Teacher-assisted open problem solving
Markus Hähkiöniemi, Henry Leppäaho and John Francisco
Previous research has developed several problem-solving models and suggested that the teacher plays a crucial role in guiding students’ problem solving. However, less is known about the particularities of problem solving and teacher guidance when dealing with open problems which include multiple possible solution pathways. The aim of this study is to understand students’ open problem-solving processes and teachers’ ways of supporting them. Data collection involved videotaping one 9th grade mathematics lesson with two video cameras and capturing the screens of the students’ computers. Seven student pairs worked on an open problem using GeoGe- bra under the guidance of a teacher trainee. We found that students had various kinds of problem-solving processes and that the teacher had a crucial role in guiding them. We elaborate on 9 ways how the teacher guided students to change between phases in open problem solving.
Dr. Markus Hähkiöniemi is university lecturer in the Department of Teacher Education, University of Jyväskylä, Finland. He is interested in classroom interaction and students’ mathematical thinking. His current project focuses on pre-service mathematics teachers’ technology-enriched inquiry-based mathematics teaching in grades 7 to 12.
Dr. Henry Leppäaho is university lecturer on the pedagogy of mathematics in the Department of Teacher Education, University of Jyväskylä, Finland. His research is focused on mathematical problem solving.
Dr. John Francisco is assistant professor in mathematics education in the School of Education at the University of Massachusetts at Amherst, USA. His research interests include students’ development of mathematical ideas and reasoning, personal epistemological beliefs and teacher learning.