Whole class interactive teaching in mathematics

last updated:September 2005

We chose this case study because it illustrates how whole class teaching can be used effectively to improve the quality of students’ learning in mathematics.

The study brought together teachers of mathematics at Key Stage 3 (11-14 years) from six secondary schools in the north of England.  They shared an interest in trying out methods of teaching mathematics which had led to high student attainment in Hungary.  They met once every half term to work with members of the mathematics department at Manchester Metropolitan University (MMU).  The group exchanged ideas with visiting Hungarian educators and some visited Hungary to observe lessons there. The Hungarian classrooms showed high levels of whole class teaching, classroom discussion and a willingness amongst students to discuss their mistakes or difficulties openly.

The British teachers visited colleagues’ lessons, watched recorded lessons on video and discussed lesson descriptions to agree on a shared vocabulary they could use to describe features of lessons.  They tried out new ideas in class and used video to record what happened.  They discussed and analysed the videos as a group to refine their theories as to what happened and why. Having identified the effective structures, strategies and activities of whole class interactive teaching in mathematics, they put them into practice in further lessons.  This, in turn, provided data for further refinement at future workshops.

Key findings from this case study

The study found that effective whole class interactive teaching involved:

• asking students to make their beliefs and difficulties public
• focusing in depth on a small number of significant problems
• focusing on key mathematical ideas and misconceptions
• promoting high levels of articulation in students of all abilities
• making changes to teaching strategies.

Making beliefs and difficulties explicit
Hungarian students regularly came to the front and demonstrated their mathematics to the rest of the class on the board. The teacher researchers did the same but were concerned about students’ sensitivities to this exposure. They made a distinction between the students and their mathematics and emphasised that the mathematics was the focus for discussion.  This encouraged co-operation and mutual support, so students felt able to expose and explain their ideas and difficulties.
Focusing in depth on a few significant problems and on key mathematical ideas and misconceptions

The group found that explanation followed by exercises made students look busy but did not help them think about their mathematics.  Learning was more effective when:

• students saw the tasks provided as interesting and worth resolving
• the task was clear and the problem easy to access, even the mathematics
• concept or content was challenging and hidden in the task
• students discussed a small number of problems in depth
• teachers focused on issues and concepts rather than just techniques
• students were allowed to fall into traps and then explored their partial understandings, beliefs, feelings, instincts and misconceptions.

Whole class interactive teaching helped students of all abilities
The researchers found that all students, including those in lower ability groups, were willing and able to discuss their mathematics openly.  A supportive environment helped everyone to discuss their own mathematical ideas and to produce explanations and justifications of their work.

Changes in teaching strategies
The researchers found the following teaching strategies helpful:

• valuing student contributions without judging them
• recognising when to facilitate discussion and when to intervene
• developing high level questioning and prompting skills
• insisting on the use of correct mathematical language.

Teachers needed to develop:

• an awareness of students’ beliefs and misconceptions
• an awareness of key mathematical ideas over and above the learning of algorithms
• an awareness of tendencies in themselves, for example, to jump in to correct students, take over explanations or explain away difficulties
• strategies for designing problems which prompted students’ awareness of key mathematical ideas.  Such problems needed to tap into students’ beliefs and be rich enough to provide a significant link to the mathematics.

      

The nature of lesson preparation changed so that teachers could be more responsive and increase their repertoire of activities and questions to help students gain insights into the topic being studied.

What were the benefits to teachers and students?

• The teachers who took part felt they gained a lot from the experience and believed, on the basis of video evidence, that their practice had improved.
• They were more alert to opportunities that emerged from student responses.
• They used class discussions much more to deepen understanding than to explain procedures.
• The participants found video helpful for individuals to see themselves clearly and for the group to work on one another’s ideas.

The teachers judged the effectiveness of their lessons on the students’ achievement.  They found that the students:

• became more effective learners and communicators than before
• became more articulate in explaining and justifying their mathematical thinking and decision-making
• could cope with harder mathematical problems than would be expected for their age.

Reference

Harrington, A. (1999) Whole class interactive teaching in mathematics Teacher Research Grant summary, 3rd year 1998-99.