Unit Outline
ESP125
Mathematics Pedagogical Content Knowledge Years 6 to 10
Semester 1, 2024
Thomas Hartley
Faculty of Education
College of Arts, Law and Education
CRICOS Provider Code: 00586B

Unit Coordinator
Thomas Hartley
Email: Thomas.Hartley@utas.edu.au
 

What is the Unit About?
Unit Description
In this unit, you will consider the theory, methods and practice of teaching mathematics (and teaching for numeracy) in Years 6-10. Curriculum documents will be a major focus (including the Australian Curriculum, and local, State and international curricula), alongside implementation strategies, related resources and expected learning outcomes. Significant topics include the teaching and learning of decimals, rational and irrational numbers, and integer arithmetic; proportional reasoning; early algebra learning; probability; statistics and probability; geometry; and principles of lesson planning.
Teaching and learning experiences involve participation in practical activities as well as an analysis of the issues related to mathematics education.
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.
distinguish the common mathematical ideas, skills, knowledge, and appropriate communication conventions that inform contemporary teaching of middle school and lower secondary mathematics
2.
exemplify the proficiencies, skills and content knowledge as described in the Australian curriculum mathematics
3.
design mathematical teaching experiences which provide formative and summative assessment of student learning
4.
analyse students understanding of mathematics through diagnostic and formative assessment, linked to the curriculum content descriptors and respond to identified areas of need
5.
collaborate with peers to reflect on the mathematical and pedagogical value of summative and formative assessment tasks
Alterations as a result of student feedback
Assessment Task Three has been changed, to encourage and reward discussion posts as part of the assessment, instead of additional workload (which was viewed as too high), with the student interview task removed to reduce workload.
The interview task which was a requirement of the former AT3as part of the WIL has been removed, so that students will have an opportunity to be more involved in clasroom activities. 
 
 

Teaching arrangements
ATTENDANCE MODE
TEACHING TYPE
LEARNING ACTIVITY
CONTACT HOURS
FREQUENCY
On Campus
Tutorial
Team Based Learning Activities associated with AT1, and mathematics content problems and group discussion
2
Weekly
Online
Online Class
Weekly video presentation and associated activities
4
Weekly
Online Class
Weekly Discussion Post associated with weekly activities, and contributing to AT3
2
Weekly
Attendance / engagement expectations
If your unit is offered On campus, it is expected that you will attend all on-campus and onsite learning activities. This is to support your own learning and the development of a learning community within the unit. If you are unable to attend regularly, please discuss the situation with your course coordinator and/or our UConnect support team.

If your unit is offered Online, it is expected you will engage in all those activities as indicated in the Unit Outline, including any self-directed learning.

If you miss a learning activity for a legitimate reason (e.g., illness, carer responsibilities) teaching staff will attempt to provide alternative activities (e.g., make up readings) where it is possible.
 
Particpation is expected in several ways. Each week (except for when the students are in sacools on WIL), there is a two-hour face-to-face tutorial on the Launceston campus. This tutorial will involve students in mathematical tasks, group work, and for three of the tutorials, completing Team Based Learning (TBL) activities associated with AT1 (a total of 15% of assessment).
In addition, each week there will be activities and content posted on MyLO, with acompanying videos from the Unit Coordinator, and other mathematics teaching staff. The expected engagement with these activities is between six and eight hours per week. (12 weeks). Included in each weeks MyLO activities is the expectation to post a refelction on at least one of the activities on the discussion boards, and respond to other students' posts,  which is assessed and contributes 24% of AT3 (2% each week). (Note: in 2024, there will only be 11 weeks assessed, because in week 12, students will be on PE).
 
 

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:
Team-Based Learning Quiz
Week 3
24 %
LO1, LO2, LO3, LO5
Assessment Task 2:
PeerWise Question Design and Analysis
Week 7
36 %
LO1, LO2, LO3, LO4, LO5
Assessment Task 3:
Discussion Posts and Reflection
Week 11
40 %
LO1, LO2, LO3, LO4
 
Assessment details
    
Assessment Task 1: Team-Based Learning Quiz
Task Description:
This assessment task will involve the use of Team-Based Learning (TBL) strategies, for three TBL activities spread evenly through the semester, taking place in weeks 1-3; weeks 4-6 and weeks 7-9, as per the Unit Schedule. You will be assigned to a group of 5-7 students. The three activities will each comprise 3 separate components, based around a reading which will be assigned on MyLO in the AT1 folder. You will be required to read this reading carefully and critically before each activity. The components of each activity will be:

An online comprehension quiz (on MyLO), of 10 multiple-choice questions based on the reading. These quizzes are known as an iRAT (Individual Readiness Assurance Test), and will be completed firstly by you individually (3% each quiz, x 3 quizzes = 9% total);

In your teams, you will revisit the questions from the iRAT, and see if collectively you can agree on correct responses, and improve your score from the iRAT. This will be conducted through the discussion posts and Collaborate online tutorial sessions [or Skype or Zoom or similar], and are known as a TRAT (Team Readiness Assurance Test). Each member of the team will gain the same mark here (2% per TRAT, x 3 quizzes = 6% total). These maybe conducted in the face-to-face tutorials if this is convenient for all students, as may the next Team Task.

