Saturday, 29 March 2014

Mathematical discourse:  Questioning

How learners ask and respond to questions reveals much about the type of information they deem important within a numeracy class.  And what learners deem as important reveals much about the goals they set for themselves, and goals, be they implicitly or explicitly defined, reveal much about the beliefs learners hold.     

And that is why this particular finding about adult learners' questioning practice is so troubling.

First let me explain the differences between good questioning and poor questioning using the model provided by Huffard-Ackels, Fuson & Sherin (2004) called the ‘math-talk community’.  To my mind this model is the most appropriate for the adult sector and has been used everywhere from young school students to University mathematical classes.

Good questioning in a numeracy class:
Student to student talk is student initiated, not dependent on the teacher.  Students ask questions and listen to responses .  Many questions are ‘why?’ questions that require justification from the person answering.  Students repeat their own or others questions until satisfied with the answers.
Poor questioning in a numeracy class: 
Teacher is the only questioner.  Short frequent questions function to keep students listening and paying attention to the teacher.  Students give short answers and respond to the teacher only.  No student to student math talk.
These two descriptions act as book-ends on a continuum.  There are two intermediate descriptions also that demonstrate how learners may transition as they move from the poor description to the good description. 

The findings

The findings of my classroom observations reveals that the greater part of the questioning discourse resembles the ‘poor’ description – disturbingly so.  This is not to say there were no exceptions.  There were some really good examples of questioning – but not many.  Overwhelmingly this is what I found:
  • Tutors asked almost exclusively polar questions while teaching
  • Learners responded to these questions with single word answers
  • Learners only responded when certain of their answer (no one risks being wrong in public)
  • On occasions when tutors asked learner to explain their thinking the learners still responded with single word answers (even when prompted).
  • Learners rarely asked questions and when they did the questions were requests for answers, not for explanations, clarifications or justifications.
  •  Learners very rarely initiated their own ‘why?’questions and when they did it was to the tutor not  each other.

The pattern is simple:  Tutor asks a closed question to the class, a learner who knows the answer answers, and the tutor carries on - over and over and over again.  This is replicated in group work environments with no tutor present.  This pattern is known as – Initiate, respond, feedback (IRF).

So, the discourse within adult numeracy classrooms resembles that of a traditional transmission-based classroom.  Given the picture above it kind of makes sense how this idea may have sneaked into our psyche. A description of this pattern has been attributed to Friere: ‘The pedagogy of the question’.  In other words a classroom culture in which questions and answers are used to control the structure, discourse and content of the class.  But, Friere is suggesting it is the teachers ‘fault’ for implementing (or conforming) to the structure.  But things are very different in this sector because the adult learners are now apply pressure to the tutor to conform to this model.  And my thinking is that this is because adult learners believe that this is how maths classes should operate and therefore both exert influence for the pattern and conform easily to it.

Are adult learners engaging in the types of discourses that promote the development of the conceptual understanding they need.

My answer: No.

Do the adult learners themselves contribute to this pattern?

My answer: Yes.

Can we as tutors change this?

My answer:  I hope so but I'm not sure how.


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