Year
2024Credit points
10Campus offering
Prerequisites
NilIncompatible
BMSC102 Numerical Reasoning
Teaching organisation
150 hours of focused learning.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 engage with authentic problems in biomedical science and learn to identify and use appropriate mathematical tools to solve them. Effective communication of the techniques used, the results obtained, and conclusions reached, are also fundamental to this unit of study.
The aim of this unit is to provide students with the skills and knowledge to understand and make informed choices about the foundational tools of mathematics broadly encountered in the practice of biomedical 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.
| Learning Outcome Number | Learning Outcome Description | Relevant Graduate Capabilities |
|---|---|---|
| LO1 | Use algebraic and graphical reasoning to describe relationships between variables related to scientific problems and extract information from and about those relationships | GC1, GC2, GC7, GC8 |
| LO2 | Use techniques and concepts from algebra, probability, statistics and calculus to model and solve problems in simple systems | GC1, GC2, GC7, GC8 |
| LO3 | Describe and discuss the appropriate tools that might be useful in the solution of more complex problems and systems | GC1, GC8 |
| LO4 | Use a spreadsheet as a computational tool to implement numerical techniques in the description and solution of simple systems | GC1, GC2, GC8, GC10 |
Content
Topics will include:
- Measurements and errors
- Mathematical expressions
- Functions and graphs
- Linear & polynomial
- Exponential & logarithmic
- Sinusoidal
- Number techniques for differentiation and integration
- Probability
- Descriptive statistics
- Data modelling
Learning and teaching strategy and rationale
This unit of study is centred around a problem-based approach to learning. Each week, students in small groups within a 3-hour workshop, investigate a set of science problems around an authentic theme or scenario. As a group, and facilitated by a tutor, they engage with these problems and use an investigative and often experimental approach to find solutions. The problems are structured in such a way to allow an easy entry into solutions, while often also allowing multiple mathematical techniques and pathways to those solutions. Furthermore, the problems in each workshop are graded, containing certain "Core" elements that are required by all students and "Extension" elements that give students the choice to develop and demonstrate more sophisticated thinking.
Online material available before the workshops will include a problem-setting scenario giving the context and rationale for the week. Help on the relevant mathematical tools will also be available online. The teaching and learning in this format is therefore not structured around mathematical themes or topics, but rather authentic issues faced by biomedical scientists.
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, students bring with them varying levels of confidence and comfort with respect to this area of study. 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 problem-based learning utilised in workshops contains a number of graded and open-ended problems that require solution. Students investigate and solve these in small groups, but as individuals write a short report that includes an outline of the issues, the methods used to solve the problems, the results and conclusions reached and any meta-thinking regarding the problem-solving process. Some of the problems presented in workshops are designated “Core”, and these require foundational skills that must be completed by all students in order to achieve a Pass. Each workshop topic also contains “Extension” problems which require deeper investigation. Students are given a choice of whether and which of these to undertake. This means the pathway to a passing achievement is clear to all students, while allowing some students to choose to pursue more sophisticated lines of enquiry and/or multiple approaches to solutions. Four of these reports are submitted for formative and summative feedback. The first of these submissions has a lower weight than the others to support students by having a lower-stakes early assessment task.
In order to pass this unit, students are required to achieve a final grade of 50% or better as an aggregate score of all points from assessment tasks in this unit.
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
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes |
|---|---|---|
Assessment 1: Report 1 Students are required to communicate satisfactory mastery of foundational skills involved in problem solving. They have the choice to also demonstrate higher-level skills by the investigative solutions of more difficult problems and communicate their results in more integrated and sophisticated ways. | 10% | LO1, LO2, LO3 |
Assessment 2: Report 2 Students are required to communicate satisfactory mastery of foundational skills involved in problem solving. They have the choice to also demonstrate higher-level skills by the investigative solutions of more difficult problems and communicate their results in more integrated and sophisticated ways. | 30% | LO1, LO2, LO3, LO4 |
Assessment 3: Report 3 Students are required to communicate satisfactory mastery of foundational skills involved in problem solving. They have the choice to also demonstrate higher-level skills by the investigative solutions of more difficult problems and communicate their results in more integrated and sophisticated ways. | 30% | LO4, LO1, LO2, LO3 |
Assessment 4: Report 4 Students are required to communicate satisfactory mastery of foundational skills involved in problem solving. They have the choice to also demonstrate higher-level skills by the investigative solutions of more difficult problems and communicate their results in more integrated and sophisticated ways. | 30% | LO1, LO2, LO3, LO4 |
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.