Self-efficacy and problem-solving skills in mathematics: the effect of instruction-based dynamic versus static visualization

ABSTRACT

This study explores the self-efficacy and problem-solving skills of middle school mathematics students. The students – 111 9th graders who were studying a unit for the analysis of function – were given mathematics instruction that was based on either dynamic or static visualization. Findings revealed a positive impact of instruction that was based on dynamic visualization that involved the use of the technological GeoGebra application, compared to instruction that was based on static visualization. The students who were exposed to dynamic visualization instruction displayed high levels of mathematics self-efficacy in real time. Improvement in the mathematics problem-solving skills of these students was shown both immediately after the intervention and three months later, demonstrating better conceptual and procedural understanding. The findings imply that exposure to instruction-based dynamic visualization contributed to closing both the affective and cognitive gaps between high and low achievers. The study offers a significant contribution to theoretical and methodological aspects, and provides practical understanding of instruction-based dynamic visualization about performance of mathematics students in both the affective and cognitive domains.

KEYWORDS:

• Dynamic visualization
• high and low achieving
• mathematics self-efficacy
• problem-solving skills
• static visualization

Acknowledgement

The authors thank the Shamoon College of Engineering (SCE) for partially supporting the fourth author as a research assistant.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 $⟨g⟩={\displaystyle \frac{\mathrm{\%}{\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}-\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}-\mathrm{\%}{\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}_{\mathrm{p}\mathrm{r}\mathrm{e}-\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}}{100-\mathrm{\%}{\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}_{\mathrm{p}\mathrm{r}\mathrm{e}-\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}}}$.

Additional information

Notes on contributors

Zehavit Kohen

Zehavit Kohen, Ph.D. is a mathematics education researcher. Her research focuses on promoting professional development and meta-cognition of high-school mathematics teachers, assessment of STEM (science, technology, engineering and mathematics) education with focus on quantitative and qualitative (mixed-method) analysis and integrating educational technology into teaching and learning of mathematics. Her doctoral research (Suma Cum Laude, 2011) focused on developing pedagogical self-regulation at preservice teachers in a technological environment, supported by reflection in different foci. During the academic year 2015–2016, she was a Visiting Scholar at the Center to Support Excellence in Teaching (CSET) at Stanford University, where she investigated the professional development (PD) of early-career mathematics teachers who participated in the Hollyhock Fellowship Program. During 2012–2017, she had been a researcher at the Technion Research and Development Foundation and at the Neaman Institute, a national policy research institute in Israel. Her research work focused on assessment of STEM education and on the choice of and retention in STEM careers.

Meirav Amram

Meirav Amram, Ph.D. is an expert in mathematics teaching and learning, and in algebraic geometry. She received her doctorate in 2000 and was the head of the mathematics unit in Shamoon college of engineering (SCE) till 10\2018. She is ranked as an excellent lecturer and has fruitful research in the area of mathematics, as well as mathematics teaching and learning.

Miriam Dagan

Miriam Dagan, M.Sc., is the head of the mathematics unit of SCE in Beer-Sheva (since it was founded in 1995). She received her M.Sc. degree from the mathematics department of Ben Gurion University in 1997. Her thesis title is “Inequalities in mathematics teaching: Deductive possibilities, learning difficulties, and the ways to cope with them”. Her research interests include tertiary education, pedagogical strategies for developing creative mathematical thinking, and graphical approaches for teaching pre-calculus. She has written more than 20 articles and books.

Tali Miranda

Tali Miranda, M.Ed, is a high school mathematics teacher with 29 years of experience. In her graduate studies in mathematics education at Levinsky College of Education, she researched the field of integrating technologies in teaching and learning mathematics, under the guidance of Dr. Zehavit Kohen. She initiated action programs among the students she was teaching and researched the effect of short-term and long-term teaching on a variety of academic and emotional aspects. She graduated her master’s degree with honors by the Dean.