Teachers'
Algebra Reasoning While Learning with Web Book
Beba (Buzina) Shternberg
bebas@cet.ac.il
The Math Team
CET  The Center of Educational Technology
Israel
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.
