Mathematical discourse

We were made to talk

When thinking about education I can't avoid working from this basic premise:  We were made to talk and laugh and have fun.  And learning was meant to be joyful and easy.  Unfortunately things in the educational world don't always turn out this way.                 

I have spent the last few months analysing discourse patterns that occur between adults (learners and tutor) within numeracy lessons.  The findings shed light on whether learners are "talking and having fun" in mathematically productive ways.  In my mind, the findings have huge implications for the tertiary sector.    

The word ‘discourse’ has several meanings relating to slightly different contexts and purposes.  My use of the word really just means the type of talking/communication that occurs between students and the tutor in classrooms.  I have analysed particular features that have emerged as important. 

Setting the scene

There is strong evidence that the quality of learner discussions has huge implications for how learners engage in, and consequently develop, mathematical knowledge.

In other words:  The type of discourse that occurs in numeracy classrooms COUNTS.

So, in adult numeracy classes do the discourse patterns enhance learning, or constrain and inhibit learning?  Well, unfortunately the discourse patterns as they relate to mathematics are particularly poor.  There are four areas of specific concern.  I’ll post the first of the four below with the other three to follow in a further post.

The source of mathematical ideas
The learners in my study believe that the tutor, and associated resources, is the only valid source of mathematical ideas.  They view the tutor as the expert who possesses the right type of mathematical knowledge.  That is, the math knowledge that is generated, owned and passed down by established academic institutions (and official mathematicians).  Because of this belief, learners see little value in generating their own ideas, sharing their ideas with others, or listening to other learners ideas. Learners do not see group problem solving as a learning opportunity and require the tutor to verify any and all answers before they celebrate success (note that whether an answer is correct or incorrect should be self-evident if learners understand the problem and answer).  Keep in mind that learners may be motivated to group problem solve due to the social aspect and a sense of fun.  They will still engage but not really believe that they will learn what they need from the experience.

The discourse patterns during group work were dominated by learners who ‘knew’ the correct method (taught to them by previous teachers and therefore authentic) and simply told the group how to solve the problem.  The group did not discuss ideas such as solution options, alternate interpretations or alternate solution strategies.  Also, once the tutor began to work through the problems the learners simply used the tutor’s ideas.  Learners very rarely spoke up and gave a new or unique method of solving or thinking about a task.  The one exception was ‘numeracy experts’, that is, those learners who had high numeracy skills and wished to show their proficiency to the class.

In essence, learners do not believe that their own mathematical ideas have any value and hence do exert energy in producing or evaluating them, nor do they exert energy in listening to other learners’ ideas.  However, research strongly suggests this is an essential process in order to develop conceptual knowledge of mathematics. Learners must generate their own mathematical ideas. However, getting them to do so requires changes to occur at a multitude of levels.  The first and not least, is to change the belief that mathematical knowledge is only produced by experts and cannot be self-discovered, a belief held by many tutors.