Elsevier

Neuropsychologia

Volume 47, Issue 2, January 2009, Pages 604-608
Neuropsychologia

Note
To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving

https://doi.org/10.1016/j.neuropsychologia.2008.10.013Get rights and content

Abstract

While there is consistent evidence from neuropsychological and brain imaging studies for an association between the left angular gyrus and mental arithmetic, its specific role in calculation has remained poorly understood. It has been speculated that the angular gyrus mediates the retrieval of arithmetic facts during problem solving, but this hypothesis has not been directly tested. In the present functional Magnetic Resonance Imaging study comprising 28 adults, we used trial-by-trial strategy self-reports to identify brain regions underpinning different strategies in arithmetic problem solving. Analyses revealed stronger activation of the left angular gyrus while solving arithmetic problems for which participants reported fact retrieval whereas the application of procedural strategies was accompanied by widespread activation in a fronto-parietal network. These data directly link the left angular gyrus with arithmetic fact retrieval and show that strategy self-reports can be used to predict differential patterns of brain activation.

Introduction

Early investigations of brain-damaged patients revealed that lesions to areas of the parietal cortex, in particular the left angular gyrus (lAG), cause deficits in mental calculation (Gerstmann, 1940). Subsequent neuropsychological and neuroimaging studies have corroborated the strong link between the lAG and arithmetic problem solving, but little is known about the particular processes this brain region supports during problem solving (Ansari, 2008). Since the lAG has been found to be implicated in language processing (Price, 2000) it has been speculated that it mediates the retrieval of verbally stored arithmetic facts (such as the multiplication table) from long-term memory (Dehaene, Piazza, Pinel, & Cohen, 2003). This assumption is supported by evidence showing that the lAG is more strongly activated during exact compared to approximate arithmetic (Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999), and shows greater activation during computation of problems with a relatively small compared to large problem size (Stanescu-Cosson et al., 2000) as well as of multiplication compared to subtraction problems (Lee, 2000). Furthermore, it has been revealed that the lAG increases in its activation after the training of arithmetic facts (Delazer et al., 2003). However, the interpretation that the lAG mediates the retrieval of arithmetic facts lacks direct empirical evidence since the effect of using arithmetic fact retrieval on the activation of the lAG has not been systematically compared with the neural correlates of less efficient procedural (calculation) strategies. In addition, the role of the lAG in fact retrieval has been disputed based on the results of some neuropsychological studies. For example, Van Harskamp, Rudge, and Cipolotti (2002) reported data from a patient with lesions in the left supramarginal and angular gyri who displayed no impairments in multiplication fact retrieval.

The present study builds on the well-established finding that children and adults apply a variety of strategies in arithmetic problem solving and that their strategy use varies on a trial-by-trial basis (Siegler, Adolph, & Lemaire, 1996). In order to evaluate whether the lAG is indeed linked to arithmetic fact retrieval, we presented healthy adults with arithmetic problems of all four operations during functional Magnetic Resonance Imaging (fMRI). Afterwards, they were required to solve half of the problems again in a paper-and-pencil test and to indicate after every problem which strategy they used. Based on the strategy self-reports in the post-scan test, we sorted the individual fMRI data into problems for which participants reported fact retrieval (“retrieval problems”) and problems that were solved using procedural strategies (“procedural problems”). In consideration of the aforementioned studies suggesting that the lAG supports arithmetic fact retrieval, it is hypothesized that retrieval problems will be associated with greater lAG activation than procedural problems. This finding would not only provide first direct evidence for a link between the lAG and arithmetic fact retrieval during calculation but would also validate the often controversial use of self-report measures to glean insights into strategy use in mental arithmetic (Kirk & Ashcraft, 2001; Smith-Chant & LeFevre, 2003).

Section snippets

Sample

Twenty-eight male adults (age between 22 and 33 years; M = 26.86, SD = 3.16) who had been screened using the Berlin Intelligence Structure Test (BIS-T; Jäger, Süß, & Beauducel, 1997) participated in the present investigation. The average IQs were 99.02 (SD = 12.46) for mathematical–numerical intelligence, 104.10 (SD = 5.60) for verbal intelligence, and 101.37 (SD = 7.47) for figural–spatial intelligence. All participants were right-handed and had normal or corrected-to-normal vision. They gave written

Experimental task performance and strategy reports

Participants solved 96.55% (SD = 2.29) of the analyzed fMRI problems correctly. From all correctly solved problems, retrieval strategy was reported in 68.76% (SD = 20.38) and a procedural strategy in 31.24% (SD = 20.38) of the problems. Strategy use was moderated by arithmetic operation, F(2.03,54.84) = 9.78), p < .001, η2 = .27, showing stronger reliance on retrieval strategies in multiplication (81.77%) and addition (75.43%) as compared with division (58.90%) and subtraction (58.50%).

Retrieval problems

Discussion

Data from neuropsychological studies with brain-damaged patients have long implicated the lAG in mental arithmetic (Gerstmann, 1940). Recently, it has been speculated that this region subserves the retrieval of arithmetic facts (Dehaene et al., 2003). However, there has thus far been no direct evidence linking arithmetic fact retrieval with activation of the lAG. In the present study we evaluated the relationship between lAG activation and retrieval by relating strategy self-reports to brain

Conclusion

The present data revealed that the self-reported use of fact retrieval strategies during arithmetic problem solving is linked with lAG activation, providing first direct evidence that the lAG mediates the retrieval of arithmetic facts. In addition, the present findings demonstrated that self-reported use of procedural strategies is associated with widespread fronto-parietal activation. These findings demonstrate the utility of self-reports as predictive measures of brain activation and have

Acknowledgements

This research was partly supported by a grant from the Provincial Government of Styria (Landesregierung Steiermark) in Austria. We thank Anna Kanape for organizing the test sessions and Michael Schneider as well as Elsbeth Stern for valuable comments on this study.

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