Digital Technologies in Designing Mathematics Education Tasks

This is a book on the benefits and drawbacks on using digital technology in designing lessons and activities in the math classroom. Over the last few decades, many ideas and teaching methods incorporating new technologies have been created in the hope of teaching math concepts to our students more effectively. One of the key issues addressed in this book is how technology can or cannot play epistemic and pedagogic roles in the classroom. As pointed out in the introduction, there are three main questions considered in the collected research papers, which are:

1. What features of the technology used can be capitalized upon to design tasks that transform learners’ experiential knowledge, gained from using the technology, into conceptual mathematical knowledge?
2. When do digital environments actually bring an essential (educationally speaking) new dimension to classroom activities?
3. What are some pragmatic and semiotic values of the technology used?

These are the main questions addressed by various scholars and leading researchers in the field of digital design.

The book is divided into four sections: Theoretical Considerations, Task Design in Dynamic Geometry Environments, Task Design in Interactive Digital Platforms, and Issues in Digital Task Design. Throughout the book, the theories and practices of designing mathematics education tasks known as Dynamic and Interactive Mathematics Learning Environments (DIMLEs), presented by Karadag et al. in 2011, are used.

In the paper, “The Planimeter as a Real and Virtual Instrument the Mediates an Infinitesimal Approach to Area,” the notion of a didactic cycle is used for students’ understanding of sequences. The activities presented are sensory-motor and symbolic. Page 125 gives a picture of the Amsler 1856 planimeter, which was a professional tool used for measuring the areas of flat shapes. It is made of two joined arms whose constraints allow only reciprocal rotation, a fixed constraint (fixed point) to which one of the arms is attached and which allows only rotation, a lens, called tracer that follows the contour of the figure whose area is to be measured, a wheel physically constrained to rotate only perpendicularly to the second arm, and a counter that keeps track of the distance travelled by the wheel. With the aid of digital technology, instructors can use a planimeter by way of GeoGebra. Figure 3 on page 127 gives us a picture of the GeoGebra Planimeter, which is a virtual model of Amsler’s Planimeter.

In “Designing Innovative Learning Activities to Face Difficulties in Algebra of Dyscalculic Students: Exploiting the Functions of AlNuSet,” Elisabetta Robotti discusses those students affected by developmental dyscalculia (DD). The paper discusses algebra not only in its syntactic aspects but also in its semantic ones. AlNuSet stands for Algebra of Numerical Sets and the research presents how DD students can make sense of algebraic notations. Pages 195–197 give a description of AlNuSet, which is made up of three tightly integrated components: the Algebraic Lines, the Symbolic Manipulator, and the Functions component. In the paper, only the Algebraic Line is used, which represents an algebraic variable as a mobile point on a line, namely, a point that can be dragged along the line with a mouse. Labeled by a letter, the point can be dragged and assumes the numerical values instantiated.

Figures 2 and 3 on pages 196–197 give us a demonstration. In Figure 2, the variable and an expression are presented on the line; by dragging \(x\) along the line, it is possible to verify the equivalence of \(2x+3x\) and \(5x\) since they belong to the same post-it for all values of \(x\). This visuospatial approach to algebra helps the student understand the dynamic representations. In Figure 3, we can see even more of the possibilities, solving \(3x+2=2x\) and \(x^2-1>x+1\).

Some other examples of digital task design are the papers on “Supporting Variation in Task Design Through the Use of Technology,” by Christian Bokhove, and “Tensions in the Design of Mathematical Technological Environments: Tools and Tasks for the Teaching of Linear Functions,” by Alison Clark-Wilson. The paper by Bokhove presents the online intervention designed at Utrecht University, which called “Algebra met Inzicht” [Algebra with Insight] and was made using the Digital Mathematical Environment (DME). In the DME, students can work and receive feedback at any time on modules that have been selected for them. The paper by Clark-Wilson explores a longitudinal study involving 15 English teachers of secondary school mathematics and 75 lesson activities. The investigation on straight lines is presented on pages 334–335, where the students were first unsure of what to do and needed prompts. Most students were able to make the connection that as the coefficient of x became larger, the line would get steeper. Hardly any of the students, however, managed to generalize to the case of fractional or negative coefficients.

This book is rich with research on the ever-growing use of digital technologies in the classroom. With the increasing variety of software, there are many options for instructors to choose from. From classroom demonstrations to having students work in groups and on homework with these technologies, the possibilities are endless. With the focus on task design within DMILEs, which expands and extends the discussion of the task design theme of Tools and Representations in ICMI Study 22, the book offers its reader a very diverse and up-to-date study of these technologies. I highly recommend this book for those instructors who want some fresh ideas or are in search for valuable digital tool-based task design approaches for students to engage in meaningful mathematical experiences. 

Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at pto2@psu.edu. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes.