Dump Most Mathematics Teaching. Teach What is Useful
The way schoolchildren are taught mathematics is a serious mistake:
- It misses many simple opportunities to help them lead tangibly better, happier lives
- It misses an important opportunity to improve political discussion among electorate and policy-makers.
- Students spend many hours on material that is quickly forgotten and of tenuous relevance.
- Most people aren’t good at mathematics. So their studies cause faltered intellectual confidence, and the adoption of misinformed self-reassuring rationales. [Eg, “I’m an artist and creative, not like you drone science types”]
First some general observations, then a proposal for what should be taught.
Make it of Practical Help
Mathematics that is compulsory should be of direct practical relevance to students’ lives. It should help them do things like:
- Understand why you should avoid borrowing unless there is a strong justification
- Understand the real cost of a loan, and decide trade off costs between paying it off early vs later
- Compare various mortgages and loans and select the cheapest one
- Understand why most insurance is a waste of money, and why normally it’s far better to pay the costs yourself when things go wrong
- When buying insurance, identify the right type and get a good price
- Figure a household budget and project savings, allowing for tax
- Figure how much food to buy for dinner, or how much money they’ll spend on holiday, or how much grass seed to buy for the lawn
- Maintain inventories
- Quantitatively assess the chances of something happening. Simple statistics as the risk of dying in a car crash, or of developing diabetes over the next 10 years if they continue their diet, or of a child accidentally dying from a gun kept at home, or of dying from a terrorist attack.
Most of today’s mathematical education up to age 15 does not help students people in this way. That costs them dearly, and I mean that literally. They suffer great stress when they haven’t figured their budgets and run out of cash. And they unwittingly and unnecessarily lavish large chunks of their income on the financial services industry.
Improve the Body Politic
The teaching of elementary statistics improves political discussion among and between the electorate and policy-makers. Debate and decision-making improves by the introduction of facts and statistics.
For example, when deciding how much to spend addressing various threats, it’s often to compare the number of people per 100,000 of population that die annually as a result of each threat.
Conversely, people who don’t understand basic mathematics are easily swayed by emotional arguments.
Most people are intimated by abstract notation, and wherever possible it should be avoided. For the sort of mathematics I propose, you can get by without it.
Drop Most of the Curriculum
Mathematics is full of important subject areas……accessible ones examples are solution to algebraic equations, set theory, calculus, matrices, and imaginary numbers.
Of course more advanced topics should be available to students. However, they should be optional, not compulsory. They should be taught to students who are good at mathematics and/or who need the topics in order to pursue other fields.
What Should be Taught?
So what should all children up to age 15 be required to study? I suggest:
- Positive and negative numbers and fractions
- Basic concepts of addition, subtraction, multiplication, and division. Only teach very basic algorithms, offload actual computation to technology
- Use of a calculator — on a computer and as a special function device
- How to estimate interest payments. This is all about polynomials of order N, but can be explained without using the intimidating mathematical notations and jargon
- Spreadsheet basics, up to and including how to calculate mortgage payments over time, and the total cost of interest and other charges
- Perhaps how to program simple custom functions in a spreadsheet using Java
- Basic geometry. Calculating areas and volumes of rectangles and cuboids, probably not more than that
- Elementary statistics. How we are often mislead by our intuitions, how to estimate the chances of things happening, and how to choose between options based on the different risks involved
All of this should be taught using everyday problems that face everyday people.