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Aug 16

## The pearls of AP Statistics 11

When a student has problems, the culprit may be narrow internal vision.

The next situation is way too familiar: the student has absolutely normal cognitive skills, knows all the theory, understands the problem statement but doesn't see the solution. And then we embark on explanations. However, in most cases the root of the problem lies elsewhere.

Internal vision is the ability to imagine and hold in the working memory a complex picture or structure. An example will help explain its importance.

Wide vision - click to see the video

There is a computer game, called Toybox, which is based mainly on simulating the laws of physics. In most cases the user has to find a move that triggers off a series of events, eventually leading to a construction collapsing. In the first video, for example, one of the canons has a red button. Pressing that button causes canons shooting, and the last cannonball destroys the castle. If you see the whole picture, spotting that special canon with a red button is easy.

Narrow vision - click to see the video

Finding the solution is much more difficult, if you don’t see the whole picture at once and have to scan it by parts, as in the second video. A person with a narrow internal vision behaves as if illuminating the picture with a narrow flashlight. When he/she sees only parts of the picture, it’s difficult to remember them and find the solution. If the student can’t solve the problem, the teacher starts thinking that perhaps he/she doesn’t know the laws of physics and explains the solution.

Nonstandard problem - click to see the video

If in the next problem there is a canon with a red button, the student will find the solution. But what if the key to solution is different, as in the third video?

The same problem occurs when studying sciences. Just having a narrow internal vision may prevent your student from seeing the solution. A wide internal vision is a prerequisite for logic and its underdevelopment may be the main culprit when logic leaves much to be desired. Making students study and repeat the theory in large pieces develops internal vision. Multiple explanations of the same theory by the teacher do not!