028239 Mathematics Education 1
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.
Credit points: 6 cp
Subject level:
Undergraduate
Result type: Grade, no marksRequisite(s): 48 credit points of completed study in spk(s): C10350 Bachelor of Arts Bachelor of Education
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 012211 Mathematics Teaching and Learning 2
Note
This subject requires completion of a basic skills mastery test in order to enrol in the subject.
Description
This subject develops students' understanding of how to work mathematically in the teaching and learning of aspects of the NSW K-6 Mathematics syllabus. Good teaching practice is modelled using hands-on collaborative tasks so students learn and can use mathematics in their teaching. Students use current approaches to develop their own understanding of number, statistics and probability concepts and to develop strategies and techniques for teaching these concepts in the primary school. Participative and collaborative learning approaches are employed each week in the workshops and the use of reflection and documentation of learning through portfolios is continued. The subject assists students to develop critical thought about, and reflection on, the teaching of mathematics in the primary school.
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. | Describe the principles of teaching and learning elementary numeration and number concepts (GTS 2.1, 3.2, 3.3, 4.1) |
| c. | Evaluate learning experiences in number, probability and statistics planned and implemented by the student (GTS 2.3, 3.3, 4.1) |
| d. | Analyse critical issues and trends in Indigenous mathematics education (GTS 1.4, 1.5, 2.4, 4.1) |
| e. | Communicate mathematical ideas using appropriate mathematical terms and clear and explicit language (GTS 2.1, 2.6, 3.4, 3.5, 4.2) |
| f. | Evaluate and select suitable assessment procedures from a range assessments in mathematics education. . (GTS 1.4, 1.5, 2.4, 4.1) |
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)
- Communicate effectively using diverse modes and technologies (GTS 2, 3, 4) (6.1)
- 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)
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 workshop 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 3, 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 content:
1. Exposure to and knowledge of mathematical concepts and the discipline of mathematics, including:
- the meaning and language of mathematical operations;
- mathematical laws and number facts;
- computation and estimation; the understanding and processing of algorisms; the use of calculators;
- the development of early numeration concepts;
- concepts and processes in the measurement of length, area, volume and capacity, mass and time; development of awareness that measurement is a process of approximation;
- Indigenous ways of doing mathematics.
2. Exposure to, knowledge of and experience in planning and implementing lesson sequences with reference to the new NSW K-6 Mathematics syllabus including:
- lesson planning;
- use of a thematic approach;
- making numeracy-literacy connections explicit;
- using working mathematically processes.
Assessment
Assessment task 1: Diagnosis of students’ understanding of number
| Objective(s): | a, b, c and e | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 35% | ||||||||||||||||||||||||
| Length: | 1700 words equivalent | ||||||||||||||||||||||||
| Criteria linkages: |
SLOs: subject learning objectives CILOs: course intended learning outcomes |
Assessment task 2: Develop a lesson for measurement
| Objective(s): | a, b, c and e | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 40% | ||||||||||||||||||||||||
| Length: | 1200 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, d and f | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight: | 25% | ||||||||||||||||
| Length: | 15 hours | ||||||||||||||||
| 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. An attendance roll will be taken at each workshop. Where possible, students should advise the lecturer in a timely manner if they are unable to attend. Students who fail to attend 8 of 9 workshops without extenuating circumstances will be refused to have their final assessment marked.
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
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2018). Teaching Primary Mathematics. 5th Edition. Pearson Australia..
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 text book (Aprroaches to mathematics teaching and learning)
Recommended text
Chapin, S. H., & O‘Connor, C. (2007). Academically productive talk: Supporting students' learning in mathematics. In W. G. Martin, M. Strutchens, & P. Elliot (Eds.), The learning of mathematics (pp. 113- 139). Reston VA: NCTM.
Nesher, P. (2015). On the diversity and multiplicity of theories in mathematics education. In E. Silver & C. Keitel-Kreidt (Eds.), Pursuing excellence in mathematics education: Essays in honour of Jeremy Kilpatrick (pp. 137-148). Cham, Switzerland: Springer International Publishing.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching in the Middle School, 12(2), 88-95.
Van de Walle et al. (2019). Chapter 2 Exploring what it means to know and do mathematics. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson.
Week 2
Required text - Chapter 3 of the text book (Numeration for whole numbers)
Recommended text
Gervasoni, A. (2002) Growth points that describe young children’s learning in the counting, place value, addition and subtraction, and multiplication and division domains. Paper presented at the Catholic Education Commission of Victoria. Success in Numeracy Education Strategy, Melbourne.
Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., & Frid, S. (2013). Chapter 3: Planning and teaching. In Helping children learn mathematics (1st Australian ed.). Brisbane, Australia: John Wiley & Sons.
Wilson, P. S. (2001). Math roots: Zero: A special case. Mathematics Teaching in the Middle School, 6(5), 300-303, 308-309.
Van de Walle et al. (2019). Chapter 8: Developing early number concepts and number sense. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson.
Van de Walle et al. (2019). Chapter 11: Developing whole number place value. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson.
