013238 Mathematics Teaching Methods 1
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Credit points: 6 cp
Result type: Grade, no marks
Requisite(s): 48 credit points of completed study in spk(s): C10404 Bachelor of Science Master of Teaching Secondary Education OR 48 credit points of completed study in spk(s): C10406 Bachelor of Technology Master of Teaching Secondary Education
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 013415 Mathematics Teaching Methods 1 AND 028259 Mathematics Teaching Methods 1
Description
The subject includes a study of secondary mathematics syllabi, lesson planning, approaches to learning, and resources for student engagement. Teacher-education students study a range of mathematics teaching strategies and content knowledge that is essential for teaching mathematics for understanding. 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 pre-service teachers with the skills and understanding required to begin to teach mathematics in a secondary school.
Subject learning objectives (SLOs)
| a. | Analyse mathematics syllabus documents to identify the particular concepts and skills secondary school learners need to develop. |
|---|---|
| b. | Analyse mathematics teaching strategies, drawing on theories of mathematics teaching and learning. |
| c. | Identify and explore a range of resources, including ICT, to enhance the teaching of mathematics and engage students in their learning. |
| d. | Plan, present and manage mathematics lessons. |
| e. | Explain mathematical ideas accurately and with clarity including use of suitable language, examples and models. |
| f. | 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.
- 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)
Contribution to the development of graduate attributes
There are three APST graduate descriptors addressed in this subject and demonstrated in relation to taught, practised and assessed.
2.1.1 Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.
Taught: Mathematical concepts are taught in every lecture. Structure of the content is taught in Week 1.
Practised: Mathematical concepts are practised in every tutorial. Structure of the content is practised in Week 1.
Assessed: Assessment task 1 criterion a, Assessment task 2 criterion a, and Assessment task 3 criterion a.
3.3.1 Include a range of teaching strategies.
Taught: Teaching strategies are taught in every lecture.
Practised: Teaching strategies are practised in every tutorial.
Assessed: Assessment task 1 criterion b and Assessment task 2 criterion b.
3.4.1 Demonstrate knowledge of a range of resources, including ICT, that engage students in their learning.
Taught: Resource use is taught in every lecture. ICT use is particularly taught in week 3.
Practised: Resource use is practised in every tutorial. ICT is particularly practised in week 3.
Assessed: Assessment task 2 criterion c.
Teaching and learning strategies
Teacher-education students are supported to learn through asynchronous lectures, practice-oriented interactive workshops, and synchronous online tutorials. Teaching and learning strategies include lecturer input, structured discussion, group work activities, asynchronous engagement with mathematics content, and assignments which critically examine and apply current thinking in mathematics education.
All teacher-education students contribute to the teaching and learning activities through engagement with Assessment Task 1, which involves teaching a problem that has been assigned for homework. The task provides teacher-education students with an opportunity to experience the responsibility associated with teaching mathematical content to a large group. Participation in the teaching and learning activities as both teacher and learner develops pre-service teachers’ metacognitive capabilities and informs their practice by offering different perspectives on the teaching and learning experience.
Teacher-education students receive ongoing formative feedback throughout the semester, in both synchronous and asynchronous activities and through questions posted in discussions and online forums.
Early on in the subject, teacher-education students are supported to diagnose their knowledge of basic mathematics. Teacher-education students are expected to pro-actively revise, and if necessary, expand and refresh their basic mathematics content knowledge by accessing resources and completing the assignments independently, and seeking support as appropriate.
All students are expected to engage with readings and other activities in preparation for each tutorial.
Content (topics)
Mathematics Teaching Methods 1 is a practical subject that draws upon mathematics education research to address the day-to-day considerations of secondary school mathematics teaching and learning, with a particular focus on Stages 4 and 5 in the NSW Mathematics syllabus.
Pre-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 students in their learning.
Teaching and learning experiences in this subject are conducted with reference to mathematics content knowledge that is taught in Stages 4 and 5, with particular emphasis on strategies that are applicable for teaching fractions and decimals, patterns and algebra, statistics and probability, and measurement and geometry. In conjunction with these teaching methods, pre-service teachers gain experience about common student misconceptions and learn techniques for supporting students to develop conceptual understandings that underpin firm mathematical foundations.
Assessment
Assessment task 1: Teaching a Homework Question
| Objective(s): | b, d, e and f | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||
| Length: | Full worked solutions (50 words each) for 10 of these MCQ or number-answer questions One in-class presentation, maximum 10 minutes, with partner Rationale and self-evaluation (max 500 words) | ||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Lesson Plan and Lesson Play
| Objective(s): | a, b, c, d and e | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||
| Length: | One lesson plan based on template, equivalent to 1500 words, with scholarly references to justify the pedagogical choices being made. One “lesson play” based on prompt, equivalent to 500 words. | ||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 3: Examination
| Objective(s): | e | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 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
A pass on each assessment task is required to pass this subject in order to meet the NESA requirement that all subject learning objectives and APST graduate standards descriptors be achieved.
In order to pass the subject, students must also attend all practice-oriented interactive workshops.
Attendance at workshops is important in this subject because the workshops offer opportunities to experience teaching and learning as practical activities. Such activities are essential for developing an appreciation of the ways in which manipulables and physical activities enrich the teaching and learning experience. In addition to this, it is important for students to experience mathematics teaching and learning as a collaborative exercise, involving the interchange of ideas with other students and the lecturer.
An attendance roll will be taken at each workshop.
Students should advise the lecturer in a timely manner if they have some extenuating reason for not being able to attend. When this occurs, the student must complete an alternate task that demonstrates understanding of the practical tasks that were covered in the missed workshop.
The workshop requirement must be met in order for students to be permitted to attempt Assessment Task 3.
Required texts
NSW Education Standards Authority (n.d.). Mathematics syllabuses. https://curriculum.nsw.edu.au/learning-areas/mathematics
References
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.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, pp. 20-26.
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. (1993). Maths anxiety. Australian Mathematics Teacher, 49(1), pp. 4-8.
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.
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.
Pagni, D. (1998). Giving meaning to multiplication and division of fractions. Australian Mathematics Teacher, 54(4), 11-13.
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.