Wednesday, March 26, 2008

Math problems of the week: Reform Math vs. other math

One way to see how Reform Math stacks up with other math programs (whether traditional American math, or math as it's still taught in other countries) is to compare specific assignments.  Once a week, OILF will do just that.


We'll rotate between different Reform programs, including Everyday Math, Investigations in Number Data and Space, MathLand, and Trailblazers, as well some of the secondary school programs.

We'll pair up a specific assignment drawn from this set with a specific assignment drawn either from a traditional series like McGraw-Hill, or from the foreign series most popular in America: Singapore Math.  

I'll try to pick assignments that take place (assuming the curriculum in question is used chronologically) at approximately the same point in the school year.  For example, I might choose two assignments from the first few weeks of first grade, or from the last few weeks of second grade, or from approximately 2/3 of the way into third grade.

I've picked Wednesdays for this weekly feature because it's the day my daughter's math homework is due.  And so it seems appropriate to kick off this series with examples from the two first grade programs she's been using, one at school and the other at home.

Tonight's homework:

1. Investigations:  Investigation 1, Sessions 4-5, Number Games and Story, Student Sheet 7.

Assignment:  "Total of Ten"
Materials:  Deck of Number Cards [each card displays a number from 0 to 10.]
Object:  Find combinations of cards that total 10.
How to Play:
1. Lay out 20 cards faceup [sic] in four rows of five. 
2. Players take turns.  On your turn, look for a combination of cards that totals ten. Remove those cards and put them aside.
3. The game is over when no more combinations of 10 can be made.
4. List all the combinations of 10 you made.

From a similar point in the Singapore Math curriculum:

2. Singapore Math:  Primary Mathematics 1B Workbook. Exercise 61, p. 142-143:

Add:

45 + 10 + 3  = 24 + 10 + 2  =
45 + 13 = 24 + 12 =

37 + 10 + 3  = 76 + 10 + 4  =
37 + 13 = 76 + 14 =

25 + 10 + 17 = 48 + 10 + 6  =
25 + 17   = 48 + 16 =

42 + 30 + 6  = 35 + 40 + 2  =
42 + 36 = 35 + 42 =

55 + 20 + 5  = 28 + 60 + 2  =
55 + 25 = 28 + 62 =

37 + 30 + 8  = 65 + 20 + 9  =
37 + 38 = 65 + 29 =

In short, a group activity (Investigations) vs. a solo assignment (Singapore Math). And a haphazard exercise in finding multiple ways to sum single-digit numbers to 10 (Investigations), vs. a structured exercise in adding two-digit numbers by breaking up one number into tens and ones (Singapore Math).

4 comments:

Dawn said...

I think that demonstrates wonderfully why Singapore Math is such a popular choice with us homeschoolers. When you're a mom with half a dozen things on your plate, "blah, blah, blah, blah,etc." just can't compare to, "add:"

lefty said...

Nicely put!

Also, many parents I know, myself included, often have a lot of trouble understanding these often very verbose and poorly written directions. If we can't understand them, then surely our children can't either.

Myrtle Hocklemeier said...

I remember the "find things that make ten" exercise in Singapore first grade. It's in the textbook, at the very beginning of the book, there is a clown holding balloons or balls and each ball has a digit on it. The child is supposed to pair up the digits whose sum is ten. That's it. No other kid involved, no cards. No distracting noises and motion. There is a corresponding coloring sheet in the activity book where they color the pairs of objects with a sum of ten.

Another "make tens" activity is on the Singapore CD rom game. The kid clicks on objects with digits on them when he can find a pair whose sum is ten. Again, his progress does not rely on the behavior of his partner and he can very quickly find many sums of ten.

We love card games at our house but let the kids play the game that they choose to play when they want to play it. That way it really is fun.

"blah, blah, blah, blah,etc." just can't compare to, "add:"

I love it!

Even at higher levels it's sometimes hard to find clear explanations and instructions.

I've been riddled lately with absolute value ailments and have been trying to puzzle my way through several different long-winded defintions. I finally had to get online and finally found the antidote which was something like "Absolute value is a distance function. Distance functions have the following four properties: symbol, symbol, symbol, and symbol.

lefty said...

Another "things that make ten" Singapore exercise that I like, also much earlier in the grade 1 curriculum than Investigations', arranges the numbers from 0 to 1 in a semi-circle, and asks the child to draw a line between pairs.

The neat geometric pattern that emerges corresponds nicely to the underlying mathematical pattern.