When you don't have to be exact: Investigating computational estimation skills with a comparison task

Ganor-Stern, Dana

doi:10.1016/j.actpsy.2014.10.010

Cited by 14 publications

(44 citation statements)

References 40 publications

(78 reference statements)

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“…Approximate computation and curriculum-based math achievement could be typically associated with math problem solving (e.g., Jordan et al, 2009 ; Jitendra et al, 2014 ). Approximate computation (e.g., 645 × 54, 90.288 ÷ 22.8) could be categorized as a type of math problem solving, because the participants could not directly retrieve answers from long-term memory nor use routine procedures to calculate answers, but instead they have to search for solutions by flexibly applying strategies (Caviola et al, 2012 ; Ganor-Stern, 2015 ). Math problem solving involves the searching the path from preconditions to solutions and is supposed to include four steps: understanding the problem, devising a plan, carrying out the plan, and looking back (Polya, 1957 ).…”

Section: Introductionmentioning

confidence: 99%

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

et al. 2017

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Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation.

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Section: Introductionmentioning

confidence: 99%

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

et al. 2017

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“…To address this issue performance on a different computational estimation task should be explored. In the estimation comparison task a multi-digit multiplication problem is presented together with a reference number and participants are asked to indicate whether they estimate the answer to that problem to be larger or smaller than the reference number [ 11 , 12 ].…”

Section: Introductionmentioning

confidence: 99%

“…It was also enhanced for smaller vs. larger reference numbers (i.e., the reference number size effect). For example, it was easier for the participants to decide that the exact answer for a problem such as 37 x 54 was larger than 400 than it was smaller than 4000 and to decide that it was smaller than 8000 than it was smaller than 4000 [ 12 , 13 ]. The ratio/distance and size effects in quantity and magnitude comparisons suggest the existence of a condensed approximate representation.…”

Section: Introductionmentioning

confidence: 99%

“…This system is assumed to be active whenever a numerical process is taking place involving either symbolic or nonsymbolic stimuli (e.g., [ 14 ]). The presence of the ratio/distance and size effects in this task might be interpreted as reflecting the involvement of the ANS in this task [ 12 , 13 ].…”

Section: Introductionmentioning

confidence: 99%

“…As to the underlying processes, Ganor-Stern [ 12 , 13 ] identified two main strategies used by college students to solve this task. The first is an approximate calculation strategy—rounding either one or two multiplicands, multiplying the rounded numbers, and comparing the product to the reference number.…”

Section: Introductionmentioning

confidence: 99%

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Solving Math Problems Approximately: A Developmental Perspective

Ganor-Stern

2016

PLoS ONE

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Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.

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Tracking practice effects in computation estimation

Ganor-Stern

Weiss

2015

Psychological Research

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The present study investigated college students' ability to estimate the results of multi-digit multiplication problems and the extent to which this ability improves with practice. Participants judged whether the results of multiplication problems composed of two-digit numbers were larger or smaller than a given reference number. The reference numbers were either close or far from the exact answer. The effects of practice, size, and distance of the reference number from the exact answer were examined using four measures of performance: speed, accuracy, eye movements, and strategy use. The results show that together with enhanced speed and accuracy with practice, participants also changed the pattern of eye movements and the strategies they used. The eye movement analysis showed longer dwell time and more frequent first fixations toward the reference number with practice, suggesting that participants relied more on the reference number to solve the task with practice. The strategy analysis revealed that with practice participants reduced their use of the approximate calculation strategy, which involves multiplying the rounded operands and comparing the product to the reference number, and increased their reliance on the sense of magnitude strategy which does not involve any calculation, but is grounded in the ANS. This was done especially for trials in which the reference number was far from the exact answer, thus exhibiting enhanced adaptivity in strategy choice with practice.

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When you don't have to be exact: Investigating computational estimation skills with a comparison task

Cited by 14 publications

References 40 publications

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

Solving Math Problems Approximately: A Developmental Perspective

Tracking practice effects in computation estimation

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