Revise-Learn-Apply: A model for teaching maths

I got into teaching because I love mathematics. My first foray into teaching was as a year 11 student tutoring a friend in year 8. I managed to help them get their grade from an E to a B and this sparked a fire in me. I wanted to help others learn about this wonderful world of numbers.

When I graduated from uni I somehow believed that in order to effectively teach Maths I needed to get my students to discover it for themselves. I felt like a magician, planning experiences that would reveal a deeper understanding of all things mathematical.

If only I knew then what I know now...
I was busy providing activities that I hoped would allow students to unearth the enigma of mathematics. I should have been actively teaching them the things I hoped they would discover. After all, I was the expert in the room.

"If a student hasn't learnt, then the teacher hasn't taught."
-Siegfried Engelmann

Like many educators, I strive to improve.

The last few years I have been considering how to best teach students Maths. I've finally settled on a framework that is supporting my students to achieve some amazing outcomes. This model is heavily influenced by Rosenshine's Principles of Instruction. It also ensures that due attention is given to each of the proficiencies of understanding, fluency, problem solving and reasoning. You will notice though that the prerequisite skills required for these proficiencies are explicitly taught to students.
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For want of a better phrase, I call it Revise-Learn-Apply.

1. Revise
In my first year of teaching I observed a colleague run a Maths lesson. He started it off with students answering 10 questions from the board. These questions covered a range of topics previously covered in his class. 
When I started using Direct Instruction programs I noticed that everything that students learnt was revisited. Rosenshine talks about the importance of daily, weekly and monthly reviews. Others frame it as retrieval practice. Whatever you call it, it is essential that we give our students the opportunity to revisit and build on their prior learning.

Inspired by the practice of Bentleigh West PS, as demonstrated in this video by David Morkunas, I spend about 20 minutes in a revise phase reviewing things I have previously taught. This part tends to be paced pretty quickly, with students' understanding being regularly checked.

One revise phase might cover the following:

• Counting by ones from different starting points.
• Counting backwards by ones.
• Subitising.
• Skip counting by 2s, 5s or 10s.
• Recalling the days of the week and saying which day comes next.
• Reading two-digit numbers and saying which of a pair is larger/smaller.
• Naming 2D shapes.
• Identifying which object is bigger/smaller.
• Addition and/or subtraction to 10.

Given the number of topics we touch on, it has to be paced quickly, and mathematical fluency is developed throughout. Students are constantly responding to questions in different ways and I am able to provide immediate feedback whenever an error occurs. I am also able to be responsive and anything that gets a high number of errors will be revisited and retaught. Any students who struggle are easily identified and provide additional support. Having said that, the success rate as we revise tends to be pretty high. 

2. Learn
The middle part of my Maths lesson (again about 20 minutes) is where the students learn because I am explicitly teaching. At the start of the year many of my foundation students didn't know how to count to 20. All of the concepts that now feature in our revise phase have been explicitly taught. During the learn phase new material is explicitly taught in small steps. Students are actively engaged as they build their knowledge about the concepts, procedures and strategies that are critical for being numerate. 

3. Apply
Once students have been taught a new concept, they need to be supported as they practice it. The apply phase provides dedicated time for students to apply their new knowledge in different situations. It is here, in the final third of our lesson, that students are supported as they solve problems and share their reasoning. It is important to note that this phase occurs after the explicit instruction. My students have been set up to succeed because they have been taught the skills they need to be successful.
​And because my students are successful at Maths, they love Maths!

Keen to learn more?
I am presenting about my experience teaching Maths at Sharing Best Practice Ballarat on October 1. Tickets have sold out but if you're attending then I'd love it if you chose to come to my session.

Think Forward Educators have set up a Maths Network and the inaugural meeting on September 14 features non other than David Morkunas! Details can be found here.