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July 24, 2015


When you get around to doing something the second time...there is always something new that happens to keep things interesting.

Last year I had worked with some 7th graders on integer subtraction by making something move from its current position to a target position. Here is a note on the same

"Children initially tend to understand negative numbers in integers as a loan. However, even a simple situation like 5-(-5)=5+5=10 becomes hard to comprehend. A number line is a better visualization for introducing negative numbers. This happens implicitly when using Scratch as it incorporates the Cartesian coordinate system. A character (sprite) when placed at (0,0) is at the center of the display. Changing x with a positive number takes it to the right correspondingly changing x with a negative number takes it to the left.
As children use a change x function they get a handle of the integers. In time they get curious and check what happens with change y with integers to get a sense of the Cartesian system.

As the children felt more confident they created a simple game with integers: the user needs to give the number to add to take a character from a start location to a target location. Though initially the children put numbers and situations they already knew e.g. two positive numbers start:5, target:10, to add:(10-5)=5. The program would then move from the start to start+to add and check that the result is the target. Once the children are comfortable enough to randomize one and then both the starting point and destination, all possibilities of subtraction scenarios arise e.g. start:10, target:5, to add:(5-10)=-5. They also clearly see the need to move left to get to the target. Similarly, start:-5 target:5 to add:5-(-5)=10 also makes sense as the target is to the right of the object."

The emphasis last time was a bit on programming and getting the strings and numbers to match up well. 

But this time the children were implicitly unconvinced about the motivation of the character (in one case) the crab to move. The crab must have had a reason to have a target, right. So they came up with their reasons. The crab was tired and wanted to sit on a rock!

There were other stories of a diver catching a fish, of a cat catching a mouse, someone looking for a key, etc). The character was at the current location and there was a visible target that the children could see is behind or ahead of the character. This helped them re-look at the result they got to see if it made sense i.e. positive number means the rock should be in ahead and a negative result is a rock behind me.

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