When you think of studying maths, what comes to your mind? You may say it’s for in-class tests, homework, and final exams. Stressed about all the learning for these; high school students can be caught off guard and struggle to go about with maths investigations. This is normal! I remember hearing sighs and confused murmurs filling up my Year 12 methods class as we were getting introduced to the investigation assessment.
Though investigations might sound a bit tricky to tackle, we’ve got you covered! Follow along to manage grey areas and you will be ready to prepare for your very first investigations.
Developing the Right Mindset
Unlike a test or exam that has specific answers to get all the marks, maths investigation often requires a trial-and-error process. You may be wondering, how does this link to set the mindset? A positive and determined mindset is prime to bring creativity, productivity, and satisfaction to your investigation. You should approach each step with an open mindset, believing that you can improve your solutions or models by learning from your mistakes.
It is important to note that there is a multitude of models and approaches to account for the practical problems in maths investigation. Though you may be afraid to show all your thought processes – don’t be! Your mathematical thinking process shapes the foundation of the evidence for your reasoning and proof.
What’s better is that mindset will in turn assist in your problem-solving skills for universities and other life events.
Planning out Brief Structure
Maths investigation can take a lot of time and effort, so it’s best to start early. This doesn't necessarily mean delving into problem-solving the minute you get the assessment. You should read the prompt carefully and create an action plan. Break down the task into manageable chunks, outlining the main problem, identifying possible strategies to find solutions, and relevant maths formulas and concepts to apply.
Setting out the brief structure of your investigation earlier will give you a clearer vision as to how you would go ahead with investigating. You will also be able to track your progress exactly for a stage of the investigation.
So, start organising early and you will thank yourself later!
Seeking for Patterns
What happens if you’re completely stuck? Here is one practical tip to avoid having a blank mind.
When breaking down the problems into smaller pieces of information, collect related examples of mathematical objects. See if you can identify patterns that result from variables. This can be an example of visual patterns such as graphing patterns (i.e., trendlines), linear relationships, or algebraic patterns (i.e., repeated sequences).
If you observe a pattern, that is great! This may lead you to explore WHY a particular pattern occurs and classify differences in the structure. This pattern-seeking method contributes to creating models to explain observations.
Understanding Key Concepts
This is probably a generic point, nevertheless, it is the first and foremost step. Understanding the main concepts thoroughly is a logical way to improve your knowledge. It is essential to comprehend the topic and its relevant concepts before linking to the investigation. You should start by reviewing class notes and textbooks to ensure you have a solid grasp of the subjects' fundamental concepts.
Understanding the concepts is much needed to recognise how they relate to the investigation’s criteria. A list or table of formulas, definitions and examples is going to be your best friend when you’re investigating!
Revise Concepts Regularly
Another tip for students is to revise regularly. Revision should serve to help you retain information and test your skills through practice tests, active recall and questions. Go over your grey areas – where can the improvements occur? You'll be surprised by the difference a solid review process can make.
This way, you can apply concepts effectively during the investigation. If you would like to prepare for investigation before the school year, here are a few tips on how to fill in gaps from previous years of content in the holidays.
Collaborate with Peers
One of the misconceptions that many students have is that your achievement is only made by working on your own. This is not true!
Collaborating with peers can be a great way to share ideas, resources and innovation to solve the problem. A good amount of communication amongst peers can make you feel less stressed. Through listening to and learning from feedback, you can help your friends succeed and reflect on your knowledge. It’s like having strategic partnerships with your friends at school!
I’m struggling to be up to date with my studies at school, what can I do to keep on top of all the concepts?
If this is the case, don’t worry there are a few measures you can take to get out of this situation. These include:
- Find a suitable method of time management for you. Is it using a calendar, sticky notes, or a diary?
- Seek additional education services outside of class. The high school offers a range of support systems for both academic study and mental health. The purpose of these is to help you with challenges that can impede your learning progress and are open to every student!
How do I understand complex maths concepts in an investigation that are an extension of the in-class content?
There are often advanced levels of problems in maths investigation for higher marks.
- Act to seek help from your school teacher if you are concerned with extension problems. Students may receive practice questions to prepare themselves for particular concepts.
- If you would like more personalised help, some maths tutors are high ATAR achievers. They can offer student-centred support and instruction outside of school. Plus, tips from their own experiences!
Do I need to work on the investigation every day?
No! Remember to take a regular break between your study. It is a common misconception that the time spent on schoolwork amounts to academic achievement. Everyone needs to recharge their minds. A good way to do so is by clearly differentiating your time between leisure and studying. Organising your workload that’s suitable for you!
Written by KIS Academics Tutor for SACE Biology and Maths Methods, Suyeon Lee. Suyeon is pursuing a Bachelor of Clinical Sciences/Doctor of Medicine at Flinders University and has received stellar reviews from her past KIS Academics students. You can view Suyeon’s profile here and request her as a tutor.