tests in school and actual learning

Say, I teach you the date of Albert Einstein's birth.  It was March 14, 1879. So, in one scheme of learning, you have learned if you say or write "March 14, 1879" when I say or write "When was Albert Einstein born?"  Of course, there are more elaborate frameworks describing learning, such as Bloom's Taxonomy of Learning Objective, where I might ask you to paraphrase your answer in other words to cut down on dry, non-comprehending memorization.  Higher up in the taxonomy, I would ask you to apply your knowledge (Al was born after the Civil War), analyze the fact (he couldn't have known Columbus or Henry VIII),  do some synthesis (write a story about Al's first brush with electricity) and evaluate the fact (not very useful, not validated or confirmed).

But what about typical testing?  What about verifying that you have learned?  We want to spend our school time mostly on student learning so the most common approach to testing is to ask the student to respond to a series test "items" and count the number or percentage that he is able to answer "correctly" (in quotes since sometimes through ignorance or pure error, the answer that gets full credit is not the actual correct answer, but rarely).

Consider a test of just 2 items:

Student	Question 1	Question 2	Test score
Circle	1	0	1
Circle	0	1	1
Triangle	0	0	0
Square	1	1	2

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The diagram shows the experience of four students on a two-question test.  The important point is that the two circle students have the same "score" but are 100% opposite in their states of knowledge.  One knows just what the other doesn't.  If we are not running a contest but instead are trying to get the students to learn, what needs to be done for one of the circles is the opposite of what the other needs. Many classrooms are un in such a way that this situation can be detected and corrected but many are not.

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Bill
Main blog: Fear, Fun and Filoz
Main web site: Kirbyvariety