Gary Rubinstein is writing a series on whether the math taught in school is useful. Americans typically study math every year, yet don’t remember most of what they learned. This is part 2, in which he identifies the “useful” part of the math curriculum.

He begins:

What if your house was burning down and you could only save one box of your things? What would you save? Fortunately most people will never have to make this decision but it is still an interesting exercise where you think about what it is in your life that really matters.

As a math educator I sometimes think what if I could only choose a small collection of the most ‘useful’ math topics to save from the entire K-12 curriculum. As I argued in the previous post, I think that at least half of the school math topics are not really ‘useful’ in the sense that you will ever actually ‘use’ them in your life. With this narrow definition of ‘useful’ and ‘useless’ an example of something that is pretty useless is to find what’s called the ‘prime factorization’ of a number like 555 and write it as 3*5*37. There might be some uses of prime factorization in some other math topics but certainly on its own it isn’t a very useful skill.

But some math topics are very ‘useful’ and I think that all students should learn them at some point throughout their schooling. In this post I’m going to make an annotated list of what those topics are. These are like the box I’m saving of ‘useful’ math. The list isn’t going to be very long which leads to the question about whether the math curriculum could be compressed so that it doesn’t take 13 years or if some of the less ‘useful’ topics should still be taught for other reasons.

In the old days, like the 1700s, a big thing that math was used for was converting different units of measurement for commerce. So converting ounces to pounds and things like that were very important and you practiced with difference currencies and things like that. Well here in the 21st century we aren’t doing those sorts of conversions very much but in this new world there are different kinds of calculations we have to do. In the news all the time we see different statistics and sometimes two different news sources interpret data in different ways so an informed citizen should have some basic ‘numeracy.’

#1: Basic adding, subtracting, multiplying, and some division. With all the options we have as consumers, it is important for us to be able to look at two competing options and decide which one is better for you. There are different ways to teach these things and I’ll address those later, but these things should be mastered by everyone.

#2: Percentages. Though percentages are really just an application of division and multiplication, I think everyone should have an understanding that 50% of something is the same as half of it while 10% of something is one tenth of it. So 50% of 400 is 200 and 10% of 400 is 40. And once you know about 10%, you can easily calculate or estimate other percentages, like 30% of 400 will be 3 times 10% of 400 which is 3*40=120. Also see how that is a little more than 25% of 400 which is one fourth of 400 or 100. Calculating tips and understanding when businesses offer 30% off or a loan that has a 2.75% interest rate and things like that are really important so consumers can make informed decisions.

#3: Basic Geometry. Knowing how to find the area of a rectangular or triangular floor is something that everyone should know. Put that skill together with multiplying and dividing and you can figure out how much carpet to order and how much it will cost.

#4: Basic statistics and probability. When you make an investment, including whether or not to play the lottery, you are taking a risk. So having some ability to measure this risk will help citizens make the right choices and not get taken advantage of.

#5: Basic ‘data science’. Nowadays we hear so many numbers on the news, but people can’t interpret these numbers without knowing how to think about them. Like we hear that crime has ‘doubled’ from last year and it sounds pretty bad. But someone who has studied this kind of data science knows what the other relevant information is. Like in this case, if crime went up from 1 incident to 2 incidents, that’s a lot different than if crime went up from 10,000 incidents to 20,000 incidents even though they are both ‘double.’ In the education research that I have done, I’ve come across papers that claim that an educational strategy resulted in ‘110 additional days of learning’ which can really mislead a reader who is not aware of the assumptions that go into these sorts of calculations.

#6: Interpreting graphs. So often, especially nowadays, data is presented in a visual form. There are scatter plots and pie charts and so many ways to use pictures to represent information. An educated citizen should be able to look at these and understand them.

Open the link and keep reading.