Interesting. My best guess right now is that this is more about how they’re seeing fractions. 0.1 is a number, but a fraction is how much OF something which could vary. So .1 could be one-tenth of 1 but it would not one-hundredth of 10. One-half was tougher because they didn’t see at first what it would be one-half of. I could certainly be wrong about this. I had difficulty distinguishing the different students. It the thoughts are along these lines they’re not seeing fractions as numbers. There is no number one-half. There is just one-half of THINGS. I’m also curious how the students were introduced to decimals.

I agree. Kids are probably exposed to lots of problems asking “What is 1/2 of X?” or “What is 20% of X?” so the concept of 1/2 and 20% as actual numbers (and “of” = multiplication) may not be clearly understood.

Sandy

I’m not sure this helps, but one thing my daughter said in 5th grade about decimals – she had one teacher who referred to decimals as ‘point 1’ which didn’t really mean anything to her. Her new teacher refers to decimals as ‘one-tenth’ or whatever their actual value is. She told me that now they make sense, she understands decimals in a clearer way. I’m a math teacher too, so it just brought home how important the language we use as teachers is in helping students understand concepts as they get more abstract.

Laura C.

Similar issue: I have students in my algebra classes who aren’t clear on whether the 0 in front of the decimal point changes the value. In other words, they’re not sure if 0.1 and .1 are the same.