Arthur Benjamin about Math Education

I found this video on my usual bookmarking sites. It got Front Page on Digg and lots of Stumbles also. The video is very interesting from my point of view as a mathematics teacher. Arthur Benjamin, a mathematics professor and also the mathemagician offers a bold proposal on how to make math education relevant in the digital age.

I think he is a really good performer but he cuts some corners and speaks like a politician convincing people of something they know very little about.

Before I utter my criticism, I have to remind you that my perspective is Finnish and our mathematics education. I probably don't know enough of the conditions in USA. I have learned that there are schools where the students don't advance very well, but on the other hand the most of the best universities are located there. Anyway calculus and statistics are universal.

The biggest problem in my opinion is that statistics is not a science we can put under the main category mathematics. It belongs to social sciences (in the University of Turku for one) and the interpretations of statistic data and their relevance has very little to do with math. Probability is a part of applied mathematics and also the calculations regarding statistics use math, but something as vague as predicting the future can not be a part of a science which gives only absolute solutions or shows that there are not any! I have a master's degree and my major is mathematics, I have even had some predoctoral studies, but I never had a single course in real statistics.

In Finland we have two different levels of mathematics the students can choose from, the short and the long course. Both levels have one course containing probability and basic statistics. The courses are very similar on both stages and I have noticed a certain trend with these courses: there are always students who get fascinated by the common-sense-math and perform much better than on the other courses BUT also some of the top students are finding this course very hard.

Calculus (we actually use the word Analysis) is taught about 2 courses on the shorter course (no integrals) and 5 on the longer course but also extra courses for those who want to choose them.

I have heard the statement: "I don't remember anything about derivatives" or: "I have not used derivatives after I left school" numerous times. I also know that most people don't, not even those who choose their career in engineering. However the basic calculus is needed in order to understand the further studies in engineering, physics, chemistry, mathematics and even statistics! A tool for the continuous probability distributions is integrals.

Teaching basic mathematical statistics is not as simple as it may sound. When I teach mean values and standard deviations the examples are either too simple to show anything about real statistics or too complicated to be handled without the calculator's built-in statistical functions. Mental mathematics skills are not very good even now, they would be worse if we take more calculators or computers in use. Regardless of the methods we use the examples take time. Typing all the input data is not so simple.

Arthur Benjamin mentions the digital age. I have a better suggestion, let's add Number Theory. It is simple, it is fun and it is a very relevant field of mathematics regarding computers, coding, cryptography and sharing secrets which will be needed in internet voting. These fields of math are hot at the moment, but the basics have been there for ages. I teach one extra course in Number theory (+ Math Logic) but there are many students who don't choose it.

It was actually Gauss (more known from the Normal Distribution) who said: "Mathematics is the queen of the sciences and number theory is the queen of mathematics."

Image credits: Wikipedia and zazzle