1. INVESTIGATION - MATHS Maths Talent Quest
June Penney
MAV - Student Activities Committee

2. INDEX What is a Maths Investigation? Why do a Maths Investigation?
VELS & Interdisciplinary Learning
Thinking Skills
Reflection of Investigation Learning
Developing Your Maths Investigation
References & Acknowledgements

3. What is a Maths Investigation?
An investigation may be defined as
“a situation originating in mathematics or the real world which lends itself to inquiry.”
Inquiry ---making observations, asking questions and pursuing
investigations has always been a fundamental approach to
understanding the world.
A mathematics investigation allows students to examine situations using various techniques and in the process of their exploration develop skills that can be applied to other problems.
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4. Why do a Mathematics Investigation?
It caters for student diversity and investigative work is viewed as a key way to engage and motivate learners.
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.
It requires students to use mathematical processes to understand the problem or situation.
First hand data – generated by the student is much better for learning than second hand data!
Students develop a systematic record of their work not only an end product.
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5. Interdisciplinary Learning (VELS, VCAA)
Communication
Design
Thinking
Integration
Creativity and Technology
ICT (Information & Communications Technology)
*Can all be included as requirements of a completed investigation.*
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6. Thinking Skills
The type of skills normally associated with investigations are generally higher order skills or processes.
These processes fall under the broad heading of Working Mathematically in VELS. (Victorian Essential Learning Standards, VCAA)
“We are preparing students for an uncertain future, there will be problems to solve that probably don’t yet exist.”
The aim of developing thinking skills through the investigation process is to provide students with the ability to apply and transfer knowledge to new and different circumstances as they arise throughout life.
To understand and act effectively in the ever changing world in which they live.
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7. Grade 4 Reflection of Investigation Learning
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Grade 4 Reflection of Investigation Learning

8. Developing Your Maths Investigation
First Decide
Getting Started
Final Presentation Format Examples
Investigation Steps
Being A Mathematician
Procedure Ideas
Investigation Model
Strategies/ Toolbox of strategies
Reflections
Self-Assessment
Log/Journal
What to include?
Assessment
A Learning Journey
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9. FIRST DECIDE Who is doing the investigation?
Class- Organisation and Roles (Maximum 30 students)
Group- Organisation and Roles (2-6 students) An example next slide.
Individual-Organisation
Will the investigation be-
A home investigation.
A school investigation.
A home/school partnership investigation.
Which investigations will be entered in the MTQ?
Every school investigation is entered.
Own School judging of investigations to select those to be
entered.
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10. Getting Started. Be Creative and Individual.
Choose something that interests you.
Use:
Mind mapping
Brainstorming
Lateral thinking
Begin:
Brainstorm Ideas and Inspiration for Investigation.
Begin a Log or Journal Clearly Explaining the Investigation, Thinking and Learning Processes and Understandings.
Generate Ideas for Topic and Related Mathematical Content.
Select Topic and Outline Investigation Content.
Ensure Acquisition and Management of Resources.
Develop a Timeline.
Consider Presentation Format.
( Posters, Booklets, Display Folders, ICT/CD and Support Materials such as Models are all acceptable. Models must relate to the mathematics not just be an artistic display “add on”.)
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11. Investigation Examples Poster, Book and Model Poster
(6 Slides)
Poster

