Oh Ordinal data, what do we do with you?
8 July 2013
Conceptualising Probability
22 July 2013

I do my own video-editing using a very versatile and complex program called Adobe Premiere Pro. I have had no formal training, and get help by ringing my son, who taught me all I know and can usually rescue me with patient instructions over the phone. At times, especially in the early stages I have felt myself wobbling along the knife-edge of competence. All I needed was for something new to go wrong, or or click a button inadvertently and I would fall off the knife-edge and the whole project would disappear into a mass of binary. This was not without good reason. Premiere Pro wasn’t always stable on our computer, and at one point it took us several weeks to get our hard-drive replaced. (Apple “Time machine” saved me from despair). And sometimes I would forget to save regularly and a morning’s work was lost. (Even time-machine can’t help with that level of incompetence.)
But despite my severe limitations I have managed to edit over twenty videos that now receive due attention (and at times adulation!) on YouTube. It isn’t an easy feeling, to be teetering on the brink of disaster, real or imagined. But there was no alternative, and there is a sense of pride at having made it through with only a few scars and not too much inappropriate language.
There are some things at which I feel totally competent. I can speak to a crowd of any number of people and feel happy that they will be entertained, edified and perhaps even educated. I can analyse data using basic statistical methods. I can teach a person about inference. Performing these tasks is a joy, because I know I have the prerequisite skills and knowledge to cope with whatever happens. But on the way to getting to this point, I had to walk the knife-edge of competence.
Many teachers of statistics know too well this knife-edge. In New Zealand at present there are a large number of teachers of Year 13 statistics who are teaching about bootstrapping, when their own understanding of it is sketchy. They are teaching how to write statistical reports, when they have never written one themselves. They are assessing statements about statistics that they are not actually sure about. This is a knife-edge. They feel that any minute a student will ask them a question about the content that they cannot answer. These are not beginning teachers, but teachers with years and decades of experience in teaching mathematics and mathematical statistics. But the innovations of the curriculum have put them in an uncomfortable position. Inconsistent, tardy and even incorrect information from the qualification agency is not helping, but that is a story for another day.
In another arena there are professors and lecturers of statistics (in the antipodes we do not throw around the title “professor” with the abandon of our North American cousins) who are extremely competent at statistical mathematics and analysis but who struggle to teach in a satisfactory way. Their knife-edge concerns teaching, appropriate explanation and the generation of effective learning activities and assessments in the absence of any educational training. They fear that someone will realise one day that they don’t really know how to devise learning objectives, and provide fair assessments. I am hoping that this blog is going some way to helping these people to ask for help! Unfortunately the frequent response is avoidance behaviour, which is alarmingly supported by a system that rewards research publications rather than effective educational endeavours.
So what do you do when you are walking the knife-edge of competence?

You do the best you can.

And sometimes you fake it.

I am led to believe there is a gender-divide on this. Some people are better at hiding their incompetence than others, and just about all the people I know like that are men. I had a classmate in my honours year who was at a similar level of competence to me, but he applied for jobs I wouldn’t have contemplated. The fear of being shown up as a fake, or not knowing EXACTLY what to do at any point stopped me from venturing. He horrified me further a few years later when he set up his own company. Nearly three decades, two children and a PhD later I am not so fastidious or “nice” in the Jane Austen meaning of the word. If I think I can probably learn how to do something in time to make a reasonable fist of it and not cause actual harm, I’m likely to have a go. Hence taking my redundancy and running!
When I first lectured in statistics for management,  I did not know much beyond what I was teaching. I lived in fear that someone would ask me a question that I couldn’t answer and I would be revealed as the fake I was. Well you know, it never happened! I even taught students who were statistics majors, who did know more than I, and post-graduate students in psychology and heads of mathematics departments, and my fears were never realised. In fact the stats students told me that they finally understood the central limit theorem, thanks to my nifty little exercise using dotplots on minitab. (Which was how I had finally understood the central limit theorem – or at least the guts of it.)
I’m guessing that this is probably true for most of the mathematics teachers who are worrying. Despite their fear, they have not been challenged or called out.
The teachers’ other unease is the feeling that they are not giving the best service to their students, and the students will suffer, miss out on scholarships, decide not to get a higher education and live their lives on the street.  I may be exaggerating a little here, but certainly few of us like to give a service that is less than what we are accustomed to. We feel bad when we do something that feels substandard.
There are two things I learned in my twenty years of lecturing that may help here:
We don’t know how students perceive what we do. Every now and again I would come out of a lecture with sweat trickling down my spine because something had gone wrong. It might be that in the middle of an explanation I had had second thoughts about it, changed tack, then realised I was right in the first-place and ended up confusing myself. Or perhaps part way through a worked example it was pointed out to me that there was a numerical error in line three. To me these were bad, bad things to happen. They undermined my sense of competence. But you know, the students seldom even noticed. What felt like the worst lecture of my life, was in fact still just fine.
The other thing I learned is that we flatter ourselves when we think how much difference our knowledge may make.  Now don’t get me wrong here – teachers make an enormous difference. People who become teachers do so because we want to help people. We want to make a difference in students’ lives. We often have a sense of calling. There may be some teachers who do it because they don’t know what else to do with their degree, but I like to think that most of us teachers teach because to not teach is unthinkable. I despise, to the point of spitting as I talk, the expression “Those who can, do, and those who can’t, teach.” One day when the mood takes me I will write a whole post about the noble art of teaching and the fallacy of that dismissive statement. My next statement is so important I will give it a paragraph of its own.

