Unit description and aim
At a time of rapid ongoing change as a result of globalisation, internationalisation and the continuing development of information communication technologies, the ability of educators and allied professionals to empower young people to develop substantive understanding of mathematics as a language to use in solving problems, making connections and communicating ideas in real life is of critical importance. In this unit, within the Mathematics specialisation of the Graduate Certificate in Education and the Master of Education, students will develop mathematical content and pedagogical knowledge for the teaching of geometry, measurement, and trigonometry in the middle years of schooling (Years 5-9). This unit reflects current mathematical pedagogies, such as inquiry-based learning, with a particular emphasis on investigation. Approaches include the effective use of digital technologies and manipulatives. Forms of argumentation and proof are highlighted. Deductive and inductive reasoning are used to solve problems and carry out investigations based upon geometry and measurement. Therefore, the aim of this unit is equip students with advanced knowledge, integrated understanding and expert skills in mathematical content and pedagogical knowledge for the teaching of geometry and measurement in the middle years of schooling.
On successful completion of this unit, students should be able to:
LO1 - Appraise the historical and cultural development of geometry and measurement and their contribution to society (GA4, GA8; APST 2.4)
LO2 - Apply theories and research informing children’s mathematical learning and children’s development of mathematical concepts and processes in Measurement and Geometry as required by Australian Curriculum: Mathematics (ACARA) and other relevant curriculum documents for the middle years (GA4, GA5, GA8, GA9, GA10; APST 1.2, 2.1, 2.2, 2.5)
LO3 - Explain geometry including Euclidean geometry as a logical system (GA4, APST 2.1)
LO4 - Use technologies and resources that will enhance understanding of geometry, trigonometry, and measurement (GA5, GA10; APST 1.2, 2.1,)
LO5 - Articulate the developmental sequence for teaching the measurement of mass, time, capacity, length, perimeter, area, surface area and volume (GA5, GA8; APST 1.2, 2.5, 3.3)
LO6 - Examine dynamic geometric systems and an ability to discuss the impact of technology (e.g., GeoGebra) on mathematics learning in geometry as well as pose challenging problems and apply geometry, trigonometry, and measurement to solve mathematical and real-world problems) (GA4, GA5, GA10; APST 2.1, 2.5, 2.6, 3.3)
LO7 - Analyse student difficulties and misconceptions and errors in learning geometry and measurement concepts in the middle years (GA4, GA5, GA8; APST 1.2, 5.1)
GA4 - think critically and reflectively
GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession
GA8 - locate, organise, analyse, synthesise and evaluate information
GA9 - demonstrate effective communication in oral and written English language and visual media
GA10 - utilise information and communication and other relevant technologies effectively.
AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS
On successful completion of this unit, students should have gained evidence towards the following standards:
1.2 Understand how students learn (Highly Accomplished)
2.1 Content and teaching strategies of the teaching area (Highly Accomplished)
2.4 Understand and respect Aboriginal and Torres Strait Islander people to promote reconciliation between Indigenous and non-Indigenous (Highly Accomplished)
2.5 Literacy and numeracy strategies (Highly Accomplished)
2.6 Information and communication technology (ICT) (Highly Accomplished)
3.3 Use teaching strategies (Highly Accomplished)
5.1 Assess student learning (Highly Accomplished)
Topics covered will give consideration to mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) and associated teaching methods, and include:
- Historical and cultural development of mathematics within geometry and measurement
- Euclidean geometry, basic premises, theorems and deductive proof
- Properties and construction of families of 2D figures and 3D solids including the Platonic solids
- Transformation geometry to include rotation, reflection and translation of 2D figures and 3D solids
- Mensuration to include perimeter, area, volume, and angle
- Pedagogical aspects of teaching and learning geometry, trigonometry and measurement through inquiry-based learning including problem posing, investigative approaches, dynamic geometry systems and manipulatives
- Diagnosing and remediating common student misconceptions and difficulties in geometry and measurement.
Learning and teaching strategy and rationale
This unit is offered in multi-mode Engagement for learning is the key driver in the delivery of this curriculum, therefore an active learning approach is utilised to support students in their exploration and demonstration of achievement of the unit’s identified learning outcomes. A range of strategies will be used to support active learning and may include: lectures, tutorials, workshops and seminars; synchronous and/or asynchronous digital engagement in reading/library tasks and presentations, learning activities, discussion forums and consultation as mediated through the LEO unit site. Other modes of delivery may include webinars and presentations.
This is a 10-credit point unit and has been designed to ensure that the time needed to complete the required volume of learning to the requisite standard is approximately 150 hours in total across the semester. To achieve a passing standard in this unit, students will find it helpful to engage in the full range of learning activities and assessments utilised in this unit, as described in the learning and teaching strategy and the assessment strategy. The learning and teaching and assessment strategies include a range of approaches to support your learning such as reading, reflection, discussion, webinars, podcasts, video, workshops, and assignments etc.
Assessment strategy and rationale
In order to successfully complete this unit, postgraduate students need to complete and submit three graded assessment tasks. The assessment strategy used allows students to demonstrate their knowledge and skill related to geometry and measurement. The first task is a mathematic investigation; the second is a clinical interview related to misconceptions in measure or geometry; the third task focuses on historical and cultural development of geometry.
Overview of assessments
|Brief Description of Kind and Purpose of Assessment Tasks||Weighting||Learning Outcomes||Graduate Attributes|
Assessment Task 1
Extended mathematical investigations (e.g. angle sum of triangles on curved surfaces) with reflection on impact of task on future teaching of the associated content
Assessment Task 2
Conduct a clinical student interview highlighting common misconceptions in measurement or geometry and critique your findings against the research literature
Assessment Task 3
An assignment highlighting the historical and cultural development of geometry and/or measurement and focusing on problem posing, investigation, and problem solution (e.g., students pose and solve two problems highlighting a cultural use of mathematics and chose and solve two historical problems (one each from measurement, geometry / trigonometry). One task should be an investigative task. Use the four tasks as a basis for a unit, to be shared with colleagues, highlighting the historical and cultural development of mathematics using teaching strategies to develop and implement engaging learning.
Representative texts and references
Duatepe-Paksu, A., Lymen, E., & Pakmak, G.S. (2012). How well elementary teachers identify parallelogram? Journal of Educational Studies, 38(4), 415-418.
Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior, 31(1), 60-72.
Fujita, T., Kondo, Y., Kumakura, H., & Kunimune, S. (2017). Students’ geometric thinking with cube representations: Assessment framework and empirical evidence. Journal of Mathematical Behavior, 46, 96-111.
Miller, S.M. (2018 online). An analysis of the form and content of quadrilateral definitions composed by novice pre-service teachers. Journal of Mathematical Behavior, 31.
Stillman, G. (2013). Problem finding and problem posing for mathematical modeling. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modeling: From theory to practice. Series on mathematics education Vol. 8. Singapore: World Scientific.