three unique fixation patterns. During addition and multiplication, participants allocated half of their fixations to the operator and one-quarter to each operand, independent of problem size. The pattern was similar on small subtraction and division problems. However, on large subtraction problems, fixations were distributed approximately evenly across the three stimulus components. On large division problems, over half of the fixations occurred on the left operand, with the rest distributed between the operation sign and the right operand. We discuss the relations between these eye tracking patterns and other research on the differences in processing across arithmetic operations.

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          Eye movements in reading and information processing: 20 years of research.

          Recent studies of eye movements in reading and other information processing tasks, such as music reading, typing, visual search, and scene perception, are reviewed. The major emphasis of the review is on reading as a specific example of cognitive processing. Basic topics discussed with respect to reading are (a) the characteristics of eye movements, (b) the perceptual span, (c) integration of information across saccades, (d) eye movement control, and (e) individual differences (including dyslexia). Similar topics are discussed with respect to the other tasks examined. The basic theme of the review is that eye movement data reflect moment-to-moment cognitive processes in the various tasks examined. Theoretical and practical considerations concerning the use of eye movement data are also discussed.
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            Using confidence intervals for graphically based data interpretation.

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              Cognitive arithmetic across cultures.

              Canadian university students either of Chinese origin (CC) or non-Asian origin (NAC) and Chinese university students educated in Asia (AC) solved simple-arithmetic problems in the 4 basic operations (e.g., 3 + 4, 7 - 3, 3 x 4, 12 divided by 3) and reported their solution strategies. They also completed a standardized test of more complex multistep arithmetic. For complex arithmetic, ACs outperformed both CCs and NACs. For simple arithmetic, however, ACs and CCs were equal and both performed better than NACs. The superior simple-arithmetic skills of CCs relative to NACs implies that extracurricular culture-specific factors rather than differences in formal education explain the simple-arithmetic advantage for Chinese relative to non-Asian North American adults. NAC's relatively poor simple-arithmetic performance resulted both from less efficient retrieval skills and greater use of procedural strategies. Nonetheless, all 3 groups reported using procedures for the larger simple subtraction and division problems, confirming the importance of procedural knowledge in skilled adults' performance of elementary mathematics.

                Author and article information

                J Numer Cogn
                Journal of Numerical Cognition
                J. Numer. Cogn.
                05 August 2016
                : 2
                : 2
                : 91-115
                [a ]Institute of Cognitive Science, Carleton University, Ottawa, Canada
                [b ]Department of Psychology, Carleton University, Ottawa, Canada
                Author notes
                [* ]Institute of Cognitive Science and Department of Psychology, Carleton University, 2217 Dunton Tower, 1-613-520-2600 ext. 2693. JoAnneLefevre@ 123456cunet.carleton.ca

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                : 29 September 2015
                : 01 February 2016
                Self URI (journal-page): https://journals.psychopen.eu/
                Research Reports

                multiplication,division,subtraction,addition,problem-size effect,mental arithmetic,eye tracking
                multiplication, division, subtraction, addition, problem-size effect, mental arithmetic, eye tracking


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