An exploration of the mechanisms underlying symbolic number order processing: The role of familiarity

Symbolic number order processing is a central aspect of early numerical development and a key predictor of later arithmetic performance. Accordingly, across three main aims, this thesis endeavoured to establish the cognitive mechanisms and strategies underlying order processing and its association with arithmetic. In my first aim, I considered the proposal that fast memory-retrieval strategies are used when processing familiar sequences, whereas slower alternative strategies (e.g., sequential magnitude comparison) are used when processing unfamiliar sequences. To test this proposal, I developed a novel measure of sequence familiarity using a comparative judgement approach in which participants compared pairs of sequences (e.g., 1-2-3 and 1-3-5) on the basis of their familiarity. Based on these comparative judgements, I was able to produce a ranking and relative scoring of each individual sequence. Then, using this familiarity measure, I found that ordinality was indeed processed faster for more familiar sequences compared to less familiar sequences. Furthermore, more familiar sequences also appeared to elicit a higher proportion of memory-retrieval strategies than less familiar sequences.

Then, to more directly establish the involvement of memory-retrieval mechanisms in order verification tasks, I used a dual-task paradigm. Specifically, because familiar sequences are considered likely to be stored in long-term memory as a verbal sequence (e.g., “one, two, three”), I tested whether loading verbal working memory via articulatory suppression would impair order verification performance both generally and in particular for more familiar sequences. Against my predictions, however, I observed no significant impact of verbal working memory load on order verification performance, nor any differential impact between familiar and unfamiliar sequences. However, it should be noted this study was underpowered and the results were in the expected direction.

Therefore, future replications of this design are needed before firm conclusions can be drawn.

In my second aim, I attempted to establish what causes both the presence and absence of the reverse distance effect – the finding that consecutive sequences (e.g., 1-2-3) are typically processed faster than non-consecutive sequences (e.g., 1-3-5). In particular, I considered the proposal that the reverse distance effect may simply be a specific instance of a more general familiarity effect whereby more familiar sequences are processed faster than less familiar sequences, irrespective of their distance. Supporting this proposal, I found that although many individuals (i.e., 28.57%) did not process consecutive sequences faster than non-consecutive sequences, each and every participant did process familiar sequences faster than unfamiliar sequences. Moreover, when using an order verification task including relatively unfamiliar consecutive sequences (e.g., 6-7-8) and relatively familiar non-consecutive sequences (e.g., 2-4-6), the reverse distance effect was no longer present at the group level.

In my final aim, I considered the proposal that it is the shared use of memory-retrieval strategies that drives the association between order verification and arithmetic fluency. In particular, certain arithmetic problems and task formats (e.g., small problems and verification formats) are thought to elicit memory-retrieval strategies more than others (e.g., large problems and production formats). Consistent with this, regression models indicated that order verification performance was better predicted by performance on i) small compared to large problems, as well as by ii) arithmetic verification compared to arithmetic production.