028241 Mathematics Education 3
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Subject handbook information prior to 2021 is available in the Archives.
Credit points: 6 cp
Result type: Grade, no marks
Requisite(s): 028239 Mathematics Education 1 AND 028240 Mathematics Education 2
These requisites may not apply to students in certain courses.
There are course requisites for this subject. See access conditions.
Anti-requisite(s): 012210 Mathematics Teaching and Learning 1
Description
The subject allows students to further develop their philosophy of teaching and learning mathematics. It examines the construction of, and builds students' understandings in, sound methodological principles for the development of concepts in introductory algebra, geometry and the number plane, and problem solving, including assessment in mathematics. The subject also identifies and analyses some of the issues in teaching students whose first language is not English, and develops an awareness of their implications for student learning. Students are encouraged to reflect on their own learning about, and teaching of, the NSW K–6 Mathematics syllabus.
Subject learning objectives (SLOs)
| a). | Describe sound methodological principles for the teaching and learning of concepts in introductory algebra, geometry and the number plane, and problem solving; (GTS 2.1, 3.2, 3.3, 4.1); |
|---|---|
| b). | Analyse issues in teaching mathematics to students whose first language is not English; (GTS 1.3, 1.4, 1.5); |
| c). | Evaluate learning experiences in geometry, patterns and algebra, the number plane and problem solving planned and implemented by the student; (GTS 2.1, 3.3, 4.1); |
| d). | Develop a variety of strategies for assessment and evaluation appropriate to the mathematical topics under consideration; (GTS 2.3, 5.1, 5.2, 5.3); |
| e). | Identify and analyse some of the 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). |
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)
3. International and Intercultural Engagement
3.1 Respond critically to national and global changes that affect learners, learning and the creation of a well-informed society (GTS 3)
6. Effective Communication
6.1 Communicate effectively using diverse modes and technologies (GTS 2, 3, 4)
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 that will promote learning in the classroom, and to strengthen their own mathematical concepts. Issues in mathematics education will be treated through student reading and reports. Students are encouraged to keep a journal in which they record reflections on their evolving beliefs about the teaching and learning of mathematics, as well as on the development of their own mathematical skills and understandings. An emphasis will be placed on collaborative learning, as students engage in workshop activities in groups, and contribute to whole class discussion. Student learning will also be supported by UTS Online which allows students to access subject information electronically.
The teaching/learning strategies employed in this subject will include lecturer input, structured discussion, workshop activities, individual research, lesson presentation by students, evaluation by students of presentations, development of lessons with revision of this in the light of practicum experiences, and assignments which critically examine and apply current thinking in mathematics teaching and learning.
In Week 2, an early formative test will be held to enable the lecturer to give feedback in Week 3 with regard to students’ current mathematical knowledge. This formative test is not an assessment task.
Content (topics)
This subject addresses the following main areas, with particular emphasis on patterns and algebra, geometry, the number plane and problem solving:
1) Exposure to and knowledge of central concepts of mathematics and the discipline of mathematics, including:
- informal and formal development of introductory algebraic concepts through the study of patterns and concrete representations, as well as equations and their application to problem solving;
- language and processes of geometry, including position, shape, classification, modelling, plane and space geometry, symmetry, tessellations, and the van Hiele levels;
- number plane in four quadrants. (PA 2.4, 4.1, 4.6, 4.10);
2) Exposure to and knowledge about mathematics pedagogies, including:
- investigation of the use of technologies to develop concepts in the above areas;
- an introduction to the teaching of mathematics through problem solving, including use of investigation techniques, the calculator and language in problem solving;
- using working mathematically processes. (PA 2.1, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 4.1, 4.6, 4.10, 5.8);
3) Exposure to, knowledge of and experience in implementing lesson sequences with reference to the NSW K-6 Mathematics syllabus, including:
- understanding the connections between Stage 3 and Stage 4. (PA 2.4, 4.1, 4.6, 4.10).
- a variety of assessment strategies including Assessment of, for and as Learning, Moderation practices; norm referencing, standards-referencing, criterion referencing and Developing marking criteria and marking guidelines
Assessment
Assessment task 1: What is the Problem?
| Objective(s): | a), c), d), e) and f) | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||||||
| Length: | 2000 words | ||||||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Development of learning resources in geometry for a small group activity
| Objective(s): | a), b), c) and f) | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 35% | ||||||||||||||||||||||||||||
| Length: | 1,500 words | ||||||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 3: Mathematics content and teaching knowledge
| Objective(s): | a) and c) | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 25% | ||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Minimum requirements
Attendance at workshops is important in this subject because it is based on a collaborative approach which involves essential workshops and interchange of ideas with other students and the lecturer.
Students must have submitted both assignments to be able to sit the examination.
In order to pass the subject, students will need to achieve an overall grade of 50% or above, including a minimum of 50% on the final examination (Assessment task 3). Students who achieve 50% or more in the assessment tasks overall, but fail to pass the final examination, will be awarded an X grade. The final examination is a critical way of confirming students’ achievement of key Graduate Teaching Standards in the areas of content and pedagogical knowledge in the subject area they are teaching.
