Adults ( N = 72) estimated the location of target numbers on number lines that varied in numerical range (i.e., typical range 0–10,000 or atypical range 0–7,000) and spatial orientation (i.e., the 0 endpoint on the left [traditional] or on the right [reversed]). Eye-tracking data were used to assess strategy use. Participants made meaningful first fixations on the line, with fixations occurring around the origin for low target numbers and around the midpoint and endpoint for high target numbers. On traditional direction number lines, participants used left-to-right scanning and showed a leftward bias; these effects were reduced for the reverse direction number lines. Participants made fixations around the midpoint for both ranges but were less accurate when estimating target numbers around the midpoint on the 7,000-range number line. Thus, participants are using the internal benchmark (i.e., midpoint) to guide estimates on atypical range number lines, but they have difficulty calculating the midpoint, leading to less accurate estimates. In summary, both range and direction influenced strategy use and accuracy, suggesting that both numerical and spatial processes influence number line estimation.
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.Keywords: eye tracking, mental arithmetic, problem-size effect, addition, subtraction, multiplication, division Basic arithmetic is important for simple computational tasks as well as a scaffold for more complex mathematical abilities. Furthermore, mental arithmetic performance is of interest to cognitive psychologists because it provides a means to examine memory (a) in an applied context, (b) in conjunction with other cognitive processes (e.g., algorithms, strategy selection), and (c) in the context of a well-defined set of stimuli. We focused on the so-called simple arithmetic facts, defined as the set of addition and multiplication problems with single-digit operands from 2 through 9 (e.g., 2 + 3; 4 x 7) and the inverse subtraction and division problems (e.g., 5 -2; 28 ÷ 4). This 'standard set' of arithmetic facts has been the focus of research on simple mental arithmetic for approximately 30 years (Ashcraft & Guillaume, 2009;Campbell, 2005). People show considerable variability in arithmetic performance across operations (i.e., addition, subtraction, multiplication, and division; Campbell & Xue, 2001). Performanceas measured by response time and error rates -also varies based on the magnitude of the operands and solutions, a finding known as the problem-size effect (Ashcraft & Guillaume, 2009; Zbrodoff & Logan, 2005). The goal of the present research was to examine how attention is allocated to problems in different operations and of different size by measuring participants' eye movements.
Adults who use mental procedures other than direct retrieval to solve simple arithmetic problems typically make more errors and respond more slowly than individuals who rely on retrieval. The present study examined how this extra time was distributed across problem components when adults (n = 40) solved small (e.g., 5 - 2) and large (e.g., 17 - 9) subtraction problems. Two performance groups (i.e., retrievers and procedure users) were created based on a 2-group cluster analysis using statistics derived from the ex-Gaussian model of reaction time (RT) distributions (i.e., μ and τ) for both small and large problems. Cluster results differentiated individuals based on the frequency with which they used retrieval versus procedural strategies, supporting the view that differences in mu and tau reflected differences in choice of strategies used. Patterns of eye movements over time were also dramatically different across clusters, and provide strong support for the view that individuals were using different mental procedures to solve these problems. We conclude that eye-movement patterns can be used to distinguish fluent individuals who readily use retrieval from those who rely more on procedural strategies, even if traditional self-report methods are unavailable. (PsycINFO Database Record
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