Math Test

On Thursday the students took their first math test of the year. Although one student made a perfect score, most were pretty disappointing. Here were the typical mistakes:

• Many students did not consistently regroup when they added. Generally I do not think they did not understand what to do, but they were trying to do the problems in their heads without using scratch paper. We will need to spend time discussing when mental math is appropriate, and when it is a bad idea.


• Estimation is still pretty shaky for many students. Some just ignore the direction to estimate altogether and find the exact answer. Others get a little puzzled about what to do when the number is somewhere around 5. We will continue to work on this.


• A consistent issue was with those problems which require pre-Algebraic thinking. Here would be a typical example. “Jack has 35 pencils and pens. He has 5 more pencils than pens. How many pencils does he have? How many pens?” This word problem is based on the algebraic equation x + (x + 5) = 35. Students will later learn to subtract the 5 from both sides of the equation and then to figure out 2x = 30 and then x=15. Based on that, they can figure out that Jack has 15 pens and 20 pencils. However, students are not quite ready for that yet, and we also want to foster at this time a certain playfulness with numbers. So we encourage them to use a “guess and check” strategy and to try substituting different numbers and see what works. We want them to get away from finding the answer instantly because, however satisfying that may be, it isn’t what mathematics is really about. There will be some more problems like this in the future.


• Related to kind of problem above are the “sum and difference” problem. Again, here’s a typical example. “Two numbers have a sum of 25. They have a difference of 5. What are the two numbers?” Again, this is really algebra: x + y = 25 and x – y = 5. The goal again is to have students play around with different number combinations until they find ones that work. Again, more problems like this will appear as homework.

While it might be tempting to just stop the sequence of math instruction and ONLY reteach some of these concepts, this is not really possible. Instead, we will need to continue to move ahead in math while going back to catch up with the missing concepts.

This means that some students will be having heavier than usual homework in math, at least for a while. But once we have had some more practice on these kinds of problems, I will retest students who need it. We will then either drop the first test or average the two tests together while weighting the second one more.

Homework: Students were given 10 math problems to do on Friday afternoon. They had to copy the problems out and do all the work. Most finished in class, but a few took them home to finish.