Getting the Formula Right
When I was a young boy, they told me that the stove top was hot and not to touch it. It was a direct instruction! “It is burny don’t touch!” they said. But my curiosity got the better of me. I needed to test what they meant. In that moment I found out what ‘burny’ was all about.
As a primary school educator of some 32 years, it can be frustrating and at a minimum ‘mind-boggling’ to see various approaches to teaching come and go. At times, debates between those passionate about certain methodology become quite heated.
At Mosman Prep we don’t get caught up in the swings and roundabouts of pedagogical practice. We adopt evidence-based teaching and learning methods to the benefit of our boys.
The author of a new report from the Centre for Independent Studies has called for a focus on traditional education methods in Mathematics, such as explicit teaching, involving the explanation and demonstration of new skills, as opposed to ‘inquiry-based learning’.
The report prompted an article in the Sydney Morning Herald last Wednesday which stated, “Maths teachers should ditch ‘faddish’ practices and focus on proven methods such as using clear and detailed instruction and teaching algorithms.”
Conversely, Australian Catholic University STEM research director Professor Vince Geiger said teachers should be able to incorporate both explicit teaching and inquiry learning into their teaching.
He states, “Research identifies we need to help our children be stronger in adaptive type thinking –taking what they learn in the classroom and being able to apply it in different situations and contexts and real-world situations. Explicit teaching by itself won’t get them there.”
There is no doubt that direct explicit instruction and teacher modelling is critical in mathematics teaching and learning. The foundational skills learned become the building blocks for future learning and problem-solving situations.
However, explicit instruction is not enough. It must occur alongside:
- mathematical teaching and learning that helps children to understand connections between concepts learned and relevance in their world.
- checking student background knowledge; overtly connecting conceptual and procedural knowledge; and providing effective feedback.
- open tasks that have the space within them for learning, not simply short tasks that students are meant to get right or wrong. Tasks that have multiple entry points, ways of seeing things, and pathways and strategies for solutions.
- the development of high-level mathematical thinking by providing opportunities for students to work in depth, not just at speed.
In addition, it must be supported by positive mindset and supportive structures such as:
- “cognitive conflict” with a growth mindset which leads to deep learning. Struggling with a new idea or concept is very productive for learning and brain development.
- grouping structures that are flexible, providing challenging and interesting work for all, and encouraging an appropriate level of instruction and high achievement.
- an environment where teachers express their belief in their students and support them when they make mistakes, so that they feel comfortable doing so.
At Mosman Prep we program a sequence of rigorous learning that follows - setting clear intentions and making connections to past learning and life; explicit teaching; joint, guided and independent learning; the use of technology; and finally feedback and reflection.
By providing explicit instruction, deep integrated mathematical teaching and learning, and an environment where our boys feel challenged but supported, we can develop the foundational skills and quantitative literacy they need to enjoy mathematics and become effective citizens and problem solvers in the 21st century.
Peter Grimes | Headmaster
References:
Myths are Undermining Maths Teaching (2022) - Centre for Independent Studies Sarah R. Powell, Elizabeth M. Hughes and Corey Peltier, University of Texas
Link - smh/forget-the-fads-maths-teachers-urged-to-focus-on-traditional-teaching-methods
Unlocking Children’s Math Potential (2019) - Jo Boaler, Professor, Stanford University; CEO, youcubed