12. Model and Books
Small Display Folder

13. Visual Arts Book
Big Book

14. Large Display Folder
Presentation Package

15. Maths of Hobbies or Interests
Maths of Arts & Crafts
Maths of Cultures

16. Investigation Steps Investigation Aim: Conclude.
A question is a problem if the procedure or method of solution is not immediately known to you but requires you to apply creativity and previous knowledge in new and unfamiliar situations.
If the procedure or solution is obvious then it is not a problem but an exercise.
Conclude.
Draw Together.
Summarise Findings.
Repeat Process.
Extend the Situation by Formulating Further Questions.
Reflections.
Explain or Justify Results.
Test Conjectures. (Use strategies)
Make Conjectures. (Formation of opinion on incomplete grounds.)
Explore Systematically. (Use strategies)
Get to Know the Situation and Formulate Questions.
Define your AIM.
Choose your TOPIC.
Begin Log or Journal.
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17. MTQ Investigation MTQ Investigations Title: Aim: Plan:
Remember to use the judging rubric.
Title:
Interesting & Worthwhile
A Concise,
Problem to
Solve
Aim:
Plan:
Outline and Guide
Investigation skills/resources used:
Mathematics Processes/
Strategies
Working document.
Raw data, methods , findings &
personal thinking.
Doing the investigation: Document the mathematics of your investigation.
*The development of your investigation must be clearly demonstrated in your log/journal.
*A final publication/presentation of your investigation is to be completed & submitted along with your log/journal.
Clearly answers aim.
Conclusion:
MTQ Investigations
Title:
Aim:
Plan:
Investigation skills used:
Maths used: Document the development of the mathematics of the investigation.
This should be demonstrated in your log/journal.
Conclusion:

18. Back to Investigation List

19. Some Procedure Ideas
*George Polya (Hungarian Mathematician) “How To Solve It”, 1945.
* See, Plan, Do, Check
An issue to explore
A question to ask
A problem to solve
A task to complete
5E’s of Investigation
Engage
Explore
Explain
Elaborate
Evaluate
Toolbox/Graphic Organiser
Garafalo & Lester (1985)
Orientation
Organisation
Execution
Verification
NSW BOS (2002)
Questioning
Applying Strategies
Reasoning & Communication
Reflecting
“Toolbox” Reference - “Work It Out,” Tom Hill, Oxford University Press.
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20. Investigation Procedure (One Model*)
See - Understanding the Problem
Plan - Deciding on a Strategy or Plan
Do - Solving the Problem
Check - Checking Your Results
(8 slides)
* George Polya- “How To Solve It”,1945

21. See Understanding the Problem
Identify the problem you want to answer.
Read the problem carefully.
Pick out the various parts of the problem.
Questions
What is the problem asking me?
Are there any words I don’t understand?
What do I already know?
What am I trying to do?

22. Plan Deciding on a Method/Plan to Get a Solution
Gather together all available information
Make some predictions or guesses.
Think about the different strategies you may use.
(Refer Strategies/Toolbox of Strategies in Index)
Decide which strategy or strategies will suit your problem.
Write down your plan.
Questions
How am I going to solve the problem?.
Have I seen the problem or a similar one before?
How can the known help me with the unknown?
Can I restate the problem?

23. Strategies for Solving Unfamiliar Problems
Trial and error.
Guessing, checking, improving.
Gathering data.
Drawings, diagrams, graphs.
Working backwards.
Looking for patterns.
Writing an equation.
Using a formula.
Simplifying the problem.
Do I know a similar problem?
Elimination of possibilities.
Using a list or a table.
Using materials.
Using models.
Acting it out.
Test conjecture by- examples and counter-examples.

24. Back to investigation List

25. Do Carry out the Plan to Solve the Problem
Work through, one step at a time.
Do each step carefully.
Explain and show how you reach your answer.
Reflect on where you are at.
Re-think and modify your strategies as needed.
Create a new plan if necessary.
Questions
What do I do next?
Have I proved I am correct?
Do I continue with my plan?
Is my plan working?
Do I need to change my plan?

