Author:

Keywords:

arithmetic; cognitive control; metacognition;numerical magnitude processing; second grade

Abstract:

In the current study, we investigated the theoretically appealing (e.g. Ashcraft, 1987; Campbell, 1995) but empirically little explored association between cognitive control and arithmetic fact retrieval. As arithmetic facts are stored in an associative network, incorrect but competing answers have to be inhibited when retrieving the answer, as a number of neighboring nodes in the semantic associative network are activated when a particular problem is presented (e.g., Ashcraft, 1987). Consequently, individual differences in cognitive control are expected to contribute to individual differences in arithmetic fact retrieval. Recent data by Rinne and Mazzocco (2014) further suggest that one’s calibration of confidence, i.e. the alignment between one’s confidence in solving a problem and the accuracy of this confidence judgement, a measure of metacognitive monitoring ability that can be considered as another important dimension of cognitive control, also predicts (adolescents) mathematical ability. To the best of our knowledge, there are no studies that have investigated the joint roles of cognitive control and calibration of confidence in children’s arithmetic fact retrieval. Furthermore, their unique roles in addition to the well-known domain-specific determinant of arithmetic, numerical magnitude processing (e.g. Vanbinst et al., 2015), remains unclear. We investigated this outstanding issue in 127 typically developing 2nd graders (7- to 8-year-olds). They all completed a single-digit addition and multiplication task at the end of second grade. We assessed cognitive control via non-numerical inhibition (animal Stroop) and updating (n-back) tasks. Calibration of confidence was measured as in Rinne and Mazzocco (2014) by asking children on a trial-by-trial basis, to verbally report their confidence in the accuracy of their answer during the arithmetic tasks (i.e., “Positively sure”, “Kind of sure”, “Not sure”). Combinations of this confidence rating and correctness of the given answer were assigned calibration scores (i.e., correct answers yielded a score of 2 if children were “Positively sure”, 1 if they were “Kind of sure”, and 0 if they were “Not sure”. This scale was reversed when the answer was incorrect). A classic symbolic number comparison task was administered as a measure of numerical magnitude processing. Measures of children’s motor speed and intellectual ability were included as control variables. Table 1 depicts the associations between the main variables under study. These data reveal that calibration of confidence and numerical magnitude processing were significantly related to addition and multiplication. Inhibition was related to addition but not to multiplication. Follow-up regression analyses revealed that calibration of confidence and numerical magnitude processing remained unique predictors of addition and multiplication, and that inhibition was a unique predictor of addition. We also calculated Bayes factors (Figure 1) to quantify the evidence in favor of the role of our different variables under study. Following the interpretation guidelines by Wetzels & Wagenmakers (2012), the current data provide decisive evidence for the unique role of both calibration of confidence and numerical magnitude processing in individual differences in arithmetic ability. These data stress the importance of children’s calibration of confidence, which should be considered as an important variable in studies on children’s arithmetic performance.