Rethinking Mathematics Instruction
This is a debate that has been raging within education for some time now and certainly shows no signs of abating. However, it is becoming increasingly obvious that the tide is turning towards the art of explicit teaching. I intentionally call explicit teaching an art form. Critics often reduce explicit teaching to a teacher standing at the front of the room scrolling through slide after boring slide of content. This could not be further from the truth.
In its most basic form, explicit teaching contains three key components: I do, we do, you do. A teacher demonstrates a concept, students then apply the newly taught skill with support, before moving towards independent practice. In reality, there are many factors to consider at each stage, along with carefully planned warm-up and plenary activities.
The Warm-Up
Each lesson entails a warm-up activity to focus students on what is to come. This may take the form of structured recall of previously covered material, or some practice of a skill that may be used in that lesson. For example, students may complete multiplication practice ahead of a lesson on equivalent fractions where the multiplication skills are used.
I do
Within the teacher-led demonstration, staff are constantly reviewing their learning intentions, making them clear to students. Staff also meticulously plan how to deliver the examples. Where to provide structure, how to balance verbal and visual prompts and how to build in necessary individual cases.
We do
The ‘we do’ phase involves students practicing the newly learned skills, applying their knowledge to problems whilst teachers constantly check for understanding. These formative checks provide a crucial checkpoint for teachers to know that students are ready to progress to independent work.
You do
Once confident that the skills have been learned, students can progress to more complex practice on their own.
This structure to a class is now widely recognised as best practice and is supported by extensive research on effective knowledge retention, whilst carefully considering learners’ cognitive load. It is certainly exciting to be part of the school’s new Instructional Framework which deeply considers all aspects of a lesson.
Certainly, for Mathematics, a subject based upon the acquisition and mastery of new skills, this approach to teaching has allowed students to flourish. The only time this method might be less effective is when students arrive at the start of a lesson already knowing the content being taught.
Mathematics is particularly challenging in this area. Whilst we cannot control the experience of every student in their primary school years, there will always be students who arrive in Year 7 who have accelerated into the Senior School curriculum. For instance, Year 7 Mathematics contains a section of work on manipulating whole numbers. Whilst these skills are vital for all students, it is not always the best use of time for a student who has already mastered these skills to participate in the instructional phase of this topic.
As a response to this growing concern in Mathematics, we are thrilled to introduce a reimagined Peninsula Grammar Mathematics Enrichment Program from 2027. This program will allow us to refine our teaching methods for those students in Years 7 to 9 who have accelerated their studies in Mathematics. The program itself will mirror the 7 to 9 curriculum but will allow those students who have previously mastered skills to spend more time on broad Enrichment activities. The program will be open to all students, but selection will be based upon results.
As we continue our journey to provide an outstanding, future-focused, holistic education based on high-quality teaching and learning, it is vital that we engage with the latest research on best practice in education. The Mathematics faculty is thrilled to be a part of this process as we look to support every one of our students to achieve their personal excellence.
Aaron Williams
Head of Mathematics
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