Using 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 computerised Decimal Comparison Test is marked automatically and the results are fed into the various games within the Decimal Games system . This means that each student is then provided with game situations which challenge their particular misconception, and the system is updated as the student learns new ideas. Teachers can read a report which is automatically generated for each student. See the Decimal Games system for instructions on installing and using the computerised test.
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. Read a summary of these misconception 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. It is especially appropriate for older students who have pvercome the more naive 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. The test also identifies students who think that repeated digits in a decimal (e.g. the 7s in 3.7777) can be ignored (and hence equal to 3.7, 3.77, etc.).
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.