A teacher who teaches from love, who truly cares about what happens to their students, even if they are struggling on the knife-edge of competence will not ruin their students’ lives through temporary incompetence in an aspect of the curriculum.

There are many ways that a teacher can have devastating effects on their students, but being, for a short time, on the knife-edge of competence, is not one of them.
Take heart, keep calm and carry on!


  1. Priscilla says:

    I just do the best I can and I am honest with my students. I tell them straight I am no expert, and point them in the direction of experts like you! They do not seem to mind one bit, infact on the odd occasion when I muck something up they like it. It makes them feel it is ok to be wrong sometimes, we are all human. I also expect that a number of my students will have more ability than I ever had, I have no problem with that. I can guide them and learn with them. A fake? That depends how you define teaching. Thanks for the post, however, I do not feel like I am on the knife edge of competence, I have enjoyed the learning. Yes it is all a bit of a mess, but we must rise above and enjoy the process. Some of the work students have produced is truly quality learning, at a much deeper level than last year.

    • Dr Nic says:

      Thanks Priscilla. I’m glad you are not on the knife-edge. I like the idea of a shared venture in learning.
      Not sure about being an expert! Maybe I’ve just been venturing a bit longer.

      • Hi Dr Nic, I return to your article whilst I attempt to gain clarity over the new external, 3.12 statistical reports. I am trying hard to rise above and see the big picture, but this year has been a bit of a nightmare. I feel like I am trying to hit a moving, invisible target. My search for clarity around the contents of this new standard is taking me far too long. So, I have visited the knife edge, and whilst I may not be doing my students harm, next year’s students will get a much better deal! This year group has been the first year for changes, each and every year that they have sat NCEA. I think some students have been disadvantaged by this process of change. So is it all worth it? I have to believe that it is. 😉

        • Dr Nic says:

          Hi Priscilla, I’ve seen your attempts to get clarity in the definition of the assessment, and I feel your pain. It seems unnecessary for things to be quite this cryptic, but hopefully it will settle down soon. I’ve also found it frustrating to have to track down the different sources of information regarding assessment in NCEA. Keep up the good work; you had to teeter on a knife-edge, not of your own making, it seems!

  2. Ian Barnes says:

    Good post Dr Nic, as usual. The undervaluing of of teaching skills in academia is rampant. In some academic circles it can be seen as “dumbing down” to state clear learning objectives which are then clearly expounded and assessed. This is not so much a “knife-edge” as a “blind-spot”.

  3. S Ellison says:

    Not sure I’m comfortable with being that close to the edge.
    It is true that change may place teachers (or statisticians) in new territory. That is part of the job, and adapting to it is part of our professional competence .
    But as a parent and as a school governor with a responsibility for what our children are taught, if someone came to me and said they were suffering from ‘temporary incompetence in some [significant] aspect of the curriculum’, I’d not want them in front of a class on that topic until they’d remedied the incompetence. And if they really cared, they wouldn’t either.
    It is our job – as employers, as education providers and – if we’re setting the curriculum – as regulators, to make sure teachers are properly equipped for their task before they teach. They have a hard enough job as it is without being pushed in front of a class without adequate training and resources.

    • Dr Nic says:

      Thanks for your comment, and appreciate your concern. I suspect that parts of the curriculum are not as important as the whole.
      For example, not quite understanding the deeper meanings of probability will make the teacher uneasy. But the student is unlikely to really “get it” anyway on the first time around, and even if well taught, many students still manage to cling to misconceptions.
      The sceptic in me thinks that there isn’t a great deal of detail that carries over from one year to the next in the student’s mind. That was certainly my experience in 20 years of teaching at university.

  4. […] unlikely to discover the possibilities at the edge of our competence. I wrote some time ago about the knife edge of competence. We don’t want to live on it, but we do need to spend some time there. I believe that if we never […]

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