013239 Mathematics Teaching Methods 2
Warning: The information on this page is indicative. The subject outline for a
particular session, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade, no marks
Requisite(s): ((96 credit points of completed study in spk(s): C10404 Bachelor of Science Master of Teaching Secondary Education OR 96 credit points of completed study in spk(s): C10406 Bachelor of Technology Master of Teaching Secondary Education) AND 013238 Mathematics Teaching Methods 1)
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 013416 Mathematics Teaching Methods 2 AND 028260 Mathematics Teaching Methods 2
Description
This subject further develops concepts introduced in Mathematics Teaching Methods 1, combining theory and practice to equip pre-service teachers with the skills and understanding required to teach senior mathematics in a secondary school. It includes a study of Stage 5, Stage 6 Standard and Stage 6 Advanced Mathematics syllabuses, with a particular focus on lesson planning and programming. Practical strategies for teaching mathematics for conceptual understanding are developed alongside philosophies underpinning current thinking in mathematics education research. This includes Indigenous ways of knowing about mathematics.
Subject learning objectives (SLOs)
| a. | Explain mathematical ideas accurately and with clarity including use of suitable language, examples and models. |
|---|---|
| b. | Identify and explore a range of mathematics teaching strategies. |
| c. | Identify, explore and create resources, including ICT, to enhance the teaching of mathematics and engage students in their learning. |
| d. | Organise content into an effective teaching and learning sequence. |
| e. | Design learning sequences and lesson plans using relevant mathematics curriculum, assessment, and reporting knowledge. |
| f. | Evaluate teaching programs to improve student learning. |
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 four APST graduate descriptors addressed in this subject and demonstrated in relation to taught, practised and assessed.
2.2.1. Organise content into an effective learning and teaching sequence.
Standard 2.2.1 is taught in Week 1, practised in Weeks 4-5, and assessed in Assessment task 1, criterion a.
2.3.1. Use curriculum, assessment and reporting knowledge to design learning sequences and lesson plans.
Standard 2.3.1 is taught and practised in Week 1, and assessed in Assessment task 1, criterion b.
3.2.1. Plan lesson sequences using knowledge of student learning, content and effective teaching strategies.
Standard 3.2.1 is taught in Week 1, practised in Weeks 4-5, and assessed in Assessment task 1, criterion c.
3.6.1. Demonstrate broad knowledge of strategies that can be used to evaluate teaching programs to improve student learning.
Standard 3.6.1 is taught and practised in Weeks 4-5, and assessed in Assessment task 2, criterion a.
Teaching and learning strategies
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 lesson inspired by an engaging puzzle or activity, or an interesting or entertaining item/excerpt from published media. The task allows students to exercise their ingenuity in recognising the breadth of mathematics that may be found in unlikely places, as well as experiencing the responsibility associated with teaching a lesson and preparing a teaching program.
Teacher-education students receive ongoing peer and tutor feedback throughout the teaching session.
A thorough understanding of senior secondary mathematics is required to fully engage with this subject. To assist with revision of these concepts, mathematics homework is 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 set 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 2 is a practical subject that adapts mathematics education research to address the day to day considerations of secondary school mathematics teaching and learning, with a particular focus on Stages 5 and 6 in the NSW Mathematics syllabus.
Pre-service teachers explore teaching strategies for concepts that are introduced in senior secondary mathematics, and develop an awareness of qualities of mathematics teaching that support students’ sense making, mathematical communication, problem solving, and reasoning. They develop lessons that draw upon rich content sources, and create teaching resources that support student-led discovery and multimodal teaching strategies.
Teaching and learning experiences in this subject are conducted with reference to mathematics content knowledge that is taught in Stage 5, Stage 6 Standard and Stage 6 Advanced, with particular emphasis on strategies that are applicable for teaching functions, trigonometry, calculus, financial mathematics, networks and vectors.
Assessment
Assessment task 1: Unit of Work
| Objective(s): | a, b, d and e | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||
| Length: | One unit of work, and three of the lessons within that unit, based on template. | ||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Online Activities
| Objective(s): | a, c and f | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||
| Length: | One online resource. Annotations on a unit of work. Two lessons. | ||||||||||||||||||||
| 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
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.
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.
Students who do not pass all assessment tasks will be awarded an X Fail grade.
Required texts
NSW Education Standards Authority (n.d.). Mathematics syllabuses. https://curriculum.nsw.edu.au/learning-areas/mathematics
References
Barnes, M. (1991a). Investigating change, Vol. 1, pp. 17-21. Curriculum Corporation.
Barnes, M. (1991b). Investigating change, Vol. 2, pp. 27-28. Curriculum Corporation.
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.
Liljedahl, P. (2020). Building thinking classrooms in mathematics. Corwin.
Skemp, R.R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, pp. 20-26.
Thurston, W.P. (1990). Mathematical education. Notices of the American Mathematical Society, 37(7), pp. 844-850.
See weekly schedule for some indicative references.
Further references will be included in online modules.