General Principles: Target examples so that Courtney realizes that she has something to learn! (e.g. she incorrectly thinks that 0.4 < 0.3, but correctly thinks that 0.12 < 0.3). Teach underlying principles with concrete models (e.g. LAB) Incorporate decimals of various lengths in the one situation wherever possible. Conduct class or group discussions on this and other misconceptions. Provide opportunities for Courtney to use her new understandings.

What does Courtney need to learn?
Courtney probably knows very little about decimals, even though she may get quite a lot of the interview and test questions correct and may be able to add and subtract decimals by following rules. This is typical of student misconceptions. She realizes that decimals perform the same function as common fractions and tries to interpret decimal notation in these terms without considering place value. In the "Talking about Place Value" interview, she shows that she has a tenuous familiarity with tenths and hundredths etc, but she does not use this in completing the Decimal Comparison Test or in the other interviews. There, she consistently interprets the decimal part as indicating the denominator of a fraction, with larger denominators creating smaller fractions. For example, she thinks that 3.12 is something like 3/12 or maybe like 3 1/12 (three and one twelfth) although she may not think it is really the same.

Courtney first needs to learn about place value, expanded notation and the "endless base ten chain".