Unit Outline

Each of EMT625 and EMT627 is the second of a pair of units that present the theory, methods and practice of teaching high school mathematics and numeracy, with EMT625 focussing on the 7-12 curriculum and EMT627 focussing on Grades 7-9. These units generally will be taken after completing the appropriate pre-requisite unit EMT525 Teaching the Grade 7-12 Mathematics Curriculum or EMT527 Teaching the Grade 7-9 Mathematics Curriculum. 

EMT625 and EMT627 focus on the learning of mathematics in secondary school classrooms, particularly Years 7 to 12 for EMT625, and Years 7 to 9 for EMT627, and will build pre-service teachers’ pedagogical content knowledge for teaching mathematics in a productive way. This unit develops an appreciation of how students in the secondary years form mathematical concepts, and how teaching can foster effective learning, with a particular focus on the “proficiencies” in the Australian Curriculum: Mathematics. It will consider issues associated with developing mathematical thinking, which includes conceptual/relational and procedural/instrumental understanding. The units will investigate ways to incorporate reasoning and problem-solving in the mathematics classroom, and how to foster higher-order thinking from students. The use of technology in relation to issues of understanding, reasoning, and problem solving is considered. These underpinning concepts will inform consideration of (i) the design and evaluation of assessment approaches at the junior and senior secondary levels and (ii) the design of appropriate sequences of lessons for units of work.

The broad aims for this unit are: 
1. To increase knowledge of how to address the mathematics proficiency strands in the Australian Curriculum, especially understanding, reasoning, and problem solving;  
2. To develop capacity and competence to identify and deliver mathematics teaching and learning experiences that develop higher order thinking and conceptual understanding; 
3. To acquire knowledge and develop skills relating to designing and evaluating assessment tasks in mathematics curriculum for Year 7 to Year 12 students; and 
4. To understand how research in mathematics education can inform practice. 
Note: EMT625 and EMT627 have similar content but there will be some distinctions in the focus of the assessment criteria.

Intended Learning Outcomes

As per the Assessment and Results Policy 1.3, your results will reflect your achievement against specified learning outcomes.

On completion of this unit, you will be able to:


1	Explain what it means to teach for different kinds of understanding and foster higher order thinking in students, and use appropriate strategies to develop these when devising teaching and learning experiences
2	Describe and use current curriculum content and contemporary teaching practices in high school mathematics education, especially in relation to reasoning and problem solving
3	Demonstrate the ability to plan, develop, and analyse mathematical assessment experiences that incorporate appropriate assessment principles
4	Assess and provide feedback on student work, and plan for further learning experiences
5	Use contemporary research in mathematics education to inform teaching practice

Requisites


REQUISITE TYPE	REQUISITES
Pre-requisite	EMT527

Alterations as a result of student feedback

How will I be Assessed?

For more detailed assessment information please see MyLO.

Assessment schedule


ASSESSMENT TASK #	ASSESSMENT TASK NAME	DATE DUE	WEIGHT	LINKS TO INTENDED LEARNING OUTCOMES
Assessment Task 1:	AT1 Evaluating and Developing Assessment	Week 5	40 %	LO3, LO4, LO5
Assessment Task 2:	AT2 Designing a Sequence of Mathematics Lessons	Refer to Assessment Description	60 %	LO1, LO2, LO5

Assessment details

Assessment Task 1: AT1 Evaluating and Developing Assessment

Task Description:

