Using graphing software to teach about algebraic forms: a study of technology-supported practice in secondary-school mathematics

Abstract

From preliminary analysis of teacher-nominated examples of successful technologysupported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater depth through case study of two teachers each teaching two lessons of this type. The practitioner model developed in earlier research (Ruthven & Hennessy, Educational Studies in Mathematics 49(1):47-88, 2002; Micromath 19 (2):20-24, 2003) provided a framework for synthesising teacher thinking about the contribution of graphing software. Further analysis highlighted the crucial part played by teacher prestructuring and shaping of technology-andtask-mediated student activity in realising the ideals of the practitioner model. Although teachers consider graphing software very accessible, successful classroom use still depends on their inducting students into using it for mathematical purposes, providing suitably prestructured lesson tasks, prompting strategic use of the software by students and supporting mathematical interpretation of the results. Accordingly, this study has illustrated how, in the course of appropriating the technology, teachers adapt their classroom practice and develop their craft knowledge: particularly by establishing a coherent resource system that effectively incorporates the software; by adapting activity formats to exploit new interactive possibilities; by extending curriculum scripts to provide for proactive structuring and responsive shaping of activity; and by reworking lesson agendas to take advantage of the new time economy.

The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom

“…As a first approach, Ruthven and colleagues (Ruthven, 2007(Ruthven, , 2009Ruthven, Deaney & Hennessy, 2009) designed a model with a focus on key structuring features that shape technology integration into classroom practice. Applications of this model (e.g.…”

Digital curriculum resources in mathematics education: foundations for change

“…Over the past decade there have been numerous research studies investigating the use of digital technologies and of digital resources for mathematics education (e.g., ClarkWilson et al 2014ClarkWilson et al , 2015Drijvers et al 2016;Ruthven et al 2009). It has been claimed (e.g., by Ruthven 2017) that the "new media do not simply replicate the functionality of the old with increasing efficiency…; (but) they make possible qualitatively different forms of interaction between user and medium, based-for example-on the introduction of new types of user interface or on the provision of instantaneous feedback on user actions" (p. 2).…”

“…First, in his ICME 13 paper, Ruthven (2017) asserts that digital technologies (and this may include DCR) are likely to influence instructional activity and interaction between teachers, students and resources through changes in the classroom environment and the mathematical tool system in play. He draws on recent studies that are said to illuminate features associated with the use of digital mathematical tools (e.g., Ruthven et al 2009); and networked classroom technologies (e.g., Clark-Wilson 2010). Many of these studies lean on the framework of Instrumental Orchestration (Drijvers 2012;Trouche 2004), others on the structuring features of classroom practice (Ruthven 2014) framework in connection with technology (e.g., Bozkurt and Ruthven 2017).…”

Graphing formulas: Unraveling experts’ recognition processes

“…Students continue to experience difficulties with seeing the relationship between algebraic and graphical representations, although graphing technology can support students' understanding in linking representations of functions (Kieran, 2006;Ruthven, Deaney, & Hennessy, 2009). In order to further improve education, we first need a domain-specific knowledge base (De Corte, 2010).…”