University of Technology Sydney

028240 Mathematics Education 2

Warning: The information on this page is indicative. The subject outline for a particular session, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.

Subject handbook information prior to 2024 is available in the Archives.

UTS: Education: Initial Teacher Education
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:
Criteria Weight (%) SLOs CILOs
Accuracy of the mathematical concepts involved in fraction misconceptions selected 20 a, c 1.2
Clarity of discussion of each misconception reflecting an understanding of fraction concepts and teaching knowledge of the literature 25 b, d 2.1
Quality of the Unit Plan 30 b, c 1.2
Appropriateness of activities for supporting the learning in order to rectify the chosen misconception 20 b, d 1.1
Cohesiveness of writing and accuracy of referencing 5 f 6.2
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:
Criteria Weight (%) SLOs CILOs
Accuracy and cohesiveness of discussion of the mathematical concepts involved in the given students' work 20 a, c 1.2
Clarity of discussion of each misconception(s) reflecting an understanding of the concepts and teaching knowledge of the literature 20 a, c 2.1
Appropriateness of activities for developing understanding of geometry 35 b, c 2.1
Clarity of teaching 20 a, c, f 1.1
Accuracy and cohesiveness of written presentation 5 f 6.2
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:
Criteria Weight (%) SLOs CILOs
Accuracy of mathematical concepts studied in the subject 40 c 1.2
Clarity in description of how to work mathematically 30 a 1.3
Appropriateness of pedagogical approaches for mathematics teaching 30 b, d 1.1
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.