Then, in your teams you will carry out a task (e.g. designing a learning activity; drawing a concept map), that reflects on the reading or the unit content from the respective weeks for the TBL activity. This will either be submitted as an answer in your team’s discussion posts, or through the MyLO submission process. Tasks will be a mixture of team responses (everyone in the team receives the same mark) and individual responses based on the teams collective work (You receive an individual mark). This will be described in the activity’s description on the AT1 MyLO site (3% each task, x 3 task = 9% total)
(Please note: the iRAT quiz will be automatically graded, the TRAT and Task will be marked by the lecturer).

Refer to the unit schedule for due dates.

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 1.1, 1.2, 2.1

Date for first AT1 Quiz 1, other dates :
TRAT 1: 4-6pm, Tues 12/3 (tut)
Quiz 2: 3pm, Mon 8/4
TRAT 2: 4-6pm, Tues 9/3 (tut)
Quiz 3: 3pm, Mon 22/4
TRAT 3: 4-6pm, Tues 23/4 (tut)
Task Length:
3 Team-Based Learning (TBL) Activities in weeks 2-11
Due Date:
Week 3 (11/Mar/2024)
Weight:
24 %
 
CRITERION #
CRITERION
MEASURES INTENDED
LEARNING OUTCOME(S)
1
Critiques commonly held theories that influence mathematics educational practice
LO1
2
Interprets meanings from written text
LO1
3
Critically reflects on literature findings, and extrapolates this to different learning contexts and personal perspectives
LO2
4
Uses literature findings to inform practice in the design of effective questions and learning tasks
LO3
5
Engages effectively with peers
LO5
 
Assessment Task 2: PeerWise Question Design and Analysis
Task Description:
This task will make use of the online learning tool PeerWise (see https://peerwise.cs.auckland.ac.nz/). Login details will be provided on MyLO. You will use PeerWise to create and explain your understanding of course -related formative assessment questions, and to answer and discuss questions created by your peers.

Part One (18%)
In part one, you will research and design two multiple choice questions that would be useful for formative assessment of student learning, on a content area of your own selection, and submit these on PeerWise. The questions will be at the Year 6-10 level (your choice), chosen from any area of the mathematical content considered in this unit. For each question:
Please provide one best-answer and three distractor choices (i.e. a standard 4-option multiple choice question). An article explaining this process is provided in the AT2 folder on MyLO (Haynes & Crouch, 2005);
Ensure the question has a conceptual understanding element to it as discussed in Week 1 and Week 2 classes, i.e. not just a pure skills-based question.
Include a brief explanation/description in PeerWise (two to three sentences) ), with reference to the Australian Curriculum Mathematics, of the year level the question is intended for, the content and knowledge it is testing, and the context for the question, e.g. what lesson it might be used in, what it might be aiming to achieve, what decisions you made in the design of the question. This should refer to the curriculum year level and content descriptors and also consider the elaborations (maximum 300 words).

Part Two (18%)
For part two, you will try out other students’ questions. You may try as many as you wish, but you will be required to review three of these, and make an insightful comment on PeerWise about how you found the question, and how effective you feel the question would be for students’ learning. You will also be asked to reflect on others’ responses to your questions, and possibly make changes based on these or not, justifying your reasons with reference to the considerations and decisions you made in designing your question. More details about the nature of this feedback will be provided in the AT2 folder on MyLO

Note: All questions and responses are anonymous to other students and administrators. Only the Unit Coordinator can identify your work.

