4.3 ACTIVE LEARNING METHODOLOGIES
All mathematics teachers have their own personal visions of what should happen in the ideal mathematics classroom and what can be achieved in the circumstances in which they teach. These visions differ, just as teachers themselves differ. An approach that suits one teacher, working with a particular class, may not suit another teacher, or indeed the same teacher with a different class. Both so-called "traditional" and "progressive" methods can be successful.
However, some teachers have found that methods that were successful in the past do not work so well with to-day's students. Some teachers would like to experiment with a broader range of teaching approaches, and would welcome guidance as to how they might do so. This section of the Guidelines addresses the issue, offers a rationale for using active learning methodologies and describes a range of such methodologies. The following sections provide concrete examples of the methodologies reflecting work done by teachers in Irish schools across a wide range of topic areas. Naturally, these approaches are meant to augment, not replace, existing ones. In particular, provision of opportunities for frequent practice (so that students' procedural skills become, and then remain, appropriately fluent) will still be an integral and essential feature in the teaching of mathematics. It is hoped that teachers will study the methodologies outlined below, apply those with which they feel comfortable, and adapt their own methods correspondingly, if necessary.
RATIONALE
As indicated in Section 3.3, the revised mathematics syllabus gives greater emphasis than did its predecessor to the following: increased depth ofunderstanding, effective communication, and appreciationand enjoyment of mathematics. Specifically, objectives C, E, G, H, and I emphasise
- relational learning
- the making of simple mathematical models and the justifying of conclusions
- the exercise of psychomotor skills
- communicating verbally
- appreciating mathematics and recognising it throughout the curriculum and beyond.
It is unlikely that these skills and learning outcomes will be achieved if mathematics teachers rely solely on a teaching methodology which is modelled on "exposition, examples and exercise." Research indicates that, where a broader range of methodologies is used,
- student confidence is enhanced and performance improved
- skills of estimation, approximation, analysis and evaluation can be practised
- a sense of ownership develops around students' own learning
- enhanced student understanding of mathematical topics occurs
- communication and dialogue improve
- more positive attitudes to mathematics develop
- a lexicon of mathematical terms can be built up gradually in a natural way for students.
RANGE OF ACTIVE LEARNING METHODOLOGIES
There is a wide range of active learning methodologies that mathematics teachers can employ to achieve increased conceptual understanding. Some of these are listed below.
- "Hands-on" activities with concrete materials
- Project work
- Mathematical games
- Problem solving
- Quiz activities
- Use of information and communication technologies, in particular multimedia
- Mathematical simulations
- Structured discussion
- Surveys, for example using questionnaires
- Visits to the Science laboratory
- Presentations
- Demonstrations
- Debates
- Visits from a mathematics expert
- Fieldwork
The lesson ideas that follow involve a number of these methodologies. In particular, many of them attempt to increase the use of practical work and concrete materials. Other lesson ideas involve student-centred investigative work, and yet others demand group work, student and teacher dialogue and project work where appropriate. The lesson ideas have been tried and tested by practising mathematics teachers in Irish schools. They are not intended to form an exhaustive list, and the range and sample can be extended in the future. Teachers are invited to contribute to this initiative by documenting lesson ideas which they have found useful and effective for a particular topic. Such ideas may relate to how a teacher might introduce a topic, how part of the topic might be taught, or how the work might be revised. For this purpose, a template is included in Appendix 4.