Achievement Test
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In principle, what should be diagnosed/evaluated in an achievement test is not the correctness of answers students made, but logical reasoning they did.
One cannot proceed a logical reasoning without understanding the meaning of subjects. Thus, if you want to test whether students properly understand the subject, then you should make such a test that obliges students to do logical reasoning to reach solutions.
What is this type of test like ? It is the test that asks "what?" and "why?" to students, explicitely or implicitely.
- The higher the grade is the more students drop out of mathematics. This measns that the higher the grade is the more it is required to understand properly the meaning of subjects.
In the beginning of learning, students might be able to follow teachers without being able to answer to "what?" and "why?" But this situation does not last long.