I am forever grateful to the teachers at my convent high school. In my first year I was required to take thirteen different subjects, one of which was typing. At the time computers were still objects mainly occurring in science fiction and operated by punch-cards, but the nuns thought we should get a wide exposure to different subjects (just in case I decided to be a typist/linguist/artist/scientist… instead of a maths teacher). Consequently I can touch-type, a skill which has been invaluable in my career as an academic. I don’t think about where my fingers are going – in fact when I do think about it, it tends to slow me down, and I make more errors. I’m grateful for all the subjects to which I was exposed, but typing is the one I use most often. When I am writing, the words go from my brain to the screen almost without effort.
Part of how this works is called “muscle memory” which “involves consolidating a specific motor task into memory through repetition”. (Wikipedia) It is a combination of stuff happening in the brain in the conscious and unconscious mind. (You can tell I am not a neuro-scientist!). We all have physical and mental skills that we use without thought. Much of the time when we are walking, riding a bicycle, driving, playing an instrument, playing sport, swimming, the processes involved do not require intervention from our conscious thought. The way we get this “muscle memory” is through repetition. A toddler learning to walk spends a lot of time practising until walking becomes fluent and unconscious. Until then they have to sit down to concentrate on something else. My son is a pianist, and spent hours on the piano as a young child, playing the same thing over and over until he could play as he wished. Now the piano is more like an extension of him, and he does not have to think about where his fingers are going. This is even more remarkable as he is totally blind and has been from birth.
Now wouldn’t it be nice if we could somehow replicate this level of competence in the area of learning mathematics, statistics and operations research. It isn’t so much “muscle memory” as mastery – becoming an expert.
I recently helped to organise a six or twelve hour Rogaine – a sporting event requiring cross-country running/hiking and navigation. At the first meeting of the committee, we were given maps of the area and asked to come up with about seventy potential checkpoints. I spent quite a bit of time studying the map, and the satellite view on Google, and managed to have some ideas. I realised what a novice I am when we met again, and Pete, one of the grand old men of rogaining, led us through the map. He could look at it and tell right away whether slopes went up or down, were steep or flat, likely to have swamps etc. I was in awe. By the end of the evening’s work my brain was mush.
This was the difference between a novice and an expert.
One of my favourite books about learning, “How People Learn: Brain, Mind, Experience and School” introduced me some years ago to the concept of novice and expert. It is a very helpful way to describe the process of mastering a skill or subject. All of us are experts in some areas. I know my times-table up to 12 automatically. Someone says 56 and automatically I think 7 times 8. Or 42, and I think 6 times 7. (Not 6 times 8 as in the Hitchhikers’ Guide to the Galaxy). I don’t have to think about it.
Similarly if I look at a histogram, it talks to me. I can see what is happening in the data, I can tell if the bin sizes are causing strange anomalies. I can tell the difference between two samples. Time series graphs are also no mystery. Trend and seasonality pop out at me. I can look at a scatter plot and have a rough idea of the correlation shown. In operations research I can hear of a problem situation, and right away I have a fair idea what techniques are going to be most appropriate in dealing with the problem. Many teachers are like this. And so we should be – as we are experts in our fields, compared to our students.
But our being experts doesn’t help students to become that way. Well not alone anyway. My experience with teaching statistics is that it takes a large number of different instances in order to see patterns. And the ability to see patterns is one of the main ways that an expert differs from a novice. It is only as I have engaged in statistical analysis and operations research that I have gained this knowledge. And it is as I have taught these subjects that I have become aware of what students find difficult.
I have previously written on the need for repetition, calling the post Drill and Rote in teaching LP and hypothesis testing. Rather than using the unpopular word “drill”, I like to talk about “well-designed repetitive practice”. I related it to two specific topics. I am currently revisiting this idea as I have been studying the NZ statistics curriculum and developing support materials for learning statistics. I have also been following the progress of a blogger who is taking a coursera course in statistics and blogging about his experiences. Though my experience of the coursera course is second-hand, I have noted a major flaw in it. (Several actually, but I’ll write a whole post about that when my friend has finished the course.) The major flaw is that there are no practice exercises, only graded assessments. This is really really bad, and I suspect that this is not an isolated example.
Too often the teaching/learning and the assessing are conflated in a way that means that neither is happening well. I suspect this happens often in NZ NCEA, but I would love to be proven wrong. Certainly it is endemic in many university courses at all levels. It’s a bit of a vicious cycle. Time-starved students tend only to put effort into activities which will affect their final grade directly. Many students do not seem to make the connection between learning in a low-stakes activity and the grade in the final assessment. Consequently they engage only in high-jeopardy activities, which behaviour is not conducive to understanding, and discourages risk-taking. Students take the “safe” road of finding out what they think the instructor wants them to say and then saying it. Instructors are torn regarding how much help they can give the students if the piece of work is meant to be the students’ own work. Consequently opportunities for teaching, coaching, questionning, discussion, and – dare I say it – learning are lost.
So where am I going with this? Teachers need to look at their curriculum plan and make sure that the students have enough learning opportunities before they are given a summative assessment activity. In the coursera course this could include providing on-line exercises and self-tests so that students can practice their knowledge. Students in turn need to avail themselves of non-assessed exercises in order to learn. It all sounds rather obvious, and idealistic.
In my “blended learning” course we found a solution that helped many of our students. It was based on the Personalised System of Instruction method, as developed by Fred Keller in the mid 1960s. There were many opportunities for students to repeat the practice tests until they gained mastery. The only way to fail the course was to fail to complete all of the assessments, correct to 80% before the end of the course. We had about the same pass/fail rate as traditional courses, a fact which I found interesting. I wonder if this could be adapted to school assessments. Students could be required to pass a “qualifiying” assessment, with which they can get help, before they are allowed to attempt the high-stakes assessment. I’d be interested to hear from teachers who may be already implementing this.
Whatever type of question is asked, is the kind of learning the students will do. For example we did not ask students to calculate standard deviations by hand, but rather got them to identify which graph showed the greatest or least variation (or consistency). We got them to critique graphs, identify flawed thinking in reports, and decide which test should be used in a specific instance. It can be tricky to assess higher order thinking, but it is possible, and over the years our questions have grown in sophistication to meet the needs we identified.
There must be multiple contexts, preferably using real data. When discovering patterns, students need to be able to tell what is general from what is specific to a given example or exercise.
Immediate feedback is very important so that students do not learn incorrect things. The on-line medium is ideal for this, and feedback can become very specifically targetted as we recognise common errors students make.
None of us like to do unpleasant tasks, and we wish to help students want to spend more time learning statistics. We continue to study motivational theory and try out different ways to help students engage. Success is a great motivator, and getting instant feedback and improving marks for repeated tries on tests works well. We are also looking at introducing some game elements.
These are the principles we are using as we develop our Statistics Learning Centre. At present we are providing materials for Level 3 NCEA Statistics in New Zealand (NZStat3), and introductory business statistics just about anywhere (See AtMyPace: Statistics)! We hope to use our experiences providing these materials to develop and fine tune them, thus providing high quality resources for all students of statistics. In this way they will be able to “train” in a safe, fun and challenging environment as they develop their statistical muscle memory.