| Effective Term: | 2024/05 |
| Institute / School : | Institute of Innovation, Science & Sustainability |
| Unit Title: | Puzzles, Patterns and Proofs (Advanced Level) |
| Unit ID: | MATHS3007 |
| Credit Points: | 15.00 |
| Prerequisite(s): | (At least one intermediate level mathematics course) |
| Co-requisite(s): | Nil |
| Exclusion(s): | (MA655 and MATHS2005) |
| ASCED: | 010101 |
| Other Change: | |
| Brief description of the Unit |
This unit is aimed at students who are interested in the role of both logic and imagination in mathematics. It 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. In the latter case this unit can be used by students interested in pursuing more advanced mathematical units. |
| 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: |
| Level of Unit in Course | AQF Level(s) of Course | | 5 | 6 | 7 | 8 | 9 | 10 | | Introductory | | | | | | | | Intermediate | | | | | | | | Advanced | | |  | | | |
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| Learning Outcomes: |
| Knowledge: |
| K1. | use elementary ideas in number theory; |
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| K2. | explain and be able to carry out proofs by mathematical induction |
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| K3. | describe the proof of the four colour theorem |
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| K4. | apply basic concepts of graph theory |
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| K5. | explain arithmetic operations from a theoretical point of view |
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| Skills: |
| S1. | express concepts, relationships and structures in mathematical form, and draw conclusions about the situations studied by abstract argument |
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| S2. | use elementary ideas about sets and their properties in problem solving |
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| S3. | investigate topological ideas |
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| Application of knowledge and skills: |
| A1. | construct mathematical proofs using a variety of proof techniques |
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| A2. | express in mathematical terms and solve a range of counting problems |
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| A3. | research and impart mathematical knowledge to others |
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| Unit Content: |
This unit introduces a broad range of mathematical concepts of wide applicability. It contains material which will be of interest and relevant to computing students who seek a theoretical understanding of their subject, as well as to mathematics students. Much of the material is starting to appear in secondary mathematics curricula, and the rest provides valuable enrichment material for those students intending to teach mathematics. |
| Graduate Attributes: |
| Federation University recognises that students require key transferable employability skills to prepare them for their future workplace and society. FEDTASKS (Transferable Attributes Skills and Knowledge) provide a targeted focus on five key transferable Attributes, Skills, and Knowledge that are be embedded within curriculum, developed gradually towards successful measures and interlinked with cross-discipline and Co-operative Learning opportunities. One or more FEDTASK, transferable Attributes, Skills or Knowledge must be evident in the specified learning outcomes and assessment for each FedUni Unit, and all must be directly assessed in each Course.
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| FED TASK and descriptor | Development and acquisition of FEDTASKS in the Unit | Learning outcomes
(KSA) | Assessment task
(AT#) | FEDTASK 1
Interpersonal | Students will demonstrate the ability to effectively communicate, inter-act and work with others both individually and in groups. Students will be required to display skills in-person and/or online in: • Using effective verbal and non-verbal communication • Listening for meaning and influencing via active listening • Showing empathy for others • Negotiating and demonstrating conflict resolution skills • Working respectfully in cross-cultural and diverse teams. | Not applicable | Not applicable | FEDTASK 2
Leadership | Students will demonstrate the ability to apply professional skills and behaviours in leading others. Students will be required to display skills in: • Creating a collegial environment • Showing self -awareness and the ability to self-reflect • Inspiring and convincing others • Making informed decisions • Displaying initiative | Not applicable | Not applicable | FEDTASK 3
Critical Thinking and Creativity | Students will demonstrate an ability to work in complexity and ambiguity using the imagination to create new ideas. Students will be required to display skills in: • Reflecting critically • Evaluating ideas, concepts and information • Considering alternative perspectives to refine ideas • Challenging conventional thinking to clarify concepts • Forming creative solutions in problem solving. | Not applicable | Not applicable | FEDTASK 4
Digital Literacy | Students will demonstrate the ability to work fluently across a range of tools, platforms and applications to achieve a range of tasks. Students will be required to display skills in: • Finding, evaluating, managing, curating, organising and sharing digital information • Collating, managing, accessing and using digital data securely • Receiving and responding to messages in a range of digital media • Contributing actively to digital teams and working groups • Participating in and benefiting from digital learning opportunities. | Not applicable | Not applicable | FEDTASK 5
Sustainable and Ethical Mindset | Students will demonstrate the ability to consider and assess the consequences and impact of ideas and actions in enacting ethical and sustainable decisions. Students will be required to display skills in: • Making informed judgments that consider the impact of devising solutions in global economic environmental and societal contexts • Committing to social responsibility as a professional and a citizen • Evaluating ethical, socially responsible and/or sustainable challenges and generating and articulating responses • Embracing lifelong, life-wide and life-deep learning to be open to diverse others • Implementing required actions to foster sustainability in their professional and personal life. | Not applicable | Not applicable |
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| | Learning Outcomes Assessed | Assessment Tasks | Assessment Type | Weighting | | 1. | K1-5, S1-3, A1, A2 | Participate in class activities | Portfolio of completed work | 0 - 20% | | 2. | A3 | Self directed or group exploration | Projects / Presentation | 30 - 50% | | 3. | K1-5, S1-3, A1, A2 | Review and skills practice | Tests / Examination(s) | 50 - 60% |
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