ABSTRACT
This chapter focuses on one particular area of mathematical knowledge for teaching: Misconceptions. Misconceptions are not the same as errors, which might be the result of misreading a question or responding too quickly. Cuoco, Goldenberg and Mark discuss the habits of mind that the people develop as mathematicians that exemplify well the messiness of the learning process. Beginning teachers need to know about misconceptions so that they can begin to understand how others learn mathematics and to enable them to be effective in the classroom. Misconceptions are a natural part of learning. They are evidence of intelligent and logical thinking as a pupil tries to make sense of new ideas drawing on their existing understanding of concepts. Real-life contexts can be helpful in giving purpose to and developing understanding of mathematical ideas. However, it can be hard for beginning teachers to know how to draw on this knowledge of misconceptions when planning and teaching.
