I have been visiting the 2nd grade and supposedly assisting with math instruction. I sit at a round table with little chairs around it and those who want help or conversation about math come over and bring their paper.
The kids understand addition and subtraction and may or may not use some sort of traditional layout of figures to be added or subtracted. They realize that four 3's is 3+3+3+3 but they don't know the word "multiplication" as such.
They have been working with common fractions but not decimal fractions. A recent worksheet asked they to decide whether one-half > ¾ . I asked one child how much a quarter was and he answered 25 cents. I asked him how much three quarters would be and he answered 75 cents. How much is half a dollar? 50 cents. So, which is bigger half or ¾. He answered ¾.
I was impressed that the whole class worked on this problem: Wagons and trikes are on a parking lot. There are 27 wheels altogether. How many wagons and how many trikes are there? No algebra, no X and Y for unknowns. Lots of simple drawings of 4-wheeled and 3-wheeled vehicles and counting going on. I taught arithmetic to four groups of 5th graders and then did it all over again the next year. During that time, we never dealt with a single problem that had more than one correct solution. These kids worked it all out, finding both solutions without any assertion that TWO solutions was an odd situation.
