I put “0.1” on the board and asked students what they’d call this. A kid said “one tenth,” but that quickly became controversial.

Question: how do you think these kids are seeing 0.1?

• 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.