Teachers' Algebra Reasoning While Learning with Web Book

Abstract

The availability of interactive web texts and the search for interactive activities that would deepen the involvement of students and teachers in investigations and guided explorations, and thus encourage creativity, have produced much anticipation for a new type of books: web books, sometimes called interactive books.

When we developed the web book "Visual Math: Functions" our aim was to create a prototype of a new kind of mathematics textbook and to let secondary school algebra teachers and students experiment with it. For the experiments to be relevant in the school environment, we chose traditional topics of functions, but organized and approached it in innovative ways. The aim of the "Visual Math: Functions" web book was to allow educators worldwide to study the many facets of interactive electronic writing with the objective of fostering the creativity and thinking habits of students, and the professional growth of teachers and curriculum developers. Under the broader view that curriculum has everything to do with teaching and learning, we consider the web book to be an environment that creates a coherent set of opportunities to learn by constructing meaning for mathematical concepts. Therefore, the web book can be a student's textbook as well as a teacher's guide.

The basis for this paper was the web activity "Vertex paths" - one of the activities that a group of 40 middle school teachers coped with in a distance learning workshop. This activity, dealing with different parametrical representations of quadratic functions, demonstrates that when students are working on traditional topics in an appropriate technological environment, they are encouraged to ask new mathematical questions.

Analysis of the teachers' responses to the activity caused us to examine the issue of algebraic reasoning: to what extent do teachers feel a need to prove their conjectures in an environment that has a potential for depicting an unlimited number of occurrences. We found that the van Hiele model of geometric thinking can be useful as a reference for analyzing the types of algebraic reasoning, while dynamic graphic representations are available to the learner.

In our presentation we will take a glance at the "Visual Math: Functions" web book and introduce the "Vertex paths" activity. We will analyze, according to the van Hiele model, the mathematical objects that were created by the teachers, and the different levels of teachers' algebraic reasoning about these objects. And we will try to expose different advantages and drawbacks of learning with dynamic web texts.