You Not Only Need a Map, You Need a Compass Too

Some time ago, in fact a very long time ago, I bought this wonderful book The Art of Thinking Clearly. If you haven't heard of the book, go to the nearest bookshop now and grab a copy. Don't bother with the library because this book is so good, that I want all the contents downloaded permanently in my brains. Ok, I digress.

As I was saying, in this book I came across a chapter "Why we prefer a wrong map to no map at all". This chapter discusses about availability bias, which is about our inclination to decide outcomes based on how easily/quickly examples come to our minds. For example, if we know of someone who had strike lottery previously, we would think that striking lottery is a highly likely possible outcome for ourselves as well, hence we buy into lottery. Another example, if an unknown (probably wrong) map is easily available to a lost traveller, he/she will most probably still try to use it in desperation despite it not knowing what he/she is looking at.

The title came to my mind immediately when I was trying to solve this past year Primary 5 SA1 Mathematics test paper this morning. I solve Primary School Mathematics problems for fun, laughter peace and joy. 


This question was not particularly difficult per se, it was made difficult because the answer provided was wrong. Here is my own worked solutions to the question.

Wanna know what was the answer given in the answer key? A = 36 and B = 42. How is it possible for Angie to have 36 after 66 stickers have been returned?

No wonder some parents are driven up the wall when trying to teach their children primary school mathematics these days. The subject itself is no doubt challenging at Primary 5 level, but when the answer key provided made no sense, how are the kids suppose to learn from the practice if there is no one else to double check? Just imagine how defeating the kid would feel when they are faced with a wrong answer key and no worked solutions to check. It is little wonder why so many kids seems to be floating in outer space with no life buoy in sight when it comes to solving Mathematics problems. I know, because I was one of them. Fortunately, like Matt Damon in The Martian, I made it back to Earth. 

Having said all these, I will still continue to use these past year test papers as their value is in the practice questions, not in the answer key provided. A quote for my favourite book, Lord of The Rings, comes to my mind, and I would paraphrase it as such: "Look for the questions. Do not trust to the answer keys. It has forsaken these test papers." 

I wish I could have such similar confidence with all the other subjects as well.

Post edit (18.4.2016): Princess feedback that when working with ratios, she prefers to work with whole number rather than decimals (i.e. 6.5 units), so I offered her another worked solution for reference as well as how to check her answers.