Breaking down the Assessment
This assignment assesses your ability to interpret, analyse and evaluate information on a specific situation or stimuli. The task involves either/both Topic 2 (Vectors and Matrices) and Topic 3 (Complex Numbers 2) from Unit 3. The assessment requires you to respond with various skills such as mathematical language, appropriate calculations, data tables, graphs and diagrams.
You are allowed a maximum of 10 pages (including tables, figures, and diagrams) and 2000 words. You are provided with 4 weeks, which includes 3 hours of class time.
The report is divided into 3 main sections: Formulate, Solve and Evaluate. I will go through each section in detail for what is required to tick off the ISMG and get full marks. When starting your assignment, I recommend beginning with the “Solve” section of the report. This allows you to understand how you complete the task and will make the other sections simpler to complete.
The assignment is marked out of 20 and is worth 20% of your Specialist Mathematics grade.
FORMULATE
This section is worth 4 out of the 20 marks in the assignment. This section sets up the problem and enables the marker to understand that you have all the tools to solve the situation.
Begin with a short paragraph detailing the purpose of your report, what the task is and how you will address it. This could involve how data is gathered, the variables that may be provided to you and crucial mathematical concepts.
Mathematical Concepts
Then, you lead into the mathematical concepts involved in the problem. You must explain all the mathematical concepts that will be used in the “Solve” section. That’s why I find it helpful to begin the report by solving the problem. The mathematical concepts you cover could include equations (e.g birth rate equation), what concepts look like and how they work (e.g matrices and how to multiply them). Diagrams, tables, equation tools and graphs are incredibly useful tools to help explain mathematical concepts. It’s important to step through concepts as if you are almost teaching them because the reader is assumed to be an average individual. A combination of visual aids and your explanations will almost force the marker to give you the top band in this criterion. The instrument-specific marking guide (ISMG) dot point that correlates is “accurate translation of all aspects of the problem by identifying mathematical concepts and techniques”.
Observations and Assumptions
Moreover, you must also document observations and assumptions about the report (in that order).
Observations are almost the equivalent of defining what certain aspects are and what you are using. For example, it may involve data that you found online and/or limits you have on data/equations. Sometimes you may need to source information for observations. But to get full marks you must explain why you have made the “observation” (may link it back to task). This is what defers the observations from being documented to statements.
Assumptions are similar to observations in their format. However, assumptions cater to the method you have used to solve the problem. This could include specific cut-offs you placed for your data, connecting your theoretical knowledge to the real world or why your data is accurate/reliable. It is okay if your assumption and observation have slight overlap in the subject covered but there should be distinct differences. Also, it's important to explain why you have made the “assumption” and it often helps relate it to the real world or utilise quantitative evidence.
For both observations and assumptions, you require 2 good ones each. However, I recommend having 3 or more as there is no penalty for having “less strong ones”. Also, present these as clearly as possible by placing a header and either presenting them as a table with the statement and explanation or in dot point format. Below are representations of this.
SOLVE
There is no one-stop method to the solution as it varies depending on the stimuli given. But utilise tables, graphs and diagrams to show data, and explain your point and information. These are powerful tools to ensure your marker knows what’s going on and can help explain your writing. Further, it’s important to showcase some sort of calculations (it is a math assignment after all!). This could include typing out equations and solving them as if you are doing a math problem in an exam, showcasing the EXCEL calculations you have completed with screenshots or showing the progression between tables/graphs by the calculations completed. This is important as it covers the criterion “accurate use of complex procedures to reach a valid solution”, which means show me your mathematical working out.
Further, the next criterion ties into the mathematical concepts you covered in the formulate. Ensure to highlight the mathematical concept and explain/show how you have used it to solve the problem. This shows that you understand the concept, know how to apply it and see its relevance to the task. Therefore, ticking off the criterion “discerning application of mathematical concepts and techniques relevant to the task”.
Lastly, its important to hit the criterion that states “accurate and appropriate use of technology”. This means utilising technology meaningfully to solve the problem. This could include using your graphics calculator for complex calculations, tables in EXCEL and/or graphs in DESMOS. It's important to state that you have used these in your assignment as it makes it very easy for the marker to tick you off.
Overall, the Solve section is really up to you and how the problem is formatted. However, it’s important to build on from the formulate and continue to build towards providing the final answer. Your last paragraph of the solve should be the answer to the task. The answer shouldn’t be a surprise but makes sense from all the information and calculations provided.
