In this work, we discuss the importance of underlying theoretical assumptions in research, focusing on the conclusions reached when analyzing data from a misconceptions constructivist (stable, unitary) perspective in contrast to a fine-grained constructivist (resources, knowledge-in-pieces) perspective. Both frameworks are rooted in the idea that…

Misconceptions in geometry are an essential problem in the understanding of geometric terms by primary and pre-primary aged children. Present research shows some misconceptions in geometry demonstrated in the understanding of circles, squares, triangles and oblongs for children in the last year of kindergarten and pupils in the last year of…

Science classes are full of abstract or challenging concepts that are easier to understand if an analogy is used to illustrate the points. Effective analogies motivate students, clarify students' thinking, help students overcome misconceptions, and give students ways to visualize abstract concepts. When they are used appropriately, analogies can…

Discussion of students' prior knowledge and its effect on analogical reasoning focuses on four case studies of high school and college students that were designed to determine factors important for success in overcoming misconceptions via analogical reasoning. Explanatory models are explained, and abstract transfer versus explanatory model…

Two astronomy professors, using the Decoding the Disciplines process, help their students use abstract theories to analyze light and to visualize the enormous scale of astronomical concepts. (Contains 5 figures.)

This document is the fourth volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 42 research reports by presenters with last names beginning between Mul and Wu:…

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…