*Reference: **Critical Thinking in Education*

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The above is the second “Self-Learning” Diagnostic Test for students in middle school and above

*Can you find the illegible numbers represented by the *’s?*

The purpose of this diagnostics is to assess the following:

- Is the student able to move beyond patterned thinking?
- Can the student think in novel ways to resolve problems?
- Is the student’s mental math techniques up to par?

Calculators are very useful. They speed up the ability to calculate. But they should augment and not replace a person’s ability to calculate mentally and on paper with pencil. The person should not get so addicted to calculators that he loses his number sense and the gut feeling when computation go wrong.

This exercise may be timed. If the student can do this exercise rapidly and accurately then his attention and self-learning potential are in good shape. No remedy is needed at this level.

If the student is unable to move beyond patterned thinking then he should review the following documents to learn that different ways of thinking are possible.

#### Mental Math Techniques for Subtraction

#### Mental Math Techniques for Multiplication

This diagnostic helps locate and fill some of the early holes in the understanding of math. Filling of such holes in a subject restores student’s eagerness to learn.

With eagerness comes the ability to self-learn.