Mathematics Teacher Educators' Perceptions and Use of Cognitive Research

Instructors (N = 204) of elementary mathematics methods courses completed a survey assessing the extent to which they value cognitive research and incorporate it into their courses. Instructors' responses indicated that they view cognitive research to be fairly important for mathematics education, particularly studies of domain‐specific topics, and that they emphasize topics prominent in psychology studies of mathematical thinking in their courses. However, instructors reported seldom accessing this research through primary or secondary sources. A mediation analysis indicated that mathematics methods instructors' perception of the importance of the research predicts their incorporation of it in their courses, and that this relation is partially mediated by their accessing of it. Implications for psychologists who have an interest in education and recommendations for facilitating the use of cognitive research in teacher preparation are discussed.     

Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison

This study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade in the representations used to perform number line estimation, numerical categorization, and numerical magnitude comparison tasks. Individual differences within each grade in proficiency for the three tasks were strongly related. Experiment 2 (27 girls and 13 boys, ages 5-6 years) replicated results from Experiment 1 and demonstrated a causal role of changes in categorization in eliciting changes in number line estimation. Reasons were proposed for the parallel developmental changes across tasks, the consistent individual differences, and the relation between improved categorization of numbers and increasingly linear representations.     

Young girls’ arithmetic and spatial skills: The distal and proximal roles of family socioeconomics and home learning experiences

The present study addressed girls’ (N = 127) early numerical and spatial reasoning skills, within the context of a critical environment in which these cognitive skills develop, namely their homes. Specifically, proximal links between distal family socioeconomic conditions and first-grade girls’ arithmetic and spatial skills were examined (mean age = 6.72 years; SD = .34). The proximal roles of two factors were considered: the general learning characteristics of girls’ homes, and the kinds of math and spatial learning activities in which girls participated. General quality of the home learning environment and specific math activities mediated the relation between family socioeconomics and girls’ arithmetic skills. In contrast, socioeconomics and home learning experiences were related to girls’ spatial skills indirectly only through their verbal skills; spatial activities were not proximal predictors of spatial skills. For both arithmetic and spatial skills, mothers’ spatial skills were a strong predictor. Future research and intervention implications of these findings are discussed.