Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software

Abstract

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its availability in classrooms also provides opportunities for positive changes to teaching and learning. Very many examples are documented in the professional and research literature, and in this paper we organize them into 10 types. These are displayed in the form of a 'pedagogical map', which further classifies them according to whether the opportunity arises from new opportunities for the mathematical tasks used, change to interpersonal aspects of the classroom or change to the point of view on mathematics as a subject. The map can be used in teacher professional development to draw attention to possibilities for lessons or as a catalyst for professional discussion. For research on teaching, it can be used to map current practice, or to track professional growth. The intention of the map is to summarise the potential benefits of teaching with technology in a form that may be useful for both teachers and researchers.

Digital Technology in Mathematics Education: Why It Works (Or Doesn’t)

“…The third and final factor concerns the educational context, which includes mathematical practices and the elements of the pedagogical map designed by Pierce and Stacey (2010). Case 2 reveals how important it is that the use of digital technology is embedded in an educational context that is coherent and in which the work with technology is integrated in a natural way.…”

“…The relevance of the educational context has later been elaborated in the notion of pedagogical map by Pierce and Stacey (2010). Concerning the teacher, she establishes a culture of PNA 8(1) discussing graphing calculator output in a format that is close to what is called a "Discuss-the-Screen orchestration" in Drijvers, Doorman, Boon, Reed, and Gravemeijer (2010) and by these means contributes to the co-construction of a shared repertoire of ways to use the graphing device.…”

Assessing the Affordances of SimReal+ and Their Applicability to Support the Learning of Mathematics in Teacher Education

“…For example, in calculus there might be less focus on skills and more on mathematical concepts (Pierce, & Stacey, 2010). In geometry, there might be emphasis on more abstract geometry, and away from facts, more argumentation and conjecturing (Pierce, & Stacey, 2010). Likewise, it may be useful to support tasks which encourage metacognition, e.g., starting with real-world applications, and using SimReal+ to generate results.…”

Assessing the Affordances of SimReal+ and their Applicability to Support the Learning of Mathematics in Teacher Education

“…• Technological affordances at the ergonomic level • Technological affordances at the functional level • Pedagogical affordances at the student level or mathematical task level • Pedagogical affordances at the classroom level or student-teacher interaction level, and • Pedagogical affordances at the subject level, that is the area of mathematics being taught There are a number of pedagogical affordances that can be provided at the student level, e.g., using the tool to freely build and transform mathematical expressions that support conceptual understanding of mathematics, such as collecting real data and create a mathematical model, using a slider to vary a parameter or drag a corner of a triangle in geometry software, moving between symbolic, numerical, and graphical representations, simulating mathematical concepts, or exploring regularity and change (Pierce, & Stacey, 2010). At this level, the motivational factor is important, especially when using visualizations to engage students in mathematical problem solving.…”