Week 3
Required text - Chapter 4 of the text book (Computation for whole numbers: additive thinking)
Recommended text
Huinker, Freckman & Steinmeyer (2003). Subtraction strategies from children’s thinking: Moving toward fluency with greater numbers. Teaching Children Mathematics, 9(6), 347-353.
Randolph, T. D., & Sherman, H. J. (2001). Alternative algorithms: Increasing options, reducing errors. Teaching Children Mathematics, 7(8), 480-485.
Van de Walle et al. (2019). Chapter 9: Developing meanings for the operations. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson
Van de Walle et al. (2019). Chapter 12: Developing strategies for addition and subtraction computation. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson
Week 4
Required text - Chapter 5 of the text book (Computation for whole numbers: multiplicative thinking)
Recommended text
Empson, S. B., & Turner, E. (2006). The emergence of multiplicative thinking in children's solutions to paper folding tasks. The Journal of Mathematical Behavior, 25(1), 46-56.
Tzur, R., Johnson, H. L., McClintock, E., Kenney, R. H., Xin, Y. P., Si, L., ... & Jin, X. (2013). Distinguishing schemes and tasks in children's development of multiplicative reasoning. PNA, 7(3), 85-101.
Van de Walle et al. (2019). Chapter 13: Developing strategies for multiplication and division computation. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson
Week 5
Required text - Chapter 8 of the text book (Measurement)
Recommended text
Bragg, P., & Outhred, L. (2004). A Measure of Rulers--The Importance of Units in a Measure. International Group for the Psychology of Mathematics Education. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2004 Vol 2 pp 159–166.
Mulligan, J., Prescott, A., Mitchelmore, M., & Outhred, L. (2005). Taking a Closer Look at Young Students' Images of Area Measurement. Australian Primary Mathematics Classroom, 10(2), 4-8.
Thornton, C. A., & Tucker, S. C. (1989). Lesson planning: The key to developing number sense. The Arithmetic Teacher, 36(6), 18.
Week 6
Required text - Chapter 8 of the text book (Measurement)
Recommended text
Linder, S. M. (2010). A Lesson-Planning Model. Teaching children mathematics, 17(4), 249-254.
Zazkis, R., Liljedahl, P., & Sinclair, N. (2009). Lesson plays: Planning teaching versus teaching planning. For the learning of mathematics, 29(1), 40-47.
Van de Walle et al. (2019). Chapter 19: Developing measurement concepts. In Primary and middle school mathematics: Teaching developmentally (1st Australian Edition.). Melbourne: Pearson.
Week 7
Required text - Chapter 8 of the text book (Measurement)
Recommended text
Cheeseman, J., & McDonough, A. (2013). Using photographs and diagrams to test young children’s mass thinking. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australiasia, Melbourne, pp. 146-153) Adelaide, SA: MERGA.
Week 8
Required text - Chapter 8 of the text book (Measurement)
Recommended text
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 9
Required text - Chapter 1 of the text book
Recommended text
Abel, K., & Exley, B. (2008). Using Halliday's functional grammar to examine early years worded mathematics texts. Australian Journal of Language and Literacy, 31(3), 227.
Bresser, Melanese & Sphar (2009). Equity for language learners. Teaching Children Mathematics, 16(3), 170-177.
Barger (2009). Gifted, talented, and high achieving. Teaching Children Mathematics, 16(3), 154-161.
Ferguson, S. (2009). Same task, different paths: Catering for student diversity in the mathematics classroom. Australian Primary Mathematics Classroom, 14(2), 32-36.
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)
References
Ameis, J. (2006). Mathematics on the Internet. A resource for K-12 teachers (3rd ed.). Upper Saddle River, N.J. : Merrill.
Bobis, J., Mulligan, J., & Lowrie, T. (2009). Mathematics for children: Challenging children to think mathematically (3rd ed.). Sydney: Pearson Education Australia.
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.
Harrison, N. (2011). Teaching and learning in Aboriginal education. (2nd edition). Melbourne: Oxford University Press.
Jorgensen, R., & Dole, S. (2011). Teaching Mathematics in Primary Schools (2nd edn). Sydney: Allen & Unwin
Marston, K & Stacey, K. (Eds.) (2001). Foundations for teaching arithmetic. Parkville: University of Melbourne.
MacMillan, A. (2009). Numeracy in early childhood: Shared contexts for teaching and learning. South Melbourne, VIC: Oxford University Press.
NSW DET. (2005). Developing Efficient Numeracy Strategies. Stage 1 (2nd ed.). Sydney: NSW DET.
NSW DET. (2005). Developing Efficient Numeracy Strategies. Stage 2 (2nd ed.). Sydney: NSW DET.
Perso, T. (2005). Improving Aboriginal literacy. Adelaide: Australian Association of Mathematics teachers.
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.
Van de Walle, J. & Lovin, L. (2006). Teaching Student-Centred Mathematics Grades 3-5. Boston: Pearson.
Other resources
Large classrooms with moveable furniture, equipped with data-projector, screen and console, group pods and nearby storage rooms.