DragginMath: When Things Happen and When Things Don’t

When using DragginMath, you enter expressions in the Top Text. This causes interactive pictures to appear. Then you drag the parts of these pictures around to make algebra happen. But sometimes, when you drag things, nothing happens, and that’s OK.

Tap the Top Text now and enter the expression 2+3+4. Be sure to tap ↲ on the screen keyboard or return on a regular keyboard when you are done typing. The resulting picture is called an operator tree. Within these pictures, the bubbles containing symbols are called nodes.

Put your fingertip on the 2 node and leave it there. See the node turn red. This color means DragginMath knows you are touching the 2 node, but you haven’t done anything with it yet. Lift your finger. Now try touching the other nodes to see what happens when you do that. Also, notice that when you touch a node, the corresponding symbol in the Top Text turns red.

Touch 2 again. Without lifting your finger, drag 2 straight to the left, away from 3. After a short distance, 2 changes from red to magenta. Lift your finger. See the node turn black and slide back where it came from. The picture now looks just like it did before you dragged the node. As far as you can tell, nothing happened, and that is exactly correct.

Touch 2 again. This time, drag it up a short distance. See it turn blue. Lift your finger. Once again, nothing happened.

Touch 2 again. This time, drag it down a short distance. See it turn green. Lift your finger. Once again, nothing happened.

These various colors are like the gearshift of a car. For example, some gear settings in a car are good for going forward at various speeds, while one gear setting is good only for going backward slowly, and another setting is good only for going nowhere. When dragging nodes in DragginMath, the color when you drag determines what kind of algebraic changes you can make at that time. If you decide you don’t want to do anything after all, just lift your finger and see everything go back the way it was before you touched the node. In other words, nothing happens.

Touch 2 again. This time, drag it straight to the right, toward 3. When you pass 3, something interesting happens: 2 turns purple. Also, 3 moves where 2 used to be. Lift your finger. See 2 move where 3 used to be. In this example, you told DragginMath to do something, and it knew how to do it, so it did. We will talk more about this particular change soon.

Touch 2 again. Drag it directly over the 4 node. Several things happen to tell you that you are on target over the 4.

1. You hear a (((click))).
2. The background color of the screen changes slightly.
3. A black border appears around a portion of the operator tree diagram.
4. A target icon 🎯 appears in the upper left corner.

After only a little experience with DragginMath, these signals become natural to you and you just know when you are on target. Now lift your finger. In this example, dragging 2 onto 4, nothing happens. Maybe you thought you were telling DragginMath to do something, but it didn’t know what you meant, so it did nothing.

To use DragginMath, you must learn which color mode to be in when you want to make a particular algebraic change. Fortunately, there isn’t much to know about that. And if you try to do something DragginMath doesn’t understand, it simply and quietly does nothing.