M. Kathleen Heid

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.

An Agenda for Research Action in Mathematics Education: Beginning the Discussion

This article by the NCTMs Research Committee presents a call for an Agenda for Research Action in Mathematics Education. The committee reviews central crosscutting issues for mathematics education research that address concerns from the political and practitioner communities regarding the coherence and utility of mathematics education research. Issues of values and feasibility are highlighted, and a broader definition of theoretical and empirical scholarship is promoted. The committee proposes that the mathematics education research community take up the mantle of authority for defining rigor and evidence in much the same way as NCTM did when facing similar criticism in earlier crises (e.g., the AgendaforAction and the Standards).

Uses of technology in lower secondary mathematics education : a concise topical survey

This topical survey establishes an overview of the current state of the art in technology use in mathematics education from an international perspective, including both practice-oriented experiences and research-based evidence. Three themes are discussed: Evidence for effect; Digital assessment; Communication and collaboration. Exploiting the opportunities provided by technology for teaching and learning requires a rethinking of educational paradigms and strategies. In the context of lower secondary mathematics, mathematical knowledge has the potential to be outsourced to powerful technologies, which challenges current curricula goals and teaching and assessment practices. We predict future possible trends in technology-rich mathematics education and provide a research agenda, looking forward to a position of effective integration of technology to support mathematics teaching and learning in lower secondary.

The impact of technology, mathematical modeling, and meaning on the content, learning, and teaching of secondary-school algebra

Abstract During each day that the secondary subgroup met, discussions were organized around a reaction to the keynote address of that day. Each of these reactions was specially prepared for the secondary group and was intended to address the concerns of secondary-level algebra.

Digital Tools in Lower Secondary School Mathematics Education: A Review of Qualitative Research on Mathematics Learning of Lower Secondary School Students

Mathematics-specific digital technology has an ever-increasing presence in school mathematics learning, and qualitative research has shed light on the potential nature of that learning. Particularly for students at the critical early teen age (ages 10–14, or lower secondary school students), the incorporation of mathematics-specific digital technology in their mathematics instruction can change the representations they see, the mathematical activity in which they engage, and the mathematical content they learn. Research on the impact of mathematics-specific digital technology on lower secondary school students has focused on the mediation of the technology on the relationships between the student and mathematical representation, mathematical activity, and/or mathematical content. To examine the nature of understanding of mathematics learning that can be gleaned from this research, a review of the qualitative research literature on the mathematics learning of lower secondary students in the context of mathematics-specific digital technology was conducted. Fifty-three relevant studies were identified and examined based on a pyramidal model describing the mediation by digital technology of the relationships between the student, and some combination of mathematical activity, mathematical representation, and mathematical content. This chapter uses selected studies from that review to represent ways in which qualitative research probes students’ mathematical work. The selected studies are used to illuminate the breadth and depth of students’ experience with mathematical activity, mathematical representation, and mathematical content, and the relationships among them.

Challenges in Teaching Praxis When CAS Is Used in Upper Secondary Mathematics

The DG focused on the relationship between CAS and mathematics in teaching and learning, educational design and the qualification of teachers’ choices concerning the use and non-use of CAS.

A Processes Lens on a Beginning Teacher’s Personal and Classroom Mathematics

This study examines the relationship between mathematical knowledge—evidenced by a teacher’s engagement in mathematical processes and actions on the products of those processes—displayed by a beginning secondary mathematics teacher (Fiona) in her personal mathematical problem solving and in her classroom instruction. This process and action approach involved analysis of Fiona’s use of four mathematical process/product pairs (representing/representation, justifying/justification, generalizing/generalization, and defining/definition). Two themes arose in the analysis of interview and classroom observation data: (a) Despite demonstrating the ability to do so, Fiona did not regularly engage in processes in her personal mathematics or classroom mathematics, and (b) Fiona focused on selected features of a product or mathematical object rather than attending to a sufficient set of relevant features. These themes suggest a treatment of mathematics as not entirely connected that limited both Fiona’s own problem solving and her students’ mathematical opportunities.