Calculation latency: The μ of memory and the τ of transformation

Campbell, Jamie I. D.; Penner-Wilger, Marcie

doi:10.3758/bf03193400

Cited by 26 publications

(44 citation statements)

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“…In part, these format costs have been attributed to reduced use of retrieval for word problems (Campbell & Penner-Wilger, 2006) and thus the format costs are interpreted as affecting mental calculation. Our results suggest that the present format manipulation (i.e., negative signs) did not influence mental calculation.…”

Section: Discussionmentioning

confidence: 99%

“…Accordingly, the problem-size effect in subtraction is typically much larger than in addition, because solvers use procedural solutions more frequently (Campbell & Xue, 2001;LeFevre et al, 2006;Seyler et al, 2003). Furthermore, problem-size effects are generally larger in atypical formats than in typical or preferred formats, because atypical formats may cause participants to rely more heavily on procedural solutions (Campbell & Fugelsang, 2001;Campbell & Penner-Wilger, 2006;LeFevre, Shanahan, & DeStefano, 2004;Mauro, LeFevre, & Morris, 2003). Thus, we used the problem-size effect to evaluate whether negative numbers influence mental calculation processes in simple addition and subtraction.…”

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confidence: 99%

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Negative Numbers in Simple Arithmetic

Das

LeFevre

Penner-Wilger

2010

Quarterly Journal of Experimental Psychology

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Are negative numbers processed differently than positive numbers in arithmetic problems?In two experiments, adults (N = 66) solved standard addition and subtraction problems such as 3 + 4 and 7 -4 and recasted versions that included explicit negative signs, that is, 3 -(-4), 7 + (-4), and (-4) + 7. Solution times on the recasted problems were slower than on standard problems, but the effect was much larger for addition than subtraction. The negative sign may prime subtraction in both kinds of recasted problems. Problem size effects were the same or smaller in recasted as compared to standard problems, suggesting that the recasted formats did not interfere with mental calculation. These results suggest that the underlying conceptual structure of the problem (i.e., addition vs. subtraction) is more important for solution processes than the presence of negative numbers.Negative Numbers -3 Negative Numbers in Simple ArithmeticAre negative numbers processed differently than positive numbers in arithmetic problems? Negative numbers are thought to be conceptually difficult for both children and adults (De Cruz, 2006). Although no one has addressed the question of whether negative numbers interfere with solving arithmetic problems, there is evidence suggesting that negative terms (e.g., 6 -x = 4) might be more difficult for students to process than positive terms in algebraic equations (Peterson & Aller, 1971;Vlassis, 2004). We hypothesized that arithmetic problems with negative numbers may be processed differently because they usually require subtraction, rather than because of the negative number, per se. Subtraction is slower and more error-prone than addition (Campbell & Xue, 2001;LeFevre, DeStefano, Penner-Wilger, & Daley, 2006;Seyler, Kirk, & Ashcraft, 2003). On this view, the conceptual structure of the problem (i.e., the mental operation that is required) is the critical determinant of processing difficulty rather than the presence of a negative number.In the present research, adults solved addition and subtraction problems in standard formats, that is 3 + 4 and 7 -4, and as addition or subtraction of negative numbers in recasted formats, that is, 3 -(-4), 7 + (-4) and (-4) + 7. In the recasted formats, the conceptual structure of the problem did not change but the format was manipulated to explicitly isolate a negative number. Shaki and Petrusic (2005) outlined two hypotheses about how people process negative numbers. According to the magnitude-polarity hypothesis, the magnitude of the number and the polarity (i.e., positive vs. negative) are processed independently, as distinct features of the stimulus. In contrast, according to the number-line hypothesis, people represent negative and positive numbers along a number line, with negative numbers extending to infinity on the left and positive numbers extending to infinity on the right. Accordingly, the negative or positive status of the number is integral to mental processing. Ganor-Stern and Tzelgov (2008) The most common use of negative signs in arit...

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Negative Numbers in Simple Arithmetic

Das

LeFevre

Penner-Wilger

2010

Quarterly Journal of Experimental Psychology

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“…One possible reason for the problem size effect is that large problems tend to be solved by procedural strategies, resulting in slower and more error prone responses (Campbell and Xue, 2001). While the exact mechanism underlying the problem size effect is still up for debate, the more salient finding is that the problem size effect is larger for problems presented in word format compared to digit format (Campbell and Fugelsang, 2001; Campbell and Penner-Wilger, 2006). Campbell and colleagues have argued that this interaction between problem size and format implies that format directly impacts calculation processes, providing support for the interactive model.…”

Section: Introductionmentioning

confidence: 99%

A Single-Boundary Accumulator Model of Response Times in an Addition Verification Task

Faulkenberry

2017

Front. Psychol.

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Current theories of mathematical cognition offer competing accounts of the interplay between encoding and calculation in mental arithmetic. Additive models propose that manipulations of problem format do not interact with the cognitive processes used in calculation. Alternatively, interactive models suppose that format manipulations have a direct effect on calculation processes. In the present study, we tested these competing models by fitting participants' RT distributions in an arithmetic verification task with a single-boundary accumulator model (the shifted Wald distribution). We found that in addition to providing a more complete description of RT distributions, the accumulator model afforded a potentially more sensitive test of format effects. Specifically, we found that format affected drift rate, which implies that problem format has a direct impact on calculation processes. These data give further support for an interactive model of mental arithmetic.

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“…The mean of the normal component reflects a uniform time demand and for simple arithmetics tasks is mainly determined by memory retrieval time. The exponential component is found to reflect the procedural strategies t h a t have been used by test takers (Campbell & Penner-Wilger, 2006).…”

Section: Applicability Of Response Time (Rt) Measurementsmentioning

confidence: 99%

Beyond test accuracy: Benefits of measuring response time in computerised testing

Gvozdenko

Chambers

2007

AJET

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This paper investigates how monitoring the time spent on a question in a test of basic mathematics skills can provide insights into learning processes, the quality of test takers' knowledge, and cognitive demands and performance of test items that otherwise would remain undiscovered if the usual test outcome of accuracy only format ("correct/incorrect") was used. Data from three tests of basic mathematics skills taken by tertiary students in 2004-2006 were analysed. Means and distributions of individual response times on parallel test questions were examined and differences were further investigated.Analysis of response time data revealed a number of surprising findings in regard to the impact of variables on preferences for written and mental calculation methods and regarding additional cognitive demands of a question. The study examined how simple statistical analysis of response time distribution can be used to investigate abnormalities of the item functioning. These findings may be of value to educators and to test producers by informing them about the potential of utilising response time measurements as a diagnostic facility in computerised tests, for the purposes of improving teaching and learning.

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Calculation latency: The μ of memory and the τ of transformation

Cited by 26 publications

References 36 publications

Negative Numbers in Simple Arithmetic

Negative Numbers in Simple Arithmetic

A Single-Boundary Accumulator Model of Response Times in an Addition Verification Task

Beyond test accuracy: Benefits of measuring response time in computerised testing

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