020213 Maths Methods for In-Service Teachers (Year 7-12)
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Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 68106 Mathematics for Secondary Education Calculus 1 AND 68103 Mathematics for Secondary Education Statistics
These requisites may not apply to students in certain courses.
There are course requisites for this subject. See access conditions.
Description
This subject explores how mathematics teaching and curriculum can be organised and managed for effective learning. It shows how theory can inform teaching practice to provide in-service teachers with the skills and understanding required to teach mathematics in a secondary school. The subject includes a study of secondary mathematics syllabuses, lesson planning, approaches to learning, and resources for student engagement. It highlights a range of mathematics teaching strategies and different forms and functions of practical work, with a focus on development of content knowledge that is essential for teaching mathematics for understanding.
Subject learning objectives (SLOs)
| a. | Analyse mathematics syllabus documents to identify the concepts and skills that secondary school learners need to develop |
|---|---|
| b. | Explain mathematical ideas accurately and with clarity including use of suitable language, examples and models |
| c. | Analyse mathematics teaching strategies, drawing on theories of mathematics teaching and learning |
| d. | Identify and evaluate a range of resources to enhance the teaching of mathematics and engage students in their learning. |
| e. | Plan, present and manage mathematics lessons |
| f. | Enhance secondary school mathematics learning with teaching methods and resources that build upon Aboriginal and Torres Strait Islander ways of teaching and learning |
| g. | Evaluate and reflect on mathematics teaching and its effectiveness. |
Course intended learning outcomes (CILOs)
This subject engages with the following Course Intended Learning Outcomes (CILOs), which are tailored to the Graduate Attributes set for all graduates of the Faculty of Arts and Social Sciences.
- Analyse: Demonstrate critical engagement with mathematical knowledge in the secondary classroom context. (1.1)
- Analyse: Critically evaluate information in the investigation of mathematical and pedagogical problems. (2.1)
- Evaluate: Appraise research in mathematics and mathematics education. (2.3)
- Analyse: Derive innovative solutions to complex mathematical and educational problems. (4.1)
- Synthesise: Through reflection, own and understand their learning journey. (4.2)
- Evaluate: Critique approaches to meeting educational needs. (4.3)
- Synthesise: Develop and Communicate complex ideas. (5.2)
- Evaluate: Integrate Aboriginal and Torres Strait Islander knowledges into professional practice and evaluate its impact. (6.3)
Contribution to the development of graduate attributes
The subject contributes specifically to the development of the following Course Intended Learning Outcomes:
- Analyse: Demonstrate critical engagement with mathematical knowledge in the secondary classroom context. (1.1)
- Analyse: Critically evaluate information in the investigation of mathematical and pedagogical problems. (2.1)
- Evaluate: Appraise research in mathematics and mathematics education. (2.3)
- Analyse: Derive innovative solutions to complex mathematical and educational problems. (4.1)
- Synthesise: Through reflection, own and understand their learning journey. (4.2)
- Analyse: Critique approaches to meeting educational needs. (4.3)
- Synthesise: Develop and communicate complex ideas. (5.2)
- Evaluate: Integrate Aboriginal and Torres Strait Islander knowledges into professional practice and evaluate its impact. (6.3)
Graduate Attribute 1. Disciplinary knowledge
Teacher-education students will engage with mathematics from the perspective of a teacher, learning to field school-student queries and diagnose mathematical misconceptions.
Graduate Attribute 2. Research, inquiry and critical thinking
Teacher-education students are encouraged to consider different models for implementing mathematics teaching and learning activities, to develop an understanding of the relative advantages offered by various teaching strategies and resources, and a sense for situations where different teaching strategies would be beneficial.
Graduate Attribute 3. Professional, ethical and social responsibility
Teacher-education students are required to reflect on the role of the mathematics teacher in the school, particularly regarding equality of educational opportunity for all school-students.
Graduate Attribute 4. Reflection, Innovation and Creativity
Teacher-education students will be given opportunities to experiment with different teaching methods and required to reflect on the effectiveness of their execution, with an aim of developing metacognitive skills to inform their future practice.
Graduate Attribute 5. Communication
Teacher-education students will develop skills required to communicate mathematical ideas clearly and confidently, using varied modes, to support secondary school-students with different learning styles.
Graduate Attribute 6. Aboriginal and Torres Strait Islander Knowledges and Connection
Teacher-education students will learn about Indigenous Australian ways of sharing knowledge and how these methods can be applied for teaching secondary school mathematics.
Teaching and learning strategies
This subject is designed for block mode delivery supported by online asynchronous study. Teacher-education students are to attend two on-campus sessions. Asynchronous learning is offered on the Learning Management System Canvas. Teacher-education students are actively involved in the asynchronous sections of this subject by contributing to online interactive elements on Canvas, where they comment on the contributions of other students.
