# Pedagogical content knowledge for Statistics

Pedagogical content knowledge means knowing how to teach a specific subject, discipline or context. There is a school of thought that the skill of teaching is transferable between subjects, so long as the teacher knows the content. However others argue that teaching strategies differ sufficiently across disciplines to create individual but overlapping bodies of knowledge, called pedagogical content knowledge. To me it is clear that different skills and approaches are needed in the teaching of different disciplines. The methods for teaching a foreign language differ largely from those for teaching history or science or cake decorating or jazz piano. There are also commonalities in all teaching, such as the need to build a relationship between the teacher and student, and building on students’ previous knowledge.

I first learned about the concept of “pedagogical content knowledge” in one of my favourite books – How People Learn: Brain, Mind, Experience and School. This book brings together research into how the brain works, and how people learn, in such a way that teachers can gain from it in their practice. Regarding pedagogical content knowledge, it states “Expert teachers know the kinds of difficulties that students are likely to face; they know how to tap into students’ existing knowledge in order to make new information meaningful; and they know how to assess their students’ progress.”

I fear that one of the reasons that the subject of statistics is not as popular as it deserves to be, is because **almost all the teachers at all levels lack pedagogical content knowledge with respect to teaching statistics**. I am not saying that the teachers are bad teachers, or ill-meaning, or unintelligent. I am saying that most teachers of statistics do not really know how to teach statistics.

Let us look at some different groups of teachers, starting with the most influential and consequently worst paid.

## Primary (elementary) school teachers)

My experience of primary school teachers is that they generally are less comfortable teaching mathematics than reading and writing. Their knowledge and understanding of statistics ranges between trivial and incorrect. Their pedagogical content knowledge for statistics is pretty low. These teachers often teach incorrect graphing methods, and may well perpetuate the idea that probability relates to dice, coins and counters. It is not really their fault. There is such a broad curriculum at that level, that it must be challenging to cover all possibilities in their training. Having said that, a well-funded initiative in professional development could address this issue.

## High school teachers

Mostly statistics at high school level is taught by mathematics teachers, from a mathematical background rather than a statistical one. I have already written about the problems when mathematicians fail to treat statistics as an allied but separate discipline from mathematics. I was greatly heartened last week to meet with forty committed teachers of high school statistics who are embracing the new approach of the New Zealand curriculum toward statistics. They have seen how interesting the subject is and are helping students to make real progress in their learning. This is testament to the dedication and collaboration of the teachers themselves, and the efforts of bodies such as Census @ School and my own Statistics Learning Centre, which are helping to support these teachers. The support from the official channels appears criminally lacking, unco-ordinated, and at times even conflicting.

These teachers were at my workshop on teaching statistical report-writing, because they were aware of their own inadequacies in this area. (Though some were doing a fantastic job already). It is hardly surprising that they feel unprepared for teaching this material when their expertise has been in teaching trigonometry, algebra, measurement and calculus. The pedagogical content knowledge for teaching statistics is very different from teaching mathematics. Statistics is, compared with mathematics, an inexact science, where context is vitally important, and where different correct approaches will produce different numbers as answers to a problem. In statistics the words used are critical, and one word can change the meaning of the sentence completely.

Fortunately there is research undertaken on how better to teach statistics, and the body of pedagogical content knowledge is increasing. Another of my favourite books is “The Challenge of Developing Statistical Literacy, Reasoning and Thinking”, edited by Dani Ben-Zvi and Joan Garfield. This brings together the results of thinking and experimentation to improve the efficacy of statistics teaching. One problem identified by Garfield some years ago was that even students who received A passes in statistics often had a very poor understanding of even the most basic concepts of the subject. It is exciting to read the progress that is being made in developing strategies for teaching statistics in a way that promotes deep understanding that transfers to other problems and disciplines. It is also exciting to live in New Zealand where the findings of the research have been applied to the development of a national curriculum in statistics.

## Khan academy

I’d just like to pop in a reference to Khan Academy because, sadly, it has a great influence. I believe that many of the mathematics Khan Academy videos are fairly well taught, in a “boy-next-door” sort of way. However the statistics videos perpetuate the mathematical view of statistics, as they are a product of an archaic curriculum. **Khan has NO pedagogical content knowledge of statistics**. This is abundantly clear in the approach and errors. I have covered this in earlier posts.

## AP Statistics

Advanced Placement Statistics is an American invention of which I have only a tenuous understanding. It appears to be a subject taken at high school level, examined nationally and can count for credit at a tertiary institution. Consequently, though the level is of first year college level, it is taught by high school teachers, which may or may not be to the advantage of the students. I suspect the level of pedagogical content knowledge among the teachers is highly skewed with a very large bulge at the low end and very thin tail to the high end. (To me the word skewed goes the wrong way, so I prefer to describe the outcome).

## Higher education

Statistics at universities is taught by a wide range of people. Teaching assistants have the advantage of recent experience learning the material and may thus be better able to see the challenges of learning the discipline. There will be truly great teachers of statistics among them. Some instructors specialise in the teaching of statistics and help to advance the corporate body of pedagogical content knowledge. Some academics really don’t care about teaching, and just present the material as painlessly (to them) as possible before they head back to their research.

# Developing pedagogical content knowledge

I fear I have stated a problem, with very little in the way of solution. Sometimes it is a good start to identify that the problem exists. Part of my aim in my workshop is to validate the efforts of teachers in what is an unfamiliar environment, and explain why they are feeling out of their depth. This diagnosis helps to remove the blame from the teacher, who are then smart enough, with a few suggestions, to work to develop a solution.

It is my intention that this blog is part of a solution. The aim is that through my musings and the comments of others we are able to encourage progress in the teaching of statistics in such a way that will thrill and excite the masses! Failing that, at least not put them off statistics altogether.

“Teaching Statistical Concepts” by Anne Hawkins et al, Longman 1992 seems to consider the problems Nic alludes to.

Your comment re skewness is intriguing. Do you think skewness implies a direction? There’s left-skew and right-skew.

My intuitive feel for the word skew is that the direction should be where the bulge is, but it is actually where the tail is. (Left skew means bulge on the left in my head, though it actually is tail on the left) So rather than get it wrong I tend to describe the shape. My experience with students is that they have similar problems (possibly from having been taught by me!)

I have had the same issue with that word “skew”, so there is some linguistic/intrinsic issue with it that we have to unfortunately live with 🙂 just like you can’t change the legacy of (many)commonwealth countries to drive on the other side of the road 🙂

It is good to know I am not alone in my view of skew.

I’m not sure Japan really classes as a commonwealth country though.

Reblogged this on roughlynormal.

Great post. It’s the same all over, I’m afraid – the need for more pedagogical content knowledge.

For example, here’s a post about the need for pedagogical content knowledge in teaching computer science. http://computinged.wordpress.com/2010/02/05/what-cs-teachers-know-pck-for-cs-ed/

An interesting extension is the TPACK framework, which adds technological knowledge: http://www.tpack.org/

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