Prof. Nigel Calder

Mobile technologies are everywhere! We use them to communicate, to work, to learn, and to play. But how might we best use them to improve the teaching and learning of mathematics? Can they make the learning experience different and if so, in what ways? How might this help students to learn?

Mobile technologies, in the form of smartphones and tablets, such as iPads, can be used to change the nature of the learning experience. There are affordances (opportunities and constraints) that are associated with this. For instance, mobile technologies can make the learning experience more visual and interactive. Students can engage with visual representations of the mathematics and move various representations around on the screen. This might be in the form of graphs, where they can easily draw a range of graphs to represent data, or might very quickly plot a series of parabolas and be able to investigate the variables that change when transforming them. This is not easily done with pencil-and-paper technology and in some cases is not possible.

The mathematics might also be done by drawing geometric shapes or angles and investigating their properties by moving them or changing their attributes such as size. As well, similar to the way CAD works in design or architecture, students can create 3-dimensional objects and manipulate them so that they can view them from different angles.

Linked to these affordances is the ease with which mathematics’ solutions can be created, evaluated and then either modified, or if appropriate, started again. When students can very easily compare and contrast mathematical models or situations, it enhances critical thinking as well as mathematical thinking. This might also lead to greater cognitive risk-taking – experimenting and exploring different mathematical problems and situations.

Another affordance is that of creating multiple representations that are linked to each other. Research has indicated that symbolic, numerical and visual representations can be worked with simultaneously, emphasising the connections and allowing students to move between them in a way that develops mathematical understanding and thinking. At a basic elementary-school level, for instance, children can put basic formulas (symbolic) for the times tables into a spread sheet, form the tables of numbers (numeric) and draw the associated line graphs (visual). If they change one number in the table, the graph will automatically change and so they can see the relationship very easily.

From our research with using mobile technologies for teaching and learning mathematics, students also use other representations such as photos (including screen shots), videos (including screen casting where the students record their thinking) and aural representations in their mathematics learning. With mobile technologies, there is also the haptic affordance, as the user can directly interact with the screen with touch, dragging or pinching movements.

These aspects lead to the potential to reshape the mathematics or the mathematics learning experience, making it more engaging.

Other research work that we have done in elementary school, secondary school and tertiary contexts with apps shows that students find it more engaging with many becoming more positive towards mathematics. Many students commented that they enjoyed doing the mathematics through apps rather than doing lots of similar examples in their books. In fact, they still do lots of examples but it can be in a fun, interactive way. They found learning this way motivating.

Photo by Garry Knight, used under CC license

However, to be most effective, the apps need to have a creative aspect, or focus on a key skill and level that the student needs. There are many poor apps available. Just having fun and not being challenged or learning is not helpful after the first burst of enjoyment is over! Teachers play a key role in this learning. They not only need mathematical and some technological knowledge (although sometimes the students can help them with this!) they also need to understand what each student understands and what learning experience or app will best help their learning. This enables them to better differentiate and personalise the learning for each child rather than teaching the same thing to everyone at the same time, even when each student has different understanding. There is an insightful statement that technology can enhance good teaching, but good technology can’t replace poor teaching (OECD, 2015).

Using mobile technologies also enables more real-life situations to be modelled and investigated. This includes the possibility of doing mathematics analysis in the field, perhaps with augmented reality apps. Using virtual technologies, an area that like robotics is growing rapidly, changes the nature of the mathematical learning situation.  Our research has also shown that using mobile technologies leads to collaborative problem solving, a key real-life process. Mobile technologies appear to be most effective as part of socio-material assemblages, with the social aspects such as discussion, and other tools being as important as the actual mobile technology. Most important is that this activity leads to greater mathematical understanding and thinking. For that’s the key purpose of teaching and learning mathematics!

Nigel Calder is Associate Professor in the Faculty of Education at the University of Waikato, New Zealand

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