Content (topics)
Mathematics Methods for In-Service Teachers is a practical subject that draws upon mathematics education research to address the day-to-day considerations of secondary school mathematics teaching and learning. In-service teachers explore teaching strategies that suit different learning styles, and develop an awareness of qualities of mathematics teaching that support students’ sense making, mathematical communication, problem solving, and reasoning. They develop lessons that implement ideas from mathematics education research, and identify and utilise teaching resources, including ICT, for engaging school-students in their learning.
Assessment
Assessment task 1: Teaching a Homework Question
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge. 2. Research, inquiry and critical thinking 3. Professional, ethical and social responsibility 4. Reflection, innovation, creativity 5. Communication | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Objective(s): | b, e and g | ||||||||||||||||||||
| Groupwork: | Individual | ||||||||||||||||||||
| Weight: | 40% | ||||||||||||||||||||
| Length: | 1. Responses to 80 questions with multiple choice or numerical responses (automatic grading). 2. Full worked solutions for ten homework questions, equivalent to 50 words per question (500 words) 3. One (individual) presentation, maximum 10 minutes (equivalent to 400 words) 4. One self-evaluation, maximum 250 words. | ||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Lesson Plan and Lesson Play
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge. 2. Research, inquiry and critical thinking 3. Professional, ethical and social responsibility 4. Reflection, innovation and creativity 5. Communication 6. Aboriginal and Torres Strait Islander Knowledges and Connection | ||||||||||||||||||||||||||||
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| Objective(s): | a, b, c, d and f | ||||||||||||||||||||||||||||
| Groupwork: | Individual | ||||||||||||||||||||||||||||
| Weight: | 30% | ||||||||||||||||||||||||||||
| Length: |
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| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 3: Maths Pedagogy
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge. 2. Research, inquiry and critical thinking 3. Professional, ethical and social responsibility 5. Communication | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Objective(s): | b and c | ||||||||||||
| Groupwork: | Individual | ||||||||||||
| Weight: | 30% | ||||||||||||
| Length: | Solutions for mathematics questions, and brief summaries of teaching methods, equivalent to 50 words per question (500 words). | ||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Required texts
NSW Education Standards Authority (n.d.). Mathematics K-10 syllabus. https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10
NSW Education Standards Authority (n.d.). Mathematics Stage 6. https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics
NSW Education Standards Authority (n.d.). Mathematics syllabuses. https://curriculum.nsw.edu.au/learning-areas/mathematics
References
Barnes, M. (1991). Investigating change Vol. 1, pp. 17-21. Curriculum Corporation.
Clarke, D., Roche, A., Cheeseman, J., and Sullivan, P. (2014). Encouraging students to persist when working on challenging tasks. Australian Mathematics Teacher, 70(1), pp. 3-11.
Dossel, S. (2016). Maths anxiety. Australian Mathematics Teacher, 72(3), pp. 40-44.
Dweck, C.S., Leggett, E.L. (1988). A social-cognitive approach to motivation and personality. Psychological Review, 95(2), pp. 256-273.
Fitzallen, N. (2015). When does 1/2 = 1/3? Australian Mathematics Teacher, 71(1), 36-40.
Goos, M., Dole, S., & Geiger, V. (2012). Numeracy across the curriculum. Australian Mathematics Teacher, 68(1), pp. 3-7.
Gray, E.M., and Tall, D.O. (1994). Duality, ambiguity and flexibility: A "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), pp. 116-140.
Horne, M. (2005). Algebra revisited. In M. Coupland, J. Anderson, & T. Spencer (Eds.), Making mathematics vital: Proceedings of the Twentieth Biennial Conference of the Australian Association of Mathematics Teachers, pp. 308-315. AAMT Inc.
Kazemi, E., Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Stenhouse.
Moloney, K., & Stacey, K. (1996). Understanding decimals. The Australian Mathematics Teacher, 52(1), pp. 4-8.
Movshovits-Hadar, N. (1988). School mathematics theorems - An endless source of surprise. For the Learning of Mathematics, 8(3), pp. 34-40.
Murray, M. (2003). Supporting mathematics learning through English language teaching strategies. Reflections, 28(1), pp. 35-40.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, pp. 20-26.
Thurston, W. (1990). Mathematical education. Notices of the AMS, 37(7), pp. 844-850.
Vincent, J., Bardini, C., Pierce, R, Pearn, C. (2016). Misuse of the equals sign: An entrenched practice from early primary years to tertiary mathematics. Australian Senior Mathematics Journal, 29(2), pp. 31-39.
Zazkis, R., Sinclair, N., Liljedahl, P. (2013). Lesson play in mathematics education: A tool for research and professional development. Springer.
Other resources
Maths equipment in Education store room (Building 10 Level 4).