NMBR140 - Introduction to Mathematical Thinking

Year

Credit points

Campus offering

Prerequisites

Incompatible

NMBR143 Introduction to Mathematical Ideas

Unit rationale, description and aim

In an increasingly technological society, an understanding of mathematics is a major asset to an individual seeking to participate fully and meaningfully. An effective teacher must be able to do the work that they assign to their students and possess mathematical content knowledge which incorporates an understanding of the mathematics they teach.

Mathematical content in this unit draws from the areas of Number, Algebraic Thinking, Geometry, Measurement, Probability, Statistics and the Application of Mathematics; and ways of mathematical thinking including reasoning, problem solving and critical thinking, and a focus on conceptual understanding. There is a particular emphasis in both content and assessment on real-world applications of mathematics.

Learning outcomes

To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.

Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.

Explore the graduate capabilities.

On successful completion of this unit, students should be able to:

LO1   demonstrate understanding and application of some elementary mathematical concepts (GA5; APST 2.1; ACECQA B3)

LO2  solve a variety of mathematical tasks (GA4, GA5, GA10; APST 2.1; ACECQA B3)

LO3  identify the structure inherent in various mathematical situations and undertake simple mathematical modelling (GA4, GA5, GA8; APST 2.1; ACECQA B3)

LO4  demonstrate an understanding of the interconnectedness of different mathematical topics and their application to real world contexts using a range of resources (GA5, GA8; APST 2.1; ACECQA B3)

LO5  communicate mathematical thinking and reasoning using mathematical language including spoken, written and visual representations (GA9, GA10; APST 2.1; ACECQA A6, B3, B9, C4).

Graduate attributes

GA4 - think critically and reflectively 

GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession 

GA8 - locate, organise, analyse, synthesise and evaluate information 

GA9 - demonstrate effective communication in oral and written English language and visual media 

GA10 - utilise information and communication and other relevant technologies effectively.

AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS - GRADUATE LEVEL

On successful completion of this unit, pre-service teachers should be able to:

ACECQA CURRICULUM SPECIFICATIONS

On successful completion of this unit, pre-service teachers should have developed the following specific knowledge:

Content

Topics will include:

• Numbers and Counting
• Place value;
• Computational strategies including mental, estimation and use of calculators
• Natural numbers, integers, fractions, factors, prime numbers, prime factorisation, divisibility tests
• Proportional reasoning, ratio
• Rational numbers and their representations as fractions and decimals, percentages, simple operations with fractions.
• Algebraic Thinking
• Figural and numeral patterns leading to generalisation
• Functions, variables and relationships
• Simplifying algebraic expressions and solving algebraic equations
• Linear and non- linear graphs
• Using technology in graphing
• Foundations of Geometry
• Classification of shapes in 2D and 3D
• Angles and angle sums of polygons
• Position

· Foundations of Measurement

• Focusing on area, length, mass, volume and time
• Metric and other measurement systems
• Relationships between units
• Foundations of Probability
• Sampling
• Fairness
• Single and multi-stage events
• Tree diagrams and two-way tables
• Representation and interpretation of data
• Population and samples
• Distribution: comparing and contrasting using measures of centre, spread and variability within the spread of data
• Summarising, analysing, presenting, interpreting data or results from empirical investigations

Embedded within each topic is the application of mathematical reasoning and problem solving

Learning and teaching strategy and rationale

This unit is offered in different formats depending on the teaching period:

• Summer or Winter term intensives
• Semester 1 or 2 comprising weekly face-to-face classes during semester or mixed mode including weekend classes.

All learning is supported by web-based learning platform LEO. Pre-service teachers are be expected to participate in online discussion and sharing via eLearning. Class resources will be available via eLearning as will access to relevant web links.

Duration

This unit includes 4 contact hours per week for 12 weeks, comprising 2 hours of lectures and 2 of tutorials.

This unit will normally include the equivalent of 24 hours of lectures together with 24 hours attendance mode tutorials.

150 hours in total with a normal expectation of 48 hours of directed study and the total contact hours should not exceed 48 hours.

Assessment strategy and rationale

The assessment tasks for this unit have been designed to contribute to high quality student learning by both helping students learn (assessment for learning), and by measuring explicit evidence of their learning (assessment of learning). Assessments have been developed to meet the unit learning outcomes and develop graduate attributes consistent with University assessment requirements. The assessment tasks provide multiple opportunities (presentation, problem solving and examination) in different ways (visual, verbal and written) for students to demonstrate:

• Knowledge of content
• Application of mathematics in real world contexts
• Development of and communication using appropriate mathematical language

Minimum Achievement Standards

The assessment tasks for this unit are designed to demonstrate achievement of each learning outcome. In order to pass this unit, students are required to complete all assessment tasks as per the Assessment policy and gain an overall pass mark.

Overview of assessments

Representative texts and references

Required text(s)

Australian Curriculum https://www.australiancurriculum.edu.au/

Australian Curriculum, Assessment and Reporting Authority (ACARA) www.acara.edu.au

McLeod, G. et al (2019). Introduction to mathematical thinking (Custom ed. eBook). Melbourne: Pearson.

Australian Curriculum Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Relevant state and territory Mathematics curriculum documents

Recommended references

Allenby, R. (1997). Numbers and proofs. Oxford, UK: Butterworth-Heinemann

Belos, A. (2010). Alex’s adventures in numberland. London, UK: Bloomsbury.

Belos, A. (2015). The grapes of math: How life reflects numbers and numbers reflect life. New York, NY: Simon & Schuster.

Boaler, J. (2019). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. New York, NY: Jossey-Bass.

Booker, G. (2011). Building numeracy: Moving from diagnosis to intervention. South Melbourne, Vic: Oxford University Press.

Burton, D. (2011). Elementary number theory (7th ed.). Boston: McGraw-Hill Higher Education

Du Sautoy, M. (2011). The number mysteries: A mathematical odyssey through everyday life (1st Palgrave Macmillan ed.). New York, NY: Palgrave Macmillan.

Eccles, P. (1997). An introduction to mathematical reasoning: Numbers, sets and functions. New York, NY: Cambridge University Press

Goldstein, L., & Schneider, A. (2013). Brief calculus and Its applications. Pearson.

Jacobs, H. R. (2002). Mathematics: A human endeavour: A book for those who think they don’t like the subject (3rd ed.). New York, NY: W. H. Freeman.

Liebeck, M. (2011). A concise introduction to pure mathematics (3rd ed.). Boca Raton, FL: Chapman & Hall/CRC Press.

Shryock-Boyke, K (2011). Introduction to plane geometry: Explorations and explanations. Pearson