Katie L. Anderson-Pence

An Examination of Children’s Learning Progression Shifts While Using Touch Screen Virtual Manipulative Mathematics Apps

The purpose of this study was to examine shifts in young childrens learning progression levels while they interacted with virtual manipulative mathematics apps on touch-screen devices. A total of 100 children participated in six mathematics learning sequences while using 18 virtual manipulative mathematics touch-screen apps during clinical interviews. Researchers developed a micro-scoring tool to analyze video data from two camera sources (i.e., GoPro camera, wall-mounted camera). Our results showed that it is possible to document evidence of shifts in childrens learning progressions while they are interacting with mathematics apps on touch-screen devices. Our results also indicated patterns in the childrens interactions that were related to the shifts in their learning progression levels. These results suggest that an open-ended number of tasks with a variety of representations and tasks at varying levels of difficulty led to children refining their understanding and shaping their concept image of mathematical ideas resulting in incremental shifts in learning. The results of this study have important implications about how mathematical tasks in touch-screen apps may prompt childrens incremental learning progression shifts to occur, and thereby promote opportunities for learning. We propose that design features in mathematics apps can be created to support and encourage these learning shifts.

Teachers’ perceptions of examining students’ thinking: Changing mathematics instructional practice

Abstract This paper seeks to illuminate teachers’ perceptions of the challenges and benefits of systematically examining students’ thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers’ perceptions of their experiences with reform-oriented mathematics instruction and systematically examining students’ thinking were analyzed. Analysis of interview data yielded five organizing themes. Findings offer insight into understanding the efficacy of examining students’ thinking as a professional development strategy.