Details for Learning Mathematics Part A
- Currently offered by Alphacrucis: Yes
- Course code: EDU414
- Credit points: 9
EDU401 Foundations in Christian Teaching and Learning, and EDU402 Human Society in the Environment: Platforms and Perspectives for the Christian Educator
The unit Learning Mathematics Part A is part of the subject area Education and is offered as a part of the following Awards: Master of Teaching (Primary) (Alphacrucis College (NSW Dept. of Education)).
The main focus of this unit is on the Pre-service Teacher as a user of mathematics and their own knowledge, skills, confidence, belief systems and values in the area of processing and communicating mathematically. In particular, it builds on the Pre-service Teacher’s own mathematical skills with a view to appreciating mathematics in everyday life and the role and nature of mathematics as a way of interpreting the world. It traces the growth and development of mathematical constructs in children through Primary school and how this aligns to the NSW K-6 Mathematics syllabus. Pre-service Teachers will be exposed to the socio-cultural and multicultural contexts of mathematics, critique a range of teaching methods including direct instruction, deductive, constructivist and socio-constructivist approaches, with a view to developing their own philosophy and teaching approach. They will investigate gender stereotypes in the maths and sciences, controversial belief systems, both historical and present day, which impact on how maths is taught in Australian schools.
- How People learn mathematics, growth and development in mathematical concept development, links between Stage 3-4
- Learning anxieties: personal math’s study skills inventory, math’s and test situations
- Truth in math’s and the sciences, numeracy across the curriculum
- Gender in the maths and the sciences
- Math’s and culture, ethno mathematics, Indigenous and cultural ways of knowing, interpreting and communicating research and statistics
- Literacy- making meaning of math’s terminology, communicating and thinking mathematically
- Personal philosophy of mathematics education and Christian worldview
Mathematical concepts, processes and teaching approaches:
- Syllabus development through Stages in Core topics; Scope and Continuum, Syllabus strands and sub-strands):- Number and Algebra (Relationships, place value, whole numbers, Hindu- Arabic, Roman, Indigenous numeration systems) rational numbers, graphs, probability and statistics, mathematical modeling, calculators and technology); Space and Geometry, (2-D, 3-D, Patterns:- symmetry, tessellation and art, drawing); and Measurement (metrics and language, standard and non standard units of measurement, money, time, angles, interpreting Data); Working Mathematically (problem-solving, every-day math’s, calculators and computers, estimating and checking), Metacognition- Thinking mathematically- questioning, interpreting, applying strategies, reflecting; Chance and Data), Communicating mathematically- numerical, geometrical, graphical, statistical, and algebraic.
- Maths in Society- being numerate (Media, community, sport, workplace, hospitality and tourism). Statistical literacy (planning, gathering, organizing, applying data to solve problems and communicate results. Numeracy and the ethics of manipulating data for society’s products and services. Indigenous and cultural ways of knowing and communicating mathematics.
- Teaching Pedagogies for Mathematical concept development:- Approaches:- deductive, inductive, direct instruction, constructivist, socio-constructivist, Skemp’s instrumental and relational learning. Problem solving heuristics (Polya, CoRT) and investigative approaches. Application of teaching and learning principles and NSW DET Quality Teaching in NSW Public Schools Discussion Paper- authentic and rich tasks, contextual, connected to learners, significance, engaging, deep intellectual quality and self monitoring for meaning making, quality learning environment. Computer- mediated learning (graphics calculators and skill development software).
This course may be offered in the following formats
Students will be engaged in analyzing NSW Board of Studies Syllabus documents and related resources, programming and planning exemplars, graphic calculators and technology assisted learning tools. They will develop lesson plans and programs in class and engage in mathematical manipulation, technology experiments and hands on mathematics learning experiences. An emphasis on modeling good practice in teaching of mathematics is integral to these learning experiences. This intensive will be residential and held at Bimbadeen, an Indigenous Conference Centre where members of the Indigenous communities in neighbouring areas will unpack Indigenous culture and mathematical understandings as well as spend informal time over the week.
Entrance Numeracy Test (5%) Due Week 1
Pre-requisites:- Entrance Numeracy Test for students who have no Tertiary mathematics subject experience.