26. SOME of the Mathematical Processes Used
Questioning
Collecting Data
Generalising
Exploring
Hypothesising
Analysing
Predicting
Reflecting
Comparing
Interpreting
Justifying
Classifying
Experimenting
Estimating
Proving
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Back to Thinking Skills

27. Check Think Carefully and Examine Your Answer
Write your answer in a complete sentence.
Questions
How can I check my result?
Have I used all the important information?
Does the answer make sense?
Does it answer the whole problem or question?
Reflections
How could the problem relate to other problems?
Is there another strategy I could use to get the answer?
How can I use this method to solve further problems?
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28. Investigation Reflections
Some Ideas:
I have learnt….
I have found….
I have discovered…
I now need to…
Today I/Tomorrow I…
Something new….
Something challenging…
Further thoughts….
Can I check this another way?
What happens if?
How many solutions?
What else can I learn from this?
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29. Self Assessment
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30. Log/Journal/Rough Workings (COMPULSORY)
Name
Title
Key question/s of investigation
Investigation Plan- Point Form
- Mind Map
Investigation Development- Ongoing demonstration and explanation of the Mathematics used.
Carefully read judging criteria
A sample investigation proforma is also available from the Mathematical Association of New South Wales website
(18 slides)
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31. Five
Log/Journal
Examples
From Previous
MTQ Investigations

32. Organise your group/class in a way that suits you.
Example One
Organise your group/class in a way that suits you.
(One Class Organisation 2007)
Writers Group
Research Group
Calculator Group
Artists Group
Photographers Group

34. Sections Example Three What is the project about?
What is the main question?
What are the other questions?
What maths is involved?
What method/s are used to investigate the problem/s?
What materials and equipment will be needed?

35. Example Four Sections Date? What are we doing for our project today?
What maths did we use?
What did we discover or learn today?
What do we need to do next?

36. Example Five
2007 Home/School Partnership Timeline Example- 1 0f 3 Pages

37. 2007 Home/School Partnership Timeline Example- 2 0f 3 Pages

38. Which investigations will be entered in the MTQ?
The above school had their own school judging of investigations to
select those to be entered.
Some schools have a school expo to display the quality of their investigations and every school investigation is entered.
While other schools submit all investigations and have a display to celebrate their maths later in the year.
2007 Home/School Partnership Timeline Example- 3 0f 3 Pages

39. Example Seven

40. What to Include? All completed investigations must have:
An investigation title.
A list of all the components of the investigation.
Each component clearly labelled.
Documented evidence of student’s investigation thoughts, processes and development to be included as separate log, journal or rough workings.
It also needs to include reference to the progress of the mathematical investigation being undertaken, the problems undertaken and the mathematical conclusions reached.
A bibliography listing all references used.
Acknowledgement of any assistance given.
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41. Assessment Assessment Format - Evaluation Rubric
Primarily based on communication, evidence of mathematical content and the understanding of the investigation appropriate to the student’s year level.
Assessment Format - Evaluation Rubric
Communication 16 points
Mathematical Content and Understanding 16 points
Ideas and Resources 8 points
Presentation 4 points
TOTAL 44 points
Download judging criteria from MAV Website-
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42. A Learning Journey
“Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost and discover more than they thought possible.”
W.S.Anglin

43. REMEMBER Curiosity and interest are the centre of inquiry!
Choose your investigation wisely!

44. Hope you are excited about your
Investigations!
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45. References Acknowledgements
“MTQ Is For You.” June Penney & Agatha Anamourlis, MAV Publications
VELS- Victorian Essential Learning Standards, VCAA, Working Mathematically (Mathematics) and Interdisciplinary Learning
Donna Ludvigsen, Working Mathematically, MAV Conference, Dec 2006
Doug Williams, Black Douglas Professional Education Services, MAV Conference, Dec 2006
“Work It Out.” Tom Hill, Oxford University Press
“How To Solve It.” George Polya, (Princeton 1945)
“Identifying problem solving in school mathematics: students’ and teachers’ perspectives.” Judy Anderson, Connected Maths, MAV Annual Conference 2008.
Acknowledgements
Thank-You To 2007, 2008 & 2009 MTQ Participants For-
A variety of 2007, 2008 & 2009 MTQ Investigation Examples.
Investigation Timeline & Self-Assessment, Mark Smith & Steve Wilson, Carey Baptist Donvale & Kew
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