Cognitive Foundations for Improving Mathematical Learning

The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance.  The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills.  The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout.

Identifies the relative influence of school and family on math learningDiscusses the efficacy of numerical play for improvement in mathFeatures learning trajectories in mathExamines the role of math language in numeracy skillsIncludes assessments of math skillsExplores the role of cognition in treating math-based learning difficulties

1. Introduction: Cognitive Foundations of Mathematics Interventions and Early Numeracy Influences David C. Geary, Daniel B. Berch, and Kathleen Mann Koepke 2. The Effects of SES, Grade-Repeating, and IQ in a Game-Based Approximate Math Intervention Josh Langfus, Alejandro Maiche, Dinorah De León, Dahiana Fitipalde, Álvaro Mailhos, and Justin Halberda 3. Role of Play and Games in Building Children’s Foundational Numerical Knowledge Geetha B. Ramani, Emily N. Daubert, and Nicole R. Scalise 4. Understanding the Link between the Approximate Number System and Math Abilities Melissa E. Libertus 5. Mathematical Development in Early Home Environment Susan C. Levine, Dominic J. Gibson, and Talia Berkowitz 6. From Cognition to Curriculum to Scale Julie Sarama and Douglas H. Clement 7. Development of Mathematical Language in Preschool and its Role in Learning Numeracy Skills David J. purpura, Amy R. Napoli, and Yemimah King 8. Early Numeracy Skills Learning and Learning Difficulties—Evidence-based Assessment and Interventions Pirjo Aunio 9. Improving the Mathematical Knowledge of At-Risk Preschool Children: Two Approaches to Intensifying Early Math Intervention Alice Klein, Prentice Starkey, and Lydia DeFlorio 10. The Use of Analogies in Mathematics Instruction: Affordances and Challenges Xenia Vamvakoussi 11. The Role of Visual Representations in Mathematical Word Problems Asha K. Jitendra and John Woodward 12. The Role of Cognitive Processes in Treating Mathematics Learning Difficulties Lynn S. Fuchs, Douglas Fuchs, Amelia S. Malone, Pamela M. Seethaler, and Caitlin Craddock 13. Explanations and Implications of Diminishing Intervention Impacts Across Time Drew Bailey