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You are using the online sample of the Teaching and Learning about Decimals CDROM.
Not all linked pages are accessible in this version. For further information about the
complete CDROM please
click here.
Using Decimal Comparison Tests
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Full Test (30 items) |
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Quick Test(13 items) |
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Zero Test (14 items) |
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About the Decimal Comparison Tests
The purpose of the Decimal Comparison Tests is to diagnose how students are thinking about decimal notation. The student is asked simply to choose the larger decimal number from pairs of decimals. Researchers estimate that only about half of 11 year olds understand whole number place value well and many less understand decimals. Comparing the size of decimals is a good task to diagnose difficulties, because the instructions for students are simple and quick to carry out, whilst the different patterns amongst the answers are very revealing.
The full Decimal Comparison Test of 30 items has been very carefully constructed. The marking instructions explain how to identify, in the patterns of right and wrong answers, most of the misconceptions about decimal notation that are known to be common in schools. Click here for a summary of these misconceptions categories. The test is quick to administer, taking less than 10 minutes for a class.
A Quick Comparison Test of only 13 items, is also available. This is easier to mark. It classifies students into three broad groups: longer-is-larger misconceptions, shorter-is-larger misconceptions and apparent-experts. Apparent-experts get nearly all the questions right and usually will have mastery of the topic. Sometimes, however, they are successfully following rules which they do not understand.
The Zero Comparison Test of 14 items identifies a different set of misconceptions. The student is now asked either to choose the larger decimal number from each of a list of pairs of decimals or to say if they are equal. This test identifies money thinkers more reliably than the standard tests, and also those students who have some of several different problems with zero.
Reliability of the tests
Children's answers are surprisingly consistent on the Decimal Comparison Tests, even across long periods of time. It is also surprising to see how many students consistently answer the separate items, following one of the known misconception patterns. We think the data from the comparison test is sufficiently valid over time for it to provide a useful guide for teaching. In one test-retest experiment (Moloney and Stacey, 1996) we found that only 6 of 50 junior secondary students changed their classification over one year. Since only 40% were experts, it was disappointing that so few changed.
Occasionally students are not consistent. Sometimes this is because they learn as the test prompts them to think more carefully about the task. Sometimes it is because they have several different ideas, which different items prompt. It is also possible that there are rare patterns of thinking about decimals that have not yet been discovered.