Fingers, blocks, pebbles and a myriad of other physical manipulatives are all tools helping students problem solve. But does that usefulness carry over when physical manipulatives give way to digital ones? The answer is a resounding yes!

In her dissertation paper “Do Gestural Interfaces Promote Thinking?” published in 2011, Ayelet Segal, confirms that interactions with touch screens are effective in helping students learn. The dissertation discusses three main types of interactions that go hand in hand with digital manipulatives: tapping, sliding, and rotating.

1. Tapping

Because the action of tapping mimics discrete counting, it can be just as effective as counting pebbles or using fingers--even more so because a student can have unlimited taps, while he or she will eventually run out of both fingers and pebbles!

But it’s essential that the taps are very closely tied to the thought process of the student. For example, tapping a screen to highlight individual pieces in an addition problem is much more effective than tapping once to highlight several pieces at a time.

2. Sliding

The act of sliding a finger across a screen can quite naturally represent the continuous increase or decrease of an amount, which makes it an ideal motion for helping students understand number lines or volume. Similar to tapping, making the cognitive connection between the mental model and movement is more important than the action itself.

3. Rotating

Rotating objects and shapes, whether in the real world or on the screen, can help students solve puzzles while reinforcing conceptual understanding and spatial awareness.

In her study, Segal found that students who rotate shapes by sliding their finger across the screen solve puzzles with more accuracy than those who tap or click to achieve the same movement.

In the video above, a student manipulates a physical object which directly translates into what is happening on screen. Learning by rotating shapes, whether digital or physical (or both!), can be a great asset in learning about 3D shapes and 3D geometry.

What it all means:

While tapping, sliding, and rotating can all be very effective in helping students model mathematical concepts, the most important factor is that the software they are using allows for the right gestures at the right time. Educational technology is at its best when movement naturally and directly relates to mental models.

For more insights on this topic, download the Digital Manipulatives Toolkit: