Conceptual Framework
Vision of Learning: Understanding student thinking about the subject matter (1.1)
As we approach the twenty-first century in an ever-expanding global economy, schools are required to prepare candidates to achieve rigorous intellectual standards. These emerging standards require that candidates engage in complex problem solving at all school levels. The standard of performance that candidates are expected to achieve does not demand merely a generic application of critical thinking. Rather, within subject matters, candidates are expected to learn to reason using the concepts and tools of particular disciplines. That is to say, for example, in mathematics students are expected to learn to reason as mathematicians do, to link mathematical ideas, and to apply mathematics to authentic and rigorous tasks. This concept of student learning for most pre-service teachers has not been a part of their own school experience. Attending to these kinds of learning outcomes requires that teachers know how to observe the myriad ways in which students demonstrate their thinking as well as how to support and to extend student thinking. Such attention may include understanding and observing demonstrations of students’ naïve theories about forces acting in the physical world as part of a unit of instruction on force and motion in physics. It might include understanding that mathematical ideas are evidenced as children use different strategies to reason about solutions to time/distance problems. It might include seeing the ways in which students’ lack of prior knowledge about spiders interferes with the kinds of inferences they make while reading a text about spiders. This kind of pedagogical knowledge is very complex, very subject matter specific, and very sensitive to developmental stages in children’s and adolescents' growth.
In course and field experiences, candidates are apprenticed to observe and draw on student thinking as they design learning opportunities for K-12 students. For example, one of our subject matter methods courses, LRN_SCI 326, Mathematics in the Elementary School from an Advanced Point of View, is taught so that candidates are able to reconstruct their own mathematical knowledge as well as develop new views of a mathematics classroom. They participate in a "model mathematics classroom" in which they work in groups, explain their thinking and strive to understand and help others understand, but at the same time reflect on mathematical pedagogy. So, for example, multidigit multiplication is taught in base 8 so that students do not know any multiplication facts and cannot automatically do their learned procedure. They use base 8 physical materials that enable them to construct their own mathematical methods of multiplying. Thus, they reconstruct their own concepts and methods of multiplication, but now with understanding. Then they discuss their new mathematical understandings, their feelings at the point of initial lack of understanding, and the role of the community in facilitating their engagement and learning.
[IPTS 1, 4, 8, 10; LAS 1, 2, 3; TECH 2, 3, 5, 6, 7, 8]