Posted by: Gary Ernest Davis on: January 23, 2011

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At the beginning of every semester I talk students through the written instructions on the website for the mathematics course they are taking. This semester, Spring 2011, those courses are Differential Equations, and Mathematical Statistics.

I talk the students through course arrangements including submission of written material using LaTeX for writing mathematics, the structure of the course, assessment procedures, and behavior in class, among other things.

As the course progresses students work on projects, of 2-3 weeks duration, and write their findings progressively on a blog.

Often I will stop the class for a short explanation of a mathematical point that is causing more than one student difficulty, or stop to explain how to format their blogs, how to write a particular expression using LaTeX, or how to use software to do a certain task.

Almost every time I do one of these things I will have at least one, student, and often several, asking me the same question that I just explained.

For example, a student might ask me how to format dy/dx as in latex, so I will stop the class and give a short explanation.

Several minutes later, another student, often several, will ask the same question over again: “How do you format dy/dx in LaTeX?”

What’s happening? Weren’t they listening?

Sometimes such questions will come later in a class, or in a following class, where I might charitably imagine they have forgotten my answer.

After many years of reflecting on this problem of students apparently not listening I have come to the conclusion that it is an issue of focus of attention.

Sometimes this is obvious: when a student is reading or clicking on, a web site, or texting on a cell phone as I am talking.

Those instances I jump on right way and remove persistent offenders from class temporarily.

Yet even this gross off-task behavior is evidence of a failure to focus attention because these issues of texting and web surfing during explanations are dealt with explicitly in writing and in talk at the beginning of the course. The offending students did not pay attention when these issues were discussed.

Sometimes students will appear to be paying attention, to be genuinely listening, and then ask me several minutes later to answer what I just discussed.

Those students, in my experience, have their thoughts elsewhere during my explanation.

In short, there are many college mathematics students who do not seem to know what it means to focus their attention and listen to a verbal explanation.

Because we currently have no way of knowing in class what is actually going through a students mind as they hear us talk, we do not know what is their focus of attention, and whether or not they are listening and processing what we are saying.

The answer, sadly, is not often.

I have observed many of my own colleagues who simply talk at students for extended periods – up to 40 minutes at a time – with very little input from students.

Even more telling (and more scientific) a brief study I carried out with several years ago with colleagues (pme30_Dalton_Davis_Hegedus) shows that many high school teachers (in fact, all those we studied) ask questions at a very high and uniform rate – about on question every 10 -15 seconds, but rarely wait any longer than 3 seconds for a student answer. Over the course of a semester this means that a high school mathematics teacher is likely to ask many thousand of times the questions asked by their students.

Mathematics teachers in other words, are in the main not listening to their students, but bombarding them with questions instead.

Then they do not wait long enough for students to come up with a thoughtful answer.

So where is listening being modeled for students?

Not by teachers, in my experience.

Mathematics is too broad and deep a subject for student to progress far by “discovering” mathematics.

Mathematical knowledge is largely cultural knowledge, obtained through the thought and work of individuals or groups of people working together on mathematical problems.

When a solution to a hard mathematical problem, or a new method for approaching a problem, is found, that knowledge is spread to other interested people by the written and spoken word.

In other words, mathematics is spread from people with ideas to others who are interested.

The issue in learning mathematics is to take on board, as your own, a procedure, method, or way of thinking, of someone else.

It is a process of bringing the outside cultural knowledge of mathematics inside your own brain, and taking on board someone else’s ideas.

This requires a strong focus of attention, and, in the case of verbal transmission, strong listening skills.

Without those skills of focus of attention and listening, learning mathematics becomes very difficult.

In one word? INTEREST

While I read in some other writings that the current generation of kids are used to stimulation that is interactive (such as those given by the computer games and such) growing up on such interactions means that their brains have been more wired to learning information in an interactive manner.

Now, I do know that I am not able to keep my focus on during the class and easily switch off or on to something else.

The only answer to this is to increase the level of interaction, though it would definitely mean more work and effort.

1 | Bernie Soong

January 23, 2011 at 2:32 pm

I am not a math teacher but your post applies to all teachers, including me! It is a good reminder as we sometimes get lost in the duties and responsibilities of the every day. And your last two sentences, awesome.