Before all the Grand Rapids Public Schools attendance issues got folks excited, I worked on a Sunday project about challenges faced by alternative education programs.
They're facing several hurdles, but the largest seems to be the state's new graduation requirements, which call for four years of math, including algebra and algebra II.
Parent Sherri Hoard wrote to tell me about some of her family's struggles. Then I heard from Brad Jolly, a former Michigander now based on Longmont, Colo.
He knows a lot about teaching math, and shared some interesting things. Here's his letter, and sharpen you pencils, because you have some homework to do.
"I saw your article about Sherri Hoard's questions, and I think I have some answers for you (and Ms. Hoard) in terms of how algebra can be successfully taught to more students.
"I have spent a lot of time in Singapore, and I have read a lot of Singapore math books. The bottom line is that they teach algebra using a very different method than the one we teach in the U.S. By fourth grade, they are doing problems like this:
"2/7 of Deb's weight is of Ed's. If Deb weighs 11 lbs. more than Ed, how much does each one weigh?
"The method they use in Singapore involves no equations and no variables, and their fourth graders get it. By the time they get to sixth grade, Singaporean students are doing the kinds of algebra (with equations and variables) that American kids typically do in eighth or ninth grade, and they are much better at it because of what they learned previously.
"I have also studied Vedic math (the kind taught in India), and again -- their methods are simply superior to the ones we use."
I was curious about this. Let's just say that when I was in high school and it came to algebra, I was a darn good social studies student.
So Brad continued:
"Here's how the Singaporean kids would solve the Deb and Ed problem below.
Step 1) The problem talks about Deb, specifically 2/7 of her weight. Let's draw the two sevenths of her weight as two boxes.
Step 2) The problem also mentions Ed, and of his weight. According to the problem, we should make of Ed's weight as big as Deb's 2/7 boxes.
"Step 3) We don't know how much Ed weighs, but clearly his weight is 3/3 of whatever it is. This is true for anybody, of course. Let's give Ed his full weight, as shown below.
"Step 4) Deb's third and fourth sevenths would be as long as Ed's second third, and Deb's fifth and sixth sevenths would be as long as Ed's final third.
"Step 5) We're not done with Deb. We owe her one final seventh, as anybody's weight is 7/7 of whatever it is. Let's add the last seventh for Deb.
"Step 6) Because Deb weighs 11 pounds more than Ed, the "overhanging" seventh represents 11 pounds.
"Step 7) Since each square is 11 pounds, Deb's total weight is 7x11 pounds, or 77 pounds. Ed, at 11 pounds less, must weigh 66 pounds.
"This is typical of the way kids do algebra in fourth grade in Singapore. No equations, no variables.
"Of course, they get into the 'traditional' method that we know in about sixth grade, but it is far easier for them after they have worked problems like this for a couple of years.
"Here are two more examples. These show how adding and subtracting fractions is taught in India. As you know, the traditional American method says the first step is to find the common denominator, and that can be hard for some students. In the Indian method, finding the common denominator is the last step, and it is immediately obvious what the common denominator is.
"Let's go through the first example: 9/16 - 5/12.
"Step 1 is to pull out whatever factor is common to 16 and 12, in this case: 4. After we pull out the 4, we writing 4 and 3 below the 16 and 12, respectively.
"Step 2 is to cross multiply and subtract: 9x3 is 27 and 5x4 is 20; 27-20 is 7. That's our numerator. We subtracted because the problem is a subtraction problem.
"Step 3 is to find the denominator, which is simply the product of the bottom row: 4x4x3 = 48. That's it.
"Here's another example:
"Step 1: Pull out the 5 from the 15 and 20, leaving 3 and 4.
"Step 2: Cross multiply and add: 11x4 + 3x3 = 53. That's the numerator of the answer.
"Step 3: Multiply straight across to find the denominator: 5x3x4 = 60.
"Most people can figure out the method in about two minutes. We would be doing our students a great favor if we taught methods like these in our schools."
Wow. This is interesting. On the downside, I now know I would struggle with math in at least two countries. There's some comfort in being consistent.
Thanks to Brad for sharing.
E-mail Dave Murray: email@example.com