Programm 361, Tasks, Mathematics, Questioning and Research

Presented and produced by Seán Delaney

Theme tune by David Vesey

This week I am joined on the programme by Professor David Clarke and Dr. Man Ching Esther Chan from the Graduate School of Education at the University of Melbourne. We discussed many aspects of research and teaching, with a focus on mathematics, tasks, questioning and language. Among the topics discussed were:

• Why a laboratory classroom was set up at the University of Melbourne
• The social unit of learning research project
• The layout of the laboratory classroom
• Negotiating of meaning in mathematics tasks (e.g. meaning of average)
• Using open ended tasks in teaching mathematics
• Marking answers to open ended mathematical tasks
• Involving students in assessing
• Sources of open-ended tasks
  • If the area of an apartment is 60 square metres, what might the five-room apartment look like?
  • Picture a bar graph where all you have are the bars and the axes but no labels of any sort. What might this be a bar graph of? Label the bar graph and explain what information is contained in the graph.
  • The average age of a family of five people is 25 and one of them is the same age as you. Who might the people be? What are their ages? And how are they related to one another?
  • The average of five numbers is 17.2. What might the five numbers be?
  • A number is rounded off to 5.3. What might the number be?
• The difference between good questions and good questioning
• Asking the question, “what is your utility function?” (i.e. that which is maximised by a system)
• Recognising the learning potential of student voice and cultural differences in how student voice is promoted and elicited
• Finding tasks that link to the curriculum
• The Lexicon project

Among the collaborators named by David and Esther were Peter Sullivan, and Neil Mercer. He also mentioned this paper on "initiating and Eliciting in Teaching: A reformulation of Telling" by Joanne Lobato, David Clarke and Amy Burns Ellis.