Forget algebra – is Statistics necessary?
Khan Academy Statistics videos are not good
30 July 2012Guest Blog: Avoid Applicable Math
14 August 2012There 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.
Afterword
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!
10 Comments
I question how you would define “statistics”, similar to the question you raise for algebra. Not necessarily formally in terms of a definition, but what concepts are the important ones that you think should be focused on, and which ones optional?
Its funny that I (and several others in the discrete math community) believe that there should be more of a focus on discrete mathematics in a student’s K-12 years. Whether it be concepts from set theory, graph theory, statistics or algorithms, I think these concepts are (1) much easier to understand and (2) have a more impact on a student’s life.
I can’t count the number of conversations I have with friends from teenagers to old men who “hate math”, but can name an NFL, NBA or MLB player’s stats inside-out, talk about sample sizes being too small to make an accurate judgement, or they’re performing in depth analysis of things like “How many times did Jason Campbell target Chris Cooley on passes between 15-25 yards, and what was Campbell’s completion percentage on said passes?” And that’s just in sports, but (as you well know) there’s a similar comparison in dieting & exercising (balancing calories/fats/carbs with workouts), cooking, travelling (shortest path algorithms, shortest travel time routes that we often argue about, least “hilly” running or biking routes), etc. And because we can set these problems up as actual questions with real world answers, we’re likely to have more engagement from the students because, although they’re going to be using and learning (discrete) mathematics to solve these problems, they’re actually interested in the outcome so (I think) they’re much more likely to WANT to do the work, as opposed to just memorizing formulas which (in their opinion) they’ll never use.
Good question. The lazy answer (for me) is to look at the GAISE report that I link to in the post. I will think about this a bit and write a post about it. The main ones off the top of my head could be: An understanding of variability and its impact on decision-making. Idea of sampling to gain information about the population. Confidence intervals. Hypothesis testing (possibly not at high school level) The relationship between correlation and causation. Critical data exploration. Communicating data through graphs and summary statistics. Probability is fun, but it is less important to be able to calculate the tricky stuff than to have an understanding of the sources and use of probability in decision-making.
Yes – a very interesting question. I’ll get back to it after my holiday (vacation).
To some extent, I think it would be useful to forget about the traditional divisions and figure out what we really believe is necessary to teach our students. I agree that both algebra and statistics contain important ideas and skills that could help our students, but what are those specifics? Clarifying these might inform the way in which we focus our teaching, and might even allow us to free up some time.
I’d argue that for most students, statistical literacy is more
important than knowing how to solve quadratic equations.
Sure, competence in relevant mathematics can help the
mastery of statistics, especially for professional use. At
some point however, different depending on the individual
student’s learning trajectory, getting some modest understanding
of statistics becomes a higher priority than learning more
mathematics. Some priority ought also to be set on computer
language skills.
More than that, syllabus priorities ought to be strongly
affected by the huge changes that are in progress outside
the classroom. The syllabi we have are to a large extent
dictated by some combination of historical priorities and
availability, at least in a few places, of teachers who can
be somewhat plausibly placed in front of a class and asked
to teach the content.
All this reinforces a demand to make better use of those
really able and skilled teachers that are available. Those
will also, in many cases, be the teachers that can be used
to drive responses to a demand for changes in syllabus
priorities.
Arising in part from my involvement with the ACT Ed Dept
experimental exercises with physics for able students, I am
convinced that the place to start inserting statistical insights
is in applied areas of the curriculum. One wants roving
statisticians, working in a team approach context, who will
show students good ways of setting up an experiment, how
to draw graphs that are effective for their data, & suggest
steps towards assessing the extent to which results may be
effected by statistical variability. Either use a team approach,
or teach statistics itself as an experimental science!
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