We ranked first for student growth in maths. What are we actually doing?
Our school has achieved outstanding results by avoiding high effort, low yield practices and investing in evidence-based practices.
Schools receive a report on how well they meet the needs of students in maths
Victorian schools receive a report on the relative growth of their students in NAPLAN Numeracy from Year 3 to Year 5. The relative growth of each student is sorted into three categories (low, medium and high) and emphasis is place on the percentage of students with high relative growth.
Why is this report significant? Because it is an objective measure of how well a school is able to meet the needs of students regardless of their starting point. All classes have students with a range of proficiency and diverse needs. All teachers have to contend with the challenge of making sure all students are making progress. Differentiation refers to efforts to teach a wide range of students, ensuring growth for all. In other words, the percentage of students in high growth is a measure of how well a school is differentiating instruction. The more effectively you differentiate instruction, the higher the percentage of students with high relative growth.
Our school ranked first for relative growth in NAPLAN Numeracy
The graph below represents relative growth achieved by Year 5 students in the period 2023-2024. The yellow bar is us. The other purple bars represent other schools with similar characteristics. 60% of our students achieved high growth, well above the 39% average for similar schools and the 25% state average. Not only are we performing above average for relative growth; the graph shows that on this measure we are ranked first when compared against similar schools.
Obviously, we’re incredibly proud of this result and the leaders and teachers at our school work incredibly hard. But I also think this result is significant because most educators would probably be surprised at what the school with the highest proportion of students with high relative growth in maths is actually doing.
Surprising things we’re not doing to maximise student growth and what we do instead
All schools put a lot of effort into various strategies to meet the varying needs of students and secure growth for all. Our school has avoided implementing many of the most common strategies directed towards this goal. Here are some reasons:
They sound intuitively right, but may not yield positive outcomes in reality
They require lots of effort for little gain
They are difficult to scale due to complexity or difficulty
They crowd out professional development of high-impact practices
Let’s look at some examples of what we’ve decided not to do and what we are doing instead:
In-class ability groups vs whole-class instruction - Perhaps the most significant thing we’re not doing is in-class ability groups. If you visited a maths classroom at our school, you wouldn’t see a low, medium and high group working on different activities. Instead, you would see whole-class instruction with the teacher explicitly teaching a common learning objective to all students. Doing this well accounts for most of our success.
This is complemented by a multi-tiered system of supports (MTSS). We administer universal screening to identify students who need extra support and provide additional small-group intervention. (The screening assessment is Acadience Math.) Classroom teachers also make adjustments to their instruction for these students: more checking in, more scaffolds, finding a couple of minutes in the day for one-to-one instruction, working more closely with specific families. For a very small number of students who need very intensive support, a systematic and collaborative effort is put into individualising goals, instruction and resources. At the other end of the bell curve, the most proficient students can opt in to an extension maths club. It’s a complex system, but a priority is to avoid compromising the quality of whole-class instruction.
Emergent curriculum vs textbooks - One other surprising thing we’re not doing is an emergent curriculum, expecting teachers to create curriculum from scratch each year based on their knowledge of students. Our teachers are not spending lots of time figuring out what to teach. Instead, our teachers use a textbook as the basis for instruction. (The textbook series is PR1ME Mathematics.) The textbook specifies clear, well-sequenced content for students to learn. The level of coherence provided by the textbook accounts for how well our school provides foundational skills and progresses learning lesson-to-lesson, month-to-month and year-to-year. (Tim Oates wrote an excellent paper on the function of textbooks in high-performing jurisdictions here.)
Spending less time on deciding what to teach opens opportunities for teachers to focus on optimising instruction. For a given specific learning objective, teachers still need to think about how to provide an effective explanation or model a procedure; what scaffolds to put in place during guided practice and how they should be faded; how to chunk and sequence learning; how to ensure students become fluent in skills; and how to support students to apply skills in problem solving situations.
It’s all about understanding trade-offs
The key to our success is understanding that every decision in a school involves trade-offs. No decision is perfect. Everything has its balance of costs and benefits, risks and opportunities. Ideas shouldn’t be judged by their intention, but their likely outcomes.
In-class ability grouping provides a good example of where we need to be more aware of trade-offs. The theoretical benefit of diverse students being provided with activities tailored to their point of need is offset by many costs and risks:
Instructional time - Probably the most significant cost of in-class ability grouping is the reduction in time in which students are actively being instructed by a teacher. In a lesson where students are organised into three groups, students get a third of the time being actively instructed they would otherwise get with whole-class instruction. This is a best-case scenario. Teachers forced to implement ability groups often lament spending most of their time reacting to off-task behaviour when they are trying to work with one group. Tim Shanahan has noted here that classes organised around grouping are less effective when it reduces the amount of teacher-guided instruction the student receives.
Workload - The fact is that planning for three groups in one lesson is more work than planning a lesson around a common learning objective. If the amount of lesson planning is a grind, it is also understandable that a teacher may sacrifice quality in order to get the work done. High-effort strategies may have a negative impact on student learning (not to mention teacher wellbeing).
Learning objectives - Students can learn more ambitious content with teacher guidance than on their own. However, lessons organised around ability groups depend on setting students up with activities they can complete independently. Less proficient students may be successfully engaging with a simpler activity, but there is a hidden opportunity cost. They could be learning more advanced content, supported by the teacher’s explanation and modelling, guided practice that begins with scaffolds that are gradually faded out and closely monitored independent practice with lots of feedback throughout.
Meanwhile, the benefits of whole-class instruction for more proficient students need to be considered:
Overlearning - We often underestimate the extent to which students can progress by continuing to practise skills in which they can demonstrate accuracy. This can lead to better retention and fluency.
Developing stronger schema - We often underestimate the extent to which students can develop stronger schema around maths skills they have acquired. They may lack the mathematical vocabulary to explain what they know with clarity and sophistication. They may lack knowledge of how an abstract procedure can be represented using various concrete materials or visual strategies. Developing schema can make future learning easier.
Learning transfer - We often overestimate the extent to which students can transfer maths skills to various problem solving situations. Even if students have already acquired the procedural knowledge being studied by the whole class, when the focus turns to explicitly teaching problem solving, these students are often learning something genuinely new.
Is this a perfect solution for everyone? No, but a perfect solution doesn’t exist. Our school has made a decision to prioritise whole-class instruction because, on balance, more learning is likely to happen with whole-class instruction than with ability groups where most students are working without direct teacher guidance.
The right choice is not always intuitive
When people think about maths instruction that meets the diverse needs of students, they don’t often think about whole-class instruction and textbooks. And yet, they are a key part of our strategy and the data indicates we are doing differentiation better than any other school. The lesson here is that schools have difficult decisions to make and we need to be guided, not by what looks like the right thing, but by what is likely to result in the best outcomes based on the evidence we have.
Brad Nguyen is a primary teacher, learning specialist and consultant.
References
Tim Oates (2014). Why textbooks count, Cambridge Assessment.
Tim Shanahan (2018). Should reading be taught whole class or small group?, Shanahan on Literacy.
