Magnitude processing of symbolic and non-symbolic proportions: an fMRI study.

BACKGROUND: Recent research indicates that processing proportion magnitude is associated with activation in the intraparietal sulcus. Thus, brain areas associated with the processing of numbers (i.e., absolute magnitude) were activated during processing symbolic fractions as well as non-symbolic proportions. Here, we investigated systematically the cognitive processing of symbolic (e.g., fractions and decimals) and non-symbolic proportions (e.g., dot patterns and pie charts) in a two-stage procedure. First, we investigated relative magnitude-related activations of proportion processing. Second, we evaluated whether symbolic and non-symbolic proportions share common neural substrates. METHODS: We conducted an fMRI study using magnitude comparison tasks with symbolic and non-symbolic proportions, respectively. As an indicator for magnitude-related processing of proportions, the distance effect was evaluated. RESULTS: A conjunction analysis indicated joint activation of specific occipito-parietal areas including right intraparietal sulcus (IPS) during proportion magnitude processing. More specifically, results indicate that the IPS, which is commonly associated with absolute magnitude processing, is involved in processing relative magnitude information as well, irrespective of symbolic or non-symbolic presentation format. However, we also found distinct activation patterns for the magnitude processing of the different presentation formats. CONCLUSION: Our findings suggest that processing for the separate presentation formats is not only associated with magnitude manipulations in the IPS, but also increasing demands on executive functions and strategy use associated with frontal brain regions as well as visual attention and encoding in occipital regions. Thus, the magnitude processing of proportions may not exclusively reflect processing of number magnitude information but also rather domain-general processes.

Using propensity score matching to construct experimental stimuli.

Propensity score matching is widely used in various fields of research, including psychology, medicine, education, and sociology. It is usually applied to find a matched control group for a treatment group. In the present article, we suggest that propensity score matching might also be used to construct item sets matched for different parameters. We constructed stimuli to illustrate the use of propensity score matching in item construction for the exemplary cases of numerical cognition research and reading research. In particular, we provide a step-by-step approach, using the statistics software R, for how to apply propensity score matching for constructing matched stimuli. This approach involves deciding on a population of stimuli, determining and calculating the covariates, and finally applying the propensity-matching method to find a set of items matched to another predefined set. Thereby, we were able to construct well-matched item sets for both examples. Hence, we conclude that the propensity-score-matching method is useful for constructing matched stimuli. Further cases of application are discussed.

Place-value understanding in number line estimation predicts future arithmetic performance.

In multi-digit numbers, the value of each digit is determined by its position within the digit string. Children's understanding of this place-value structure constitutes a building block for later arithmetic skills. We investigated whether a number line estimation task can provide an assessment of place-value understanding in first grade. We hypothesized that estimating the position of two-digit numbers requires place-value understanding. Therefore, we fitted a linear function to children's estimates of two-digit numbers and considered the resulting slope as a measure of children's place-value understanding. We observed a significant correlation between this slope and children's performance in a transcoding task known to require place-value understanding. Additionally, the slope for two-digit numbers assessed at the beginning of grade 1 predicted children's arithmetic performance at the end of grade 1. These results indicate that the number line estimation task may indeed constitute a valid measure for first-graders' place-value understanding. Moreover, these findings are hard to reconcile with the view that number line estimation directly assesses a spatial representation of numbers. Instead, our results suggest that numerical processes involved in performing the task (such as place-value understanding) may drive the association between number line estimation and arithmetic performance.

The influence of math anxiety on symbolic and non-symbolic magnitude processing.

Deficits in basic numerical abilities have been investigated repeatedly as potential risk factors of math anxiety. Previous research suggested that also a deficient approximate number system (ANS), which is discussed as being the foundation for later math abilities, underlies math anxiety. However, these studies examined this hypothesis by investigating ANS acuity using a symbolic number comparison task. Recent evidence questions the view that ANS acuity can be assessed using a symbolic number comparison task. To investigate whether there is an association between math anxiety and ANS acuity, we employed both a symbolic number comparison task and a non-symbolic dot comparison task, which is currently the standard task to assess ANS acuity. We replicated previous findings regarding the association between math anxiety and the symbolic distance effect for response times. High math anxious individuals showed a larger distance effect than less math anxious individuals. However, our results revealed no association between math anxiety and ANS acuity assessed using a non-symbolic dot comparison task. Thus, our results did not provide evidence for the hypothesis that a deficient ANS underlies math anxiety. Therefore, we propose that a deficient ANS does not constitute a risk factor for the development of math anxiety. Moreover, our results suggest that previous interpretations regarding the interaction of math anxiety and the symbolic distance effect have to be updated. We suggest that impaired number comparison processes in high math anxious individuals might account for the results rather than deficient ANS representations. Finally, impaired number comparison processes might constitute a risk factor for the development of math anxiety. Implications for current models regarding the origins of math anxiety are discussed.

Methodological aspects to be considered when measuring the approximate number system (ANS) - a research review.

According to a dominant view, the approximate number system (ANS) is the foundation of symbolic math abilities. Due to the importance of math abilities for education and career, a lot of research focuses on the investigation of the ANS and its relationship with math performance. However, the results are inconsistent. This might be caused by studies differing greatly regarding the operationalization of the ANS (i.e., tasks, dependent variables). Moreover, many methodological aspects vary from one study to the next. In the present review, we discuss commonly used ANS tasks and dependent variables regarding their theoretical foundation and psychometric features. We argue that the inconsistent findings concerning the relationship between ANS acuity and math performance may be partially explained by differences in reliability. Furthermore, this review summarizes methodological aspects of ANS tasks having important impacts on the results, including stimulus range, visual controls, presentation duration of the stimuli and feedback. Based on this review, we give methodological recommendations on how to assess the ANS most reliably and most validly. All important methodological aspects to be considered when designing an ANS task or comparing results of different studies are summarized in two practical checklists.