Units

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Sample subject outline - Semester 1 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

The broad range of topics addressed in this unit reflects the need for mathematics education today to encompass more than an understanding of traditional basic skills. Teachers and the wider community need to broaden their perspective on what constitutes good mathematical skills and develop effective ways of measuring these. We need to ensure that students are prepared for success in a technologically based information age, by providing them with early and democratic access to powerful mathematical ideas. We also need to recognise and nurture a broader range of mathematical talents.

Aims

Through a mixture of lectures, workshops, informal discussion groups, and virtual learning communities, this unit will provide participants with the content knowledge and pedagogical strategies to promote the mathematical development (both cognitive and social) of their students. The lectures will provide the theoretical framework for the workshops. The workshops will provide students with the opportunity to participate in collaborative problem tasks that illustrate the content addressed in the lectures. There will be a focus on participants developing a broader range of thinking and reasoning processes as they work with the mathematical content presented. Students will be encouraged to critically evaluate ideas, reflect on their learning during the unit, and to freely express their personal viewpoints.

Objectives

On completion of this unit, students should:

1. Be confident and knowledgeable about the teaching and learning of the topic areas addressed during the semester; 1.1

2. Demonstrate an understanding of the mathematical ideas and principles behind these topics; 3.3

3. Analyse critically the latest theories on how students learn and apply mathematics; 1.7

4. Be critical and analytical in selecting and implementing learning activities, including technological tools, to develop students' mathematical understanding and reasoning processes; 1.6, 1.7

5. Be able to use the internet in a critical and constructive manner to access appropriate educational materials, and to collaborate with other teachers in improving the mathematics education of their students; 1.3 , 3.5, 4.5

6. Be able to plan and implement appropriate mathematical learning experiences to meet the needs of all learners. 3.1, 3.2

Content

This unit covers the following topics:

The beginning mathematics processes: These include key underlying experiences of elementary mathematics, such as working with attributes to match, sort, compare, order, and construct patterns; also included here is an introduction to early number ideas.

Whole number numeration: A teaching model for developing place value is examined and used to analyse teaching sequences for 2-digit through 7-digit numbers. This is extended to include other numeration activities such as seriation, renaming, comparing and ordering, and rounding.

Operation concepts and number facts: A language approach for teaching mathematics concepts is examined and applied to the teaching of the four mathematics operations. The use of strategies to develop mastery of number facts is explored.

Computation - mental and paper and pencil: The use of computation as a natural extension of number facts and working with numbers is examined; the development of mental computation through the use of number sense discussions is also included here.

Decimal and common fractions: The teaching model used for whole numbers is applied to decimal fractions and common fractions.

Mathematical reasoning, problem solving, and problem posing: These include a range of important thinking processes such as critical, reflective, creative, flexible, and logical reasoning; together with pattern generation, problem representation, problem solving and posing, and mathematical modelling.

Statistical reasoning and notions of chance: These include basic statistical concepts, graphs, critical analysis of data, and basic probability concepts and processes.

Measurement: This includes concepts and processes, and links to the decimal-fraction teaching model.

Spatial reasoning: Included here are spatial concepts, models, constructions, and reasoning processes.
The use of technological tools in a critical and constructive manner is addressed during the course of the above topics.

Approaches to Teaching and Learning

Graduate pedagogy is applied in this unit. This provides students with opportunities to contribute to the mathematics education knowledge community of their group by participating in ideas analysis, critical inquiry, problem solving, and problem posing. Students can study the unit in either internal or external mode. The internal mode comprises a mix of lectures, workshops, and virtual learning activities. The external mode comprises self-paced study using the OLT site on-line tutor.

The lectures are video-streamed for both external and internal mode.

Assessment name: Assessment 1
Description: Knowledge and understanding of primary mathematics curriculum
Word Length:1500-2000 words
Internal and external students address a number of questions on the teaching and learning of mathematics from the set textbook.
Relates to objectives: 1 & 2
Weight: 30%
Internal or external: Both
Group or individual: Individual
Due date: Early - Mid semester

Assessment name: Assessment 2
Description: For internal students: In groups of four, students are to present a seminar on the teaching and learning of one key idea from the topic areas of EITHER measurement OR spatial reasoning. The seminar presentation is accompanied by a written paper, addressing the following components:
(a) Introduce and explain the concept/s and processes being addressed and indicate why they are an important component of the mathematics curriculum;
(b) Design or select from the literature, an appropriate activity that would develop children's understanding of the concept/s and process/es, and justify why you chose the activity;
(c) Demonstrate the activity by implementing it with the students in the tutorial class;
(d) Indicate briefly how you would assess children's learning from the activity.

For external students, individual written papers addressing the above issues are required.
Word Length: 1500-2000 words
Relates to objectives: 1, 2, 3, 4, 5, & 6
Weight: 20%
Internal or external: Both
Group or individual: Group with Individual Component
Due date: End of semester

Assessment name: Assessment 3
Description: Both internal and external students complete an examination
Relates to objectives: 1, 2, 3, 4, & 6
Weight: 50%
Internal or external: Both
Group or individual: Individual
Due date: End of semester

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

Basic text
Booker, G., Bond, D., Briggs, J., & Davey, G. (2003). Teaching primary mathematics. Melbourne: Longman

Background Reading
Baroody, A. J. (1998). Fostering children's mathematical power: An investigative approach to k-8 mathematics instruction. Mahwah, NJ: Lawrence Erlbaum.

Bobis, J., Mulligan, J., Lowrie, T., & Taplin, M. (1999). Mathematics for children: Challenging children to think mathematically. Australia: Prentice Hall.

English, L. D. (Ed.). (2004). Mathematical and analogical reasoning of young learners. Mahwah, NJ. Lawrence Erlbaum.

English, L. D. (Ed.). (2002). Handbook of international research in mathematics education: Directions for the 21st century. Mahwah, NJ: Lawrence Erlbaum.

English, L. D. (Ed.). (1997). Mathematical reasoning: Analogies, metaphors, and images. Mahwah, NJ: Lawrence Erlbaum Associates.

English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. Mahwah, NJ: Lawrence Erlbaum Associates.

Mannigel, D. (1992). Young children as mathematicians: Theory and practice for teaching mathematics. Wentworth Falls, NSW: Social Science Press.

Owens, D. T. (Ed.). (1993). Research ideas for the classroom: Middle grades mathematics. New York: Macmillan.

Sawyer, A. E. (1993). Developments in primary mathematics teaching. London: David Fulton.

Steen, L. A. (1997). (Ed). Why numbers count: Quantitative literacy for tomorrow's America. New York: College Entrance Examination Board.

Risk assessment statement

There are no out-of-the-ordinary risks associated with the general conduct of this unit.

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 31-Oct-2012