Module: Mathematical Thinking

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Mathematical Thinking
Module Code	MS147 (ITS) / MTH1031 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Sinead Breen
Module Teachers	Brien Nolan, Emma Owens
NFQ level	6	Credit Rating	5
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 the nature and use of logic in mathematics, mathematical language, mathematical modelling and problem solving in mathematics.

Learning Outcomes

1. Apply logic in mathematical arguments
2. Demonstrate an appreciation of the importance and nature of proof in mathematics
3. Demonstrate insights on different views of the nature of mathematics
4. Develop proficiencies in problem solving and in the teaching of problem solving
5. Learn how to use mathematical language correctly
6. Develop an awareness of the concepts of growth and fixed mindsets and how these impact the learning of mathematics

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	10	Lectures on course material.
Tutorial	10	Workshops
Independent Study	95	Independent work on course material and exercises.
Online activity	10	Asynchronous activities
Total Workload: 125

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

Mathematics: history & philosophy
Introduction to philosophies of mathematics and their historical development, with a focus on the emergence of axiomatic approaches and mathematics as a problem solving activity

Mathematical logic, language and mathematical proof.
The role of definitions in mathematics; mathematical statements; the need for mathematical proof; mathematical logic; 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.

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

Mathematical Mindsets
Fixed and growth mindsets in mathematics.

Assessment Breakdown
Continuous Assessment	100%	Examination Weight	0%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Workshop assignments.	30%	As required
Participation	Completion of assigned tutorial tasks.	20%	As required
Assignment	Problem solving assignments	40%	As required
Assignment	Complete online course on Mathematical Mindsets	10%	Week 3

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 1

Indicative Reading List

J. Mason,L. Burton,K. Stacey: 2011, Thinking Mathematically, Pearson Higher Ed, 027372892X
Philip J. Davis and Reuben Hersh: 1981, The Mathematical Experience, Penguin,

Other Resources

43866, Website, 0, St Andrew's History of Mathematics Website, http://www-groups.dcs.st-andrews.ac.uk/~history/, 43867, Website, Pearson Education Online, 0, MyMathLab, http://global.mymathlabglobal.com/,