Upon the Shoulders of Giants

Unit Outline (Higher Education)

Level of Unit in Course

AQF Level(s) of Course

Level of Unit in Course

Introductory

Intermediate

Effective Term:

2024/05

Institute / School :

Institute of Innovation, Science & Sustainability

Unit Title:

Upon the Shoulders of Giants

Unit ID:

MATHS1000

Credit Points:

15.00

Prerequisite(s):

(VCE Mathematics or equivalent)

Co-requisite(s):

Nil

Exclusion(s):

(ENCOR1015 and MATHS2000 and SCCOR1300)

ASCED:

010101

Other Change:

Brief description of the Unit

This unit allows students to see the relevance of mathematics in scientific and technical practice, with a historical overview of the development of mathematical thought. Various concepts and techniques in elementary mathematics that will equip students for further mathematical and technical unitss will be introduced/reviewed. The unit would be particularly valuable to prospective teachers of mathematics at primary and secondary level and to students interested in improving their understanding of basic mathematical principles and techniques.

Grade Scheme:

Graded (HD, D, C, P, MF, F, XF)

Work Experience Indicator:

No work experience

Placement Component:

Supplementary Assessment:Yes

Where supplementary assessment is available a student must have failed overall in the Unit but gained a final mark of 45 per cent or above, has completed all major assessment tasks (including all sub-components where a task has multiple parts) as specified in the Unit Description and is not eligible for any other form of supplementary assessment

Course Level:

Learning Outcomes:

Knowledge:

K1.	Describe the development of the concept of number.

K2.	Explain the structure of numbers.

K3.	Outline the historical development of sets and functions as ways of describing mathematical entities.

K4.	Discuss some of the historical underpinnings of Euclidean geometry and its applications.

K5.	Describe the significance and evolution of the idea of `chance`.

Skills:

S1.	Perform calculations, using appropriate technology, to investigate number properties.

S2.	Perform algebraic manipulations, including factorisation and solution of quadratics.

S3.	Describe relations and functions and related ideas.

S4.	Find the sum of arithmetic and geometric series.

Application of knowledge and skills:

A1.	Use ideas about sets and their properties in problem solving.

A2.	Discuss the significance of mathematicians` work in the context of their lives and times.

A3.	Present mathematical knowledge to other student.

Unit Content:

Topics in this unit may include an introduction to the concepts of number, function, probability and geometry through a guided exploration of the development of these ideas from an historical perspective. Throughout the unit, the ideas will be developed using practical applications. Topics to be covered in this unit will be taken from the following: early number systems and symbols, geometry and arithmetic from the early civilizations, the development of number theory and foundations of algebra, solving equations, geometry and trigonometry, geography and navigation, astronomy and trigonometry, combinatorics, logarithms, kinematics, sequences and series, probability and statistics, the foundations of calculus, the beginning of structure - groups, rings and fields, set theory, analysis and topology.
•The changing concept of number in the development of society.
•The contribution made by different cultures to the development of mathematics.
•Concepts in algebra, trigonometry and geometry.
•The development and application of calculus.
•Mathematical models for the real world using functions, relations and sets.
•Ideas in geometry that influence the world in which we live.
•Concepts of probability with a discussion of historical and contemporary applications.
•The historical context underpinning the development of mathematical topics found in typical school curricula.

Graduate Attributes:

	Learning Outcomes Assessed	Assessment Tasks	Assessment Type	Weighting
1.	K1-5, S1-4, A1	Participate in class activities.	Portfolio of completed work	10 - 30%
2.	K1-5, S1-4, A1-3	Self directed or group exploration.	Projects	10 - 30%
3.	K1-5, S1-4, A1, A2	Review and skills practice.	Tests / Examinations	40 - 60%

Adopted Reference Style:

APA

Professional Standards / Competencies:

Standard / Competency

Threshold Learning Outcomes - Mathematics: Initial

Attribute			Assessed	Level
1 Understanding
	1.1 Demonstrate a coherent understanding of the mathematical sciences.
		1.1.2 Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to development of the mathematical sciences.	Yes	Introductory
2 Knowledge
	2.1 Exhibit depth and breadth of knowledge in the mathematical sciences.
		2.1.1 Knowledge of the principles and concepts of a broad range of fundamental areas in the mathematical sciences.	Yes	Introductory
4 Communication
	4.1 Communicate mathematical and statistical information, arguments, or results for a range of purposes using a variety of means.
		4.1.2 Appropriate presentation of information, reasoning and conclusions in a variety of modes, to diverse audiences (expert and non-expert).	Yes	Introductory
5 Responsibility
	5.1 Demonstrate personal, professional and social responsibility.
		5.1.1 Ability to self direct learning to extend their existing knowledge and that of others.	Yes	Introductory
		5.1.2 Ability to work effectively and responsibly in an individual or team context.	Yes	Introductory
		5.1.3 Ethical application of mathematical and statistical approaches to solving problems.	No	Introductory