The use of open problem-solving tasks in mathematics education challenges teachers’ beliefs, knowledge and practices. This article examines the practices of two primary teachers and their 3rd to 5th grade classes during a three-year in-service teacher training project aiming to increase mathematical problem-solving in class. Three lesson videos and two interviews with each teacher were used to provide the data for this study. The results show how different teachers in terms of their beliefs, knowledge and practices during the problem-solving activities can produce mathematically different learning opportunities. Teacher Ann saw mathematics as too rigorous, and to combat this, gave her pupils a great deal of autonomy. Her pupils were encouraged to come up with creative solutions. Teacher Beate emphasized mathematical understanding. Her pupils were guided cognitively and they came up with mathematically elegant solutions. In teaching open problem-solving both autonomy and cognitive guidance are needed.
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