013240 Mathematics Teaching Methods 3
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Subject handbook information prior to 2024 is available in the Archives.
Credit points: 6 cp
Result type: Grade, no marks
Requisite(s): 120 credit points of completed study in spk(s): C10404 Bachelor of Science Master of Teaching Secondary Education AND 013238 Mathematics Teaching Methods 1 AND 013239 Mathematics Teaching Methods 2
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 013417 Mathematics Teaching Methods 3 AND 028261 Mathematics Teaching Methods 3
Description
Mathematics Teaching Methods 3 further develops pre-service teachers’ skills and understandings that are required to fully participate in decision making, advocacy and leadership in secondary school mathematics. With a particular focus on the design, implementation and influences of assessment, this subject explores content from the Stage 6 Advanced, Extension 1 and Extension 2 mathematics syllabuses and continues the emphasis on teaching mathematics for conceptual understanding.
Subject learning objectives (SLOs)
| a. | Explain mathematical ideas accurately and with clarity including use of suitable language, examples and models. |
|---|---|
| b. | Analyse syllabus documents to identify the particular concepts and skills learners need to develop. |
| c. | Identify and explore teaching strategies and resources to enhance the teaching of mathematics and engage students in their learning. |
| d. | Identify and explain the purpose of different ways of assessing student learning. |
| e. | Evaluate student work and provide constructive feedback. |
| f. | Apply moderation processes to support consistent and comparable judgements of student learning. |
| g. | Apply assessment information to modify teaching practice. |
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.
- Know secondary school students and how they learn, with an advanced ability to critically evaluate the physical, social and emotional dimensions of learners (1.1)
- Know the content and how to teach it, demonstrating an advanced knowledge of a teaching program in one or more disciplines to critically evaluate its delivery (1.2)
- Plan for and implement effective teaching and learning with an advanced knowledge of educational practice, pedagogy, policy, curriculum and systems (1.3)
- Assess, provide feedback and report on student learning (1.4)
- Plan and carry out extended analysis, and undertake independent research, of issues related to content-specialisations and teaching theories and practices (2.1)
- Communicate effectively using diverse modes and technologies in academic, professional and community contexts (6.1)
Contribution to the development of graduate attributes
There are five APST graduate descriptors addressed in this subject and demonstrated in relation to taught, practised and assessed.
5.1 Demonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning
Standard 5.1 is taught in the Week 1 lecture, practised in the Week 5 tutorial, and assessed in Assessment task 3, criterion c.
5.2 Demonstrate an understanding of the purpose of providing timely and appropriate feedback to students about their learning.
Standard 5.2 is taught and practised in Week 4, and assessed in Assessment task 1, criterion c.
5.3 Demonstrate understanding of assessment moderation and its application to support consistent and comparable judgements of student learning.
Standard 5.3 is taught and practised in Week 4, and assessed in Assessment task 1, criterion b.
5.4 Demonstrate the capacity to interpret student assessment data to evaluate student learning and modify teaching practice.
Standard 5.4 is taught and practised in Week 1, and assessed in Assessment task 1, criterion e.
5.5 Demonstrate understanding of a range of strategies for reporting to students and parents/carers and the purpose of keeping accurate and reliable records of student achievement.
Standard 5.5 is taught and practised in Week 4, and assessed in Assessment task 2, criterion d.
Teaching and learning strategies
Teaching and learning strategies include lecturer input, structured discussion, group work activities, asynchronous engagement with mathematics content, and assignments which develop teacher- education students’ identities as professional mathematics educators.
All teacher-education students contribute to the teaching and learning activities through engagement with Assessment Task 2, which involves creating and presenting an assignment or investigation-style task that is suitable for Stage 6 assessment. The task requires consideration of the delicate balance that must exist between practicality, adherence to syllabus requirements, fairness and integrity in assessment construction, and effectiveness for school-student interest and engagement. In so doing, it provides a valuable opportunity for teacher-education students to exercise their creativity and ingenuity to introduce new ideas that contribute to growing and developing their collective understanding of possibilities for mathematics education.
A thorough understanding of senior secondary mathematics is required to fully engage with this subject. To assist with revision of these concepts, mathematics homework will be offered throughout the course. Teacher-education students are expected to pro-actively revise their basic mathematics content knowledge by accessing resources and completing the homework independently, and seeking support as appropriate.
All teacher-education students are expected to engage with readings and online learning activities in preparation for each tutorial. Attendance at workshops is important in this subject because it is based on a collaborative approach which involves essential workshopping and interchange of ideas with other students and the lecturer.
