028241 Mathematics Education 3
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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 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
This subject examines the construction of, and builds students' understandings in, sound methodological principles for the development of concepts in statistics, probability, decimals, fractions, percentage, proportion, patterns, algebra and problem solving. Students are introduced to ways of teaching and learning these concepts. 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. | Interpret and apply understanding of the content of relevant NSW Mathematics curriculum K-6 and initiatives in planning for teaching. |
|---|---|
| b. | Apply theories about primary aged student’s development of mathematical concepts and proficiencies to create powerful learning experiences for students studying the NSW Mathematics Curriculum K-6. |
| c. | Evaluate and plan for effective use of a range of learning activities, teaching approaches and resources including new technologies, to enable students to learn mathematics appropriate to their needs. |
| d. | Use language, symbols, resources including ICT as tools to design learning sequences and lesson activities to support student’s mathematical learning as required by the NSW Curriculum K-6. |
| e. | Plan Units and Lessons appropriately for students at varying stages of mathematical and statistical development. |
| f. | Design and implement an understanding of formal assessment procedures suitable in mathematics education, including Best Start, SENA 1 and SENA 2, NAPLAN, Building Block for Numeracy. |
| g. | Communicate mathematical ideas using appropriate mathematical terms and clear and explicit language. |
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)
- 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)
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 Canvas 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 examines two main areas:
1. Exposure to and knowledge about mathematics and the mathematics discipline, including:
- concepts and processes in statistics and probability,
- concept and processes in patterns, algebra and problem solving;
- rational number concepts, including application of percentage, ratio and proportions, basic operations for common and decimal fractions, and the relationship amongst them; and their applications;
2. Exposure to the NSW K-6 Mathematics syllabus, the new Australian Curriculum and to relevant pedagogies, including:
- approaches used in teaching measurement concepts, including questioning techniques to support student learning, listening to students and engaging them in discussion;
- assessment in the primary school classroom of understanding of these concepts;
- theories of learning in mathematics education, including co-operative learning and working mathematically; use of computer technology to investigate these topics of;
- an introduction to the teaching of mathematics using inquiry techniques, the calculator and appropriate language and mathematical terms.
Assessment
Assessment task 1: What is the Problem?
| Objective(s): | a, b, c, d, e, f and g | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||||||
| Length: | 2000 words equivalent | ||||||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Mathematics video for classroom use
| Objective(s): | a, b, c, d, e, f and g | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 30% | ||||||||||||||||
| Length: | 1200 words equivalent per student (4 minutes) | ||||||||||||||||
| 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: | 30% | ||||||||||||||||
| 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 (Approaches to mathematiocs teaching and learning)
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 (Problem Solving)
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 of textbook (Algebra and algebraic thinking)
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.
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 5
Required text - Chapter 6 of textbook (Numeration and computation for fraction ideas)
Recommended text
Griffin, L. B. (2016). Tracking decimal misconceptions: Strategic instructional choices. Teaching Children Mathematics, 22(8), 488-494.
Lai, M. Y., & Murray, S. (2015). Hong Kong grade 6 students’ performance and mathematical reasoning in decimals tasks: Procedurally based or conceptually based? International Journal of Science and Mathematics Education, 13(1), 123-149.
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 2015(38), 201-221.
Roche (2006). Longer is larger: Or is it? Australian Primary Mathematics Classroom, 10(3), 11-16.
Wright, V., & Tjorpatzis, J. (2015). What's the point?: A unit of work on decimals. Australian Primary Mathematics Classroom, 20(1), 30-34.
Week 6
Required text - Chapter 6 of textbook (Numeration and computation for fraction ideas)
Recommended text
Ercole, L. K., Frantz, M., & Ashline, G (2011). Multiple ways to solve proportions. Mathematics Teaching in the Middle School, 16(8), 482-490.
Parish, L. (2010). Facilitating the development of proportional reasoning through teaching ratio. In L. Sparrow, B. Kissane, & C. Hurst (Eds.) (2010), Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, pp. 469-476). Fremantle, WA: MERGA.
Holbrook, E. L. (2010). Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics: Grades 6-8. Reston, National Council of Teachers of Mathematics, 16 p.254-254.
Singh, P. (2000). Understanding the concept of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 43(3), 271-292.
Week 7
Required text - Chapter 10 of textbook (Statistics and probability)
Recommended text
Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305-225.
Marshall, L., & Swan, P. (2006). Using M & Ms to develop statistical literacy. Australian Primary Mathematics Classroom, 11(1), 15-24.
Hourigan, M., & Leavy, A. (2016). Practical Problems: Using Literature to Teach Statistics. Teaching Children Mathematics, 22(5), 282-291.
Persezzini, D., & Bassett, J. (1996). Assessing students through data exploration tasks. Teaching Children Mathematics, 2(6), 366-371.
Week 8
Required text - Chapter 10 of textbook (Statistics and probability)
Recommended text
Barnes, M. (1998). Misconceptions about probability. Australian Mathematics Teacher, 54(1), 17-20.
Bryant, P., & Nunes, T. (2012). Children's Understanding of Probability: A Literature Review (full Report). Nuffield Foundation. (Accessible via Google Scholar)
Edwards, T. G., & Hensien, S. M. (2000). Using probability experiments to foster discourse. Teaching Children Mathematics, 6(8), 524-529.
Jones, G. A., & Thornton, C. A. (2005). An overview of research into the teaching and learning of probability. In Exploring Probability in School (pp. 65-92). Springer US.
Week 9
Required text - N/A
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.