028240 Mathematics Education 2
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particular session, location and mode of offering is the authoritative source
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Subject handbook information prior to 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade, no marks
Requisite(s): 028239 Mathematics Education 1
These requisites may not apply to students in certain courses.
There are course requisites for this subject. See access conditions.
Anti-requisite(s): 012212 Mathematics Teaching and Learning 3
Description
This subject examines the construction of, and builds students' understandings in, sound methodological principles for the development of concepts in rational number, measurement, graphing, and mental arithmetic. Students are introduced to ways of teaching and learning concepts in measurement and rational number. The study of mathematical concepts in this subject involves the modelling of participative and collaborative learning approaches. Students are encouraged to reflect on their own learning about, and teaching of, the NSW K–6 Mathematics syllabus. The link with the school-based field component of the corresponding professional experience subject enables students to apply and reflect upon mathematics teaching and learning episodes.
Subject learning objectives (SLOs)
| a. | Explain the primacy of working mathematically in the teaching and learning of mathematics; (GTS 1.3, 2.1, 2.5); |
|---|---|
| b. | Demonstrate an understanding of a variety of assessment procedures suitable in mathematics education, including Best Start, Count Me In Too, SENA 1 and SENA 2, NAPLAN and informal methods of assessment; (GTS 2.3, 5.1, 5.2, 5.3, 5.4); |
| c. | Describe the principles of teaching and learning of geometry concepts; (GTS 2.1, 2.6); |
| d. | Evaluate learning experiences in rational number, geometry, graphing and mental arithmetic planned and implemented by the student; (GTS 3.3, 4.1); |
| e. | Analyse critical issues and trends in Indigenous mathematics education; (GTS 1.4, 1.5, 2.4, 4.1); |
| f. | Communicate mathematical ideas using appropriate mathematical terms and clear and explicit language. (GTS 2.1, 2.6, 3.4, 3.5, 4.2). |
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.
- Operate professionally in a range of educational settings, with particular emphasis on their specialisation (GTS 1, 2) (1.1)
- Design and conduct effective learning activities, assess and evaluate learning outcomes and create and maintain supportive and safe learning environments (GTS 1, 2, 3, 4, 5) (1.2)
- Make judgements about their own learning and identify and organise their continuing professional development (GTS 3, 6) (1.3)
- Analyse and synthesise research and engage in inquiry (GTS 3) (2.1)
- Exhibit high-level numeracy and literacies (GTS 2) (6.2)
Contribution to the development of graduate attributes
This subject addresses the following Course Intended Learning Outcomes:
1. Professional Readiness
1.1 Operate professionally in a range of educational settings, with particular emphasis on their specialisation (GTS 1, 2)
1.2 Design and conduct effective learning activities, assess and evaluate learning outcomes and create and maintain supportive and safe learning environments (GTS 1, 2, 3, 4, 5)
1.3 Make judgements about their own learning and identify and organize their continuing professional development (GTS 3, 6)
1.4 Act as a developer of learning with colleagues and possess collaborative skills (GTS 7)
2. Critical and Creative Inquiry
2.1 Analyse and synthesise research and engage in inquiry (GTS 3)
6. Effective Communication
6.2 Exhibit high level numeracy and literacies (GTS 2)
Teaching and learning strategies
Investigative workshop activities, lectures and associated readings will allow students both to develop strategies which will promote learning in the classroom, and to strengthen their own mathematical concepts. An emphasis will be placed on collaborative learning, as students engage in workshop activities in groups, and contribute to whole class discussion. Students will investigate the classroom use of various technologies and the use of flipped learning as a teaching strategy. Students will also use UTS Online, the UTS electronic communication tool, to access content and interact electronically. The workshops provide opportunities for students to receive ongoing formative feedback from their peers as well as tutors each week, including early feedback before census date.
Content (topics)
In this subject, students focus on a range of topics relevant to the teaching of mathematics in the primary classroom. These topics include:
- The NSW Mathematics Syllabus K-6 and the Australian Curriculum;
- the metric system and measurement;
- the use of ICT in mathematics teaching and learning;
- fractions, discrete and continuous contexts, equivalent and decimal fractions;
- addition and subtraction of fractions;
- geometry, including poisition, shape, classification, symmetry, tessellations, the van Hiele levels;
- number plane in four quadrants;
- mental arithmetic concepts;
- assessment of mathematics in the primary school;
- theories of learning in mathematics education;
- inquiry gtechniques, the calculator and mathematical terms.
Assessment
Assessment task 1: Unit planning for fractions
| Objective(s): | a, b, c, d and f | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||
| Length: | 1800 words | ||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Development of learning resources for geometry
| Objective(s): | a, b, c and f | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 30% | ||||||||||||||||||||||||
| Length: | 1000 words equivalent per student | ||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 3: Mathematics content and teaching knowledge
| Objective(s): | a, b, c and d | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 30% | ||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Minimum requirements
Attendance at classes is essential because the subject takes a collaborative approach which involves an interchange of ideas with other students and the lecturer.
Students must have submitted both assignments to be able to sit the examination. An overall grade of 50% or above is required to pass the subject. However, failure to achieve a minimum of 45% on the final examination will result in a fail; this minimum must be gained in students’ demonstration of knowledge of mathematical concepts and pedagogical approaches that have been studied in the subject.
Required texts
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2015). Teaching primary mathematics. Pearson Higher Education AU.
NSW Education Standards Authority Mathematics K–10 syllabus (download from the NESA website http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/ or purchase from bookshop.
