Unit rationale, description and aim
Working in the 21st century requires high levels of mathematics, numeracy and reasoning skills, essential for participating in a globalised and technological world. Teachers play a crucial role in developing successful lifelong learners who possess the knowledge and skills for future success. Effective teachers of mathematics must possess Mathematical Knowledge for Teaching (MKT) and a positive disposition.
This unit introduces preservice teachers to subject matter knowledge a domain of MKT which involves understanding how mathematical ideas are structured, represented, and communicated across the content strands of the Australian Curriculum Mathematics and state-based syllabi. Preservice teachers will explore number concepts, the historical development of our number system and cultural aspects of mathematics, including Indigenous perspectives, and the foundations of algebraic thinking, geometry, space, measurement, data, and chance. Building mathematical proficiencies of understanding, fluency, strategic competence and reasoning which foster a positive mathematical disposition through the exploration of mathematics in the real world and through problem-solving is undertaken.
The aim of this unit is to provide a strong foundation subject matter knowledge that develops preservice teachers' deep understanding of mathematics, ability to justify solutions, select appropriate resources, and discern appropriate learning experiences which supports future pedagogical decision-making. This knowledge prepares students for subsequent units focused on curriculum, pedagogy, and assessment, where they will integrate their content knowledge with effective teaching practices.
Learning outcomes
To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.
Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.
Explore the graduate capabilities.
Apply foundational concepts of mathematics (number...
Learning Outcome 01
Apply mathematical proficiencies (understanding, f...
Learning Outcome 02
Justify problem-solving strategies and solutions u...
Learning Outcome 03
Research and explain common misconceptions and err...
Learning Outcome 04
Reflect on the importance of a positive mathematic...
Learning Outcome 05
Content
Topics will include:
- Mathematics and numeracy in the real world
- Building a positive disposition towards mathematics
- Proficiency in mathematics: understanding, fluency, reasoning and problem-solving
- Mathematical processes: thinking, reasoning, communicating, problem-solving and investigation process skills
- Researching common misconceptions in learning and understanding mathematics
- Exploring early number concepts, including number history and Indigenous understanding of number
- Place Value conventions – whole number
- Fraction concepts and constructs
- Place Value conventions – decimal fractions
- Understanding operations – arithmetic vs algebraic thinking
- Understanding operations – multiplication and division
- Geometry – 2D and geometric language
- Geometry – 3D and location
- Measurement concepts and the measuring process
- Data and statistics
- Chance and probability
Assessment strategy and rationale
The assessment tasks and their weightings are designed to allow preservice teachers to progressively demonstrate achievement against the unit learning outcomes.
The assessments involve a variety of tasks to challenge students’ learning and enable differentiation of achievement and be equitable and ethical. The Hurdle incorporates a diagnostic test which enables students to prepare for the LANTITE Numeracy test.
Assessment task 1 facilitates demonstration of problem-solving strategies, articulating mathematical thinking and reasoning through diagrams, mathematical notation and written explanations. Assessment task 2, written examination enables demonstration of mathematical knowledge and understanding expectations for primary teaching.
The assessment tasks for this unit are designed to demonstrate achievement of each learning outcome. To pass this unit, you are required to submit all assessment tasks and achieve a minimum overall passing grade of 50%.
As this unit contains practical, skill-based content, engagement with 80% of mathematics laboratory tutorials is recommended as per Section 5.9h of the ACU Assessment Procedure. For students in the online mode, there will be a nominated schedule of mathematics tutorial exercises equivalent to mathematics laboratory tutorials.
Overview of assessments
Hurdle Task: Online Numeracy Quiz Complete a for...
Hurdle Task: Online Numeracy Quiz
Complete a formative online numeracy quiz aligned to the testing framework for LaNTITE: Numeracy.
Complete/Incomplete
Assessment Task 1: Problem-solving Folio Comple...
Assessment Task 1: Problem-solving Folio
Complete six extended tasks drawn from tutorial experiences and covering the different strands of mathematics covered in the unit (number and algebra, measurement, geometry, probability and statistics). For each task, you will need to:
(1) solve the problem,
(2) justify the solution with mathematical reasoning, and
(3) reflect on personal learning and future progression.
50%
Assessment Task 2: Written Examination Demonstra...
Assessment Task 2: Written Examination
Demonstrate subject matter knowledge and mathematical proficiency across the content strands of the Australian Curriculum Mathematics.
50%
Learning and teaching strategy and rationale
Learning and teaching strategies include a mix of student-centred problem-based learning, collaborative inquiry-based learning, and challenge-based learning. Learning and teaching will take place through a combination of self-directed studies, including online content, video clips, academic readings, weekly tasks, and reflection on learning experiences, and weekly contact hours for collaboration and discussion of problem-solving approaches and strategies.
Learning and teaching strategies are designed to be flexible and promote both collaborative learning and self-regulated and guided learning:
- Self-directed content online to enhance mathematical content knowledge
- Tutorial/workshop activities to engage in learning through active collaboration, designed to encourage and develop mathematical argumentation through peer learning to develop mathematical knowledge for teaching
- Reading/webinar/podcast schedule with recommendations that involve directed reading/viewing as well as self-directed study suggestions
Representative texts and references
Recommended Text and Documents
Zager, T. J. (2017). Becoming the math teacher you wish you’d had: Ideas and strategies from vibrant classrooms. Hawker Brownlow Education.
Oxford University Press UK (2013). Oxford Student’s Mathematics Dictionary. Oxford, UK: Oxford University Press
Recommended References
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.
Beswick, K., & Goos, M. (2018). Mathematics teacher educator knowledge: What do we know, and where to from here? Journal of Mathematics Teacher Education, 21, 417-427.
Clements, D. H., & Sarama, J. (2020). Learning and teaching early math: The learning trajectories approach (3rd ed.). Routledge.
Royer, J. M. (2003). Mathematical cognition. Information Age Publishing
Suggate, J., Davis, A. & Goulding, M. (2010). Mathematical knowledge for Primary teachers. Taylor and Francis Group.
Zager, T. J. (2017). Becoming the math teacher you wish you’d had: Ideas and strategies from vibrant classrooms. Routledge.