EVALUATE
The main goal of this section is to “evaluate” how reasonable your answer to the problem is. This comes in different sections.
1) The first criterion is “evaluation of the reasonableness of solutions by considering the results…” and ties into the last criterion “justification of decisions made using mathematical concepts”.
Most times the easiest method to prove the reasonableness of your results is to compare them to the real world, is your answer realistic? In some cases, you will be given a task that has direct real-world applications, in others you could be given a more arbitrary task that implies a realistic application. It’s important to assess with your answer whether it fits current data and can be deemed reasonable. This could be as simple as a strong R^2 value or could require further research into the topic and what current data may provide. By utilising a mathematical concept to evaluate your reasonableness it ticks off two criteria in the ISMG, reducing your word count and making it easy for your marker. However, if you deem that it is unreasonable you should change your answer and/or solve section as it is required for your answer to be reasonable.
2) The rest of the first criterion that isn’t addressed yet is the “evaluation of the reasonableness of solutions by considering…assumptions and observations”
The best and safest way to complete this to attain full marks is simply altering your assumptions and observations. What happens if you change them? Does it cause your answer to change? Does it make it less or more accurate and/or reliable? Does your answer make sense if you change them?
It is perfectly fine if your answer changes (hopefully it actually does as it shows your observations and assumptions are important) but it should make your answer less reliable, less accurate and/or not make sense practically.
By changing your assumptions and observations you are effectively testing them. You should change 2 of each to make the criterion (or more if you have words/space).
3) This criterion is the “documentation of relevant strengths and limitations of the solution and/or model.
This can be formulated similarly to your observations and assumptions in the formulate. Therefore, you require reasoning/proof as to why it’s a strength or limitation (e.g strong R^2 value, validity/reliability claims and why, changing your assumption/observation could also help with this using the change in data, qualitative reasoning is better). Much like the observations and assumptions in the formulate, 2 good ones are required but I recommend having at least 3 each.
4) Lastly, the conclusion. There is no specific criterion for it, however, it does come under the communication mark much like the introduction.
Here restate the report’s purpose, how you completed the task, the results and the evaluation of the results. It's important you incorporate quantitative evidence here to get that top mark.
FINAL TIPS AND TRICKS
- Label all screenshots, tables, graphs, diagrams and equations with captions as per genre conventions. This is important for your communication criterion mark.
- Ensure the data and the report is readable when printing in A4 size as that is how your marker will be reading it.
- Visual aids are your best friend here. Screenshots, diagrams, tables, graphs, equations and big matrices (if applicable) help the marker understand what’s going on (a picture does paint 1000 words) and help make you look more professional.
- I recommend giving your finished report to a sibling or parent even if they have no idea about what's going on or the maths. Your report should be readable for them and they should understand it from start to finish. If they have to ask questions or things are unclear then you should edit your report as the average individual should be able to read and understand it.
Get inspired by a 99+ ATAR student’s study routine!
FAQs
How do I stay under the word count for my PSMT?
To stay under the word count, below is a screenshot of what does and doesn’t count to “words” in your report, taken from the QCAA website. I found it extremely helpful to put numbers as digits (e.g “1” instead of “one”) and utilise symbols instead of words (e.g “%” instead of “percentage”). Remember you only have 2000 words and 10 pages so utilising pictures and these tricks will help immensely.
Where can I find examples of a top mark PSMT?
Take a look at the annotated example on the QCAA website. This helps understand the ISMG. However, I recommend only seeking examples after having written a plan or parts of your report to avoid plagiarism. Remember there’s no one right answer!
Where do I begin with my Specialist Mathematics PSMT?
Don’t start with a Word document and from the formulate. Begin by answering the problem on your own (but this time you can ask your friends for help too), much like doing a regular math problem. This could be as simple as taking a pen and paper out to calculate the answer or utilising DESMOS/EXCEL to create your answer. It’s best to stay away from the Word document until you have found an answer to the problem.
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Written by KIS Academics Tutor for QCE Specialist Mathematics and Mathematical Methods, Ragulan Gnanavel. Ragulan is currently pursuing a Bachelor of Actuarial Studies and Commerce at UNSW. He has outstanding credentials as a tutor, and you can view Ragulan’s profile here and request him as a tutor.
