The VCE General Maths exams are over for another year - congratulations to you and your students.
As one Reddit user pointed out, someone at VCAA likes the Olympics, dropping it into the exam! So, let’s jump, dive and plunge into an analysis of this year’s Exam 1.
First up, and a big change for 2024, there’s only 4 options provided for all multiple-choice questions (A, B, C and D) - down from the 5 options of previous years. This was of course announced by VCAA back in March 2024, so it was no surprise, and should’ve made Exam 1 simpler for students.
Overall the exam struck a happy medium of being challenging but not tricky. But getting top marks is no simple feat - VCAA carefully design each exam to spread students across the bell curve.
As we know all multiple-choice response options (apart from the correct response) on the VCAA General Maths exam 1 are constructed around common misconceptions or errors that students are likely to make. The wrong answers are not arbitrary, they’re designed to separate students out across the bell curve.
So let’s break down Question 18 (see below) on calculating interest, to see why students might not have picked Answer B as the correct answer.
If a student chooses Answer A (0.75%) they have assumed there are too many zeros in the weekly interest rate multiplier 1.00075 and simplified it incorrectly to 0.75%, without considering the correct process for converting to an annual rate.
Answer C (4.5%) means a student has rounded the multiplier 1.00075 to 1.0008 during their calculations. This minor rounding error has skewed the outcome, giving an incorrect annual interest rate of 4.5% - a simple misconception applied to significant figures.
Lastly, if a student chooses Answer D (7.5%) they have made a simple but significant error by placing a decimal point incorrectly between the 7 and 5, resulting in 7.5%.
Back to the Olympics - if you’re practising, say, high jump, your coach is going to instruct as much on what to do, as what not to do (don’t have too long a run up, jump off from the correct foot… you get it!)
In Maths we need to do the same, by getting students to understand what is wrong, as much as what is right.
We do this for 3 reasons:
A simple activity teachers can try is to give the class or groups of students wrong answers that are based on misconceptions, and get them to explain why this is wrong. Students often really struggle with confidence in Maths, and this can be a great strategy for tackling this. They’ll love pulling apart errors as much as they love getting a question right!
Building up students’ Maths misconception muscles takes time - and needs to start from Year 7. That way students are progressively building the depth of knowledge they’ll need to tackle, and succeed in senior Maths.
This is why at Edrolo we bake misconceptions into every part of what we do in Year 7-10 Maths.
At the start of each chapter, we introduce a misconception table. It highlights common errors and misunderstandings that students are likely to encounter. This sets the stage for a deeper learning experience where students are more aware of potential pitfalls and better equipped to navigate them.
For all our multiple-choice questions, incorrect answers are intentionally created to reflect common student misconceptions. We don't use random or arbitrary numbers; instead, each distractor is crafted to address a specific misunderstanding that students frequently have.
This approach mirrors the standards set by VCAA, ensuring that students are well-prepared for their final exams. Let’s see how we do exactly this for Year 10 on the same topic of compound interest - and what misconceptions would lead to a student not selecting Answer C as the correct response.
If a student picks Answer A ($13,327.03) they have only divided the annual interest rate by 4 (for quarterly compounding) but failed to apply the compounding effect correctly over multiple periods.
Any student picking Answer B ($14,332.50) has not taken into account the compounding periods correctly for the interest rate and time period. They have used the annual interest rate without adjusting for quarterly compounding.
Lastly, any student picking Answer D ($14,332.50) has applied the time period by multiplying it by 4, as if compounding for eight years instead of 2, and not dividing the interest rate by quarterly too. This overestimates the compounding effect and leads to a much higher future value than expected.
Ultimately, our goal is to create resources that empower students to overcome challenges, understand their learning paths, and excel. By focusing on misconceptions, we align with VCAA's commitment to high-quality assessments and equip students with the skills and awareness they need for academic success.
In mathematics education, understanding what lies beneath the surface of a wrong answer is just as important as getting the right one. It’s how students will really win when it comes to mastering maths, being ready for the final exams and pursuing a lifelong love of maths.
My Maths teaching colleagues at Edrolo have spent the last 4 years building a skills-focused system for teaching maths from Years 7-10, email [email protected] if you’d love to take a look - I’d be happy to show it to you.
