How children learn basic skills such as discriminating between different quantities and counting? According to the dominant Approximate Number System (ANS) theory,humans are born with the ability to discriminate between discrete quantities (i.e.,numbers). Accordingly, early math curriculum should focus on discrete quantities. This theory guides many early-math curricula worldwide. We provide a review of empirical evidence challenging the ANS theory and introduced a more recent theoretical framework, the Approximate Magnitude System (AMS). This theory suggests that continuous magnitudes (such as area, density, volume, etc.) are more intuitive and acquired earlier then the ability to understand numbers. Using examples from early math education practices, we emphasize and demonstrate the potential benefits of taking the AMS approach and using magnitudes as a scaffolding for understanding numbers and more complex math concepts. Insights gained from studies that combines both cognitive psychology and educational research, with the active participation and contribution of early-math teachers, may be of assistance to both cognitive psychologists, interested in how math abilities develop, and to educators, looking to improve math curriculum. We hope that this article will inspire others to consider research in this direction and start a productive discussion on the role of continuous magnitudes in teaching math.
Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics
