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Mathematics Matters Lesson Accounts
A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.
 

Mathematics Matters Lesson Accounts - Values & Principles

Each lesson account has associated values and principles, below are explanations of all the values and principles.

Values

Fluency in recalling facts and performing skills
For example:
Memorising names and notations
Practising algorithms and procedures for fluency and 'mastery'
Conceptual understanding and interpretations for representations
For example:
Discriminating between examples and non-examples of concepts
Generating representations of concepts
Constructing networks of relationships between mathematical concepts
Interpreting and translating between representations of concepts
Strategies for investigation and problem solving
For example:
Formulating situations and problems for investigation
Constructing, sharing, refining, and comparing strategies for exploration and solution
Monitoring one’s own progress during problem solving and investigation
Interpreting, evaluating solutions and communicating results
Awareness of the nature and values of educational system
For example:
Recognising different purposes of learning mathematics
Developing appropriate strategies for learning/reviewing mathematics
Appreciating aspects of performance valued by the examination system
Appreciation of the power of mathematics in society
For example:
Appreciating mathematics as a longstanding part of worldwide human creativity
Creating and critiquing ‘mathematical models’ of situations
Appreciating uses/abuses of mathematics in social contexts
Using mathematics to gain power over problems in one’s own life
 

Principles

Teaching is more effective when its ....

Builds on the knowledge learners already have
This means developing formative assessment techniques and adapting our teaching to accommodate individual learning needs.

Exposes and discusses common misconceptions and other surprising phenomena
Learning activities should expose current thinking, create ‘tensions’ by confronting learners with inconsistencies and surprises, and allow opportunities for resolution through discussion.
Uses higher-order questions
Questioning is more effective when it promotes explanation, application and synthesis rather than mere recall.
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Collaborative group work is more effective after learners have been given an opportunity for individual reflection. Activities are more effective when they encourage critical, constructive discussion, rather than argumentation or uncritical acceptance. Shared goals and group accountability are important.
Encourages reasoning rather than ‘answer getting’
Often, learners are more concerned with what they have ‘done’ than with what they have learned. It is better to aim for depth than for superficial ‘coverage’.
Uses rich, collaborative tasks
The tasks we use should be accessible, extendable, encourage decision-making, promote discussion, encourage creativity, encourage ‘what if’ and ‘what if not?’ questions.
Creates connections between topics both within and beyond mathematics and with the real world
Learners often find it difficult to generalise and transfer their learning to other topics and contexts. Related concepts remain unconnected. Effective teachers build bridges between ideas.
Uses resources, including technology, in creative and appropriate ways
ICT offers new ways to engage with mathematics. At its best it is dynamic and visual: relationships become more tangible. ICT can provide feedback on actions and enhance interactivity and learner autonomy. Through its connectivity, ICT offers the means to access and share resources and - even more powerfully - the means by which learners can share their ideas within and across classrooms.
 
 

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Lesson Accounts
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Lesson Accounts Introduction

Mathematics Matters - What constitutes the effective learning of mathematics? find out more

 

Discover the 'Mathematics Matter' Project Forum