But WHAT is different? Can you give me a specific example? HOW are they making it conceptual? To be honest, what it sounds like is that they just aren't doing much teaching at all, either of tools or of concepts. Navel-gazing isn't teaching, and that's the impression I'm getting of it (albeit perhaps wrongly).
I don't call word problems conceptual (and those have always been around anyway). Is there more to it than that?
Hi Kriston,
My sons' school uses a spiral system called Everyday Mathematics (EM). These systems are called "Reform Mathemathics." I wrote a letter to the school detailing my ideas about EM's weaknesses. I used specific examples from the books. If anyone wants a copy, PM me and I'll send it.
Overall, EM has a "spiral" approach that spins from one topic to the next. So in 1st grade they do, say, classical addition for a few days and move to learning shapes. Then they go on "numeracy" which is taught using a grid that looks like a calendar and goes from 1 to 100. Etc. etc. They evertually work back to slightly more advanced classical addition problems and the spiral starts again.
EM books are wordy and include exercises that ask kids to cut pictures of triangles out of magazines or write the name of the presidents and mottos on various coins.
They have a limited number of numerical operations. This increased in the 2nd grade book, but all the problems in the 1st half were 1st grade level from what I could tell (entire pages of 8+4, 11+8 etc).
Critics argue that reform maths systems are superficial and that they don't allow ideas to sink in. Many originally relied heavily on calculators, even in 1st grade. I think the resulting uproar *may* have killed the worst of the calculator stuff. I'm not sure; my kids' school just skips the calculator stuff.
Google "Math wars" and you'll see what I mean.
My feeling is that the Reform systems are a swing of the pendulum in the opposite direction from too much rote drilling.
ALso, EM has a lot of exercises that look mathematical on the surface but really aren't. For example, in grade 1, they cut out a ruler and measure 3 things at home. When they hand in the homework, the teacher has *no way of knowing if the measurements are accurate*. Sure, the parents should have helped, but what if they didn't for some reason or didn't pay close attention?
Why can't the book just draw a few lines and get the kids to measure the lines? If the goal is to teach them how to measure something, there has to be a way to *assess learning*.
One of my biggest problems with EM was the number grid approach to addition. This is a twist on counting on a number line, and kids are supposed to "hop" "forward" to add and "backward" to subtract.
The grid has 10 row of 10 numbers from 1 to 100 (no zero). Because it starts at 1, 10 is on the same line as 1-9 and 20 is on the same line as 11-19, etc. This approach completely fails to show kids that 10, 20, etc. begin new groups of ten. And of course, 100 is on the same line as 91-99.
Also, I'm not sure why moving across a grid and then down a row to add, say, 8+3, is a better way to teach addition than just using a pile of bingo chips or drawing some circles. Ditto for subtraction, which is less intuitive than addition and requires that you start with a pile of bingo chips (or whatever) and then take something away.
Also, the grid forces kids to count by ones to add and doesn't TEACH the idea of addition. I think the idea is let them figure it oiut for themselves. But the system is too complicated and many kids can't see the forest for the trees.
EM makes an assumption that children can understand certain concepts intuitively when they can't. Moving backwards and up a row to do 11-3 is NOT intuitive the way that watching a pile get smaller is.
So overall, these systems can look attractive to people weary of drill and kill. But they are deceptive and close inspection shows their weaknesses.
Hope that answers your question?
Val
