EDMA111 - Introductory Mathematics

Year

Credit points

Campus offering

Prerequisites

Unit rationale, description and aim

Students wishing to pursue a teaching career need to meet required admission prerequisites to initial teacher education programs.

In this unit, students will develop conceptual understanding, procedural fluency and mathematical reasoning skills in the areas of simple functions, elementary algebra, proportional reasoning, measurement, statistics and probability. Topics are introduced using an inquiry approach with an emphasis on application, mathematical modelling and investigation. Graphical, numerical, and algebraic representations are emphasised particularly through the appropriate use of digital technologies.

The aim of this unit is to provide students with learning outcomes and unit learning activities specifically designed to demonstrate the achievement of Australian Qualifications Framework Level 5 for 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 linear, quadratic, and simple exponential functions, and apply these functions to a range of contexts (GA5, GA6, GA7, GA8, GA10).  

LO2 - Create equations to express the relationships between variables in geometric, numeric and measurement related contexts, and apply algebraic methods to solve problems in those contexts (GA5, GA6, GA7, GA8, GA10).  

LO3 - Solve problems with proportions as a specific type of linear relationship, particularly in contexts with rates and ratios, using numeric methods (equivalent fractions, percentages, decimals, ratios) and graphical methods (gradient as rate of change) (GA5, GA6, GA7, GA8, GA10).   

LO4 - Carry out statistical investigations and probability experiments to answer questions and solve problems, using category data, discrete and continuous numeric data, and time series data, display the data with appropriate graphs and tables to detect patterns and relationships in the data and report findings (GA5, GA6, GA7, GA8, GA10).  

LO5 - Solve problems and model situations using International System of Units and other measurement systems (GA5, GA6, GA7, GA8, GA10).  

Graduate attributes

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

GA6 - solve problems in a variety of settings taking local and international perspectives into account

GA7 - work both autonomously and collaboratively 

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

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

Content

Topics will include:

• Connecting functions, their equations, and graphs (linear, simple quadratic and exponential);
• Creating linear, quadratic and simple exponential equations to express relationships between and among variables in contexts that are spatial, numeric or measurement related;
• Solving problems modelled by linear, quadratic, and simple exponential equations, using a variety of techniques including changing the subject, factorisation, simultaneous equations, and graphical methods;
• Connecting equivalent fractions, decimals and percentages as different representations of the same number, recognising the difference between part-whole and part to part relationships.
• Solving problems with rates and ratios, using a variety of techniques including ratio tables, double number lines, percentages, and equations as appropriate
• Gathering multi-variate categorical, numerical and time series data to answer investigatory questions, with an appreciation of sampling techniques;
• Display data using a range of appropriate graphical representations; column (bar) and pie for categorical data, stem and leaf, dot plot, histogram, scatterplots, box and whisker for numeric data, and line graphs for time series or other continuous data;
• Report findings from data-driven investigation appropriately with an appreciation of uncertainty;
• Relate experimental results to theoretical models to estimate probabilities with an understanding of randomness and long-run frequency, including the use of tree diagrams, two-way tables, frequency tables, and the normal distribution;
• Connect the commonly used standard units for length, area, volume and capacity, mass, time, temperature, speed, pressure, and density (including population), and convert between common measurement systems;
• Solve a variety of problems in context.

Learning and teaching strategy and rationale

Students will be involved in a variety of teaching-learning strategies to progress and demonstrate their understandings in this unit. This unit includes 3 contact hours per week over 12 weeks, comprising 1 hour of lecture, and 2 hours of tutorials.

Students are required to actively participate in all lectures, tutorials and assigned learning activities to achieve the learning outcomes.

Assessment strategy and rationale

The assessment tasks and their weightings are designed to allow students to progressively demonstrate achievement against the unit learning outcomes and to develop graduate attributes consistent with University assessment requirements.

A range of assessment procedures are used, consistent with University assessment requirements.

Minimum Achievement Standards

The assessment tasks and their weighting for this unit are designed to demonstrate achievement of each learning outcome. In order to pass this unit, students are required to submit all assessment tasks, meet the learning outcomes of the unit and achieve a minimum overall passing grade of 50%.   

Electronic Submission, Marking and Return

Assessment task submission and return of marked assessment will be done through Turnitin on LEO (unless otherwise specified). Tasks will be marked and returned within three weeks after the assessment is completed.

Overview of assessments

Representative texts and references

Barnes, M. (1994). Investigating change. [Units 1-10, 2 teachers’ handbooks]. Melbourne: Curriculum Corporation.

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

Demana, F., Waits, B. K., Foley, G. D., & Kennedy, D. (2011). Precalculus: Graphical, numerical, algebraic (8th ed.). Boston, MA: Pearson.

Eccles, P. (1997). An Introduction to Mathematical Reasoning: Numbers, sets and functions. New York, NY: Cambridge University Press.

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.

Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. Hoboken: Taylor and Francis.

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