Many theories about human number representation stress the importance of a central semantic representation that includes the magnitude information of small integer numbers, and that is conceived as an abstract, compressed number line. However, thus far there has been little or no direct evidence that units and teens are represented on the same number line. In two masked priming experiments, we show that single-digit and two-digit Arabic numerals are equally well primed by an Arabic numeral with the same number of (...) digits as by an equally distant Arabic numeral with a different number of digits (e.g. the priming effect of 7 on the target 9 is the same as the priming effect of 11 on the target 9). The finding was obtained both with a number naming task and with a parity judgement task. This is in line with the hypothesis that units and teens are part of a continuous number line. (shrink)

6 and 14 recently proposed taxonomies that distinguish between four processing states, based on bottom-up stimulus strength and top-down attentional amplification. The aim of the present study was to empirically test these processing states using the priming paradigm. Our results showed that attention and stimulus strength significantly modulated priming effects: either receiving top-down attention or possessing sufficient bottom-up strength was a prerequisite for a stimulus to elicit priming. When both top-down attention and sufficient bottom-up strength were present, the priming effect (...) was boosted. The origins of the observed priming effects also varied between different processing states. We can conclude that our empirical study using the priming paradigm confirmed the presence of four processing states, which displayed a differential pattern of response priming effects and differential origins of the response priming effects. (shrink)

6 and 14 recently proposed taxonomies that distinguish between four processing states, based on bottom-up stimulus strength and top-down attentional amplification. The aim of the present study was to empirically test these processing states using the priming paradigm. Our results showed that attention and stimulus strength significantly modulated priming effects: either receiving top-down attention or possessing sufficient bottom-up strength was a prerequisite for a stimulus to elicit priming. When both top-down attention and sufficient bottom-up strength were present, the priming effect (...) was boosted. The origins of the observed priming effects also varied between different processing states. We can conclude that our empirical study using the priming paradigm confirmed the presence of four processing states, which displayed a differential pattern of response priming effects and differential origins of the response priming effects. (shrink)

Math anxiety results in a drop in performance on various math-related tasks, including the symbolic number ordering task in which participants decide whether a triplet of digits is presented in order (e.g. 3-5-7) or not (e.g. 3-7-5). We investigated whether the strategy repertoire and reaction times during a symbolic ordering task were affected by math anxiety. In study 1, participants performed an untimed symbolic number ordering task and indicated the strategy they used on a trial-by-trial basis. The use of the (...) memory retrieval strategy, based on the immediate recognition of the triplet, decreased with high math anxiety, but disappeared when controlling for general anxiety. In the study 2, participants completed a timed version of the number order task. High math-anxious participants used the decomposition strategy (e.g. 5 is larger than 3 and 7 is larger than 5 to decide whether 3-5-7 is in the correct order) more often, and were slower in responding when both memory- and other decomposition strategies were used. Altogether, both studies demonstrate that high-math anxious participants are not only slower to decide whether a number triplet is in the correct order, but also rely more on procedural strategies. (shrink)

Clarke and Beck discuss in their sections on congruency and confounds literature that has challenged the claim that the approximate number system represents numerical content. We argue that the propositions put forward by these studies aren't that far from the indirect model of number perception suggested by C&B.

Cohen Kadosh & Walsh (CK&W) argue that numerical representation is primarily non-abstract. However, in their target article they failed to consider recent behavioral priming experiments. These priming experiments provide evidence for an abstract numerical representation under automatic conditions.