Designing digital technology tasks for the development of functional thinking
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ORIGINAL ARTICLE
Designing digital technology tasks for the development of functional thinking Stephan Michael Günster1 · Hans‑Georg Weigand1 Accepted: 25 June 2020 © The Author(s) 2020
Abstract In this paper we introduce a theoretical framework concerned with fostering functional thinking in Grade 8 students by utilizing digital technologies. This framework is meant to be used to guide the systematic variation of tasks for implementation in the classroom while using digital technologies. Examples of problems and tasks illustrate this process. Additionally, results of an empirical investigation with Grade 8 students, which focusses on the students’ skills with digital technologies, how they utilize these tools when engaging with the developed tasks, and how they influence their functional thinking, are presented. The research aim is to investigate in which way tasks designed according to the theoretical framework could promote functional thinking while using digital technologies in the sense of the operative principle. The results show that the developed framework—Function-Operation-Matrix—is a sound basis for initiating students’ actions in the sense of the operative principle, to foster the development of functional thinking in its three aspects, namely, assignment, co-variation and object, and that digital technologies can support this process in a meaningful way. Keywords Functional thinking · Operative principle · Task design · Digital technologies · Empirical investigation
1 Introduction Functions are a common thread that runs through all of mathematics education and acts as a guideline throughout the whole mathematical curriculum (e.g. Core-PlusMathematics Project 2015). Through exposure to functions, students acquire a variety of topic-related and universal mathematical skills. They recognize and describe functional relationships in different situations, analyze, interpret and compare various representations of functions, characterize functions by their properties and solve realistic problems with the help of functions. The development of the function concept in school is based on a wide spectrum of phenomena and depictions. Learners develop an idea of the function concept in relation to different situations and representations and come to understand how these are interwoven with the technical
* Hans‑Georg Weigand [email protected]‑wuerzburg.de Stephan Michael Günster stephan.guenster@uni‑wuerzburg.de 1
Julius-Maximilians-University, Würzburg, Germany
aspects of the concept. Hence, the concept of function develops on various abstract levels. While developing mathematical concepts in the classroom, tasks play a very important role. They substantiate educational objectives and skills associated with understanding the concept. However, the term ‘task’ covers a wide range of applications in mathematics education. A task can vary from a single question asked by a teacher, over a system of exercises, to a whole project or to “rich learning tasks” (Flewelling and Higginson 2003), as Leuders (2015)
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