Reverse Thinking

Tuyet is in Year 5. She has not heard the "th" sound in the decimal column names, and therefore sees another whole number to the right of the decimal point, but mirrored about the ones column. Her judgments about the size of the decimal number are affected by what she perceives to be the columns with the largest value, that is, the rightmost columns. Reverse thinking is one of the longer-is-larger misconceptions.

Look at Tuyet's answers to the Decimal Comparison Test. (You can double-click on the yellow notes for her reasons.)
Interviews with Tuyet
Talking About Place Value Video Images with text
Making the Biggest and Smallest Numbers Video Images with text

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

Lesson ideas appropriate for students like Tuyet.

Research on our Australian sample detected reverse thinking in only 1% of students across the years on the Decimal Comparison Test. However, quite frequently we come across reverse thinking in other tasks (e.g. writing decimals). Different misconceptions are displayed by different tasks because knowledge is not well integrated. A full description of reverse thinking.