Student Services - Investigating: Mathematics 2009
For students from Pre-School to Year l2

WHAT IS THE INVESTIGATING: MATHEMATICS COMPETITION?

The Investigating: Mathematics competition is open to all primary and secondary students in NSW. The competition aims to promote interest in mathematics and foster positive attitudes amongst students, teachers and parents. The focus is on the process of mathematical investigations.

Looking at real life situations and finding that mathematics is everywhere captures the imagination of both teachers and students. The Competition allows students to investigate mathematics on an individual / group / class basis with the chance to have fun, see mathematics in real life situations and receive some recognition in the process. The work involved in investigations can assist students with the Working Mathematically component of the syllabus.

Entries closed on Friday 29 May 2009

All entrants receive certificates of participation and first, second and merit awards are given at each level. There is an awards ceremony early in September. The best entries at State level are entered into the National Maths Talent Quest.

2009 results

• NSW Investigating: Mathematics 2009 Winners

2008 results

• NSW Investigating: Mathematics 2008 Winners

2007 results

• NSW Investigating: Mathematics 2007 Winners
• National MTQ winners

2006 results

• NSW Investigating: Mathematics 2006 Winners
• National MTQ winners

2005 results

• NSW Investigating: Mathematics 2005 Winners
• National MTQ winners

MORE INFORMATION ABOUT THE INVESTIGATING: MATHEMATICS COMPETITION

WHO CAN ENTER?

All students from Preschool to Year 12 can enter the competition, which is conducted in year levels.

Entries can be from:

• individuals or,
• groups (of no more than 6 students), or
• classes of no more than 35 students

If two or more classes at the same year level have investigated a common theme, entries should be submitted separately for each class, ensuring that the entries address a different aspect of the investigation.

Where group or class entries involve mixed year levels, they are placed in the higher year level category.

Entry levels for students in non-standard classes

Students following a non-standard pattern of study, for example students in composite classes, home schooling students, accelerated students and students in special programs, may choose to enter the competition in the class or year grouping that relates to their age, or they may choose to enter an older division.

Entries from composite classes are to be entered at the age / year level that corresponds to the age of the oldest student in the group or an older level if it is more appropriate for the group.

PRIZES

A Certificate of Participation is awarded to every student at State level.  State level First, Second and Merit Certificates can be awarded in all categories, to individuals, groups and class entries. The judges reserve the right not to make awards if the standard of entries is not sufficiently high. The judges’ decision is final and no correspondence will be entered into.

The top entries for each level are then forwarded to the National Maths Talent Quest held later in the year.

Schools will be notified (by fax or e-mail) of winning entries. Please ensure that a school fax number or e-mail address is on your application form.

The names of winning students, groups or classes and their school will be reported in the MANSW Newsletter and on the MANSW Website www.mansw.nsw.edu.au .  Photographs of winning students may be placed on the MANSW Website or used in the MANSW journals, Reflections and Square One.

Non-winning entries can be collected from the MANSW Office after 4 August.  Entries sent by post will be returned to the school by post.

ENTRY FORMATS

Entries may be presented in many different formats, eg essays, reports, poems, songs, stories, audiovisual presentations, models, posters, games etc. It is important to ensure that, no matter what method of presentation chosen, the mathematics of the investigation is not lost and that appropriate documentation of the process is required.

Some guidelines for particular formats are given below. This does not exclude other formats.

Models

• Static or working models must have clear assembly instructions and need to reinforce a mathematical principleas part of the project.
• Models must be accompanied by appropriate documentation, e.g. notes outlining mathematical aims, rules, the process of investigation, conclusions, bibliography and acknowledgements.
• Models must not exceed 10 Kg or be more than 0.7m in any dimension – larger entries will NOT be accepted.  If you have a model larger than this, please submit photographs, either electronic or hard copies. The model must be able to fit through a normal doorway and be able to be carried by one person.

Posters

• Posters need to have a sequence of ideas with clear starting and finishing points with a clear indication of the mathematics involved.
• They must be accompanied by appropriate documentation,  eg notes outlining mathematical aims, the process of the investigation, conclusions, bibliography and acknowledgements
• Posters must be no larger than a standard A1 sheet (594cm x 841cm)
• Posters must be able to be rolled into a Postpak cylinder

Games

• Games need to show the development of the mathematical ideas behind the game from both the developer and the player’s perspectives.
• They must be accompanied by appropriate documentation,  e.g. notes outlining mathematical aims, the process of the investigation, conclusions, bibliography and acknowledgements
• Games must be exceptionally creative and original.

Technology supported mathematics

• In general, a technology-based entry should not be submitted unless the technology highlights an aspect of the mathematics and is not purely a presentation tool.
• The entry must be accompanied by appropriate documentation, e.g. notes outlining mathematical aims, the process of the investigation, conclusions, bibliography and acknowledgements
• Any mathematics involved must be able to be checked by the judges. Programming entries will be acceptable if they form an integral part of a multi-media presentation
• Must be submitted in Windows format.
• The entry must run self-contained from a single floppy disk or CD-ROM on standard equipment (standard screen resolution and sound cards).  Please test CD-ROMS in another computer after burning.
• The entry must not install any items onto the host computer’s hard drive
• Relevant runtime version or executable files must be supplied.
• Accompanying notes giving clear operation instructions for users not familiar with the medium used must be supplied.
• Technology entries should also include a hard copy if possible.

Film, video or audio tape presentations

• These items must illustrate the development of the mathematical ideas of the producers.
• They must be accompanied by appropriate documentation,  e.g. notes outlining mathematical aims, the process of the investigation, conclusions, bibliography and acknowledgements.
• There must be a script and a description of the editing, acting, dubbing and camera operation as appropriate.
• Videos should be VHS format and Maximum running time is 15 minutes.
• An indexed commentary should be provided (e.g. 000-040 introduction, 040-060 definition of polygons etc).

