Name: Yoann Henri Le TeuffName: Yoann Henri Le TeuffSubject: MathematicsSubject: MathematicsCore tutor: Jeanette PerryCore tutor: Jeanette Perry

University of Warwick Secondary PGCE University of Warwick Secondary PGCE 2004-20052004-2005

CA1: professional portfolioCA1: professional portfolio

Task Number: 7Task Number: 7Title: Key SkillsTitle: Key Skills

Key Skills & MathematicsKey Skills & Mathematics

Key SkillsKey Skills CommunicationCommunication Application of numberApplication of number Information Technology (ICT)Information Technology (ICT) Working with othersWorking with others Improving own learning & performanceImproving own learning & performance Problem solvingProblem solving

Mathematics is ideal to develop these Mathematics is ideal to develop these skills.skills.

CommunicationCommunication

In Mathematics, there is the need to:In Mathematics, there is the need to:

Explain and share concepts & methods.Explain and share concepts & methods.

Devise a logical reasoning: the thinker Devise a logical reasoning: the thinker must be subtle, clear & articulate.must be subtle, clear & articulate.

Understand and use numerous Understand and use numerous conventions, ancient and foreign conventions, ancient and foreign alphabets, abstract symbols, etc.alphabets, abstract symbols, etc.

Application of numberApplication of number Mathematics is the subject of number Mathematics is the subject of number

manipulation and application “par manipulation and application “par excellence” (especially via Statistics).excellence” (especially via Statistics).

Pupils must develop the following Pupils must develop the following judgements on use of numbers:judgements on use of numbers:– How many decimal places are meaningful?How many decimal places are meaningful?– Which convention is best to write numbers Which convention is best to write numbers

(1.12(1.12××101022, , 2, 3.274658738, 2, 3.274658738, ¾¾, ∞, etc)?, ∞, etc)?– When to use and not to use numbers (algebra, When to use and not to use numbers (algebra,

with substitution of letters by numbers)with substitution of letters by numbers)– Meaning of a number (size, ratio, probability, Meaning of a number (size, ratio, probability,

etc.)etc.)

Information Technology (ICT)Information Technology (ICT)

ICT is very effective for demonstrations in ICT is very effective for demonstrations in Mathematics: it provides a feel for what Mathematics: it provides a feel for what abstract concepts represent:abstract concepts represent:

GeometryGeometry: constructions and properties : constructions and properties (dynamic-geometry software)(dynamic-geometry software)

GraphingGraphing (plotting software) (plotting software)

Data handlingData handling (spreadsheets with (spreadsheets with statistical functions): for statistics and statistical functions): for statistics and probabilitiesprobabilities

Working with othersWorking with others

Mathematics is not a solitary activity! Mathematics is not a solitary activity! Group Group work is essential in many mathematical activities:work is essential in many mathematical activities:

CourseworkCoursework: individual work benefits from group : individual work benefits from group discussions on certain problems.discussions on certain problems.

Investigation activitiesInvestigation activities: teamwork requires : teamwork requires exchange of ideas and hypotheses within the exchange of ideas and hypotheses within the team.team.

Elaboration of proofsElaboration of proofs: does the current logical : does the current logical reasoning hold to others’ scrutiny?reasoning hold to others’ scrutiny?

Improving own learning & Improving own learning & performanceperformance

Investigative tasks enhance one’s ability Investigative tasks enhance one’s ability at problem solving.at problem solving.

Assessment of one’s weaknesses: straight Assessment of one’s weaknesses: straight forward; one needs to practice more what forward; one needs to practice more what one did wrong.one did wrong.

Performance can be improved by sharing Performance can be improved by sharing efficient methods and tricks with others.efficient methods and tricks with others.

Learning is always progressive as one can Learning is always progressive as one can build on what one has already learnt.build on what one has already learnt.

Problem solvingProblem solving

Forms bulk of mathematical activities.Forms bulk of mathematical activities. Investigative workInvestigative work CourseworkCoursework Solving equationsSolving equations Deriving/using propertiesDeriving/using properties Devising better solving methodsDevising better solving methods Getting an answer!Getting an answer!

ConclusionsConclusions

Mathematics enables the expression Mathematics enables the expression and acquisition of all key skills and acquisition of all key skills without contrivance.without contrivance.

The context where these key skills The context where these key skills are involved can be found in are involved can be found in professional life (e.g., Statistics and professional life (e.g., Statistics and numerical-problem solving): little numerical-problem solving): little adaptation to ‘real life’ is required.adaptation to ‘real life’ is required.