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Abstract
Two studies were conducted to explore mathematical precocity in young children. Study 1 examined mathematically gifted first and third graders' working memory development. The results showed that mathematically gifted children's working memory growth was similar to that expected of their age peers. Study 2 examined changes in mathematically gifted children's conceptual structures. Mathematically gifted children were roughly a year ahead of their age peers in the rate of development of conceptual structure in the numerical domain. A neo‐Piagetian theory of intellectual development was used to explain these seemingly conflicting findings. The relation between working memory growth and conceptual development was discussed throughout the paper.
Acknowledgements
We thank Nancy M. Robinson, Robert D. Abbott, Virginia W. Berninger and Julie Busse for making their Math Trek data available. We also thank the children and faculty at Pinecrest School Thousand Oaks.
Notes
1. This is equivalent to Case's ‘central conceptual structure in the numerical domain’. Central conceptual structures are domain‐specific in content but at the same time subject to system‐wide constraints.
2. These measures require that participants carry out an action while trying to memorize target numbers or spatial layouts.
3. This system is typically described in Case's theory as consisting of four levels or sugstages: predimensional, undimensional, bidimensional and integrated bidimensional substages. These correspond to Levels 1 through 4, respectively.
4. This level is referred to as vectorial and includes rational numbers and negative numbers.
5. The gifted children participated in Project Math Trek (see Robinson et al., Citation1996).
6. These children participated in the Case project (see Case & Okamoto, Citation1996).
7. Item 5 should have included two sub‐items. However, a single item of this type was administered in the non‐gifted study.
8. Because our items are dichotomous, the data lend themselves to violations of normality. Various methods have been developed to estimate from such data, for example, the categorical variable methodology (Muthén, Citation1984) and the asymptotically distribution‐free (ADF) estimator (Browne, Citation1984). However, these estimation methods require a much larger sample size. We thus used the ML method.