I don’t like the Khan Academy videos about statistics. But I can see why some people do. Some are okay, though some are very bad. I’m rather sorry they exist though, as they perpetuate the idea of statistics as mathematics.
Khan Academy, critics and supporters
Just in case you have been living under a rock, with respect to mathematics education, I will explain what Khan Academy is.
Sal Khan made little YouTube videos to teach a family member maths. Other people watched them and found them useful. Bill Gates discovered them and threw money at them. Now there are heaps of videos, with some back up exercises, and some people think this is the best thing to happen to maths (and other) education. Other people think that the videos lack pedagogical content knowledge. Sal agrees – he says he just makes them up as he goes along.
Diane Ravitch linked into the Khan Academy debate, beginning with this post, which is what got me looking into this. Two mathematics teachers made videos after the style of Mystery Science Theater 3000 starring two of Khan’s poorer mathematical contributions. The one on multiplying negative numbers was particularly poor and has since been replaced. Critiques of Khan seem to meet with two kinds of comments. One group is people who know about teaching, who are pleased that someone is pointing out that the emperor, though not naked, is poorly clad. The other lot are generally telling the mean teachers to leave Khan alone, that he is the saviour of mathematics teaching, and they would never have understood mathematics without him. The supporters also either suggest vested interest (for people who make educational materials) or that the writers should try to do better (for those people who don’t make educational materials). To be fair, the first group are also calling for other people to make better videos and put them out there.
For a good summary of the pros and cons of KA, here is a recent article in the Washington Post: “How well does Khan Academy teach?”
Khan Academy Statistics videos
So I took a look at Khan Academy statistics videos. I know something about the teaching of statistics. I have many years of experience of successful teaching, I have done research and I have read some of the literature. I have pedagogical content knowledge (I understand what makes it hard for people to learn statistics.) And I have made my own statistics teaching videos, which have been well received. I wrote some time ago about the educational principles based on research into multimedia, which have been used in developing these videos. Unlike Khan I have thought hard and long about how to present these tricky concepts. I have written and rewritten the scripts. I have edited my audio to remove errors and hesitations, I have…anyway – back to Khan Academy.
To be fair, statistics is one of the most difficult subjects to teach, so I didn’t have high hopes.
To start with the list of topics under the statistics heading showed a strong mathematics influence. This may reflect the state of the curriculum in the United States, but in no way reflects current understanding of how statistics is best understood. I couldn’t find anything about variation, levels of measurement and sampling methods, which are all foundation concepts of statistics. I think it would be more correct to call the collection of videos “the mathematics of statistics”. It starts with the “Mean, Median and Mode.” Not exactly a great way to enter the exciting world of statistics. And he mispronounces the adjectival use of “arithmetic”, which is a bit embarrassing.
Reading Pie Graphs
I summoned up courage to view the video on reading Pie Graphs. It was not good. The example was percentages of ticket sales for Mediterranean cruises over a year. That data should never have been put into a Pie Graph. For two reasons! First there are too many slices of pie. A pie chart should never be used for that many categories. But worse than that, the categories are ordinal – they are months. The best choice of graph is a bar or column chart, with the months in order, as you would then be able to see trend! (I have to stop myself here or I could rave on much longer). My point is that Khan has used a very BAD graph as his example. This is one of the worst things a teacher can do, as it entrenches in the students’ minds that this is acceptable. The only thing good about the graph was that it was not three dimensional, and it is not exploding. It didn’t even have a title. Bad, bad, bad. (Sorry I was meant to be stopping)
I am tempted to say Khan is arrogant to think he can produce something after a few minutes thought. Actually I was tempted to say something rather stronger than that. I have to admit I haven’t watched many of the videos, but I really don’t want to spend too much of my life doing that. I chose one on Confidence Intervals, which nearly had me throwing things at the computer. It never explains what a confidence interval is. The bumbling around was so painful I couldn’t watch the video in its entirety. I’m pretty sure he got it wrong. He was so confused by the end that I can’t say for sure. My own confidence intervals video is one of my earlier ones, so it is a little rough, but I’d wager most people understand better what a confidence interval is after watching it. (UPDATE: Since writing this post I have made a better video about confidence intervals. It explains what confidence intervals ARE!) You can watch it here:
So then I decided I should look at the video entitled p-value and hypothesis tests. This is something I know many people struggle with. It is crucial to understanding inferential statistics. I have spent many hours working out ways in which to teach this that will help people to understand.
The p-value and hypothesis testing
Well I watched most of the p-value video, and was pleasantly surprised. The explanation of how we get the p-value is sound, and once he gets into his flow, the hesitations get less irritating. There is a small error – talking about 100 samples, rather than a sample of 100 observations. Also it is a bad idea to have a sample size of 100 in an example as this can get confused with the 100 in the expression of the confidence interval as a percentage. But it does give a good mathematical explanation of how the p-value is calculated. I’m not sure how well it helps students to understand what a p-value is. For a mathematically capable student, this would probably be enlightening. I have my doubts about most of the business students I have taught over the last two decades.
My main criticism is that the video is dull. It doesn’t provide anything more than the mathematics. But apart from alienating non-mathematical students it isn’t harmful. In fact if I had a student who wanted to know the mathematics behind the statistics, I would be happy to send them there. People have commented that my videos don’t tell you how the p-value is calculated. This is true. That is not the aim. Maybe I’ll do one about that one day, but I figured it was more important to know what to do with one.
Khan Academy videos on statistics aren’t good
My point is, surely we can do better than that! Bill Gates has thrown money at the Khan Academy. Wouldn’t it be wonderful if it were the purveyor of really good practice rather than mediocrity? One blogger suggests that if Khan Academy could use really good videos, it really could be useful.
I have gone on long enough.
I realise now, that asking a busy person to watch my videos is a bit of a cheek. They aren’t that long though. They are funny and clever. They are NOT like Khan Academy. I think they are worth the six to ten minutes each.
Here are links to my three most popular ones. Enjoy.