When Lewis was in Grade 4, the exactness of language was a concept to which most adults — including his teachers — in his world did not subscribe. When it came to word problems in math, he struggled with giving an answer because there was a lack of exactness in the way the questions were asked by his teacher that year.
Why his teacher wasn’t able to understand that the questions relating to probability and fractions were flawed, rather than the answers, is beyond me to this day. However, it was easy to understand what the problems were and as Lewis perceived them to be.
The original question his teacher had crafted was:
You have a bag of jelly beans with 15 jelly beans inside. There are fewer green jelly beans than red jelly beans and there are fewer red jelly beans than blue jelly beans. Express this as a fraction.
It seemed to be a very straight-forward question and of all the questions on the quiz that day, the first question was the only one Lewis felt confident he could answer … assuming all the information was provided in the original question.
He determined that the fraction was 1/3. With green jelly beans having the fewest and blue jelly beans having the most, Lewis determined his answer would have to reflect the unbalanced situation. He wrote down that green jelly beans would make up 1/6 of the bag, red jelly beans would make up 2/6 of the bag and blue jelly beans would make up 3/6 of the bag. Of course, 2/6 becomes 1/3 and so one-third of the jelly beans in the bag were red jelly beans was his answer.
The next question was:
There are as many yellow jelly beans in this bag as there are orange jelly beans. How many of each are there? Express this as a fraction.
At this point, Lewis hit a roadblock. He worked hard at answering the question but alas, he was unable to come up with an answer with which he felt confident.
Finally he called the teacher over to his desk and, according to what the teacher told me, Lewis said, “You changed the question completely. There are 15 jelly beans but you haven’t told me how many colours of jelly beans are in that bag. My first answer is wrong if there are any yellow or orange jelly beans in the bag. My first answer is right if the answer to the yellow or orange jelly beans is 0/6. So, how many different colours of jelly beans are in the bag anyway?”
Lewis reasoned that his teacher had not provided all the facts which meant that Lewis could not answer the questions correctly. He pointed out that the second question required people to guess at how many differently coloured jelly beans were in the bag of 15 jelly beans, since the second question indicated that there were more than just green, red and blue jelly beans in the bag as implied in the first question.
The teacher claimed that Lewis was just being difficult and rude, and alleged that Lewis had found a way to avoid answering questions. He went as far as to state that Lewis had done this because he didn’t understand how to determine probability and express that probability as a fraction.
What his teacher didn’t understand was that he, as the teacher, was not using exact language; he was not clear in his description of the situation. No one would be able to answer his questions with so much information missing.
Upon arriving home that day, Lewis told me his version of the situation. He was adamant that when incomplete information is provided in a question put to a second party, the second party cannot give a correct answer no matter how knowledgeable the second party may be on the subject. And that response was as right then as it is now.
If you haven’t got all the information with which to make a definitive and final answer, then the answer is flawed — and most likely incorrect — no matter how you look at it.
What people need to take into consideration when actual results fall short of the anticipated results is whether they had all the information on hand prior to projecting what the end result would most likely be … whether it has to do with baking a cake, building a skyrise, planning an event or determining how many jelly beans of different colours are found in a bag.
The exactness of words could save all of us a lot of time that’s wasted undoing and redoing things in life that didn’t need to be undone and redone had everything been considered from the start.
It’s not every day that a 9-year-old boy is able to figure that out when so many adults struggle with the concept well into their twilight years.