Mathematics and statistics lessons about elections

Study elections in mathematics because it is important

Too often mathematics is seen as pure and apolitical.  Maths teachers may keep away from concepts that seem messy and without right and wrong answers. However, teachers of mathematics and statistics have much to offer to increase democratic power in the upcoming NZ general elections (and all future elections really). The bizarre outcomes for elections around the world recently (2016/2017 Brexit, Trump) are evidence that we need a compassionate, rational, informed populace, who is engaged in the political process, to choose who will lead our country. Knowledge is power, and when people do not understand the political process, they are less likely to vote. We need to make sure that students understand how voting, the electoral system, and political polls work. Some of our students in Year 13 will be voting this election, and students’ parents can be influenced to vote.

There are some lessons provided on the Electoral Commission site.   Sadly all the teaching resources are positioned in the social studies learning area – with none in statistics and mathematics. Similarly in the Senior Secondary guides, all the results from a search on elections were in the social studies subject area.

Elections are mathematically and statistically interesting and relevant

In New Zealand, our MMP system throws up some very interesting mathematical processes for higher level explorations. Political polls will be constantly in the news, and provide up-to-date material for discussions about polls, sample sizes, sampling methods, sampling error etc.


It would be great to hear from anyone who uses these ideas. If you have developed them further, so much the better. Do share with us in the comments.

Suggestions for lessons

These suggestions for lessons are listed more or less in increasing levels of complexity. However I have been amazed at what Year 1 children can do. It seems to me that they are more willing to tackle difficult tasks than many older children. These lessons also embrace other curriculum areas such as technology, English and social studies.

Physical resources

Make a ballot box, make a voting paper. Talk about randomising the names on the paper. How big does the box need to be? How many ballot boxes are being made for the upcoming election? How much cardboard is needed?

Follow the polls

Make a time series graph of poll results. Each time there is a new result, plot it on the graph over the date, and note the sample size. At higher levels you might like to put confidence intervals on either side of the plotted value. A rule of thumb is 1/square root of the sample size. For example if the sample size is 700, the margin of error is 3.7%. So if the poll reported a party gaining 34% of the vote, the confidence interval would be from 33.3% to 37.7%.

You can get a good summary of political polls on Wikipedia.

From NZ maths  – On the Campaign Trail (CL 4)

Figure it Out, Number sense  Book 2 Level 4 – has an exercise about finding fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.

From NZ maths – Whose News (CL 4)

This is a guide to running an analysis on the level of representation of different geopgraphic areas in the news. The same lesson could be used for representation of different parties or different issues.

Graphical representations

The newspapers and online will be full of graphs and other graphical representations. Keep a collection and evaluate them for clarity and attractiveness.

How many people will be employed on election day?

This inquiry uses a mixture of internet search, mathematical modelling, estimation and calculation.

  • How many electorates are there?
  • How many polling booths per electorate?
  • How many people per booth?
  • How long are they employed for?

Fairness of booth provision

  • Is the location of polling booths fair?
  • What is the furthest distance a person might need to travel to a voting booth?
  • What do people in other countries do?

The mathematics of MMP

This link provides a thorough explanation of the system. A project could be for students to work out what it is saying and make a powerpoint presentation or short video explaining it more simply.

Overhang and scenario modelling

Overhang occurs when a party gets more electoral MPS elected than their proportion allows. Here is a fact sheet about overhang and findings of the electoral review. Students could create scenarios to evaluate the effect of overhang and find out what is the biggest overhang possible.

Small party provisions

How might the previous two election results have been different if there were not the 5% and coat-tailing rules?


Different ways of assigning areas to electorates get different results. The Wikipedia article on Gerrymandering has some great examples and diagrams on how it all happens, and the history behind the name.

Statistical analysis of age and other demographics

Statistics should be analysed in response to a problem, rather than just for the sake of it.
Suggested Scenario: A new political party is planning to appeal to young voters, under 30 years of age. They wish to find out which five electorates are the best to target. You may also wish to include turn-out statistics in your analysis.

Resource: Enrolment statistics by electorate – some graphs supplied, percentages for each electorate.

