Maurice’s selected thoughts.

I mentioned Innumeracy: Mathematical Illiteracy and Its Consequences a few posts ago. I just finished reading the book this weekend so I thought I’d give my final impression of it.

Basically I’d say it is worth a read if you are interested in mathematics education, statistics, or possibly just math in general. The author basically argues that most people are innumerate and gives many examples to illustrate. The examples are the best part of the book since they often show instances that illustrate a general concept. I became more mindful of the misuse of statistics by others, and particularly the media while reading this book. I can’t say I agree with everything in the book. The author seems to believe that introducing more games and jokes into math curriculum will draw students into the subject. I believe that without a deeper commitment to showing students why a subject will be useful to them they will not engage with the subject. This is basically true of every subject. Full engagement cannot be achieved through jokes.

This weekend my ten year old became a little more engaged in math when she realized that math was important for the woodworking project we are building. She was already interested in the project. I just used this interest in the project to expand her interest in math. I will agree with the author that math teachers need to be better educated. However, with the current trend toward strictly test based assessment in public schools I have little doubt that the situation will remain grim. In order to leverage existing interests there must be a place for those interests in the learning environment. Preparation for standardized tests leaves little room for such endeavors, particularly when teachers are assessed by student performance on the exams. “Extra curricular” activities have been nearly eliminated. It seams most schools foster an environment where there is no room for fun, or at least the one concept most students learn very well is that whatever is going on at school should not be fun. Add to this the shameful level of pay for teachers, and you have an environment that is disappointing even to those who are willing to accept the low pay for the opportunity to make a difference.

This is a book that will make you think, and possible inspire you to help someone else think a little more rationally. Overall I rate the book at about two beers. It loses a few because it is a little unfocused at times. I think it should have been two books. One on misinterpreting statistics, and a second on the inadequacies of the educational system.

I just took a look around my work area to see what the most useful thing has been over the past week. It has been a rather long week since I’ve been studying for an exam. There is nothing I hate worse than exams. They are the least practical way to evaluate real knowledge that I can think of, but that is another story. What I found to be most useful is How to Prove It: A Structured Approach, a book that does a good job of presenting a very important skill for anyone working toward a degree in Computer Science (or math I imagine). I really wish I had known about this when I was getting my Bachelor’s degree. It would have helped a great deal with the “introductory” courses in discrete math, computer science theory, and graph theory.

I have found that writing proofs, much like writing code, is kind of an art. Most either get it or they don’t. I have been lucky since I have always just got it when it comes to code. Unfortunately I’ve had to be able to write proofs as well. Proofs I did not get. Why is another story but I think it has a lot to do with the cultural innumeracy described in Innumeracy: Mathematical Illiteracy and Its Consequences.

How To Prove It is a book for those of us that did not come to proofs naturally, and I must say Daniel J. Velleman has captured on paper easily understandable incites that allowed me to build the new skill of writing proofs atop the well trodden skill of writing code. Basically if you grok code and the process of creating it all you need is to study this book in order to achieve the same status for proofs. For me this has opened up a very important area for potential application to my research. Having a real understanding of proofs has allowed me to begin reading math (and understanding instead of glossing over proofs), and math like it or not is the foundation of computer science. These of course have been the long term benefits of having purchased and read the book several months ago. What made it the most reached for item over the last week has been the four page summary of proof techniques conveniently listed in the back of the book. If you are looking for a great guide to mathematical proofs and by extension reading and writing math, this is it. If you’re trying to win an argument with your wife keep looking, these are not those kind of proofs (I can’t prove it but I believe those kind of proofs don’t exist).

For the last week being an excellent reference and most used item I’d rate this book 5 beers, but overall I’d have to say 4 beers. It is eye opening for those with limited proof skills, but the reference value could have been raised significantly by printing the proof techniques on the insides of the cover, or in some other easy to reach location.