While the studies mentioned above have focused on how numerical information is represented and manipulated, individual differences in number processing have generally not been considered in this regard. If increased exposure to certain stimuli can produce information processing biases, as has been shown with emotional Stroop task paradigms (e.g. Edwards, Burt & Lipp, 2006), individual differences relating to mathematics should also influence numerical information processing. Patterns observed in emotional Stroop task paradigms demonstrate, for example, that anxious individuals show an involuntary attentional bias for anxiety related stimuli (e.g. Edwards et al., 2006). This bias is thought to result from increased focused attention and memory for anxiety related stimuli above other
stimuli. Thus if, as according to Ashcraft (2006), automaticity of processing for certain stimuli (e.g. anxiety related words) develops as a result of rehearsal and memory, increased mathematics experience could lead to a similar processing “bias” for numerical information.
Although numerical competence is a complex skill, relying on various abilities (e.g. Mazzocco, 2008), the argument that practice and memory lead to increased proficiency with numbers is held by most leading theorists in the area of numerical cognition. Dehaene (1997), for example, argues that it is unlikely that some individuals are biologically predisposed to be mathematics proficient and emphasises the role of memory and practice. For ‘prodigies’, for example, numbers are so practised that the presentation of nearly every number activates learned facts stored in memory about that number. In such cases, Dehaene (1997) argues, it is the extensive exposure and practice with numbers that result in their superior abilities, rather than a predisposed numerical aptitude. Similarly, Butterworth (1999) is of the view that there is no evidence relating mathematics achievement to innate intellectual advantages. Instead, the best predictor of mathematics achievement is practice and training. Furthermore, Stevenson and Stigler (1992) noted that the emphasis placed on innate numerical ability varies cross-culturally. In Japan, for example, effort and learning is emphasised in school performance, whereas American parents often emphasise innate talents and limitations. These cultural differences seem to profoundly influence mathematics achievement, with the Japanese showing an advantage in numerical achievement compared to the American; which further strengthens the case for practice and memory.
Acquiring advanced numerical concepts seem to be particularly difficult, in comparison with language acquisition, for example, which emphasises the need for extensive practice and rehearsal in order to master numerical concepts. Learning to count is easy for children as they are already competent in the necessary activities that they need to engage in to achieve this, such as searching, verbal labelling and one-to-one correspondence. However, equations beyond simple addition require skills that humans are ill-equipped for such as memorisation of large numbers and remembering various different facts that are easily confused with one another (e.g. multiplication tables; Dehaene, 1997). In comparison with literacy development, which mostly involves adding new words to existing concepts of word classes and grammar, mathematical abilities often require developing completely new skills that add on to previously acquired skills, but are conceptually distinct (LeFevre, 2000). Number representation and calculation, for example, require the abilities to read, write and transcode between different symbolic numerical notations (Deheaene, 1992). It seems that at this point in development, mathematics education and cultural variables would greatly influence numeracy. Formal numerical manipulation thus requires an “increasingly sophisticated understanding of numerosity” (Butterworth, 2005, p. 15).
Studies of individual differences in numerical cognition have mostly come from a developmental perspective. However, studying adult samples can be informative of how the experiences encountered earlier in life can influence later numerical information processing. For example, great variability in the processing of basic probability and numerical concepts (numeracy) exists among even highly
educated adult populations (e.g. Jukes & Gilchrist, 2006; Lipkus, Samsa & Rimer, 2001; Peters, Västfjäll & Slovic et al., 2006). This suggests that while children can acquire the necessary skills for performing formal mathematics, they may still not be able to apply these skills to novel situations in adulthood (Dehaene, 1997).
Overall, there seems to be a lack of consideration for mathematics experience in adult numerical cognition studies of both lower level number processing (e.g. number comparison), as well as more advanced number manipulation (e.g. calculation). Mathematics experience, however, seems important to consider, as differences in exposure to numerical information should influence the automaticity with which underlying number meanings are accessed from symbolic formats. For example, if individuals with greater mathematics experience are more proficient at accessing number meaning from a variety of different numerical formats (e.g. arabic digits, number words, quantifier words etc.) it would lend more support to models which assume an underlying analogue code for all numbers (e.g. McCloskey’s Abstract Code model, 1992). If all numbers are translated to an internal amodal code an advantage with numbers should not discriminate between formats. On the other hand, if processing differences between numerical formats (e.g. arabic digits and number words) differ at different levels of mathematics experience, it would be more in line with the accounts which postulate that different numerical formats assume separate representational codes, without the need for a uniform analogue code (Campbell & Clark’s Encoding Complex Model, 1995; Dehaene’s Triple Code model, 1992). Practice with a particular format would thus strengthen its processing
(e.g. arabic digits), while not necessarily influencing the processing of another (e.g. number words).