Students will need to show evidence of Tertiary Mathematics subject experience to be exempted from taking the NSW On-line Mathematics Test in Week 1 of the course.
Self Appraisal (30%) Due Week Week 13
The purpose of this assessment is to encourage you to monitor and develop your own knowledge, skills and values in the area of mathematics as part of your development as a Reflective Practitioner.
Gather data at the outset of the course from a range of sources including commercial instruments (you may require a fellow student or colleague to perform your assessment). Diagnose your strengths and weaknesses in your knowledge, skills and attitudes, in relation to the maths content of the NSW syllabus. Show steps taken to remediate and enhance your personal development; for example, math’s anxiety, or specific concept development. Post test yourself or get another colleague to perform your assessment at the end of the Program (e.g. after EDU424 and EDU400) and analyse for any growth or change.
Include an Appendix showing the Raw Data such as commercial tests and an Appendix of a Glossary of Mathematical terms indicating the suitability for communicating to pupils at each stage (from 1-3).
Conclude with any insights you have gained that will impact on how you will teach. Your discussion should consider not only your own emotional and concept development experiences, but a critique of the testing instruments you used and their validity.
(Note students will be asked periodically to share their own data and experiences in class discussion).
Approaches Assignment (65%) Due Week 10
Critically review three different approaches to teaching mathematical concept development, identifying strengths and weaknesses of each approach. Include key research and writers in the area, past and present. (1,000 words)
Part B (Class Teacher interview)
Interview a class teacher teaching an age group of your choice:
- Interview him/her about their rationale and goals and outcomes for his/her current class.
- Select a Stage and concept the teacher plans to teach (refer to the NSW Maths Syllabus), noting what prior knowledge would have been expected and what the pupil could expect to follow on with.
- In light of the pedagogies outlined in the NSW DET Quality Teaching in NSW Public Schools Discussion Paper, analyse the teacher’s planning of a unit of work (e.g. series of three or four lessons), choice of pedagogies, and pre and/or post testing assessments and reporting.
- Where possible observe the teacher teaching one or more of the lessons. Note how he/she introduces the concept and how he/she caters for different abilities, culturally and linguistically diverse children, and integrates technology to mediate learning
- Discuss with the teacher what you understand from your research (Part A) into writers in the field of mathematics education, might reflect his/her approach.
- Write a summary of this teacher’s approach citing the researchers and writers it either aligns with or differs from. (500 words)
Compose your own Philosophy Statement of the teaching approach(es) you intend to follow in your own classroom in relation to mathematics and how it reflects/ embraces a Christian Worldview. (300 words)
- Department of Education and Training (2003). Quality Teaching in Public Schools Discussion Paper. Sydney: Professional Support and Curriculum Support Directorate.
- NSW Board of Studies (2002). Mathematics K-6 Syllabus. Sydney: Author.
- NSW Board of Studies (2002). Mathematics K-6 Support Documents. Sydney: Author.
- NSW Board of Studies (2005). Primary Curriculum Foundations Statements. Sydney: Author.
- Reys, E.R., Suydam, M.N., & Lundquist, M.M. (2003). Helping Children Learn Mathematics, 7th edn,Needham Heights, MA : Allyn & Bacon.
- Van Brummelen, H. (1998), Walking With God in the Classroom: Christian Approaches to Learning and Teaching, 2nd edn, Seattle, WA : Alta Vista College Press.
- Australian Journal of Reading: Focus Issue- Language in Mathematics, (1989), vol. 12, no. 2, Australian Reading Association.
- Arem, C. (1993) Conquering Math Anxiety: A Self-Help Workbook, Pacific Grove, California : Brooks/Cole Publishing Company.
- Boaler, J. (1997) Experiencing School Mathematics: Teaching Styles, Sex and Setting, Buckingham : Open University Press.
- Board of Studies NSW (2002) Mathematics K-6 Syllabus. Sydney : Author.
- Cockcroft, W.H. (1982) Mathematics Counts: Report of the Committee Inquiry into the Teaching of Mathematics in Schools. London : H.M.S.O.
