Spontaneous Focusing

On quantitative Relations (SFOR) has been found to predict the development of

rational number conceptual knowledge in primary students. Additionally, rational

number knowledge has been shown to be related to later algebra knowledge. However,

it is not yet clear: (a) the relative consistency of SFOR across multiple

measurement points, (b) how SFOR tendency and rational number knowledge are

inter-related across multiple time points, and (c) if SFOR tendency also predicts

algebra knowledge. A sample of 140 third to fifth graders were followed over a

four-year period and completed measures of SFOR tendency, rational number

conceptual knowledge, and algebra knowledge. Results revealed that the SFOR was

relatively consistent over a one-year period, suggesting that SFOR is not

entirely context-dependent, but a more generalizable tendency. SFOR tendency

was in a reciprocal relation with rational number conceptual knowledge, each

being uniquely predictive of the other over a four-year period. Finally, SFOR

tendency predicted algebra knowledge three-years later, even after taking into

account non-verbal intelligence and rational number knowledge. The results of

the present study provide further evidence that individual differences in SFOR

tendency may have an important role in the development of mathematical knowledge,

including rational numbers and algebra.

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