Contribution: This study focuses on microcontroller circuits and aims to: 1) investigate the impact of formal reasoning on students' post-knowledge using catastrophe theory; 2) compare the different combination sequences of tangible user interface (TUI) and graphical user interface (GUI); and 3) assess the usability of both interfaces and explore…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

A longitudinal study of students' developing understanding of decimal notation has been conducted by testing over 3000 students in Grades 4 to 10 up to 7 times. A pencil-and-paper test based on a carefully designed set of decimal comparison items enabled students' responses to be classified into 11 codes and tracked over time. The paper reports on…