- deBono, E. ‘The CORT thinking program’ in Thinking and Learning Skills: Relating Instruction to Basic Research Vol. 1, ed.J. W. Segal, S. F. Chipman, & R. Glaser, Hillside, New Jersey : Erlbaum.
- Issler, K & Habermas, R. (1994) How We Learn: A Christian Teacher’s Guide to Educational Psychology, Grand Rapids, MI : Baker.
- Howell, R., Bradley, J. & Bradley, W. (2001) Mathematics in a Post Modern Age- a Christian Perspective. Grand Rapids, MI : Eerdmans.
- Lamb, S. & Fullarton, S. (2002) Classroom and school factors affecting mathematics achievement: A comparative study of Australia and the United States using TIMMS. Australian Journal of Education, 46(2), pp. 154-171.
- Martin, H. (1997) Integrating Mathematics Across the Curriculum, Cheltenham, Vic :Hawker Brownlow Education.
- Murdoch, K. (1998) Classroom Connections: Strategies for Integrated Learning, Armadale, NSW : Eleanor Curtin.
- Nickel, J. (2001) Mathematics: Is God Silent?, Rev.2nd edn, Vallecito, California : Ross House Books.
- Reesink, C. (1998) Teacher-Made Aids: Elementary School Mathematics Vol. 3, National Council of Teachers of Mathematics, VA, USA : Reston.
- Rushdoony, M. S. (2001). Whence Freedom? School Mathematics, Philadelphia, PA : Chalcedon.
- Ryan, T. (1993). Thinkfest. A Hands-on Problem-Solving Adventures for the Classroom and Home, Fingal, NSW : HeadFirst Publishing
- State of New South Wales, Department of Education and Training, Professional Support and Curriculum Directorate, (2003) Teaching about angles
- Wahl, M. (1998), Maths For Humans, Melbourne, Vic : Hawker Brownlow Education.
- Bransford, J., Brown, A., & Cocking, R. (2000) How People Learn: Brain, Mind, Experience, and School, Washington, D.C., USA : National Academy Press.
- Carr, K. (1996) Using video to help children reflect. Waikato Journal of Education Vol 2.
- De Klerk, J. (2002) Illustrated Maths Dictionary for Australian Schools, 3rd ed., Cheshire, Melbourne : Longman.
- Goldhaber, D.D. & Brewer, D.J. (2000) Does teacher certification matter? High School Teacher Certification status and student achievement. Educational Evaluation and Policy Analysis, 22(2), 129-145.
- Grootenboer, P., & Lowrie, T. (2002) Pre-service primary school teachers’ views on mathematics and mathematics education. In D. Edge & B. H. Yeap (Eds.). Mathematics education for a knowledge-based era: Proceedings of the Second East Asia Regional Conference on Mathematics Education and Ninth Southeast Asian Conference on Mathematics Education (pp. 232-238). Singapore: National Institute of Education.
- Naismith, L., Longsdale, P., Vavoula, G & Sharples, M. (2004) Literature review in mobile technologies and learning. (Nests Future Lab series. Report 11), http://elearning.typepad.com/thelearnedman/mobile_learning/reports/futurelab_review_11pdf/ accessed 9 October 2006.
- Overman, C. (1996) Assumptions that Affect Our Lives, Luisiana, Missourie : Charleston Publishing Group.
- Pobl, M. (1997) Teaching Thinking Skills in the Primary Years, Melbourne, Vic : Hawker Brownlow Education.
- Sire, J. W. (2000) Habits of the Mind: Intellectual Life as a Christian Calling. Downers Grove, Illinois :InterVarstity Press.
- Tucker, K. (2005) Mathematics Through Play in the Early Years: Activities and Ideas, London: Paul Chapman Publishing.
- Van Brummelon, H. (2002) Stepping Stones to Curriculum: A Biblical Path, 2nd edn,Colorado Springs, CO : Purposeful Design Publications.
- Australian Primary Mathematics Classroom
- Mathematics Teaching
- Journal for Research in Mathematics Education
- Australian Association of Mathematics Teachers http://www.aamt.edu.au/
- Mathematical Association of Victoria http://www.mav.vic.edu/au/
- ACU Mathematics Teaching And Learning Centre
- Mathematics Education Research Group Of Australasia http://aww.merga.net.au