Recommended texts
Week 1
Required text - Chapter 11 of textbook
Recommended text
Sullivan, P. (2011). Dealing with differences in readiness. In P. Sullivan (2011), Teaching Mathematics: Using research-informed strategies (pp. 40-47). Melbourne, Victoria: Australian Council for Educational Research. (Accessible via Google Scholar)
Downton, A. (2015). Developing an overall school mathematics plan. Prime Number, 30(1), 6-9.
Sullivan, P., Clarke, D. J., & Clarke, D. M. (2012). Teacher decisions about planning and assessment in primary mathematics. Australian Primary Mathematics Classroom, 17(3), 20-23.
Week 2
Required text - Chapter 4 of the textbook
Recommended text
Gould, P. (2013). Australia's Next Top Fraction Model. Australian Primary Mathematics Classroom, 18(3), 5-12.
Siebert, D., & Gaskin, N. (2006). Creating, Naming, and Justifying Fractions. Teaching Children Mathematics, 12(8), 394-400.
Wright, V. (2013). In search of the prototypical fraction. Australian Primary Mathematics Classroom, 18(2), 27-33.
Week 3
Required text - Chapter 5 of the textbook
Recommended text
Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138.
Clarke, Roche & Mitchell (2008). Ten practical tips for making fractions come alive and make sense. Mathematics Teaching in the Middle School, 13(7), 372-380.
Jigyel, K., & Afamasaga-Fuata'i, K. (2007). Students' Conceptions of Models of Fractions and Equivalence. Australian Mathematics Teacher, 63(4), 17-25.
Siemon, D. (2002). Partitioning—The missing link in building fraction knowledge and confidence. Mathematics~ making waves, 411.
Week 4
Required text - Chapter 6 of textbook
Recommended text
Clarke, D. (2006). Fractions as Division: The Forgotten Notion?. Australian Primary Mathematics Classroom, 11(3), 4.
Lewis, R. M., Gibbons, L. K., Kazemi, E., & Lind, T. (2015). Unwrapping students’ ideas about fractions. Teaching Children Mathematics, 22(3),158-168.
Wyberg, T., Whitney, S. R., Cramer, K. A., Monson, D. S., & Leavitt, S. (2012). Unfolding fraction multiplication. Mathematics teaching in the Middle School, 17(5), 288-294.
Week 5
Required text - Chapter 9 of textbook
Recommended text
Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Learning and teaching geometry, K-12, 1-16.
Lehrer, R., & Curtis, C. L. (2000). Why Are Some Solids Perfect?. Teaching Children Mathematics, 6(5), 324-324.
Wright, V., & Tjorpatzis, J. (2014). What's the point?: A unit of work on decimals. Australian Primary Mathematics Classroom, 20(1), 30-34.
Week 6
Required text - Chapter 9 of textbook
Recommended text
Hourigan, M., & Leavy, A. (2015). What's a Real 2D Shape? Designing Appropriate Geometric Instruction. Australian Primary Mathematics Classroom, 20(1), 24-29.
Leavy, A., Pope, J., & Breatnach, D. (2018). From Cradle to Classroom: Exploring Opportunities to Support the Development of Shape and Space Concepts in Very Young Children. In Forging Connections in Early Mathematics Teaching and Learning (pp. 115-138). Springer, Singapore.
Renne, C. G. (2004). Is a rectangle a square? Developing mathematical vocabulary and conceptual understanding. Teaching Children Mathematics, 10, 258–263.
Week 7
Required text - Chapter 9 of textbook
Recommended text
Browning, C. A., Garza-Kling, G., & Sundling, E. H. (2007). What's your angle on angles?. Teaching Children Mathematics, 14(5), 283-287.
De Villiers, M. D. (1993). Transformations: A golden thread in school mathematics. Spectrum, 31(4), 11-18.
Fyhn, A. B. (2008). A climbing class’ reinvention of angles. Educational Studies in Mathematics, 67(1), 19-35.
Siew, N. M., & Abdullah, S. (2012). Learning Geometry in a Large-Enrollment Class: Do Tangrams Help in Developing Students’ Geometric Thinking?. Journal of Education, Society and Behavioural Science, 239-259.
Week 8
Required text - Chapter 9 of textbook
Recommended text
Alagic, M. (2003). Technology in the mathematics classroom: Conceptual orientation. Journal of Computers in Mathematics and Science Teaching, 22(4), 381-399.
Serow, P., & Callingham, R. (2011). Levels of use of interactive whiteboard technology in the primary mathematics classroom. Technology, Pedagogy and Education, 20(2), 161-173.
Van de Walle et al. (2019). Chapter 20: Geometric thinking and geometric concepts. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson
Week 9
Required text - Chapter 1 of textbook
Recommended text
Clarke, D. M., & Wilson, L. (1994). Valuing what we see. Mathematics Teacher, 86(7), 542-545
References
Anghileri, J. (2006). Teaching number sense (2nd ed.). London: Continuum.
Brown, T., & Liebling, H. (2014). The really useful maths book: a guide to interactive teaching (Revised ed.). London: Routledge.
Jacobs, H. R. (1994). Mathematics – a human endeavour. (3rd ed.). New York, NY: Freeman.
Klein, M. (2000). Teaching mathematics against the grain: investigations for primary teachers. Katoomba, NSW: Social Science Press.
Other resources
Classrooms with freestanding desks and equipped with IT facilities and internet connection.