Column Overflow thinking

Brad is in Year 6. He has learnt the correct column names for decimal numbers, but attempts to write too many digits into a column. Just as 12000 has three zeros after the 12 to indicate thousands, Brad thinks that the number of zeros after the decimal point indicates the name of the decimal. So 0.12 is 12 tenths (as there is no zero after the point) while 0.012 is 12 hundredths (as there is one zero after the point). In effect, he is squeezing the number 12 into a single column. Column Overflow thinking is one of the longer-is-larger misconceptions.

Look at Brad's answers to the Decimal Comparison Test. (You can double-click on the yellow notes for his reasons)

Interviews with Brad
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
Attempt a short decimal comparison test to check your understanding of Brad's thinking. This will help you learn to diagnose this error.
Lesson ideas appropriate for students like Brad.
Research on our Australian sample shows that about 5% of students* in Years 4 and 5 think like Brad, decreasing to about 1% of Year 10. This proportion varied considerably - at one school 15% of the Year 6 students were diagnosed this way.
* This group includes both column overflow thinkers and zero makes small thinkers, who cannot be separated with the basic decimal comparison test. The interviews show Brad is a column overflow thinker.