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 1.2, 2.1, 5.1, 5.4

Part One due (18%) Mon 15/4

Part Two Due (18%) Mon 12/4 (note this is first day of prac, so should submit before)
Task Length:
Part One: Research, design and submit two formative multiple-choice questions on PeerWise (4-6 hours): no word limit for the question itself, but questions should be consistent with formative assessment and multiple-choice guidelines discussed in class. Maximum 300 words for your description. Part Two: Try out other students’ questions and review three of these questions, making a brief comment on each, three to four sentences for each (2-4 hours, maximum 200 words each response). Critically reflect on responses to your own questions and justify any changes you may or may not make to your questions based on this feedback (2-4 hours, maximum 500 words between the two questions, may be unevenly split, e.g. 200 words for one; 300 for the other)).
Due Date:
Week 7 (15/Apr/2024)
Weight:
36 %
 

 
CRITERION #
CRITERION
MEASURES INTENDED
LEARNING OUTCOME(S)
1
Aligns questions with appropriate year levels and content descriptors from the Australian Mathematics Curriculum
LO2, LO3
2
Undertakes pedagogical analysis and design of mathematical questions, with a clear focus on mathematics and conceptual development
LO3, LO4, LO5
3
Demonstrates correct mathematical understandings
LO1, LO2, LO3, LO4, LO5
4
Critically reflects on your learning and responds to feedback
LO5
5
Engages effectively with peers
LO5
 
Assessment Task 3: Discussion Posts and Reflection
Task Description:
Weekly Discussion Posts and Reflection

Part One: Weekly Discussion Prompts

Part Two: Reflection on Discussion responses, against Unit ILOs.

Part One: 24% (2% each week)
Part Two: 16% (500 to 1000 words)

For Part One, you will be given a series of Discussion Board prompts which relate to each week’s activities (12 weeks). You will be asked to make a comment about your experiences in respect to the prompt for at least one activity each week, and also respond with a comment to at least one other students’ discussion post.

For Part Two, you will reflect on your own discussion posts over the semester, as well as those of your classmates to whom you have responded. In your reflections, you will consider how these have helped your learning in respect of the ILO’s for the unit, and your future teaching.

Your reflection should make explicit reference to the ILO’s, and draw from your own reflections.

If you use Generative AI (eg ChatGPT) in your reflection, you should include with you reflective piece any prompts you provided in generating your work, and also describe how you amended it to make sense. If you use any references for this piece of writing, you should write a brief sentence or paragraph describing why this reference is relevant or why you chose it to support your reflection


Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 1.2, 2.1, 3.2, 3.4, 5.1, 5.4

The due date is set for the end of week 11, because students will be on prac in week 12, 2024. However, a later submission can be negotiated with the UC, as long as it does not interfere with prac.
Task Length:
1800 words
Due Date:
Week 11 (17/May/2024)
Weight:
40 %
 
CRITERION #
CRITERION
MEASURES INTENDED
LEARNING OUTCOME(S)
1
Conducts a student interview and marks it accurately, with effective comments
LO2, LO4
2
Correctly classifies the interviewed students' performance based on data from the decimal comparison test: Q1 on the interview protocol
LO2, LO4
3
Correctly identifies and explains the interviewed students' misconceptions, based on interview data and written responses
LO2, LO4
4
Develops appropriate teaching and learning activity to address a student's specific learning needs showing a range of teaching strategies and targeted resources for current understanding, to correct misconceptions and facilitate further development
LO1, LO2, LO3, LO4
 
 
 

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. 
 
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.
 
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.
 
Review of results and appeals
You are entitled to ask for a review of the marking and grading of your assessment task if there is an irregularity in the marking standards or an error in the process for determining the outcome of an assessment. Details on how to request a review of a mark for an assignment are outlined in the Review and Appeal of Academic Decisions Procedure.
 
 
 

Required Resources
Required reading materials
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2022). The Australian Curriculum: Mathematics (Version 9.0). Sydney, NSW: Author. https://v9.australiancurriculum.edu.au/
Goos, M., Stillman, G., & Vale, C. (2017).
Teaching secondary school mathematics: Research and practice for the 21st century (2nd ed.). Crows Nest, NSW: Allen & Unwin. [Note the 2007 1st Edition is OK if you already have a copy].
University of Tasmania (2015). APA 7th edition.
Referencing guide. https://utas.libguides.com/referencing/APA7th
(We recommend you purchase these as additional resource texts as they provide “Horizon Knowledge’, see week one lectures, Ball et al. 2008).
  1. Especially useful for those considering teaching at Year 11 &12, with a wonderful chapter on Calculus by a UTAS lecturer Robyn Reaburn: Hine, G., Reaburn, R., Anderson, J., Galligan, L., Carmichael, C., Cavanagh, M., Ngu, B., & White, B. (2016). Teaching Secondary Mathematics. Cambridge University Press.
  2. For help with understanding students’ prior knowledge, extends to Year 8, and especially useful for those of you who may well end up teaching at lower years, e.g. Year 6. Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2015). Teaching mathematics: Foundations to middle years (2nd Revised Edition). South Melbourne, VIC: Oxford University Press.
  3. Very useful for teaching about fractions & decimals, especially for your AT3. Sullivan, P. (2021). Building Engagement in Middle Years Mathematics EBook. Oxford University Press Australia & New Zealand.
 
