I agree that we must keep in mind the common core standards. And in fact the standards themselves about fractions are reasonable. But I notice that the Draft Progressions is brand new (August 2011). When the first drafts of the Common Core came out 4-5 years ago, there were pages with examples and then these pages were abruptly removed from the internet. (I had written several responses with details about some of the inadequacies of the examples for the algebra: expressions and equations so I still have that set.)
Now I am looking at this Draft Progressions and I see several similar problems. It seems to me that the people who write these things have never taught kiddies in the classroom (I myself have never taught young ones - I get the older kids who are the result of this teaching and I simply start over.)
My complaints about the Draft Progressions after a brief look at it.
(a) There is no verbalization. Teaching is done verbally - particularly fractions. Any explanation should include how to actually talk about fractions. Two years ago, I made a video about my pet peeve about people talking fractions: http://youtu.be/xOQWmLGPmWQ , i.e. how do you say "1/4". Many people say "one over four". What does that mean? "One-fourth" is a picture in my head; "one over four" is 3 words.
(b) I also looked at the pictures in this draft progressions. They take fractions out of context. We teach kids at a very early age that we cannot compare an apple to an orange. They understand this and they understand that if we have 2 apples and 2 oranges that we DO have the same number of each type of fruit but we DON'T have the same fruit. But apparently a child will compare 1/4 of a giant pizza to 1/2 of a small pizza and conclude that 1/4>1/2 (see page 4). I simply cannot believe this. (I might believe they think 1/4>1/2 since 4>2, but not from a silly pizza example - please correct me if I am wrong.)
From this - in the very next paragraph - it goes on to explain how important it is to compare 2/5 > 2/7 (which indeed is a much, much harder concept) and use this example in SPITE of the fact that the standards specifically state: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
Then this draft continues onto 4th grade and immediately they go on to the stuff that (I think) Sue was talking about: complicated expressions "over" complicated expressions.
There is no way to understand this reasoning in terms of defining fractions as parts of a whole and it is easy to see exactly where we lose them. First we lose the teachers, who then lose the kiddies.
(The draft progression actually mentions presenting to 4th graders
which (I think) is ridiculous at that age and again in SPITE of the fact that the standards specifically state: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
So while keeping the standards in mind, we need to focus on teaching methods that really communicate what fractions are and how they help us function; teaching methods that work in the classroom and have been used by real teachers teaching grades 3 and 4.
