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

As a technological society, the world is rapidly changing, making it difficult to predict what specific knowledge and skills will be needed other than in solving a variety of unforeseen problems and in learning new information and skills. Our world is shaped by increasingly complex, dynamic, and powerful systems of information, requiring the development and use of models to interpret and explain our world, think and reason in mathematically diverse ways and with representational fluency, and use sophisticated equipment and resources.

This unit focuses on the knowledge and pedagogy teachers require to enable students to have access to the deep ideas and key processes that lead to success in and beyond school, that will encompass, visual thinking, algebraic reasoning, numerical reasoning, and algorithmic processes. It uses mathematics as a rich source of experiences in which powerful reasoning processes and general problem-solving skills can be developed, experiences that are not confined to formal, abstract mathematics but are abundant even in the mathematical world of young children. An important component of this development is to go beyond the acquisition of factual information to the construction of effective mental representations, such as analogies, metaphors, and images, which facilitate mathematical reasoning.

Aims

The aim of this unit is to assist you in developing powerful means of interpreting, thinking mathematically and using technology, and in designing and implementing classroom problem solving environments in order to be able to effectively teach the mathematics of tomorrow.

Objectives

On completion of this unit, you should have acquired:

1. An appreciation of the thinking power of mathematics and an awareness of the multiplicity of problem-solving roles it plays in our society. [EPAs 1.4]

2. A knowledge of some of the current theories and research on thinking, reasoning, learning, and problem solving in the mathematics domain. [EPAs 1.4, 3.1, 3.2]

3. A knowledge and appreciation of some of the major representations used in mathematical reasoning, including analogies, metaphors, and images. [EPAs 3.1, 3.2]

4. More effective mathematical reasoning, problem-solving and modelling skills and skills with technology and virtual knowledge objects. [EPAs 2.4, 3.1,3.2]

5. Competence in identifying and analysing the reasoning processes that a diverse range of children employ in solving mathematical problems and in developing effective reasoning, problem solving and modelling activities for a wide range of students. [EPAs 2.1, 2.2, 2.3, 2.4, 2.5]

6. An ability to reason, model and solve problems, to work independently and to present information in an engaging and scholarly manner. [EPAs 3.2]

Content

The content to be covered in this unit includes:

1. The essential components of thinking, reasoning and working mathematically.
2. The growth of mathematical thinking throughout the last 100 years and the nature
and scope of mathematical reasoning, problem solving and modelling.
3. The nature, role, and development of representations in mathematical reasoning, problem solving and modelling.
4. Analysis of students' reasoning, problem solving and modelling in mathematical situation.
5. Use of computers and the development of virtual objects for mathematics instruction.
6. Applying research to the development of mathematical reasoning, problem solving and modelling in the classroom, workplace, and informal environments.

Approaches to Teaching and Learning

This unit will adopt an interactive format in which you will actively participate in all discussions and workshop experiences.

Assessment

Formative assessment will be via the tutorials, feedback on drafts and on the first assessment item.

Summative assessment consists of two items:

Assessment name: Project proposal
Description: The preparation of a project proposal, for promoting thinking and reasoning in the classroom for a particular aspect of the mathematics curriculum.
Length: approximately 3000 words.
Relates to objectives: 1, 2, 3, 4, 5, & 6
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: Progressive

Assessment name: Presentation of the project
Description: Length: equivalent of 2,000 words
Relates to objectives: 1, 2, 3, 4, 5, & 6
Weight: 40%
Internal or external: Internal
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

Texts:

There is no text for this unit.

References:

Anderson, J. et al (2007). The Origo handbook of mathematics education. Brisbane: Origo Education.

Burrill, G. & Elliott, P. (Eds). (2006). Thinking and reasoning with data and chance. Reston, VA: National Council of Teachers of Mathematics.

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

Stiff, L. & Curcio, F. (1999). Developing mathematical reasoning in grades K - 12. Reston, VA: National Council of Teachers of Mathematics.

Risk assessment statement

There are no out-of-the-ordinary risks associated with the general conduct of this unit. Workplace health and safety protocols in relation to computer use will apply.

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