by Dana Hanna, Associate Dean (Education)*
First-year university mathematics has a familiar problem. At one end of the grading scale, students scrape through with the minimum required marks but arrive in second-year courses underprepared for what comes next. At the other end, students earn high distinctions without ever having to demonstrate the deeper conceptual understanding those grades are supposed to represent. And for many students, the moment they discover their approach to learning mathematics wasn’t working is the final exam itself — when it’s too late to do anything about it. This is a familiar story for many courses, especially first year where students are transitioning from high-school learning environments to higher education.
This was the situation facing MATH1013, ANU’s introductory calculus and linear algebra course taken by 300–400 first-year students each semester, most of whom are studying mathematics as a service course for another discipline. A team from the ANU Mathematical Sciences Institute (MSI) has spent the past two years redesigning the course’s assessment structure around the principles of mastery learning — and the early results suggest the change is working.
The problem with a single high-stakes exam
Historically, MATH1013 was assessed mostly through exams: a mid-semester exam worth 20–30%, a final exam worth 40–50% with a low hurdle requirement, and the remaining 30% from quizzes, tutorials and assignments.
A close look at past exams revealed the structural issue. The exam was designed so that around 40% of the final exam’s marks sat at pass-level difficulty, with the remaining questioned aim at the higher difficulty levels. However, partial credit on harder questions meant students could accumulate enough marks to pass without potentially having mastered the basics. Meanwhile, the final exam covered mostly second-half content, so a student’s grasp of foundational material from earlier in the semester was barely tested at all by the time it counted.
Mastery learning: an old idea, newly applied
Mastery learning isn’t new — the concept dates back to Benjamin Bloom in the 1960s, and has been applied in various university mathematics contexts over the decades, including more recent work in Australia. Its core premise is that success in a subject depends less on aptitude and more on the time and support a student needs to reach a required standard. Rather than one summative exam at the end, students sit shorter “mastery” exams earlier in the course, set at a high pass bar (commonly around 80%). If a student doesn’t meet that bar, they’re given further attempts — with additional support and revision in between — before moving on. If you’re interested in more information on mastering learning, competency based assessment and transition learning, a great starting place is the Transition Pedagogy Handbook (2010) by K. Nelson, T. Creagh, S. Kift & J. Clarke
What changed in MATH1013
For 2024–25, the MATH1013 team restructured the course’s assessment around this model:
- 20% — Two Mastery Hurdle Exams, covering the first and second thirds of course content respectively. Each consists of 20 questions marked simply correct or incorrect, all set at baseline pass-level difficulty. Students need 16/20 on each to clear the hurdle, with up to three (or four) attempts available during the semester and additional support offered between attempts.
- 32% — Online quizzes, tutorials and assignments, continuing the ongoing-engagement component of the course.
- 48% — Final exam, with no hurdle requirement, but explicitly assuming that a student at a bare-pass standard has already secured roughly 42 of 52 available marks earlier in the course. Question parts are stratified to test learning outcomes at pass, credit, distinction and high-distinction levels.
The effect is to separate two things that a single exam had been trying to do at once: confirming that every student has the baseline skills they need, and distinguishing between levels of deeper understanding for grading purposes.
Early results
Comparing the 2024–25 offerings to previous years, the team reported several encouraging shifts: a significant reduction in students withdrawing after the census date, fewer fail grades among students who remain enrolled, fewer students requiring supplementary assessment, and a higher confidence in the grade levels given to students at the completion of the course.
Practical Aspects
When students don’t achieve the minimum required grades for the mastery exams in the first instance they are provided a second opportunity approximately two weeks later. A third attempt is organized, but due to timing this occurs in the final exam block and often after the final exam (which is less than ideal). While originally the maximum mark (10/10) could be achieved regardless of how many attempts were made, this was changed to a maximum of 9/10 for the second attempt and 8/10 for the third attempt. This change increased the proportion of students who achieved satisfactorily the first attempt and again in the second attempt.
Currently the setup of these mastery exams are handled by the academics involved in this course. The additional support that is made available to students between the exam attempts is provided by casual tutoring staff. Exams are also hand-written on specific exam sheets (i.e. not using exam booklets) and scanned to gradescope for ease of marking[1].
Why it matters beyond MATH1013
The MATH1013 redesign is a useful case study in transition pedagogy and mastery learning — the idea that curriculum and assessment should be deliberately designed to support students gaining confidence in a set of skills that will form the foundation of future courses, rather than assuming they’ll adapt unaided or ‘figure it out’. By giving students an early, low-stakes signal about whether their foundational skills are where they need to be — and the support to close the gap before it’s too late — the mastery learning model addresses a problem that will be recognisable to anyone teaching large first-year quantitative courses, or courses where new skills are being developed in their initial phase.
This post summarises a presentation by Dr Griffith Ware and Assoc. Prof. Adam Piggott of the ANU Mathematical Sciences Institute (ANU) as was written with the aid of Claude-AI. If you’re interested in pursuing an assessment design founded in mastery or competency based assessment, you’re encouraged to connect with the CBE Associate Dean (Education).
[1] If you are interested in exploring Gradscope further – please contact the CBE Associate Dean (Education) for further information.