Denominator Focussed Thinking
 Ricardo is in Year 6. He has learnt the names of the place value columns and appreciates that the value of the columns decreases by a factor of ten as he moves to the right. This allows him to correctly order 0.1 and 0.01 as one tenth is larger than one hundredth. However, he has incorrectly generalised that any number of tenths is greater than any number of hundredths, for example, 0.1 is greater than 0.24. Denominator Focussed thinking is one of the shorter-is-larger misconceptions.
Look at Ricardo's answers to the Decimal Comparison Test. (You can double-click on the yellow notes for his reasons.)
Interviews with Ricardo
 Talking About Place Value Video Images with text Making the Biggest and Smallest Numbers Video Images with text Number Between Video Images with text Hidden Numbers Video Images with text

See how Ricardo would count from 1 to 2 with decimals and compare with other students.

Attempt a short decimal comparison test to check your understanding of Ricardo's thinking. This will help you learn to diagnose this error.

Lesson ideas appropriate for students like Ricardo.

Research on our Australian sample shows that the percentage of denominator focussed students is about 4% in Years 5 and 6 and then decreases to about 1% of Year 10 students. A full description of denominator focussed thinking.