*Reference: **Critical Thinking in Education*

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

*Can you compute the three addition problems above on paper with pencil?*

The purpose of this diagnostics is to assess the following:

**Is the student’s attention well focused?****Is the student confident of his/her answer?****Is the student’s mental addition techniques up to par?**

In this diagnostics, the student

**Adds the numbers from top to bottom to get the sum.****Adds the numbers from bottom to top to verify the sum.****Checks his answers against those provided on the right.**

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’s focus and confidence in math needs improvement then he should practice mental addition on a gradient as follows.

**Practice adding two single-digit numbers.****Practice adding a single-digit number to a double-digit number.****Practice adding two double-digit numbers**

It all boils down to knowing the sum of two single-digit numbers. And, for that, there are limited numbers of combinations. The rest is attention and technique.

The techniques for mental addition help develop basic number sense. The student is then able to rapidly add two numbers, while also verifying the sum at the same time. This skill is then carried forward to rest of the basic math operations. This builds up a confidence that is hard to shake.

This exercise develops the fundamental thinking skill on which subsequent math skills are built. It fills an early hole in the understanding of math.

The following document provides basic mental addition techniques and exercises. After learning these techniques, the student may develop his own techniques.

#### Mental Math Techniques for Addition

This diagnostic helps locate and fill one 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.

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