MATH APPRECIATION

AND SKILLS TRAINING

ALEX ESCANILLA ALFONSO

OBJECTIVES• Establish an agreed set of valued learning outcomes and an agreed set of

principles, grounded in evidence, that underpins the learning of mathematics• Produce a collection of lesson accounts from a range of different settings in

order to illustrate what the values and principles might look like in the classroom

• Ascertain the relative values put onto the different learning outcomes in an ideal case and to compare these with perceptions of relative values in practice

• Identify any barriers to the values and principles being translated into practice, and to propose strategies for overcoming them.

• Promote spirit of curiosity and a love for Mathematics

The Mathematics Learning Area includes interrelated knowledge and skills:

■ Knowledge:

• numbers, operations and relationships;

• patterns, functions and algebra;

• space and shape (geometry);

• measurement; and

• data handling.

■ Skills:

• representation and interpretation;

• estimation and calculation;

• reasoning and communication;

• problem posing;

• problem solving and investigation; and

• describing and analysing.

Mathematics is a human activity that involves observing, representing and investigating patterns and quantitative relationships in physical and social phenomena and between mathematical objects themselves. Thus, new mathematical ideas and insights are developed.

OUTCOME-FOCUSED LEARNING

• fluency in recalling facts and performing skills• conceptual understanding and interpretations for representations• strategies for investigation and problem solving• awareness of the nature and values of the educational system• appreciation of the power of mathematics in society.

Learning outcomes sought Types of learning activity impliedFluency in recalling facts and performing skills • Memorising names and notations

• Practising algorithms and procedures for fluency and ‘mastery’

Conceptual understanding and interpretations for representations

• Discriminating between examples and non-examples of concepts• Generating representations of concepts• Constructing networks of relationships between mathematical concepts• Interpreting and translating betweenrepresentations of concepts

Learning outcomes sought Types of learning activity implied

Strategies for investigation and problem solving • Formulating situations and problems forinvestigation• Constructing, sharing, refining, and comparingstrategies for exploration and solution• Monitoring one’s own progress during problemsolving and investigation• Interpreting, evaluating solutions andcommunicating results

Awareness of the nature and values of the educational system

• Recognising different purposes of learningmathematics• Developing appropriate strategies for learning/reviewing mathematics• Appreciating aspects of performance valuedby the examination system

Learning outcomes sought Types of learning activity implied

Appreciation of the power ofmathematics in society

• Appreciating mathematics as human creativity(plus historical aspects)• Creating and critiquing ‘mathematical models’of situations• Appreciating uses/abuses of mathematics insocial contexts• Using mathematics to gain power over problemsin one’s own life

VALUES• SOCIAL

Mathematics enables learners to participate in life both at work and at home. (J.Back)• PERSONAL

…learners seeing themselves as mathematicians. (S.Feller)• INTRINSIC

…confidence in strategies to approach and solve problems. (J.Golding, B.Murphy)

“Too much time is spent developing “fluency in recalling facts and performing skills” to the detriment of other aspects”1. Society’s attitude towards Mathematics2. Teachers’ subject and pedagogical subject knowledge3. A taught curriculum defined by assessment4. The style and quality of textbooks and other resources

OBSTACLES TO PROGRESS

SUGGESTED WAYS FORWARD

• Improve the provision and quality of professional development opportunities

• Develop and share experience and resources for learning• Use professional standards to inform others about the teaching

and learning of Mathematics• Influence the extent and quality of key stage assessments and

public examinations

REFERENCES1. Ahmed, A. (1987). Better Mathematics: A Curriculum Development Study. London: HMSO.

2. Cockcroft, W. H. (1982). Mathematics Counts. London: HMSO.

3. DfES. (2005). Improving Learning in Mathematics.

London: Standards Unit, Teaching and Learning Division.

4. QCA. (2007). Mathematics: Programmes of Study for Key Stage 3 & 4 and attainment targets.

5. Smith, A. (2004). Making Mathematics Count: The Stationery Office Ltd.

SKILLS ENHANCEMENT

REPRESENTATION AND INTERPRETATION• Translating words into algebraic expressions• Tabular Matrix• Problem Solving

ESTIMATION AND CALCULATION• Rounding off numbers• Basic operations and Mental Math• Solving Linear Equation using different Methods

REASONING AND COMMUNICATIONIs it TRUE?A + B = C4A – 3A + 4B – 3B = 4C – 3C4A + 4B – 4C = 3A + 3B – 3C4 (A + B – C) = 3 (A + B – C)Hence,4 = 3 ?

DESCRIBING AND ANALYSING

• Statistical Problem solving“There are 3 types of lies – lies, damn lies, and statistics”“Figures don’t lie, but liars figure”

PROBLEM SOLVING AND INVESTIGATION

• Proving Theorems and Other Related Facts• Pascal’s Triangle vs. Fibonacci Series• Travel time