BMSD102 - Numerical Reasoning

Year

Credit points

Campus offering

Prerequisites

Incompatible

BMSC102 Numerical Reasoning

Teaching organisation

Unit rationale, description and aim

The ability to reason numerically is fundamental to the practice of science. All science involves some or all of measurement, mathematical manipulation and analysis of measurements, interpretation and presentation of numerical data, and drawing conclusions from numerical data.

The focus of the unit is heavily towards the conceptual understanding and practical use of mathematical tools rather than as a study of these as an end in themselves. The approach is therefore one of applied mathematics, with a particular emphasis on spreadsheet-based numerical techniques. Students will develop the skills and knowledge in various mathematical 'scripts', graphical interpretation and presentation of data, manipulation of equations, functions, descriptive statistics, probability, basic modelling techniques and differential and integral calculus.

This unit provides students with the skills and knowledge to understand and use the foundational tools of mathematics broadly encountered in the practice of science.

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 - Use algebraic and graphical reasoning to describe relationships between variables related to scientific problems and extract information from and about those relationships (GA4, GA5, GA8, GA9)

LO2 - Use techniques and concepts from algebra, probability, statistics and calculus to model and solve problems in simple systems (GA4, GA5, GA8)

LO3 - Describe and discuss the appropriate tools that might be useful in the solution of more complex problems and systems (GA4, GA5, GA8)

LO4 - Use a spreadsheet as a computational tool to implement numerical techniques in the description and solution of simple systems (GA4, GA5, GA8, GA9, GA10)

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.

Content

Topics will include: 

• Number and measurement 
• Mathematical expressions 
• Functions and graphs 
• Linear & polynomial 
• Exponential & logarithmic 
• Trigonometric 
• Manipulating and solving equations 
• Differentiation and integration 
• Concepts & applications 
• Simple numerical techniques 
• Probability 
• Statistics 
• Summary and descriptive statistics 
• Graphical representation of data 
• Modelling 
• Using tools above to model data for description and prediction 
• Numerical spreadsheet-based techniques  

Learning and teaching strategy and rationale

This unit of study predominantly engages students in active approaches to their learning. Weekly lectures provide opportunities for students to see numerical reasoning modelled by experienced practitioners, to regularly undertake well defined practice activities commonly involving pair-wise or small group discussion, and to ask questions of staff.  

A weekly workshop session provides an opportunity for greater individual attention for students as they apply the skills and knowledge in a particular topic to graded problems that are grounded in their application to science wherever possible. These classes also allow for discussion of open-ended problems and issues that more genuinely reflect the circumstances of real world situations of numerical reasoning. 

Students engage with spreadsheet-based numerical techniques in weekly practical classes held in a computer laboratory. These exercises, like the workshop exercises above, are graded in difficulty, include real world situations, and allow students to develop the skills and confidence with these important and ubiquitous mathematical tools.  

Online support, supplementary materials and channels of communication are provided to students via LEO.  

Further to this, to ensure students are ready to transition from the Diploma and articulate into the second year of undergraduate study, transition pedagogies will be incorporated into the unit as the key point of differentiation from the standard unit. This focuses on an active and engaging approach to learning and teaching practices, and a scaffolded approach to the delivery of curriculum to enhance student learning in a supportive environment. This will ensure that students develop foundation level discipline-based knowledge, skills and attributes, and simultaneously the academic competencies required of students to succeed in this unit.

Assessment strategy and rationale

While Year 12 maths or equivalent is a requirement for course entry, amongst students there is a very large spread of background, facility and comfort level with maths. Some students have previously undertaken calculus-based courses while others have completed maths methods type courses. This presents a particular challenge for this unit of study which aims to bring all students to a level where they can understand and implement - at a basic level - the concepts and techniques commonly used in science.  

The unit is designed to provide enough time for students with less background to master the more difficult concepts while simultaneously providing enough challenge and extension for students with a more sophisticated maths background. The assessment strategies support this aim in a number of ways: 

Maths Foundations (Assessment 1) consists of structured exercises supported by small group teaching. Students with greater background may choose to submit these as a single submission early in semester. The Maths Foundations also include a series of more challenging optional exercises that are suitable for this group of students. Other students, with less prior exposure, may choose to make a series of smaller submissions through the semester and thereby allow greater opportunity to develop these foundational skills and knowledge over an extended period of time. Students choosing this second alternative are provided with intensive small group teaching in each topic. At the end of a topic, they demonstrate satisfactory completion, or this may be extended a further week to provide a further buffering time for mastery.  

The Excel Exercises (Assessment 2) also require the conceptual understanding of Maths Foundations implemented with various spreadsheet-based numerical techniques. Students make a submission at the end of semester and the content of the assessment is tightly linked to small group supported teaching throughout the semester. The exercises also include more challenging problems and applications that are available to students aiming for Distinction level grades. In this way, students who have come to the unit with little prior experience can achieve success, while more advanced students can be significantly extended and challenged.  

The end-of-semester examination (Assessment 3) allows students to demonstrate the basic skills and knowledge that are required for this unit. The examination, like the other assessments, also include questions that are designed to be more challenging for students who have had significantly greater prior experience.  

Strategies aligned with transition pedagogies will be utilised to facilitate successful completion of the unit assessment tasks. For each assessment, there will be the incorporation of developmentally staged tasks with a focus on a progressive approach to learning. This will be achieved through activities, including regular feedback, particularly early in the unit of study to support their learning; strategies to develop and understand discipline-specific concepts and terminology; in-class practice tasks with integrated feedback; and greater peer-to-peer collaboration.

Overview of assessments

Representative texts and references

Alldis B. K., & Kelly V. A. (2012). Mathematics for technicians(7th ed.).  McGraw Hill.

Banks R. (2013). Towing icebergs, falling dominoes, and other adventures in applied mathematics. Princeton University Press. https://doi.org/10.1515/9781400846740

Bellos A. (2010). Alex's adventures in numberland. Bloomsbury. https://ebookcentral.proquest.com/lib/acu/reader.action?docID=5222774

Croft A, Davison R. (2002) Foundation maths. Prentice Hall.

Croft T., & Davison R. (2020). Foundation maths (7th ed.). Pearson. https://ebookcentral.proquest.com/lib/acu/reader.action?docID=6009853

James, G., & Dyke, P. P. G. (2016). Modern engineering mathematics (6th ed.). Pearson Education Limited. https://ebookcentral.proquest.com/lib/acu/reader.action?docID=6036640

Kahneman D. (2013). Thinking, fast and slow. Anchor Canada. 

Liengme, B. V. (2016) A guide to Microsoft® Excel 2013 for scientists and engineers. Academic Press/Elsevier. 

Stewart, J. (2019). Calculus: Concepts and contexts (Student edition. 4th ed.). Cengage. 

Stewart, J., Redlin, L., & Watson, S. (2017): Precalculus: Mathematics for calculus. (7th ed., metric version). Cengage Learning.