Recommended reading materials
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2016). National literacy and numeracy learning progressions. https://www.australiancurriculum.edu.au/resources/national-literacy-and-numeracy-learning-progressions/
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special?
Journal of Teacher Education, 59(5), 389-407. doi: 10.1177/0022487108324554
Beswick, K. (2006). The importance of mathematics teachers' beliefs.
Australian Mathematics Teacher, The, 62(4), 17.
Beswick, K. (2006). Changes in preservice teachers' attitudes and beliefs: The net impact of two mathematics education units and intervening experiences.
School Science and Mathematics, 106(1), 36-47.
Booker, G. (2011).
Building numeracy: Moving from diagnosis to intervention. Oxford University Press.
Campbell, A., Craig, T., & Collier-Reed, B. (2019) A framework for using learning theories to inform ‘growth mindset’ activities,
International Journal of Mathematical Education in Science and Technology, DOI: 10.1080/0020739X.2018.1562118
Chick, H. L. (2003). Counting on Frank and Fermi: Using Fermi questions in the classroom. In B. Clarke, A. Bishop, R. Cameron, H. Forgasz, & W. T. Seah (Eds.),
Making Mathematicians (Proceedings of the 40th annual conference of the Mathematical Association of Victoria, pp. 89-97). Melbourne, VIC: MAV.
Chick, H. L., Pham, T., & Baker, M. K. (2006). Probing teachers’ pedagogical content knowledge: Lessons from the case of the subtraction algorithm.
Identities, cultures and learning spaces, 139-146.
Chick, H. L. (2007). Teaching and learning by example. In J. Watson & K. Beswick (Eds.),
Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, pp. 3-21). Sydney: MERGA.
Chick, H., & Pierce, R. (2012). Teaching for statistical literacy: Utilising affordances in real-world data.
International Journal of Science and Mathematics Education, 10, 339 - 362. DOI: 10.1007/s10763-011-9303-2.
Forgasz, H., Leder, G. C., & Halliday, J. (2013). The make it count project: Naplan achievement evaluation. Proceedings of the
36th annual conference of the Mathematics Education Research Group of Australasia, Melbourne, Australia: http://www.merga.net.au/documents/Forgasz_et_al_MERGA36-2013.pdf
Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms.
The Journal of Mathematical Behavior, 22(1), 73-89. doi: http://dx.doi.org/10.1016/S0732-3123(03)00005-1
Lowe, I., Johnston, J., Kissane, B., & Willis, S. (1995).
Access to Algebra. Books 1,2,3,4 and two Teacher’s Guides. Carlton, Vic: Curriculum Corporation.
Marshman, M., & Porter, G. (2013). Pre-service Teachers' Pedagogical Content Knowledge: Implications for Teaching. Proceedings of the
36th annual conference of the Mathematics Education Research Group of Australasia, Melbourne, Australia: http://www.merga.net.au/documents/Marshman_et_al_MERGA36-2013.pdf
Morgan, C., Watson, A., & Tickly, C. (2004).
Teaching school subjects 11-19: Mathematics. London: Routledge Falmer.
Muir, T., & Wells, J. (2019). Are athletes getting better over time?
Australian Primary Mathematics Classroom, 24(3), 15.
Stacey, K. (2005). Travelling the road to expertise: A longitudinal study of learning. In Chick, H. L. & Vincent, J. L. (Eds.), Proceedings of the
29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 19-36). Melbourne: PME.
Stacey, K., Ball, L., Chick, H., Pearn, C., Steinle, V., Sullivan, P., & Lowe, I. (2007-9).
Mathematics Developmental Continuum P-10. http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/continuum/Pages/mathcontin.aspx
Steinle, V. (2004). Detection and Remediation of Decimal Misconceptions. In B. Tadich, S. Tobias, C. Brew, B. Beatty, & P. Sullivan (Eds.),
Towards Excellence in Mathematics (pp. 460-478). Brunswick: The Mathematical Association of Victoria.
Watson, A. (2006)
. Raising achievement in secondary mathematics. Maidenhead, UK: Open University Press.
Watson, A., & Mason, J. (2005).
Mathematics as a constructive activity: Learners generating examples. New York: Routledge.
Watson, J. M. (2006).
Statistical literacy at school. Mahwah, NJ: Lawrence Erlbaum.
 
Other required resources
Technology: Free graphical and algebraic software:
Geogebra: (a bit complex, but has great sliders etc which allow us to vary properties & see the effects): https://www.geogebra.org
Desmos (really simple to use, draws great graphs, really worth exploring): https://www.desmos.com/
See also (from discussion posts) http://www.visnos.com/demos some awesome interactives