Required texts
Jorgensen, R., & Dole, S. (2011). Teaching Mathematics in Primary Schools (2nd edn). Sydney: Allen & Unwin.
Mathematics K–10 syllabus from the NSW Board of Studies website (download from http://syllabus.bos.nsw.edu.au/mathematics/mathematics-k10/)
Recommended texts
Week 1
Required text - Chapter 1 of the textbook
Recommended text
Clarke, D. M., Clarke, D. J., & Sullivan, P. (2012). Reasoning in the Australian Curriculum: Understanding its meaning and using the relevant language. Australian Primary Mathematics Classroom, 17(3), 28.
Ginsberg, H. P. (2009). The challenge of formative assessment in mathematics education: Children's minds, teachers' minds. Human Development, 52(2), 109-128.
Heng, M. A., & Sudarshan, A. (2013). “Bigger number means you plus!”—Teachers learning to use clinical interviews to understand students’ mathematical thinking. Educational Studies in Mathematics, 83(3), 471-485.
Suurtamm,C., Koch, M., & Arden, A. (2010). Teachers’ assessment practices in mathematics: classrooms in the context of reform. Assessment in Education: Principles, Policy & Practice, 17(4), 399-417.
Suurtamm, C. (2012). Assessment Can Support Reasoning & Sense Making. Mathematics Teacher, 106(1), 28-33.
Way (2008). Using questioning to stimulate mathematical thinking. Australian Primary Mathematics Classroom, 13(3), 22-25.
Week 2
Required text - Chapter 2 of textbook
Recommended text
Nunokawa, K. (2005). Mathematical problem solving and learning mathematics: What we expect students to obtain. The Journal of Mathematical Behavior, 24(3-4), 325-340.
Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say?. Procedia-Social and Behavioral Sciences, 8, 142-151.
Week 3
Required text - Chapters 7 and 11 of textbook
Recommended text
Brown, J. (2008). Structuring mathematical thinking in the primary years [Keynote Address]. In J. Vincent, R. Pierce, & J. Dowsey (Eds.), Connected maths, Proceedings of the 45th annual conference of the Mathematical Association of Victoria (MAV), (pp. 40-53). Melbourne: MAV.
Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teaching children mathematics, 6(4), 232.
Rivera, F., Knott, L., & Evitts, T. A. (2007). Visualizing as a mathematical way of knowing: Understanding figural generalization. The Mathematics Teacher, 101(1), 69-75.
Taylor-Cox, J. (2003). Algebra in the early years. Young Children, 58(1), 14-21.
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 4
Required text - Chapter 7 of textbook
Recommended text
Wilkie, K. J., & Clarke, D. M. (2016). Developing students’ functional thinking in algebra through different visualizations of a growing pattern’s structure. Mathematics Education Research Journal, 28(2), 223-243. (Focus on the Results and Implications)
Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teaching children mathematics, 6(4), 232.
Rivera, F., Knott, L., & Evitts, T. A. (2007). Visualizing as a mathematical way of knowing: Understanding figural generalization. The Mathematics Teacher, 101(1), 69-75.
Week 5
Required text - Chapter 7 of textbook
Recommended text
Watson, A. (2007). Key understandings in mathematical learning: Algebraic reasoning. (Accessible via Google)
van den Kieboom, L. A., & Magiera, M. T. (2012). Cultivating Algebraic Representations. Mathematics Teaching in the Middle School, 17(6), 352-357.
Week 6
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 7
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 8
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 9
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
References
Ameis, J. (2006). Mathematics on the Internet. A resource for K-12 teachers(3rd ed.). Upper Saddle River, N.J. : Merrill.
Bennett, A. B., & Nelson, L.T. (2001). Mathematics for elementary teachers: An activity approach(5th ed.). Boston: McGraw-Hill.
Billstein, R., Libeskind, S., & Lott, J. (2010). A problem solving approach to mathematics for elementary teachers (10th edn). Upper Saddle River, NJ : Pearson Addison-Wesley.
Bobis, J., Mulligan, J., & Lowrie, T. (2009). Mathematics for children: Challenging children to think mathematically (3rd ed.). Sydney: Pearson Education Australia.
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). Teaching Primary Mathematics(4th ed.). Frenchs Forest: Pearson Education Australia.
MacMillan, A. (2009). Numeracy in early childhood: Shared contexts for teaching and learning. South Melbourne, Vic.: Oxford University Press.
Reys, R.E., Lindquist, M.M., Lambdin, D., Suydam, M.N. & Smith, N.L. (2007). Helping Children Learn Mathematics(8th ed.). New York: Wiley.
Sarama, J & Clements, D. (2009). Early childhood mathematics education research: Learning trajectories for young children.New York: Routledge.
Sherman, H., Richardson, L., & Yard, G. (2005). Teaching Children Who Struggle With Mathematics: A Systematic Approach to Analysis and Correction. Upper Saddle River: Pearson Education.
Simeon, D.,Beswick, K.,Brady, K.,Clark, K., Faragher, R. (2015). Teaching Mathematics Foundations to Middle Years.Australia , Oxford University Press
Van de Walle, J. & Lovin, L. (2006). Teaching Student-Centred Mathematics Grades 3-5. Boston: Pearson.