The phrase I despise more than any in popular use (and believe me there are many contenders) is “Those who can, do, and those who can’t, teach.” I like many of the sayings of George Bernard Shaw, but this one is dismissive, and ignorant and born of jealousy. To me, the ability to teach something is a step higher than being able to do it. The PhD, the highest qualification in academia, is a doctorate. The word “doctor” comes from the Latin word for teacher.

Teaching is a noble profession, on which all other noble professions rest. Teachers are generally motivated by altruism, and often go well beyond the requirements of their job-description to help students. Teachers are derided for their lack of importance, and the easiness of their job. Yet at the same time teachers are expected to undo the ills of society. Everyone “knows” what teachers should do better. Teachers are judged on their output, as if they were the only factor in the mix. Yet how many people really believe their success or failure is due only to the efforts of their teacher?

For some people, teaching comes naturally. But even then, there is the need for pedagogical content knowledge. Teaching is not a generic skill that transfers seamlessly between disciplines. You must be a thinker to be a good teacher. It is not enough to perpetuate the methods you were taught with. Reflection is a necessary part of developing as a teacher. I wrote in an earlier post, “You’re teaching it wrong”, about the process of reflection. Teachers need to know their material, and keep up-to-date with ways of teaching it. They need to be aware of ways that students will have difficulties. Teachers, by sharing ideas and research, can be part of a communal endeavour to increase both content knowledge and pedagogical content knowledge.

There is a difference between being an explainer and being a teacher. Sal Khan, maker of the Khan Academy videos, is a very good explainer. Consequently many students who view the videos are happy that elements of maths and physics that they couldn’t do, have been explained in such a way that they can solve homework problems. This is great. Explaining is an important element in teaching. My own videos aim to explain in such a way that students make sense of difficult concepts, though some videos also illustrate procedure.

Teaching is much more than explaining. Teaching includes awakening a desire to learn and providing the experiences that will help a student to learn. In these days of ever-expanding knowledge, a content-driven approach to learning and teaching will not serve our citizens well in the long run. Students need to be empowered to seek learning, to criticize, to integrate their knowledge with their life experiences. Learning should be a transformative experience. For this to take place, the teachers need to employ a variety of learner-focussed approaches, as well as explaining.

It cracks me up, the way sugary cereals are advertised as “part of a healthy breakfast”. It isn’t exactly lying, but the healthy breakfast would do pretty well without the sugar-filled cereal. Explanations really are part of a good learning experience, but need to be complemented by discussion, participation, practice and critique. Explanations are like porridge – healthy, but not a complete breakfast on their own.

## Why statistics is so hard to teach

“I’m taking statistics in college next year, and I can’t wait!” said nobody ever!

Not many people actually want to study statistics. Fortunately many people have no choice but to study statistics, as they need it. How much nicer it would be to think that people were studying your subject because they wanted to, rather than because it is necessary for psychology/medicine/biology etc.

In New Zealand, with the changed school curriculum that gives greater focus to statistics, there is a possibility that one day students will be excited to study stats. I am impressed at the way so many teachers have embraced the changed curriculum, despite limited resources, and late changes to assessment specifications. In a few years as teachers become more familiar with and start to specialise in statistics, the change will really take hold, and the rest of the world will watch in awe.

In the meantime, though, let us look at why statistics is difficult to teach.

- Students generally take statistics out of necessity.
- Statistics is a mixture of quantitative and communication skills.
- It is not clear which are right and wrong answers.
- Statistical terminology is both vague and specific.
- It is difficult to get good resources, using real data in meaningful contexts.
- One of the basic procedures, hypothesis testing, is counter-intuitive.
- Because the teaching of statistics is comparatively recent, there is little developed pedagogical content knowledge. (Though this is growing)
- Technology is forever advancing, requiring regular updating of materials and teaching approaches.

On the other hand, statistics is also a fantastic subject to teach.

- Statistics is immediately applicable to life.
- It links in with interesting and diverse contexts, including subjects students themselves take.
- Studying statistics enables class discussion and debate.
- Statistics is necessary and does good.
- The study of data and chance can change the way people see the world.
- Technlogical advances have put the power for real statistical analysis into the hands of students.
- Because the teaching of statistics is new, individuals can make a difference in the way statistics is viewed and taught.

I love to teach. These days many of my students are scattered over the world, watching my videos (for free) on YouTube. It warms my heart when they thank me for making something clear, that had been confusing. I realise that my efforts are small compared to what their teacher is doing, but it is great to be a part of it.

Unfortunately there are always a few poor teachers who give the rest a bad name. I would also add that many teachers do not know how to teach mathematics (and by extension, statistics). That said, I am not speaking with hard data – just consistent anecdotal evidence.

Statistics becomes enjoyable when you get to experience the thrill of discovery. Of traversing new areas. Applying new techniques. Thinking outside the box and experimenting. Then debating whether the analysis was appropriate. First year stats is boring. 🙂

Back to teaching. The only way to determine whether you truly know a subject is to teach it. (And why I also dislike the statement quoted.) This is why I am disappointed with the lack of excited mathematics students and, in particular, the large proportion of students who exit school hating mathematics. Does this not imply that the maths teachers a) don’t know the subject well enough to teach it, b) the requirements to teach maths are too low, or c) something else like low salary results in not drawing the best candidates?

Society would likely function much better if more people understood mathematics, probability, and basic risk assessment.

“The only way to determine whether you truly know a subject is to teach it.”

This exactly. I studied maths, and one semester I did an exchange in Germany. Tuition was in german, so I studied for my exams in german, but I recall explaining things to my boyfriend (also studying maths) over skype – even though he only understood the bits in english, explaining the concepts aloud to someone helped me better understand what I was learning.

Math and statistics both, unfortunately have a prejudice working against them. It is not hard to imagine a conversation of four or five well educated, well read individuals, where one of them will readily admit a lack of prowess in mathematics. This indicates a comfort level in revealing this shortcoming. At the same time it would be difficult to imagine one of these same well read individuals admitting a deficiency in grammar or spelling. These is something about our society that makes it okay, even acceptable to be deficient in mathematics. Every math teacher has had a student that says ” I just do not have a mathematical mind”. Why is it acceptable to admit this, while admitting one is a poor speller or poor at grammar would be an embarrassment? (I hope I’ve spelled everything correctly)

Doing statistical consulting at the University of Wollongong, I was approached by a lecturer in English for some statistical advice. She readily admitted that she could barely add up. What I should have replied (but of course didn’t think of until later) is ‘Oh, you poor thing! I guess that you can’t read either!’ She would have been horrified by this, but my response would have been that humans were counting long before they were reading. (Even if the counting was as basic as ‘Hey, he’s got more than me!’)

I think that we have to stress more the absolute fundamentalism of mathematics in society.

Ken Russell

Ken Russell