Think about the topic under investigation

Math investigations will often be presented in multiple parts, usually 3 to 4 is common. These parts either all lead on from the previous part OR they form separate sub-topics of a chapter. What do I mean by this? 

Let’s look at an example:

If time permits, do some research into the topic you’re supposed to be investigating. For example, in an investigation that explores the features of a polynomial, the topic itself should give you a good indication as to what topic the teacher is looking for you to explore. You should then look ahead in your textbook, look online for the features of polynomials that you may be looking into in this investigation. What do they mean by a polynomial with a real factor? Distinct roots.. What are those? If you’re asked to explore polynomials with multiple degrees, why? What is different about each degree and what is the same? There must be a pattern or a reason they are leading you to look into this topic. Have there been other similar topics you can draw knowledge from?

“A strong Directed Investigation should take the reader through the concise journey you underwent to discover the new concept & conjectures you are presenting. “

Formatting your report

Let’s start with formatting. Depending on your school and your year level, you will be expected to format your investigation in a particular way. Of course, each school and teacher might have different requirements so always make sure to check your Task Sheet and Marking Rubric. Generally an investigation should include the following:

• Introduction: Give an outline of the problem and give context. Introduce the topic of mathematics you will be exploring and introduce each part of the investigation. Ensure to include if you will be using any tools or technology to aid your investigation. 
• Results and data: Format this section to present data in a similar way to how the task has been presented to you. For instance, if the Task had 3 distinct parts, make the results for each part clear here. Often the teacher would have included guiding questions, use those to form this section and include relevant equations, diagrams and figures. Ensure to include annotations and labels.
• Discussion & Analysis : I have noticed many students get stuck at this point. This is where the reader will be able to distinguish a student who can simply just perform calculations and follow instructions from a student who is able to critically link the concepts together and demonstrate they understand this investigation with depth. A few things to write about here: What did your results show? How do they connect to each other? How are they relevant to the topic being investigated? Were your results consistent with your conjectures? What were your assumptions? Are there any limitations to your investigation? How reasonable were your results? Could further investigations improve these findings? If so, how?
• Conclusion: New ideas can not be introduced here. In conclusion, make sure to present your main findings, explain how your results meet the objectives that were set earlier and is an opportunity for you to tie everything together. Any further investigations?
• References: A good investigation should include a list of references for any sources of information included in your writing. The referencing format should follow your school’s Referencing Guidelines.
• Appendices:   

Final tips and thoughts

• Unless otherwise indicated, avoid using personal pronouns.
• Sometimes when you stare at your own work for too long, you begin to skip through and miss mistakes. It goes without saying that if possible, have someone such as your teacher (if they’re allowing drafts), your tutor, your parent, a sibling, a friend, proofread your work and glance over your calculations.
• Look at the assessment criteria for tips on what the teacher will be marking. For instance, if they have listed “Use of electronic technology to find solutions to mathematical problems”, make sure you have shown in your work that you attempted to do this. 
• Follow the instructions! If it says “with aid of a diagram..”, use a diagram!! 
• Label and introduce your graphs and figures in an appropriate, consistent and professional manner. Refer to these in your discussion. 
• Don’t lose marks on the little things! I have seen some brilliant students come back to laugh with me at the silly little, preventable marks they lost. Check your page formatting, check that your axis are labelled, check that your units are listed and consistent! Check, Check, Check!
• SACE also have Assessment task exemplars available on their site, have a look.
•  A strong Directed Investigation should take the reader through the concise journey you underwent to discover the new concept & conjectures you are presenting. 

Best of luck!