Why Can not Johnny Problem Solve

You have heard the expression "He has a lot of book knowledge, but not much commonsense." What is commonsense? I think it is the ability to reason something out, to problem solution. This problem solving ability has nothing to do with how much you know. It does have everything to do with the mental connections you make with the information you know. I have been thinking a lot lately of math anxiety. Math anxiety is a block to effective problem solving using numbers. Take for instance this example. I have a BA in Mathematics. I can factor polynomials in my sleep. I can find the first, second and third derivation of a complex quadratic formula, but I could not solve this simple math problem. The answer eluded me.

The problem was this. Eight of us were taking a boat trip for three days. I had to buy enough loaves of sliced ​​bread for sandwiches for the eight of us for three lunches. Assuming 1 s sandwiches per person I calculated that I needed 72 slices of bread. But how many loaves of bread did I need? I was stumped. What was the ratio of slices to loaf? Finally, my friend suggested that I just count the number of slices of bread in the loaf I was interested in buying and then I could figure out how many loaves I needed. Count the slices in the loaf! It seemed too obvious. Of course it worked, but how come that did not dawn on me? I have too much book knowledge and not enough problem solving. When I learned math in this case word problems, I was always given all the information I needed and precise instructions on where to plug in the numbers in the formula in order to solve the problem. Math become rote, plug the numbers into the formula and, "Voila!" there is your answer. Real life does not work that way. I was missing a piece of the puzzle. It did not dawn on me that I would have to supply the missing piece myself.

Now let's look at math in elementary school. First, we are lead to believe there is only one way to solve a problem. If we venture to solve it another way, right or wrong, the answer is wrong because we did not do the problem the way the book said to. One day I was in a multiple learning styles class. We were required to figure out how many steps two people would each need to take to be back in sync on the same foot, given that one person's stride was 2/3 the other person's stride. Because it was not a math class and we were not given the formula to figure it out, we saw numerous ways to resolve this problem. Some people stood up and paced it off with a friend. Some drew a picture. Others stared at the tiled ceiling. Someone was even beating a rhythm. Occasionally everyone who attempted to solve the problem came up with the correct answer. The only ones in the group who did not get an answer were those who were stumped because they did not know the formula. No one told them how to solve the problem, so they could not solve it. They did not know how to start.

Second, we are lead to believe that there is only one right answer. This is not necessarily correct. There exists different numbers that have the same value like and and 2/4. Both mean b but how many times has 2/4 been marked wrong just because the answer sheet stated that the answer was.. Sometimes the correct answer can be a close estimate. For instance one third of 1 1/3 is equal to 4/9. That's the correct answer. But if I was making one third of a cake recipe that called for 1 1/3 cups, I would just use a c cup. It is close enough. Beside my measuring cups do not have measures for 1/9 cup. How do I know that c cup is close enough because half of 9 is equal to 4.5? The next closest measure is 1/3 cup and that's only 3/9. You decide. Which is closer to 4/9, 1/3 or 1/2? Remember, we're only making cake. Now how many people would have been stopped from making the cake because of the fraction calculation? How many would have been stopped because they could not measure accurately 4/9 cup? Of course, if I was measuring an explosive and a drug, I might want to be a little more accurate. But we are talking cake here, not rocket science.

Last, we are lead to believe that life will give us all the information we'll need to solve the problem. That is not necessarily correct either. Sometimes we have to get the numbers for ourselves or make a best guess. For my loaf problem above, I could have estimated 30 slices per loaf. Then I would have needed to buy bread with at least thirty slices per loaf or I would have needed to recalculate the numbers of loaves based on the actually slices per loaf. Of course the calculation is pretty straight forward. But what if I had wanted to serve different breads for each lunch? What if the different bread required that I allot two sandwiches per person? All these factors can affect the calculation. But how many people are stumped by problems like this everyday? How many people willingly state that they're no good at math and do not even try to the problem solve? Why can not Johnny problem solve? I do not think he was ever tried how.