Module:

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

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Module Title
Module Code	(ITS)
Faculty		School
Module Co-ordinator	Semester 1: Brien Nolan Semester 2: Brien Nolan Autumn: Brien Nolan
Module Teachers	Brien Nolan
NFQ level	6	Credit Rating
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None
Array

Description

This module introduces students to some different general aspects of mathematics, including its history, the nature and use of mathematical language, problem solving in mathematics and in mathematics teaching and the concept of mathematical mindsets.

Learning Outcomes

1. Gain a deeper insight into the nature of mathematical problem solving
2. Develop proficiencies in problem solving and in the teaching of problem solving
3. Learn how to use mathematical language correctly and develop an appreciation of the importance and nature of proof in mathematics
4. Learn a variety of proof techniques
5. Develop an awareness of the concepts of growth and fixed mindsets and how these impact the learning of mathematics
6. Discuss key historical milestones in the development of mathematics
7. Learn about different ways that maths is present in our culture

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	10	Lectures on course material.
Seminars	8	Workshops
Independent Study	122	Independent work on course material and exercises.
Online activity	30	Asynchronous activities
Total Workload: 170

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Introduction
What is mathematics and where does it come from? How much maths can there be? A brief chronologyof mathematics. Applications of mathematics. The classification of mathematics.

Mathematical problem solving.
Structured approaches to problem solving in mathematics: Mason's Rubric Writing. Approaches to teaching problem-solving in mathematics.

Mathematical language and mathematical proof.
The role of definitions in mathematics; mathematical statements; the need for mathematical proof; different types of proof: induction, working forwards-backwards, proof by contradiction, proof by contrapositive argument; nomenclature: conjectures, lemmas, propositions, theorems, corollaries etc; the philosophy of mathematical proof; the creation of new mathematics.

History of mathematics.
An overview of the history of mathematics and its role in the natural and human world, from pre-history to the 21st century.

Numeracy skills.
Students will use an online system to develop proficiency and confidence in numeracy, focussing on basic numerical and algebraic skills.

Assessment Breakdown
Continuous Assessment	%	Examination Weight	%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Workshop assignments.	20%	As required
Participation	Completion of assigned tutorial tasks.	10%	As required
Assignment	Problem solving assignment	20%	As required
Group project	Develop a presentation on a topic from the history of mathematics	20%	Week 10
Assignment	Complete online course on Mathematical Mindsets	10%	Week 3
Essay	Book report	20%	Week 6

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category

Indicative Reading List

Philip J. Davis and Reuben Hersh: 1981, The Mathematical Experience, Penguin,
W.S Anglin: 1994, Mathematics: A Concise History and Philosophy, Springer-Verlag,
DA Brannan: 1996, A First Course in Mathematical Analysis, CUP, 9780511573200
Reuben Hersh: 1997, What is Mathematics, Really?, OUP,
Anthony Croft and Robert Davison: 2010, Foundation Maths, 5th, Pearson Education,

Other Resources

40742, Website, 0, St Andrew's History of Mathematics Website, http://www-groups.dcs.st-andrews.ac.uk/~history/, 40743, Website, Pearson Education Online, 0, MyMathLab, http://global.mymathlabglobal.com/,