Is inquiry-based teaching working in the maths classroom?
Our founder's analysis of New Zealand's PISA 2022 data, and why we teach explicitly.
The question
New Zealand's maths results in PISA, the OECD test of 15-year-olds, fell for the third time in a row in 2022. Over the same decade, classrooms moved towards inquiry-based teaching, where students explore and question ideas with less direct instruction. Our founder asked a simple question of the data: does the teaching style a student experiences most of the time predict their maths score?
The study was completed in 2024 as a Summer Research Scholarship (SUMRESCH 301) in the Department of Mathematics at the University of Auckland, supervised by Dr Tanya Evans.
The study in brief
- TitleIs Inquiry-Based Instruction working in the Mathematics Classroom? An analysis of New Zealand's education using PISA 2022
- DataPISA 2022, New Zealand 15-year-olds, 3,828 students
- ComparedInquiry-based teaching against teacher-directed teaching
- Controlled forSocio-economic status (the PISA ESCS index)
- MethodHierarchical multiple regression
- WhereUniversity of Auckland, Department of Mathematics, 2024
How teaching style was measured
PISA asks students how often their maths teacher does certain things, from "never or almost never" to "every lesson or almost every lesson". Six of those questions were combined into two scores.
Students explore, the teacher prompts
- The teacher gave problems from everyday life involving numbers and asked us to make a decision about the situation
- The teacher encouraged us to think about how a problem from everyday life could be solved using mathematics
- The teacher encouraged us to think about how to solve problems in different ways than demonstrated in class
The teacher shows, students practise
- The teacher taught us to memorise rules and apply them to solve mathematics problems
- The teacher taught us how to use mathematical logic when approaching new situations
- The teacher showed us how problems that look difficult can be solved more easily by understanding how the number system is organised
Each student's answers were averaged into a score from 1 to 5 for each style. Scores of 4 and 5 ("more than half of the time" and "every lesson") tell us a student really is in that kind of classroom; lower scores only tell us they are not.
What it found
After allowing for socio-economic status, teaching style still predicted maths scores, and the two styles pulled in opposite directions.
- +20.3 pointsper step on the teacher-directed scale: the more often the teacher explained, modelled and had students practise, the higher the maths score
- −20.1 pointsper step on the inquiry-based scale: the more often students were left to explore with little direct teaching, the lower the maths score
- 21.9%of the variation in scores explained by the final model (socio-economic status plus the two teaching styles); every effect significant at p < 0.001
Above the national mean
Students who experienced teacher-directed teaching most of the time or every lesson scored above New Zealand's mean of 491.6 points.
Below the national mean
Students who experienced inquiry-based teaching most of the time or every lesson scored below the mean. On average; individual students in any classroom can do very well.
Not just a wealth effect
Socio-economic status was the strongest single predictor, as it always is. Teaching style added to it: adding the two styles to the model raised the explained variation from 16.6% to 21.9%.
The finding matches earlier international work on PISA science data (Oliver, McConney and Woods-McConney, 2021; Hwang and colleagues, 2018), which also found inquiry-heavy classrooms doing worse on average.
What the study does not claim
The data comes from students' own reports of what their teacher does, and 15-year-olds are not trained observers of teaching method. The study leans on the students at the ends of the scale, who experience one style nearly every lesson, because their answers are the most reliable. It shows association, not proof of cause, and it says nothing against inquiry as a tool for deeper thinking once the foundations are secure.
The study's own conclusion is a balanced approach: explicit teaching to build and secure the skills, with inquiry built on top of it rather than instead of it.
Open questions
- Is the pattern the same in other countries, or particular to New Zealand?
- How do schools built around inquiry compare with schools that kept direct teaching?
- Which parts of inquiry help, and at what point in learning a topic?
Why we teach explicitly
This is why every Cell Tuition lesson runs as "I do, we do, you do". The tutor explains and models the idea first. Tutor and student work through problems together. Then the student practises on their own with feedback on every step. It is the teacher-directed pattern that scored highest in the data, it is our founder's own teaching philosophy, and since 2025 it is a core part of the New Zealand curriculum refresh.
Our founder trains every tutor in this approach, whatever the subject, and keeps the team up to date with research in mathematics education.
Evidence we build on
- Teacher-directed teaching predicts higher maths scores in New Zealand (PISA 2022)
- One-on-one tutoring works: 87% of 96 randomised trials improved results
- Online tutoring works: gains of 0.2 to 0.3 SD in randomised trials
- Spaced practice beats cramming, so homework is five minutes a day
- Immediate feedback fixes errors before they set, so lessons are one-on-one
See the difference for yourself
One free lesson, no contract, and PDF notes afterwards.
