We identified that Non-Routine Problem Solving (NRPS) was a learning tool that could better support students in taking in and understanding new ideas. NRPS complements the College’s existing mathematics teaching and assessment structures. Although traditional tests remain a core measure of learning, elements of NRPS have now been incorporated into these assessments. Tests at Years 7, 8 and 9 now include three distinct sections, challenging the students in not only routine and complex elements from the current unit of work but also problems of a similar nature to those encountered in the Team Competition.
Since the introduction of NRPS in 2023 with the Year 7 and Year 9 cohorts, followed by the inaugural Team Competition later that year, all Middle Years mathematics classes have since engaged with elements of the NRPS model.
In 2026, selected components of the NRPS model have begun to be carefully introduced in the Preparatory School. Phase One is already well established, with strong engagement evident across the targeted year levels.
This has been integrated in student learning through a three phase developmental model.
Phase 1: Individual Learning and Teacher Guidance
Students begin by attempting carefully selected problems individually. These problems are then explored through structured whole class discussion, during which the teacher explicitly models optimal approaches to the thinking, reasoning, and writing processes. Students subsequently apply these cognitive processes to similar problems, enabling them to refine and strengthen the accessibility of the ideas required.
Phase 2: Team Competition
Students participate in a NRPS Teams Competition, engaging collaboratively to create strategies to solve a series of problems. Through this, they gain insight into how their peers think, reason, and learn. The competition takes place under a time restriction, and when complete, solutions are submitted, marked, and teams are ranked, with prizes awarded accordingly.
Phase 3: Battles
While year level team competitions promote collaboration, they offer limited opportunities for students to perform their mathematical thinking publicly. The NRPS Battles require students to present their reasoning verbally in front of an audience. As well as further enhancing problem solving skills, these events build students’ capacity to communicate mathematical ideas coherently, confidently, and engagingly, while also contributing to a highly energetic and enjoyable learning environment.
Measuring Success
Excitingly, the NRPS initiative has brought positive student engagement and objective impact on the outcomes for all students. This can be seen in the clear positive shift in Year 9 NAPLAN Numeracy outcomes. The cohort involved in the inaugural 2023 NRPS program went on to achieve the highest Year 9 Numeracy score in the state in 2024. The 2025 Year 9 cohort also demonstrated notable improvement, achieving a higher average result than the 2024 cohort. Similar gains have been seen in the Year 7 results. The NRPS initiative has increased students’ familiarity, competence, and confidence.
