Module FOUD0751: Maths and Statistics for Teachers

Department: Foundation Year (Durham)

FOUD0751: Maths and Statistics for Teachers

Prerequisites

• None

Corequisites

• None

Excluded Combination of Modules

• Foundations of Statistics

Aims

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

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) and surds.
• 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,
• Quadrilaterals, Symmetry, order of rotational symmetry.
• Sampling - Distinctions between sample and population, sample selection.
• Tabulation - Discrete/continuous data, Tally charts, frequency and grouped frequency tables, Class intervals and Implications of grouping.
• Representation - Bar Charts, Pie Charts, Histograms, Recognising visual misrepresentation.
• Measures of location - Mean,mode and median for raw data and frequency distribution, Median for raw data.
• Measures of Spread - Range, Quartiles, Inter-quartile range, Variance, standard deviation for raw data, frequency distribution, cumulative frequency.
• Correlation - Scatter diagrams +ve, -ve, or lack of correlation, line of best fit (by eye) through (x,y), interpolation and extrapolation.
• Tests - Chi squared, Normal distribution, Contingency tables.
• Probability - Venn diagrams. Range 0-1, impossible to certainty, Probabilities of equally likely events, Probability as a limit to relative frequency. Simple Addition and Multiplication of probabilities as appropriate, Tree diagrams. Venn diagrams
• Introduction to computer use for statistics.

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 different forms of sampling, tabulation and visual representation (SSK6)
• Understanding of the distinctions and implications of using different forms of sampling, tabulation and visual representation (SSK7)
• Knowledge of calculations required for measures of central location, spread, correlation and significance testing (SSK8)
• Understanding of implications and appropriateness of use of different statistical measures (SSK9)
• Knowledge of probability, including calculations of equally likely events and simple addition and multiplication as appropriate (SSK10)
• Knowledge of some probability diagrams including Tree diagrams, Venn diagrams and probability space tables. (SSK11)
• Knowledge of alternative number systems (SSK12)

• use a calculator appropriately in relation to problems faced. (SSS1)
• confidently manipulate items listed on the attached syllabus in a range of contexts.(SSS2)
• construct accurate graphs from data or calculation and analyse by interpolation or extrapolation and rate of change calculations. (SSS3)
• carry out a range of statistical procedures as listed on the attached syllabus. (SSS4)
• conduct a survey and analyse results statistically. (SSS5)

• be able to communicate effectively in writing. (KS1)
• be able to demonstrate problem solving skills. (KS2)
• have improved their own learning and performance. (KS3)
• be able to apply number both in the tackling of numerical problems and in the collecting, recording, interpreting and presenting of data (KS4)
• be able to use a computer package to improve learning (KS5)

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 and seminars.
• Much of the learning, understanding and consolidation will take place through the use of structured exercise during seminar sessions and students' own time.
• Design, implementation and statistical analysis of surveys will be consolidated and assessed through the independent production of the projects.
• Short in-class formative tests covering aspects of the previous week’s work will be set usually on a weekly basis. These tutor marked tests allow rapid feedback and build confidence. These tests enable students to reflect on their own performance, identify areas of weakness, and practice some of the skills and techniques which will be required in the longer invigilated tests.
• Small coursework tasks developing or consolidating the previous week’s work will be set on a weekly or fortnightly basis. Like the tests, these tutor marked tasks allow rapid feedback and build confidence. Additionally, they ensure that students master specific skills to an appropriate level prior to their requirement in more complex tasks or other modules. As an example, the first task usually involves the plotting of three graphs. Tutor feedback from this task ensures that students are ready to draw further graphs in Biology or Chemistry.
• Students undertake a project in which they explore research questions by applying appropriate statistical concepts and techniques that they have been taught, to numerical data they have obtained. They then interpret their statistical findings to reach meaningful conclusions. The project, thus, both consolidates and assesses a range of statistical procedures.
• Manipulative skills and ability to recall, select and apply mathematics and statistics will be assessed by the two invigilated tests in addition to the portfolio of tasks and in-class tests.
• The Portfolio covers SSK 1-12, SSS1-4, KS 2-5
• The Invigilated Tests cover SSK 1-12, SSS1-4, KS2-4
• The Project covers SSK6-9, SSS1, SSS4, SSS5, KS 1-4

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will be given self-testing units on a weekly basis in the form of worksheets with answers and/or DUO quizzes. In-class tests and Portfolio tasks with a rapid marking turnaround fulfill a formative as well as summative role (See Section 14). Students have access to two or more mock papers and answers to help prepare for the invigilated tests. The project is submitted in two parts so that early feedback on the Introduction and method can be used to inform the second part of the project.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University