028259 Mathematics Teaching Methods 1
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Credit points: 6 cp
Subject level:
Postgraduate
Result type: Grade, no marksRequisite(s): 48 credit points of completed study in spk(s): C10350 Bachelor of Arts Bachelor of Education
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 013047 Mathematics Teaching Methods 1 AND 013415 Mathematics Teaching Methods 1 AND C10209 Bachelor of Educational Studies
Description
This subject explores how mathematics teaching and curriculum can be organised and managed for effective learning. The subject combines theory with practice to provide students with the skills and understanding required to begin to teach mathematics in a secondary school, and is associated with professional experience. The subject includes study of secondary mathematics syllabuses, lesson planning, approaches to learning and teaching, and different forms and functions of practical work and its role in learning and teaching mathematics. This subject is a prerequisite for the other mathematics teaching methods subjects.
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.
- Operate professionally in a range of educational settings, with particular emphasis on their specialisation (GTS 1, 2) (1.1)
- Design and conduct effective learning activities, assess and evaluate learning outcomes and create and maintain supportive and safe learning environments (GTS 1, 2, 3, 4, 5) (1.2)
- Make judgements about their own learning and identify and organise their continuing professional development (GTS 3, 6) (1.3)
- Act as a developer of learning with colleagues and possess collaborative skills (GTS 7) (1.4)
- Communicate effectively using diverse modes and technologies (GTS 2, 3, 4) (6.1)
Contribution to the development of graduate attributes
This subject addresses the following Course Intended Learning Outcomes:
1. Professional readiness
1.1) Operate professionally in a range of educational settings, with particular emphasis on their specialisation
1.2) Design and conduct effective learning activities, assess and evaluate learning outcomes and create and maintain supportive and safe learning environments
1.3) Make judgements about their own learning and identify and organize their continuing professional development
1.4) Act as a developer of learning with colleagues and possess collaborative skills
1.5) Employ contemporary technologies effectively for diverse purposes
6. Effective communication
6.1) Communicate effectively using diverse modes and technologies
Standards addressed in this subject and demonstrated in relation to Taught, Practised and Assessed:
1.2.1 Demonstrate knowledge and understanding of research into how students learn and the implications for teaching.
2.1.1 Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.
3.3.1 Include a range of teaching strategies.
3.4.1 Demonstrate knowledge of a range of resources, including ICT, that engage students in their learning.
Standard 1.2.1 will be taught and practised in Weeks 1 and 2 assessed in Task 1 criteria b and c, Task 2 criteria b and c.
Standard 2.1.1, Mathematical concepts are taught in every lecture. Structure of the content is taught in week 1.
Mathematical concepts are practised in every tutorial.Structure of the content is practised in week 1. Assessed in:Task 1 criterion a,Task 2 criterion a, and Task 3 criterion a.
Standard 3.3.1, Teaching strategies are taught in every lecture.Teaching strategies are practised in every tutorial.
Assessed in:Task 1 criterion b, Task 2 criterion b, andTask 3 criterion b.
Standard 3.4.1,Resource use is taught in every lecture. ICT use is particularly taught in week 3.Resource use is practised in every tutorial. ICT is particularly practised in week 3. Assessed in Task 2 criterion c.
Teaching and learning strategies
The teaching/learning strategies employed in this subject will include lecturer input, structured discussion, workshop activities, individual research, lesson presentation by students, evaluation by students of presentations, development of lessons with revision of this in the light of practicum experiences, and assignments which critically examine and apply current thinking in mathematics teaching and learning, as well as using examples from the NESA K-10 Mathematics Syllabus.
Students will receive ongoing peer and tutor feedback throughout the teaching session.
Students are expected to pro-actively revise their basic mathematics content by accessing resources independently and seeking support as appropriate.
Gaps in knowledge of basic mathematics lead to considerable difficulty with this subject. Therefore, in Week 2, an early formative test will be held to enable the lecturer to give feedback in Week 3 to each student about any areas that they may need to revise. This formative test is not an assessment task.
Content (topics)
Students will typically experience the learning in this subject through the following processes and/or content that will be covered: a combination of tutorial and online discussions, cooperative group work, workshops, observations of workplace practices; practical activities, readings and short lectures specific to each of the objectives listed above, using examples from the Stages 4 and 5 of the Years 7-10 Mathematics Syllabus (2012).
Content:
- Yr 7-10 Mathematics syllabuses
- Content knowledge
- Structure
- Lesson planning
- Lesson Structure
- Teaching a lesson
- Strategies to evaluate teaching program to improve student learning
- Reflection on the teaching of the lesson
- Working Mathematically
- Inclusion in lesson planning and implementation
- Teaching strategies and approaches
- Selection and adaptation of resources
- Books
- Systemic materials
- Multi-media
- Selecting and using learning technologies
- Using ICT in the classroom
- Lesson planning with ICT activities
- ICT teaching/learning practices
- Literacy in Mathematics
- Integrating literacy and numeracy strategies in Mathematics
Assessment
Assessment task 1: Teaching a Homework Question
| Objective(s): | b, d, e and f | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||
| Length: | Homework questions with multiple choice or numerical responses. Full worked solutions for ten homework questions. One presentation, maximum 10 minutes, with partner. One 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
In order to pass the subject, students must:
- 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.
- Achieve a minimum of 50% for Assessment Task 3.
50% on Assessment Task 3 represents the minimum level of both knowledge of the teaching content and knowledge of effective teaching practice.
- Achieve an overall mark of 50% or above.
Students who achieve an overall mark of 50% or above, but fail to satisfy one of the other two minimum requirements, will receive an X grade.
Required texts
Board of Studies NSW (2012). Mathematics K-10 syllabus. https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10/content
Goos, M., Vale, C., & Stillman, G. (2017). Teaching secondary school mathematics (2nd edition). Routledge.
References
Dweck, C.S., Leggett, E.L. (1988). A social-cognitive approach to motivation and personality. Psychological Review, 95(2), pp. 256-273.
Gray, E.M. & 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.
Further readings will be linked to each week's workshops.