Can horses do maths?

Imagine if one day with a new class I pulled you aside and said “listen, there are a couple of special students in here”.  You’re intrigued and I tell you, “on the entrance tests we also tested for IQ and these five students did incredibly well!” while handing you a list with the names of five students. Would you be surprised if these students ended the course with great marks?

Now imagine I told you that I had selected those students at random. That’s impossible, you think, not only did those students do the best on the test, but they were also the best in class. Moreover, the only person who knew that the students were ‘special’ was you, the teacher.

Clever Hans  was a horse who could do maths. Hans’ owner used to ask Hans maths questions and Hans would bang his hoof to answer. This amazed people who saw it. The horse was not only capable of understanding human language but also of answering complex (for a horse) questions!

Hans actually couldn’t do maths, not at all, but he was fairly clever. When Carl Stumpf investigated and subjected the horse and owner to various control tests he discovered that Hans was picking up on subtle messages being given by the questioner. The owner’s body language (leaning forward, raising his eyebrows, etc) were all giving Hans the hints he needed to produce the right answer.

Han’s owner himself had no idea he was giving these unconscious messages. And teachers are similarly unconscious of the fact that our expectations can shape student performance. This is called the Pygmalion effect and it was researched in 1968 by Rosenthal and Jacobson who suggest that students will conform to our expectations of them. Students for who teachers hold high expectations will achieve highly and vice-versa. The effect was more apparent in younger children, but all children selected as being  “special” showed greater gains than the other students. 

So how does this happen? According to this video there are four things which teachers do which affect students. Firstly they are nicer to those students for which they have high expectations. Secondly, they teach them more. That is they give more time and input to these students. Thirdly, teachers give “good” students more chances to respond in class and finally the teachers give more positive feedback to “good” students and conversely “are willing to accept low quality responses” from students who they expect less from.  
In class this week I was thinking about a group of boys who sit together, who I have come to see as perhaps not as capable and perhaps not as hardworking as others. It then struck me that these kids are actually in the highest level class, and are also students of a public university, meaning that they  certainly have above average English ability nationally and are in the top third for the University as a whole. Despite this, I’d somehow mentally pigeon-holed them. I now need to reevaluate my attitude towards these students because I’m pretty sure I’m probably guilty of having lower expectations for them, which could, according to this research,  actually lead to them doing worse. 

Once the perception is in place, confirmation bias will do the rest. Every time a ‘good’ student forgets homework you will think, -ah well they probably had a good reason to, while you will be less charitable about the a student who you perceive to be less able ‘Oh, well it’s not surprising he’d forget his homework!”. In the same way when a student who we perceive has lower ability, answers a question we may think ‘wow, impressive -for her.’ As Mark Twain put it “give a man a reputation as an early riser and he can sleep ’till noon.”

I haven’t seen much criticism of this theory so if you know any please direct me to it. I do wonder about the Hawthorne (observer) effect and if teachers could have been influenced to ‘make sure’ those students who were predicted to do well would do well, (or conversely how bad it would look for the teacher if they didn’t). This study by Claiborn failed to replicate the findings. Though Smith and Luginbuhl (1976, 265) claim that “the effect is observed often enough that its importance should not be discounted.”
On a related note, this doesn’t just apply to teachers and students it likely also applies to your job and how your boss sees you. If your boss sees you as being a capable and reliable member of staff then you’ll probably conform to those stereotypes to some extent. You’ll also be given more responsibility and probably more nuanced feedback when you get things wrong. conversely, if your boss sees you as slightly less capable or a bit unreliable then they may well be what you become.

So, no, horses can’t do maths, but teachers’ attitudes towards their students can affect students in quite remarkable ways. 

update: See how far we’ve come!

2 thoughts on “Can horses do maths?

  1. Thanks for putting such care and time into this post — really eloquently argued (last October). I've got something related coming (how the identities we co-construct with our students determines their success), but I have to finish setting up my website first (self-learning). I suspect the support for this argument you're looking for can be found, albeit maybe implicitly among the social-interactionists. More recently, there's this, which reminded me of the famous blue eye/brown eye classroom experiment, which may really be qwhat's going oon here:


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s