Module FOUN0407: MATHEMATICS FOR TEACHERS

Department: Foundation Year

FOUN0407: MATHEMATICS FOR TEACHERS

Pre-requisites

Corequisites

Excluded Combinations

Aims

• To introduce and develop a bank of mathematical skills, which students can apply in a range of contexts.
• To provide a foundation for future study in Education.
• To develop students' learning skills.
• To develop a problem solving approach.
• To encourage students to develop confidence in their own abilities in maths.

Content

• Number: Arithmetic (+,-,x,/) directed whole numbers, fractions and decimals. Introduction to alternative number systems
• Efficient accurate use of a calculator.
• Ratio, proportion (direct and inverse and using graphs).
• Percentages.
• Estimation, approximation and accuracy.
• Index notation (integer indices).
• Surds and rational indices.
• Standard Index notation (a x 10m).
• Introduction to logarithms.
• Calculations using scientific formulae.
• Algebra: Symbols.
• Algebraic formulae, evaluation of terms.
• Formulation and solution of algebraic equations in one unknown.
• Use of brackets, collecting terms etc, algebraic expansion, elementary factorisations.
• Simultaneous linear equations in two unknowns.
• Graphs: Cartesian coordinates, linear graphs, the equation y=mx + c.
• Graphs from formulae, graph plotting, Rate of Change. Use of computer packages for graph generation and investigation
• Solving equations graphically.
• Exponential growth and decay.
• Mensuration: Measurement, length, area (triangles, quadrilaterals, circles), Volume.
• Angles, triangles, Pythagoras' theorem, Sine, Cosine and tangent for acute angles, Radians/degrees.
• Quadrilaterals, Symmetry, order of rotational symmetry.
• Matrices. Introduction to discrete analysis

Learning Outcomes

• Knowledge of directed whole numbers, fractions, decimals and percentage and their use (SSK1)
• Understanding of estimation and approximation and conventions associated with this (SSK2)
• Understanding of a range of tests for direct and inverse proportion including graphical methods (SSK3)
• Knowledge of a range of algebraic techniques as listed in the syllabus (SSK4)
• Knowledge of simple indices, logarithms and Standard index form. (SSK5)
• Knowledge of simple matrix addition, subtraction and multiplication (SSK6)
• Knowledge of alternative number systems (SSK7)
• Knowledge of a critical path technique (SSK8)

• By the end of the module the students will have acquired the skills to be able to:
• use a calculator appropriately in relation to problems faced.
• confidently manipulate items listed on the attached syllabus in a range of contexts.
• carry out investigations on a range of topics

• By the end of the module the students will:
• be able to communicate effectively in writing (KS1)
• be able to demonstrate problem solving skills (KS2)
• be able to use a computer package to improve learning (KS3)
• be able to apply number both in the tackling of numerical problems and in the collecting, recording, interpreting and presenting of data (KS4)
• Test covers SSK 1-8, SSS1, SSS2, KS1, KS2, KS4
• Portfolio SSK 6, SSK7, SSK8, SSS1, SSS2, SSS3, KS1-4

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures.
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Ability to use and apply concepts and techniques will be tested in the end of the module test.
• Work on alternative number systems, matrices, discrete maths and computer generation of graphs will be developed and assessed through short investigative tasks.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment

Students will be given self-testing units on a weekly basis.