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Pickering, Jayne; Adelman, James S.; Inglis, Matthew – Journal of Numerical Cognition, 2023
Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by…
Descriptors: Number Concepts, Multiplication, Symbols (Mathematics), Mathematics Skills
Hurst, Chris; Hurrell, Derek – Mathematics Education Research Group of Australasia, 2016
Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…
Descriptors: Multiplication, Number Systems, Teaching Methods, Number Concepts
Carrier, Jim – School Science and Mathematics, 2014
For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…
Descriptors: Multiplication, Logical Thinking, Abstract Reasoning, Cognitive Structures
McCrink, Koleen; Spelke, Elizabeth S. – Cognition, 2010
A dedicated, non-symbolic, system yielding imprecise representations of large quantities (approximate number system, or ANS) has been shown to support arithmetic calculations of addition and subtraction. In the present study, 5-7-year-old children without formal schooling in multiplication and division were given a task requiring a scalar…
Descriptors: Number Systems, Arithmetic, Multiplication, Young Children

Confrey, Jere; Smith, Erick – Journal for Research in Mathematics Education, 1995
Presents a covariation approach to learning exponential and logarithmic functions based on a primitive multiplicative operation labeled splitting that is not repeated addition. Suggests that students need the opportunity to build a number system from splitting structures and their geometric forms. (30 references) (MKR)
Descriptors: Concept Formation, Exponents (Mathematics), Functions (Mathematics), Learning Theories