## ED1SS1-Subject Specialism 1: Mathematical reasoning

Module Provider: Institute of Education
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Autumn term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Module version for: 2016/7

Module Convenor: Mr Marc Jacobs

Summary module description:
This module sets the expectation that students develop as independent, autonomous mathematicians, able to persevere and apply problem solving strategies. It aims to ensure that students are confident to extend the mathematical reasoning of all children within and beyond primary school expectations. Using geometry and number theory as vehicles, students are introduced to the nature and various types of mathematical proof. It also develops students’ understanding of the history of mathematical development, across time and cultures.

Aims:
•To gain insight into key principles of mathematical reasoning
•To enhance students’ enjoyment of and confidence in using mathematics and increase their ability to solve problems
•To develop algebraic skills and understanding
•To develop students’ understanding of Euclidean geometry and its place in the primary and secondary curriculum
•To develop an understanding of number theory and its modern day applications
•To recognise the role of different cultures and contexts in the development of mathematics over time

Assessable learning outcomes:
On successful completion of the module, students will be able to:
•Apply Euclidean geometry to solve a wide variety of problems in two and three dimensions
•Apply techniques of proof in a variety of geometric and number theory contexts
•Outline key people, cultures and stages in the development of mathematics

Students will increase their ability to develop their own mathematical ideas through investigation and individual and corporate study. They will reflect critically on their own development as a mathematician, identifying targets for personal development. Throughout the module, students will be encouraged to link higher level mathematics with its origins in the primary school, and reflect upon pedagogical strategies.

Outline content:
•Euclidean Geometry in both two and three dimensions
•Elementary number theory including prime numbers, composite numbers, factorization, introduction to encryption codes
•Types of proof, including direct proof, proof by exhaustion, disproof through counter example, proof by induction, proof by contradiction, proof by the contra-positive
•Origins of mathematics/mathematical development: eg the history of zero, development of algebra, cross-cultural and chronological development

Brief description of teaching and learning methods:
This module will be delivered in interactive sessions, which include lecturing, discussion and practical activities. Sessions will require some pre-reading, and students should be prepared to contribute their views and work collaboratively in order to make presentations. Working on problem sheets both independently and collaboratively will be an integral element of the module, alongside more extended investigation and enquiry.

Contact hours:
 Autumn Spring Summer Lectures 56 Tutorials 5 5 Guided independent study 134 Total hours by term 195.00 5.00 Total hours for module 200.00

Summative Assessment Methods:
 Method Percentage Written assignment including essay 40 Set exercise 60

Other information on summative assessment:
• Selected problem sheets and investigations (2,500 words equivalent).

Formative assessment methods:
Throughout the module students will complete problem sheets to provide students with regular formative feedback on their work.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Length of examination:
N/A

Requirements for a pass:
An overall mark of 40%.

Reassessment arrangements:
Resubmission of a comparable assignment during the summer resit period.