Rose Mary Zbiek

How Might Computer Algebra Systems Change the Role of Algebra in the School Curriculum

Computer Algebra Systems (CAS) are software systems with the capability of symbolic manipulation linked with graphical, numerical, and tabular utilities, and increasingly include interactive symbolic links to spreadsheets and dynamical geometry programs. School classrooms that incorporate CAS allow for new explorations of mathematical invariants, active linking of dynamic representations, engagement with real data, and simulations of real and mathematical relationships. Changes can occur not only in the tasks but also in the modes of interaction among teachers and students, shifting the source of mathematical authority toward the students themselves, and students’ and teachers’ attention toward more global mathematical perspectives. With CAS a welcome partner in school algebra, different concepts can be emphasized, concepts that are taught can be done so more deeply and in ways clearly connected to technical skills, investigations of procedures can be extended, new attention can be placed on structure, and thinking and reasoning can be inspired. CAS can also create the opportunity to extend some algebraic procedures and introduce and assist exploration of new structures. A result is the enrichment of multiple views of algebra and changing classroom dynamics. Suggestions are offered for future research centred on the use of CAS in school algebra.

Prospective Secondary Mathematics Teacher Preparation and Technology

A systematic literature review suggests three positive conclusions. First, engagement with technologies could enhance PSMTs’ understanding of subject knowledge and develop their positive attitudes toward using technologies. Second, incorporation of mathematics technology and practice-based video cases in teaching methods courses could help PSMTs develop their pedagogical knowledge and knowledge about student learning. Moreover, incorporating technologies in mathematics and methods courses and connecting courses with field experiences could promote PSMTs’ awareness of implementing student-centered mathematics instruction and help them identify as technology innovators. Third, PSMTs’ progress in facilitating student thinking, reasoning, and problem solving seemed elusive. Preparing PSMTs to teach secondary mathematics with technology remains an important endeavor and an emerging research area in need of systematic studies and a global effort to develop a cohesive body of literature.

Contemporary Framing of Technology in Mathematics Teaching

Many types of powerful digital technologies have been part of secondary school mathematics classrooms and mathematics teacher education in many places for decades. However, research on technology in teacher preparation continues to be sparse and challenging to synthesize. To organize and probe ideas, researchers and practitioners need better ways to frame their work. In this chapter, a blend of three conceptual tools is connected to existing literature to describe prospective secondary mathematics teachers’ (PMSTs’) professional growth in technology, content, and pedagogy in integrated and dynamic ways. The blending of Technological, Pedagogical, and Content Knowledge (TPACK); Mathematical Understanding for Secondary Teaching (MUST); and Play, Use, Recommend, Incorporate, and Assess (PURIA) perspectives underscores the complexity of learning to teach mathematics with technology.

Summary and Looking Ahead

Throughout the survey one can see that there is a steady growth in the research around prospective secondary mathematics teacher education. Also several of the studies were repeated in at least two of the sections due to the nature of the factors that were studied. It is difficult to write about teacher knowledge without some acknowledgment of how knowledge or lack of knowledge can impact teachers’ mathematics identities. Furthermore, field experiences are contexts in which PSMTs’ knowledge and identities are impacted and shaped. In addition, the survey revealed that mathematics education researchers are thinking more deeply about how to foster the growth of effective mathematics teachers in a myriad of ways.