For this assessment task, you will need to obtain a copy of a mathematics assessment instrument (artefact) being used in a school. This might be an end-of-unit test, an open-ended task, a project, a set of practice exam questions, etc. The main requirement is that it is being used to assess students on a particular topic (not the whole of a course), and is a "substantial" instrument (not a quick quiz, for example). For this assignment you will need to do the following:
1. Conduct an analysis of the assessment artefact, in terms of what kind of assessment it involves, what understanding is assessed, its diagnostic capacity, any strengths or weaknesses, its level of demand, its usefulness for differentiated assessment, etc. You should also analyse how the assessment artefact allows students to engage in problem solving and reasoning.
2. Produce a set of exemplary/model solutions for the assessment artefact.
3. Prepare four additional tasks that could be added to the artefact that address the same content but add value to the artefact as an assessment instrument. At least one of these tasks must clearly allow students to use problem solving and reasoning skills, rather than being routine.
4. Conduct an analysis of your four additional tasks, in terms of what kind of assessment they involve, what understanding is assessed, their diagnostic capacity, any strengths or weaknesses, their level of demand, their usefulness for differentiated assessment etc. This analysis should also discuss how the tasks allow students to engage in problem solving and reasoning.
5. Produce a set of exemplary/model solutions for the four additional tasks.
6. Develop a marking scheme/rubric for the the four additional tasks. Make sure criteria are clearly identified. Justify your choices.
7. Conduct an analysis of supplied student responses to a separate task (the task and responses will be provided on MyLO, together with additional instructions).
Where applicable, please ensure that ideas are referenced (e.g., if ideas for the alternative task came from the internet or if you refer to any of the literature we discussed in the unit).

Your choice of assessment for parts 1-6 should be appropriate for a content area determined by your unit enrolment:
If you are enrolled in EMT625 you should consider content from Years 9-10 of the Australian Curriculum: Mathematics, or from a suitable Year 11 or 12 mathematics unit.
If you are enrolled in EMT627 you should consider content from Years 7-9 of the Australian Curriculum: Mathematics.

Details of exact requirements (including word counts and criteria) will be provided on MyLO.

The final product could be uploaded to, or linked to from, your portfolio.

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 1.2, 1.5, 2.3, 3.1, 5.1, 5.2, 5.4, 5.5

Task Length:

1600 words (nominal) (because this assignment includes worked solutions and an assessment artefact, it is difficult to nominate a definitive word count; guidance will be provided on MyLO)

Due Date:

Week 5

Weight:

40 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Analysis of the original assessment artefact and the quality of the solutions.	LO3, LO5
2	Appropriateness of the design and analysis of the additional assessment tasks.	LO3, LO4, LO5
3	Appropriateness of the marking scheme/rubric for the additional assessment tasks.	LO3, LO5
4	Quality of feedback and appropriateness of teaching approaches in response to students’ work.	LO4

Assessment Task 2: AT2 Designing a Sequence of Mathematics Lessons

Task Description:

This assessment task involves preparing a sequence of lessons for a unit of work on a mathematical topic of your choice for one of the grade levels relevant to EMT625 (Grades 9-12) or EMT627 (Grades 7-9). Your unit of work should comprise 5 to 8 lessons. You will submit a written component for this assessment and will participate in an interview with your unit coordinator about the lesson sequence, as described below.

Written component (30%):
• Lesson sequence: Clearly identify the grade level, and overarching objectives for the sequence. Give a brief description of each lesson (1-1.5 pages per lesson), clearly indicating, for each lesson, (a) the lesson objectives, (b) the focus, structure and teaching approaches for the major components of the lesson, (c) how technology will be used, and (d) at least two examples of typical tasks/skills that students will be able to do following the lesson. The sequence must incorporate tasks that become increasingly challenging and incorporate spacing and retrieval practice; and you must show a complete set of student tasks for one of the lessons. At least one lesson must have a substantial problem-solving focus (or indicate clearly—on a separate page—how problem solving will be addressed across the sequence). At least one lesson must have a significant component that addresses one of the mathematical processes (computational thinking, mathematical modelling, statistical investigation, or probability experiments and simulations).
• Research considerations: Write 300 words that considers at least two key research articles about students’ learning of the topic being covered in the unit of work, and indicate how you have taken this knowledge into account in your planning.