Content (topics)
Mathematics Teaching Methods 3 is a practical subject that considers mathematics teaching and learning from a perspective of oversight and advocacy. In particular, the purpose of assessment and its influence upon learning is considered alongside teaching methods for mathematics content from Stage 6 Advanced, Extension 1 and Extension 2: methods of proof, applications of the binomial theorem, parametric equations, projectile and simple harmonic motions, trigonometric identities, complex numbers, vectors, inverse functions, and further calculus.
With an underlying philosophical focus on the implications of mathematics assessment practices, the teaching and learning experiences in this subject develop a metacognitive awareness of how learning can be shaped by assessment. The potential for assessment tasks to guide the learning experience is explored in depth and questions are raised regarding the appropriateness of different assessment mechanisms and the impacts these may have on different kinds of learner.
Assessment
Assessment task 1: Grading Student Work Samples
| Objective(s): | a, e, f and g | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||||||
| Length: | 1500 words or equivalent | ||||||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Stage 6 Integrated Teaching, Learning and Assessment Task
| Objective(s): | a, b, c, d and f | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||||||
| Length: | 1000 words (excluding outcomes list and reference list). Worked example, figures, appendices as appropriate. | ||||||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 3: Exam: Mathematical concepts and teaching strategies
| Objective(s): | a | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Weight: | 20% | ||||||||
| Length: | The exam is designed to be 2 hours long. Students will be given a maximum of 4 hours to complete the paper. | ||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Minimum requirements
Students must pass all assessment tasks to pass this subject because the tasks collectively assess the Subject Learning Objectives and Graduate Attributes (both APST graduate descriptors and CILOs) covered in this subject. External accrediting bodies (NESA and AITSL) require all tasks to be satisfactorily completed in order to demonstrate achievement against NSW Graduate Teacher Standards. Students who do not pass all assessment tasks will be awarded an X Fail grade.
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
Recommended texts
Goos, M., Vale, C., & Stillman, G. (2017). Teaching secondary school mathematics (2nd ed.). Allen & Unwin.
References
Archbald, D.A. & Newmann, F.M. (1988). Beyond standardized testing: Assessing authentic academic achievement in the secondary school (Introduction and Chapter 1). National Association of Secondary School Principals.
Black, P. & Wiliam, D. (2010). Inside the Black Box: Raising standards through classroom assessment. Phi Delta Kappan, 92(1), pp. 81-90.
Brown, S. (2004). Assessment for Learning. Learning and Teaching in Higher Education, 1, pp. 81-89.
Buckingham, J. (2012). Keeping PISA in Perspective: Why Australian Education Policy Should Not Be Driven by International Test Results. https://www.cis.org.au/publications/issue-analysis/keeping-pisa-in-perspective-why-australian-education-policy-should-not-be-driven-by-international-test-results/
Clarke, D., Mitchell, A., Roche, A. (2005). Student one-to-one assessment interviews in mathematics: A powerful tool for teachers. MAV Annual Conference 2005. https://w.mav.vic.edu.au/files/conferences/2005/doug-clarke.pdf
Ferguson, H.J. (2013). Journey into ungrading. In J. Bower and P.L. Thomas (Eds.), De-testing and de- grading schools: Authentic alternatives to accountability and standardization.
Hattie, J. (2003). Teachers make a difference. What is the research evidence? Keynote presentation at Building Teacher Quality: The ACER Annual Conference, Melbourne, Australia.
Hattie, J. & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), pp.81-112.
Leung, F.K.S. (2014). What can and should we learn from international studies of mathematics achievement? Mathematics Education Research Journal of Australasia, 26(3), pp. 579-605.
Ley, J. (2015). A five-question approach to teaching mathematics. Reflections, 40(4), pp. 1-5.
Manitoba Education, Citizenship and Youth (2006). Rethinking classroom assessment with purpose in mind. Winnipeg, Manitoba: Author.
Rohrer, D., Dedrick, R.F., Stershic, S. (2015). Interleaved practice improves mathematics learning. Journal of Educational Psychology, 107(3), pp. 900-908.
Skemp, R.R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, pp. 20-26.
Smith, G., Wood, L., Coupland, M., Stephenson, B., Crawford, K., Ball, G. (1996). Constructing mathematical examinations to assess a range of knowledge and skills. International Journal of Mathematical Education in Science and Technology, 27(1), pp. 65-77.
Wisconsin Department of Public Instruction (n.d.). Understanding depth of knowledge and cognitive complexity. https://dpi.wi.gov/sites/default/files/imce/assessment/pdf/Forward%20Bloom%27s%20Taxonomy%20and%20Webb%27s%20DOK%20Doc.pdf
Wormeli, R. (2011). Redos and retakes done right. Educational Leadership, 69(3), pp. 22-26.