ABSTRACT
In this book, I have related the teaching and learning experiences of students in two schools to the knowledge, beliefs, and understandings they developed as evidenced in a range of assessments. There are a number of theoretical perspectives that might be used to explain or interpret the findings from these schools. For example, the two approaches could be taken as examples of constructivist and nonconstructivist teaching. I have chosen to analyze the results from a situated perspective because this provided a framework that enabled me to address the ways in which individuals dealt with different situations. The breadth of this framework was fundamental in understanding why students used mathematics in one setting and not another; why they appeared to have knowledge, but they did not always choose to use it; and how their learning practices came to influence their practices elsewhere. The findings of this study, interpreted within this framework, illustrate the inherent complexity of the learning process – and, crucially, that it is wrong to believe that assessments merely indicate whether a student has more or less knowledge. Evaluations and analyses of mathematics teaching and learning need to include consideration of the different forms of knowledge that learners develop, the practices in which they engage as learners, and the relationships that such practices afford with the discipline of mathematics (Boaler & Greeno, 2000).