Other formats

• It is important to ensure that, no matter what method of presentation chosen, the mathematics of the investigation is not lost.
• The entry must be accompanied by appropriate documentation, e.g. notes outlining mathematical aims, the process of the investigation, conclusions, bibliography and acknowledgement.

PLEASE NOTE

The supervising teacher must verify that the work submitted in all formats is the work of a student or group of students.  All students must be made aware of the perils of breach of copyright.

HINTS TO GET YOU STARTED

• Appoint an Investigating: Mathematics coordinator for your school
• Discuss the Investigating: Mathematics organisation at the faculty level or with a team of interested teachers at a teaching team level
• Include Investigating: Mathematics in the faculty programs
• You could involve one entire year level in Investigating: Mathematics and allocate some class time to it.
• Class teachers can give students ideas and inspiration for investigation preparation. However, students should carry out their own investigations of a particular theme following formal class lessons in that area.
• Initiate brainstorming with the students and teachers from different subject areas e.g. Art, Music, English etc.
• Excursions to various places can initiate valuable ideas for a practical project, e.g. building sites, the zoo, a museum, the Art Gallery, local businesses or industries.
• Investigation of the mathematical content in a hobby or sport could be encouraged.
• At all times, consideration must be given to the mathematical content, originality and presentation of entries

ASSISTANCE FOR STUDENTS

• One of the most difficult parts of the documentation is keeping a diary of the investigation.  There is a sample proforma investigation diary on the MANSW website www.mansw.nsw.edu.au that can be adapted and used by schools / students (download the sample diary as a PDF or download the sample diary as a Word document).  However, use of the diary is NOT a requirement.
• You can also contact the Mathematical Association of Victoria (MAV) www.mav.vic.edu.au to purchase their resource books designed for Primary and Secondary entries.

WHAT IS INVOLVED IN A MATHEMATICS INVESTIGATION?

A mathematics investigation allows students to examine ‘a situation originating in mathematics or the real world that lends itself to inquiry’.  It involves a series of steps:

• getting to know the situation and formulating questions
• exploring systematically
• making conjectures
• testing conjectures
• explaining or justifying results
• extending the situation by formulating further questions
• summarising the findings

Investigations require students to use mathematical processes to understand the problem/situation.  The types of processes developed by work on investigations include;

• data collection
• symbolising
• classifying
• simplifying
• abstracting
• following / ending patterns
• conjecturing
• communicating
• justifying / proving
• generalising / hypothesising
• predicting

The important difference between a mathematics investigation and a mathematics problem solving task is that students need to formulate their own questions from a given situation.  By formulating their own questions, students give teachers a clear indication of their level of knowledge and / or understanding of the topic.

Finally, students should be encouraged to systematically record their work, not only the end results.  This may take the form of a diary or learning log / journal.

STATE JUDGING CRITERIA

The judges look primarily for evidence of originality, mathematical content and understanding appropriate to the year level.

Originality

Some of the factors considered include

• To what extent is the research taken from one or more references?
• What is the evidence for the students’ active involvement in research for the entry?
• Does a model, if included, really enhance the entry and demonstrate the student’s originality and understanding of the project?

Mathematical content and understanding

First and foremost, it is important that entries reflect non-trivial mathematical content, concepts and processes appropriate to the students’ level of mathematical development.  This does not imply that many different topics need to be covered, but it is expected that students will demonstrate depth and breadth in their exploration of the mathematics
Some of the factors considered include:

• Evidence of appropriate use of mathematical terms, graphs, tables, diagrams, formulae, estimation, measurement, problem solving, calculation etc. as relevant tot the investigation’s aims
• Evidence that the investigation is an integrated   piece of works (especially in group and class entries)
• Are the conclusions reached logical and supported by the mathematics used?  Do they suggest further investigations and, if so, to what extent has the student identified these?
• Mathematical accuracy

Communication

It is likely that the students will engage in a number of activities over a period of time. The entry need not include all of these. The final submission should encapsulate the spirit and nature of the mathematics involved without unnecessary detail. It is important that students are encouraged to draw together explicitly the mathematical findings, understanding and ‘surprises’ arising from their explorations.

Entries submitted by more than one student, i.e. by a small or whole-class group, need to reflect the cooperative group learning processes that underpinned the completion of the task. A ‘whole class’ entry should not entail a repetitious collection of the same piece of work from all class members. Not all tasks lend themselves naturally to group work. The results of such a task must illustrate excellent cooperation by the students, a sensible division of the topic into cohesive and interconnected aspects and a logical and comprehensive pulling together of all aspects at the end.

A diary or leaning log / journal should accompany each entry.  It is not intended as a day-by-day entry of “what I did today and how long it took me”.  This affords entrants an opportunity to outline their planning and thinking, to explain their goals,, to discuss both successes and problems that arose and to talk about how they solved these problems. The diary / log is a vehicle for entrants to make their thinking, mathematical ideas and learning quite explicit.
Some of the factors considered include:

• How clearly are the aims of the investigation stated and its conclusions explained?
• How thoroughly are reference sources (including Internet sources) listed?
• Has the student adequately acknowledged help given by teachers, parents and friends?

Presentation

A polished, word-processed entry with computer generated graphs and diagrams may enhance an excellent project, but it is not essential. Many of the winning entries in previous years have been hand written.  The judges will, of course, take overall presentation into account, but what is more valued is an entry which is clearly the student’s own work, with the student’s own voice coming through the discussion.
Some of the factors considered include:            

• How well is the project organised and presented
• Does it have visual impact and neatness