The hierarchical relations among mathematical competencies: From fundamental numeracy to complex mathematical skills.

Abstract

Mathematical competencies can be conceptualized as layers of knowledge, with numeracy skills as the foundational core and more complex mathematical skills as the additional layers over the core. In this study, we tested an expanded hierarchical symbol integration (HSI) model by examining the hierarchical relations among mathematical skills. Undergraduate students (N = 236) completed order judgement, simple arithmetic, fraction arithmetic, algebra, and verbal working memory tasks. In a series of hierarchical multiple regressions, we found support for the hierarchical model: Additive skills (i.e., addition and subtraction) predicted unique variance in multiplicative skills (i.e., multiplication and division); multiplicative skills predicted unique variance in fraction arithmetic; and fraction skills predicted unique variance in algebra. These results support the framework of the HSI model in which mathematical competencies are related hierarchically, capturing the increasing complexity of symbolic mathematical skills.

Research and Pedagogies for Early Math

“…For example, teaching only non-constrained and higher-level skills may be counterproductive given that "lower-level" knowledge may be necessary for effective learning and use of higher-level processes, perhaps especially in hierarchical content domains such as math, e.g., [39,74,75]. Further, researchers of color have argued that avoiding lower-level skills and knowledge may not serve the needs of some communities because they have not had equitable opportunities to learn them [76,77].…”