Adaptive number knowledge in secondary school students: Profiles and antecedents

Abstract

The present study aims to examine inter-individual differences in adaptive number knowledge in secondary school students. Adaptive number knowledge is defined as a well-connected network of knowledge of numerical characteristics and arithmetic relations. Substantial and relevant qualitative differences in the strategies and expression of adaptive number knowledge have been found in primary school students still in the process of learning arithmetic. We present a study involving 879 seventh-grade students that examines the structure of individual differences in adaptive number knowledge with students who have completed one year of algebra instruction. Results of a latent profile analysis reveal a model that is similar than was previously found in primary school students. As well, arithmetic fluency and the development of arithmetic fluency are strong predictors of adaptive number knowledge latent profile membership. These results suggest that adaptive number knowledge may be characteristic of high-level performance extending into secondary school, even after formal instruction with arithmetic concludes.

Developing a Stealth Assessment System Using a Continuous Conjunctive Model

“…Adaptive expertise in arithmetic is defined as the ability to apply procedures flexibly and adaptively to solve mathematics problems (Hatano & Oura, 2003;McMullen et al, 2019). Adaptive expertise in arithmetic consists of two main components -flexibility and adaptability (Nunes et al, 2016).…”

“…Adaptive number knowledge entails a variety of mathematic skills such as the ability to locate magnitude representation and find "nice numbers" (conduct estimations; McMullen et al, 2016). It is the underlying ability that allows one to choose the best problem-solving strategy from a range of available options (McMullen et al, 2019). Adaptive number knowledge can better equip students to think adaptively and flexibly to choose the best solution in different problem-solving contexts (McMullen et al, 2016).…”

Associations Between Adolescents' Subjectively Experienced Emotions and Psychophysiological Reactions in Achievement Situations

“…Raven's test consists of diagrams with one part missing. In this study, only half the items were used and alternating items were picked for presentation (see also McMullen et al, 2019). Responses were scored correct or incorrect; the maximum score was 30 (α = .81).…”