General Principles: Target examples so Brad realizes that he has something to learn! (e.g. he incorrectly thinks that 0.9 < 0.12, but correctly chooses 0.3 < 0.45). 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 Brad to use his new understandings.

What does Brad need to learn?
Brad has made the decimal-fraction link, and knows a lot about place value but not quite enough. He writes (correctly) 8 tenths as 0.8, 9 tenths as 0.9, but then (incorrectly) 10 tenths as 0.10, 11 tenths as 0.11, 12 tenths as 0.12. Similarly, with the hundredths, he would write 0.08, 0.09, 0.010, 0.011 and 0.012. In effect, Brad squeezes the number 12 into one column. This is why we call it column overflow. As Brad said in his "Talking about Place Value" interview about 4.067, "When there are two zeros at the start, that's when it moves into thousandths".

Brad's misconception is likely to occur because it also arises from over-generalising procedures with whole numbers; in this case, naming the decimal number from the left, just as we name a whole number from the left (456 is "in the hundreds", so 0.456 could be "in the tenths").

Brad is a sophisticated thinker - it should not be hard to put him on track.