Here is a simple story problem. Rose has 5 pennies. Eva has 9 pennies. How many more pennies does Eva have than Rose? I have posed this problem to many, many children. More than a few of them have answered, “Eva has 9. You just told me that.” Those children didn’t understand the question. It is not simply that they got the wrong answer. It is not simply that they made a minor mistake. Those children really didn’t understand what I was asking. Here is another problem. Trixie has 3 baskets. There are 4 cherries in each basket. How many cherries does Trixie have altogether? I often ask children to draw pictures to represent story problems. For this problem, I have seen children draw 3 baskets, draw 4 cherries in each basket, and then miscount the cherries – maybe they count 11, or maybe 13. Of course, 11 is not right. And 13 is not right. But compare those children who miscount with those children who start out by drawing 4 cherries and 3 baskets. Miscounting is one thing – everyone makes minor mistakes. But children who draw 4 cherries and 3 baskets don’t understand the question. Those children need help.Read More