It's back to school for millions of kids all over the world. Time to get all the bags, pencil cases and other paraphernalia and of course the various text books. At this time I tend to reminisce on my own school days. I remember a particular day during my first week of class two in primary school. That day we were given a particularly challenging piece of maths homework. As we looked through the questions at the end of the day, one kid exclaimed, " Wait, look the answers here in the back of the book!"
We all stopped dead in our tracks checking our copies to make sure that we all had the same edition. Sure enough, the answers were right there. Suddenly homework had become a ten or fifteen minute affair rather than hours of work. It was truly a 'God send' as far as we were concerned. The next day in class we showed up grinning, we had finished the homework and knew we would all get 100% and teacher, well she would be none the wiser. Of course teacher duly collected the homework and then casually mentioned that we could all have checked our answers as they were given in the back of the book. We went into shock at that moment, how did she know about that? Who spilled the beans? It's amazing when you are eight that you think that in spite of the teacher using a text book for the last 20 years, that YOU would be the first to discover the 'secret.' At that time though we saw it as a clear proof of teacher omniscience.
Suddenly we had no idea what our marks would be. Luckily teacher went easy and gave us all our marks, but we were told that next time we had to show all of our 'working'. That seemed a daunting prospect but we soon learnt how to beat the system. Once we knew the answer we would just manipulate the numbers to get the 'right' result. So the next week we did just that. At primary school there are just four things you can do with numbers, add, multiply divide or subtract that's it. With a little numerical gymnastics you are bound to find the right answer sooner or later. Words of explanation were never needed, we learnt that 'working' did not mean justification of what you did.
As the year went on and we got more confident, quite often we would do the sums only using the answers as a check. There was one day though where the homework assignment really through a 'spanner into the works.' One particular answer in the book had all the students baffled. We had done this type of question many times throughout the term but this time the answer just was not working out. We had answer 24 and the book had answer 34. That morning before class there was a raging argument among us. There were one or two kids who actually had got the book answer, but they had used the numerical gymnastics trick and couldn't explain why they did what they did. But they were quite happy, they had the answer in the book and they couldn't understand what the argument was about. About seven or eight kids recognising that time was running out before class, erased their original responses and copied from the kids with the book answer, smiling at having been saved before the bell. They had the right answer and working that's all teacher was looking for.
However there were still about six students left who were truly in a dilemma. We were not convinced that the methods used to get the 'right' answer were correct. It just didn't make sense to us. Still it was what the book had and the book was the authority. Therefore it must be that we just didn't understand. We weren't getting it, maybe we weren't as smart as we thought. Slowly as the minutes past many of us gave in and decided to go with the book answer, I was one of them. However there was one student who stuck to her guns. Her view was she wanted to understand where she went wrong, she might sacrifice a grade but at least she would learn something and not make the same mistake again . We all looked at her like she was crazy and wondered why she would throw away her marks like that.
Soon the teacher arrived and we went through the homework and we all waited for that fateful question. "By the way", the teacher remarked," the answer in the back of the book was wrong, the right answer is 24." We were all speechless. How could that be? How could the book answer be wrong? Surely people who wrote maths text books knew far more maths than a set of eight year old kids? In all the discussion and argument never did anyone, even the girl who by now had become a hero, consider that the book answer might be incorrect. We all except for the one wise girl lost our marks as a result." Don't assume all the book answers are right," the teacher concluded.
I learnt a lesson that day that went far beyond maths or algebra. A lesson which has stayed with me until today. People continue to show me a book which they say has all the right answers in back, front and middle. A book whose mathematics is perfect and whose old English language can be translated without error. They tell me that the number of available paths is not greater than one by showing me the book says 'the way' and not 'a way.' They tell me the answer of 14 billion I calculated is wrong, 6000 is the absolutely correct answer. But the working they show me has been backward engineered. They show me how they calculate but not why they choose to add certain numbers together or interpret certain writings the way that they do.They also never say why they completely ignore the new maths and science of today or the more recent history books.
So, I remember my former classmate and tell them I will stick to the answers I have spent hours working out. Just like the wise girl said then, it's not because I am sure I am right but because it represents the world as I now understand it. If a teacher can one day show me the step in my calculations where I went wrong I will be happy for the opportunity to increase my understanding. Until then I will carry my 'working' with me and I am prepared to explain my methods and reasoning to anyone.I will not be swayed by a book presented to me that just lists answers 1 to 10 without words of justification. I now know that books even written by the best experts can be wrong. I also know books can lead us to state answers as being absolutely right although it's a complete mystery to us as to how the writer arrived at them. Perhaps most importantly, I know that when everyone else is following the book, a minority of even one can often be right.
My decision to stick with my answers has not gone down too well with many of those in my class. Scores of my colleagues shake their heads at me for throwing away the easy marks. A large portion have even told me I will be severely punished when the teacher comes back. I am assured that I will be given a big 'F' and sent to eternal detention. All the revelations are in the back of the book, they tell me, and I am a fool not to change my answers to fit the text. In spite of all this I am still not convinced that the teacher will show up when the bell rings. It's a shame because that would mean I will never get the chance to hear her tell the class one more time that you should never put all your trust in those textbook answers.