Telling stories: The perils and promise of using verbal reports to study math strategies.

Kirk, Elizabeth; Ashcraft, Mark H.

doi:10.1037/0278-7393.27.1.157

Cited by 151 publications

(170 citation statements)

References 40 publications

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“…The self-report methodology has nonetheless been criticised on the grounds that, when asked to describe mental processing, people may change or be unable to accurately describe their behaviours (Kirk & Ashcraft, 2001;Smith-Chant & LeFevre, 2003). Additionally, individual differences and instructional demands may bias verbal reports and the solution procedures that are reported (Kirk & Ashcraft, 2001;Smith-Chant & LeFevre, 2003).…”

Section: Introductionmentioning

confidence: 99%

Simple arithmetic processing: The question of automaticity

Jackson¹,

Coney²

2005

Acta Psychologica

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In adult simple arithmetic performance, it is commonly held that retrieval of solutions occurs automatically from a network of stored facts in memory. However, such an account of performance necessarily predicts a uniform reaction time for solution retrieval and is therefore not consistent with the robust finding that reaction time increases with problem size and difficulty. Additionally, past research into arithmetic performance has relied on tasks that may have actually induced and measured attentional processing, thereby possibly confounding previous results and conclusions pertaining to automaticity. The present study therefore, attempted to more reliably assess the influence of automatic processing in arithmetic performance by utilizing a variant of the well-established semantic word-priming procedure with a target-naming task. The overall results revealed significant facilitation in naming times at SOAs of 240 and 1500 ms for congruent targets i.e., targets that represented the correct solutions to problems presented as primes (e.g., 6 + 8 and 14). Significant inhibition in comparison to a neutral condition (0 + 0 and 17) was also observed at 120 and 240 ms SOAs in naming incongruent targets (e.g., 6 + 8 and 17).Furthermore, response times were found to vary as a function of both arithmetic fluency and problem size. Differences in performance to addition and multiplication operations and implications for cognitive research and education are considered.

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Section: Introductionmentioning

confidence: 99%

Simple arithmetic processing: The question of automaticity

Jackson¹,

Coney²

2005

Acta Psychologica

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“…To what extent multiplication problems are solved by retrieval in adults is a matter of considerable debate (e.g., Kirk & Ashcraft, 2001;. If multiplication problems are not solved primarily by retrieval but by such strategies as repeated addition or multiplication by 10 followed by subtraction [e.g., 9 ϫ 8 ϭ (10 ϫ 8)Ϫ8], it might be that some or even all of the major effects could be attributed to nonretrieval strategies.…”

Section: Retrieval and Nonretrievalmentioning

confidence: 99%

Interacting neighbors: A connectionist model of retrieval in single-digit multiplication

2005

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“…For this purpose, verbal reports of the strategy used by each participant were collected. However, because it has been observed that the method of verbal report alters the strategies that participants would have spontaneously used (Kirk & Ashcraft, 2001), verbal reports were collected in a separate session administered after the experimental sessions. Our main analyses focused on those participants who reported retrieving the answer of all the very small additions studied by Barrouillet and Thevenot (2013) and almost all the small additions (i.e., with a sum 6 10).…”

Section: The Present Studymentioning

confidence: 99%

Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval?

2016

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a b s t r a c tContrary to a widespread assumption, a recent study suggested that adults do not solve very small additions by directly retrieving their answer from memory, but rely instead on highly automated and fast counting procedures (Barrouillet & Thevenot, 2013). The aim of the present study was to test the hypothesis that these automated compiled procedures are restricted to small quantities that do not exceed the size of the focus of attention (i.e., 4 elements). For this purpose, we analyzed the response times of ninety adult participants when solving the 81 additions with operands from 1 to 9. Even when focusing on small problems (i.e. with sums 610) reported by participants as being solved by direct retrieval, chronometric analyses revealed a strong size effect. Response times increased linearly with the magnitude of the operands testifying for the involvement of a sequential multistep procedure. However, this size effect was restricted to the problems involving operands from 1 to 4, whereas the pattern of response times for other small problems was compatible with a retrieval hypothesis. These findings suggest that very fast responses routinely interpreted as reflecting direct retrieval of the answer from memory actually subsume compiled automated procedures that are faster than retrieval and deliver their answer while the subject remains unaware of their process, mistaking them for direct retrieval from long-term memory.

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Telling stories: The perils and promise of using verbal reports to study math strategies.

Cited by 151 publications

References 40 publications

Simple arithmetic processing: The question of automaticity

Simple arithmetic processing: The question of automaticity

Interacting neighbors: A connectionist model of retrieval in single-digit multiplication

Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval?

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