Interview component (30%): You will have an interview with the unit coordinator on the following aspects of your plan:
• Focus of the unit of work: What are you expecting students to learn as a result of this unit of work? What areas do you think are going to be difficult/require the most attention? What learning activity in the unit plan is going to be especially critical for student learning and why? How does this unit connect with other areas of mathematics, and other areas of the curriculum? Why is it important for students to learn this material?
• Problem-solving, reasoning, and understanding: Discuss how problem solving and reasoning feature in your sequence. Discuss which aspects of your sequence develop instrumental and relational understanding.
• Start a lesson: Demonstrate how you would conduct the start of one of the later lessons in the sequence, which includes a review of the previous lesson as well as a launch into the present lesson.
• Model how to do one of the typical tasks in your plan and discuss likely student difficulties with the task.
• Technology use: What are the affordances and limitations of the technology you have used in the unit plan? Why are you using the technology and how? What will students need to know to make effective use of the technology?
• Mathematical processes: Discuss when and how your lesson sequence addresses at least one of computational thinking, mathematical modelling, statistical investigation, or probability experiments and simulations.

Written component due: Week 10
Interview: Week 11 or Week 12

Task Length:

2400 words total (1600 words for the submitted sequence and 800 words for the interview)

Due Date:

Refer to Assessment Description

Weight:

60 %

How your final result is determined

To pass this unit, you need to demonstrate your attainment of each of the Intended Learning Outcomes, achieve a final unit grade of 50% or greater, and pass any hurdle tasks.

Academic progress review

The results for this unit may be included in a review of your academic progress. For information about progress reviews and what they mean for all students, see Academic Progress Review in the Student Portal.

Submission of assignments

Where practicable, assignments should be submitted to an assignment submission folder in MYLO. You must submit assignments by the due date or receive a penalty (unless an extension of time has been approved by the Unit Coordinator). Students submitting any assignment in hard copy, or because of a practicum finalisation, must attach a student cover sheet and signed declaration for the submission to be accepted for marking.

Academic integrity

Academic integrity is about acting responsibly, honestly, ethically, and collegially when using, producing, and communicating information with other students and staff members.

In written work, you must correctly reference the work of others to maintain academic integrity. To find out the referencing style for this unit, see the assessment information in the MyLO site, or contact your teaching staff. For more detail about Academic Integrity, see Important Guidelines & Support.

Requests for extensions

If you are unable to submit an assessment task by the due date, you should apply for an extension.

A request for an extension should first be discussed with your Unit Coordinator or teaching support team where possible. A request for an extension must be submitted by the assessment due date, except where you can provide evidence it was not possible to do so. Typically, an application for an extension will be supported by documentary evidence: however, where it is not possible for you to provide evidence please contact your Unit Coordinator.

The Unit Coordinator must notify you of the outcome of an extension request within 3 working days of receiving the request.

Late penalties

Assignments submitted after the deadline will receive a late penalty of 5% of the original available mark for each calendar day (or part day) that the assignment is late. Late submissions will not be accepted more than 10 calendar days after the due date, or after assignments have been returned to other students on a scheduled date, whichever occurs first. Further information on Late Penalties can be found on the Assessments and Results Procedure.

Required Resources

Required reading materials

You will need to be able to access the mathematics curriculum area of the Australian Curriculum, and you will need Improving learning in mathematics: Challenges and strategies for Week 3. The other resources have informed the preparation of this unit and will be beneficial to you, but are not essential.

Australian Curriculum, Assessment and Reporting Authority (ACARA). (2022). The Australian Curriculum. Sydney, NSW: Author. https://v9.australiancurriculum.edu.au/

Boaler, J. (2010). The elephant in the classroom: Helping children learn and love mathematics. London: Souvenir Press.

Goos, M., Stillman, G., & Vale, C. (2017, 2nd Edition). Teaching secondary school mathematics: Research and practice for the 21st century. Crows Nest, NSW: Allen & Unwin. [Note the 2007 first edition is suitable if you already have a copy].

Swan, M. (2005). Improving learning in mathematics: Challenges and strategies. London: Department for Education and Skills Standards Unit. Freely downloadable from https://www.stem.org.uk/elibrary/resource/26057