University of Technology Sydney

013415 Mathematics Teaching Methods 1

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.

UTS: Education: Initial Teacher Education
Credit points: 6 cp

Subject level:

Postgraduate

Result type: Grade, no marks

There are course requisites for this subject. See access conditions.
Anti-requisite(s): 013047 Mathematics Teaching Methods 1 AND 028259 Mathematics Teaching Methods 1

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.

  • 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

This subject addresses the following Course Intended Learning Outcomes:

1. Professional readiness

1.1) Know students and how they learn, with an advanced ability to critically evaluate the physical, social and emotional dimensions of learners

1.2) 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

1.3) Plan for and implement effective teaching and learning with an advanced knowledge of educational practice, pedagogy, policy, curriculum and systems

1.6) Exhibit recent technological pedagogical and content knowledge with creativity and initiative

6. Effective communication

6.3) Are effective communicators, highly skilled in new literacies, able to justify and interpret professional decisions to specialist and non-specialist audiences

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: 30%
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:
Criteria Weight (%) SLOs CILOs
a. Homework questions: Correctness of mathematics; and clarity, accuracy and cohesiveness of written communication, including the use of suitable calculations, diagrams, and other modes of expression as appropriate. 50 e 1.2
b. Teaching: Appropriateness of strategies to promote relational understanding of mathematical concepts. 20 b 1.3
c. Teaching: Strength of justification of strategies to engage learners 20 d 1.1
d. Self-evaluation: Depth of reflection on the presentation. 10 f 1.3
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: 30%
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:
Criteria Weight (%) SLOs CILOs
a. Correctness and appropriateness of references to NSW 7-12 mathematics syllabus documents. 5 a 1.2
b. Depth of analysis and interpretation of the teaching strategies, with APA referencing for scholarly literature that is used to justify pedagogical choices. 20 b 1.3
c. Strength of justification of strategies to engage learners, including appropriate and judicious use of teaching resources and ICT. 20 c 1.1
d. Appropriateness of strategies to promote relational understanding of mathematical concepts. 35 e 1.2
e. Clarity, accuracy, conciseness and cohesiveness of lesson plan, and appropriateness and reasonableness of language in “lesson play”. 20 d 1.3
SLOs: subject learning objectives
CILOs: course intended learning outcomes

Assessment task 3: Examination

Objective(s):

b and e

Weight: 40%
Length:

2.5 hours

Criteria linkages:
Criteria Weight (%) SLOs CILOs
a. Effectiveness of explanation of mathematical concepts, substance and structure of the content, and teaching strategies. 50 e 1.2
b. Depth of knowledge of how students learn and the implications for teaching. 50 b 1.1
SLOs: subject learning objectives
CILOs: course intended learning outcomes

Minimum requirements

In order to pass the subject, students must:

  1. 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.

  1. 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.

  1. 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.