General Principles: Use targeted examples so Ricardo realizes that he has something to learn! Teach underlying place value principles with concrete models (e.g. LAB). Often use decimals of various lengths in the one situation. Conduct class or group discussions on this and other misconceptions. Provide opportunities for Ricardo to use his new understandings.

What does Ricardo need to learn?
Ricardo has a good knowledge of place value names, but has difficulty coordinating the size of the numerator and denominator of a fraction. He understands, for example, that 0.2 =2 tenths and that 0.36= 36 hundredths and knows that tenths are larger than hundredths. He wrongly concludes that 0.2 is greater than 0.36 because he thinks only about the size of the parts (the tenths or hundredths) and cannot simultaneously consider how many parts there are. This is why we call him a "denominator-focussed" thinker.

Ricardo probably has difficulty with fractions as well. Peled and Shahbari (2003) found that 78% of the denominator focussed students in their study were unable to correctly compare common fractions. Ricardo needs help to coordinate the influence of the numerator and denominator for fractions. This is associated with the ability to unitise and reunitise. See decimal-fraction link for more information.

Make sure that Ricardo is faced with problems that he will get right and problems that he will get wrong. For example, he incorrectly thinks 0.36 < 0.2 but correctly chooses 0.12 < 0.4. It is important that he understands that his basic interpretation of the numbers is faulty - he is NOT just making careless mistakes.

Ricardo needs to see decimals in many equivalent forms, using expanded notation e.g. to see 0.36 as 36 hundredths and also as 3 tenths and 6 hundredths. See here for more information.