Tool Use and the Development of the Function Concept: From Repeated Calculations to Functional Thinking

Abstract

ABSTRACT. The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how the use of computer tools may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a point of departure and the notions of emergent modeling and instrumentation as design heuristics, a potentially rich technology-intensive learning arrangement for grade 8 students was designed and field-tested. The results suggest that the relationship between tool use and conceptual development benefits from preliminary activities, from tools offering representations that allow for progressively increasing levels of reasoning, and from intertwinement with paper-and-pencil work.

What Mathematics Education May Prepare Students for the Society of the Future?

“…Next to the computer tools developed by the group of Hoyles cum suis (e.g. Bakker, Kent, Noss & Hoyles, 2009), and the Simcalc software developed by Kaput and associates, we may refer to the computer tools developed in design experiments some of us have been involved in, e.g., on Data Analysis (Cobb, McClain, & Gravemeijer, 2003), calculus (de Beer, Gravemeijer & van Eijck, 2015;Doorman & Gravemeijer, 2009), and functions (Doorman, Drijvers, Gravemeijer, Boon & Reed, 2012). In our view, the goal of coming to grips with key ideas, and the potential of tailor-made educational computer tools to reach this goal, has to be taken into account when considering which subject matter might be feasible for the majority of students.…”

Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

“…According to Doorman, Drijvers, Gravemeijer, Boon, and Reed (2012), the aspect of the dynamic process of co-variation is shown in the Shanghai lower secondary school textbook. Ronda (2009) states directly that to describe students' understanding, efforts should be made to examine its properties and representations.…”

Improving Grade 7 Students’ Achievement in Initial Algebra Through a Technology-Based Intervention

“…The Algebra Arrows Applet The Algebra Arrows applet is designed to offer students the possibility of constructing and using chains of operations on numbers and algebraic formulas, and as such to foster students' view of function as an input-output chain of operations representing a dependency relationship (Doorman et al 2012). If f is a given function, f(x)=c represents an equation in one variable and it can be interpreted as: which input value in the chain of operations defined by f provides c as an output value?…”

“…In algebra education, ICT use contributes significantly to its learning and teaching (Rakes et al 2010). For example, use of digital tools in algebra education can promote students' development both of symbol sense and of procedural skills (Bokhove and Drijvers 2010b), can be effective for improving conceptual understanding and procedural skills of secondary school students (Bokhove and Drijvers 2012) and may foster the development of the notion of function (Doorman et al 2012). Furthermore, use of a digital environment can support students' mathematical problem-solving skills and can contribute to their ability to solve informal algebra problems Van den Heuvel-Panhuizen et al 2013).…”