Problem Solving

Problem solving. What does it mean exactly? If you were good at solving problems, what kind of problems would you be able to solve? If you're seven years old, how hard is too hard? Where is the point reached where we can say that developmentally, most seven-year-olds are not ready for a particular kind of problem?

These questions are going around my head this afternoon after a long day of problem solving with my second graders. Our county has a goal of higher achievement in problem solving, as evidenced by the NSRE tests that the fourth graders take every year. A lot of focus is put on learning how to think through problems, explain answers, find alternatives, etc. We found out today that our school has a 28% pass rate in problem solving on the NSRE tests. That sounds terrible until you consider the fact that the county average is half that and the national average is only 20%. When we were told that at our faculty meeting this afternoon, our initial reaction was one of "YAY!" and "Let's pat ourselves on the back!" This is the third consecutive year of hearing data such as this on how our fourth graders achieved on these tests. I'm not so excited; more - confused. The source of my confusion?

Has anyone considered that perhaps if the national average for fourth graders on this test is 20% (and has been that way for years), then MAYBE, JUST MAYBE the test may be above the level of most fourth graders? Is this really a test that Japan's nine-year-olds are scoring like 90% on?

Here's an example question:

Many people fertilize their lawns to make the grass healthier. The Garden Center recommends that you use 5 lbs. of fertilizer per 200 square feet of lawn. Fertilizer costs $1.09 per lb. Determine how much fertilizer needs to be purchased and how much it will cost to purchase that amount of fertilizer for the shaded area of this yard. The yard measures 150 feet by 90 feet and the house measures 40 feet by 28 feet.

And another:

A cylindrical water tower is 7/8ths filled with water. The water tower is 10 feet tall and has a diameter of 9 feet. If 1 cubic foot of water weighs 62.4 pounds, what is the weight of the water in the tower?

On that note, as a school, we have begun kicking up our problem solving from kindergarten on up in an effort to achieve better on the NSRE tests. I did a problem solving activity with my second graders this morning that I felt was on their ability level. This was the problem I gave them:

A triangle = 1 cent

A square = 5 cents

A rhombus = 10 cents

A hexagon = 25 cents

A trapezoid = 8 cents

A long, thin rhombus = 17 cents

Make a picture using only these shapes that equals 63 cents and prove that your picture is worth 63 cents.

Out of 18 kids, 5 kids really struggled and needed a lot of support. So about 72% of my kids were able to complete a 63-cent picture AND prove it using words and numbers. I think that this accurately assesses who is struggling with problem solving and communicating explanations in words and numbers. It was challenging for most kids and very difficult for a few.

Later in the afternoon, the kids were given a county-wide assessment that was very similar to this problem. I am under the impression that this assessment was supposed to prepare kids for the NSRE tests by giving them a similar type of problem but on a "second-grade level". This was the question:

1. If a triangle is worth 2 cents, how much is a hexagon worth?

2. What if a triangle is worth 5 cents? Then how much is a hexagon?

3. How much are 2 hexagons?

This is clearly a multi-step problem because first kids have to realize the relationship between triangles and hexagons - that 6 triangles equals one hexagon. Then they have to count by 2's to find the answer, change the 2's to 5's and count by 5's for the next answer. And finally add two hexagons (which two? who knows?) to find the last answer.

Doesn't seem so difficult right? Keep in mind most of these kids are 7. Keep in mind that if you ask them how many sides a hexagon has, many of them have no idea. Guess how many of my kids were able to figure this out without support (as will be the case with the NSRE tests in 2 years)? ONE. One kid saw the relationship right away between triangles and hexagons and knew what this problem was asking. All 17 other kids needed a great deal of support to figure this out. Similar results were found in the 6 other second grade classes. Does this mean it's a problem with the kids? Clearly they were able to solve the problem we did earlier in the day. Does this mean it's a problem with the teachers? Or does this mean it's a problem with the test?

As our country is pushing for higher and higher achievement, how far is too far? When are kids just developmentally not ready for a particular kind of question? Are we TRYING to stump them? I mean, I think that last problem solving question is a fantastic activity as an extension activity or a challenge. But should it be used as an assessment that says "this is what we expect 7-year-olds to be able to do on their own?"