Statistical analysis of turn out

In the interests of better democracy, we wish to have a better voter turnout. Find out the five electorates with the best voter turnout and the worst, and come up with some ideas about why they are the best and the worst. Test out your theory/model by trying to predict the next five best and worst. Use what you find out to suggest how might we improve voter turnout.

Resource: Turn out statistics – by electorate or download the entire file

Happy teaching, and fingers crossed for September.


Forget algebra – is Statistics necessary?

There is the popular (amongst statisticians) statement from H.G.Wells. Usually it is quoted as: “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.”

According to a paper in Historia Mathematica, what Wells actually said (in 1929) was:

“The time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world wide states that are now developing, it is as necessary to be able to compute, to think in averages and
maxima and minima, as it is now to be able to read and to write.”

Not quite as pithy as the paraphrase, and sadly he didn’t mention statistics specifically. But – the point is, he was correct – or would have been if he had actually said what he is attributed as having said.

Statistical understanding is a fundamental literacy for the twenty-first century.

My blog post title today is intentionally provocative, and based on the blog by Andrew Hacker, in the New York Times, “Is Algebra Necessary?”. This article has many academics and others quite exercised at the thought that algebra might not be essential to all students. Or even that someone could dare to suggest that this might be the case. As it is not clear to me what the term “algebra” encompasses, I find it difficult to decide one way or the other. Some aspects of algebra are really handy, and I teach them in my Quantitative methods for business course. (Much to the disgust of some of my students.) But an awful lot of algebra though fun and useful for many professions, is not really essential for the general populace. To me it is more important for someone to be able to interpret statements of causation correctly than to be able to solve a quadratic. Hacker’s point is that this obsession with algebra for all is providing a barrier to students who are otherwise talented and capable.

It seems that people on team: “Algebra for all” have a somewhat privileged view of the populace. They are concerned for College students and particularly physicists, engineers and biologists. And they seem to be focussed on occupational concerns more than citizenship. Surely the subjects that everyone is required to master, should be the subjects needed for being an “efficient citizen,” to borrow Wells’s phrase.  What skills and attitudes and knowledge do we want all our citizens to have, regardless of their career path? I think an understanding of variability and data are pivotal to effective decision-making.

By the time a person leaves compulsory schooling they should have a working understanding of the nature of variation in the universe and the implications of this variation. They should be able to examine data presented in various forms and make judgments from it. The Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report of 2005 states: “Every high school graduate should be able to use sound statistical reasoning to intelligently cope with the requirements of citizenship, employment, and family and to be prepared of a healthy, happy, and productive life.” How does algebraic reasoning fit in that sentence? It is more difficult to see the direct benefit to citizenship, though for some employment it would be needed.

The study of the discipline of statistics teaches a wide range of skills:
Number skills, writing, critical thinking, application, lateral thinking, argument, reasoning, visual interpretation, communication, persistence, coping with ambiguity. These are skills important for citizenship.

Andrew Hacker, in his controversial article “Is Algebra necessary?” said, “Ours is fast becoming a statistical age, which raises the bar for informed citizenship. ”

And Rob Knop commented in his response to the Hacker article, “So, yes, I would agree that we could and perhaps should de-emphasize algebra in favor of making time for statistical awareness, and perhaps in filling in the basic number sense that students failed to get out of elementary school.”

It is interesting that both sides of the argument agree on the necessity of statistics in education.

In New Zealand the curriculum area previously known as Mathematics is now called Mathematics and Statistics, and statistics is getting a much greater emphasis at all levels of schooling. However there are mathematics teachers who still perceive statistics as one of many sub-branches of mathematics, though this is not how statisticians perceive their discipline. (For more about this maths/stats divide, see an earlier post, “Hey mathematics – leave the stats alone.“) There are problems arising, as many of the teachers are not as familiar with statistics as they would like to be. It has been interesting reading the bulletin boards where teachers express their concerns. The transition will be challenging for many. And there may arise a new breed of teacher who specializes in teaching statistics.

This is an exciting time to be a statistics educator. The research is there, the will is there, the technology is there and the need is there. Move over, Algebra. Statistics is coming through.


For any loyal followers who tune in each week, there will be a break for a few weeks unless I can convince my colleague to do a guest post. See you in September!