I am on Charlotte Wilkinson's mailing list, as I respect her research and writings, and have her permission to share her thoughts and writings.
Her latest epistle (April Newsletter) https://www.wilkieway.co.nz/blog/post/163475/april-newsletter-2026/ asks us to Question and Reflect on Teaching Approaches we may have thrust on us or encouraged to implement as its "best for the students" see her final paragraph.
Beware The Science of Maths
Riding on the wave of the popular “Science of Reading” there is now a movement calling itself the Science of Maths.
Information for this newsletter is taken from The Science of Maths Reconsidered: A critical examination of foundational claims. by Kate Raymond (University of Oklahoma USA) and Melissa Gunter (Central Connecticut State University USA)
While there is much common ground between the “Science of Maths” (SOM) and current research in maths education most arguments made by SOM are based on scant evidence.
Areas of agreement: There is a need for high quality instruction, large scale research of instructional practices, and clear goals and direction for students.
SOM conclude that these goals can only be achieved through the use of direct instruction, they fail to demonstrate that inquiry, discovery, or other student-centred approaches cannot accomplish the same goals.
SOM claims it is a myth that students should not be exposed to procedural instruction until they have demonstrated adequate conceptual understanding.
This is a long standing debate within maths education - when in fact effective mathematics teaching focuses on the development of BOTH conceptual understanding and procedural fluency. Conceptual knowledge and procedural knowledge work in tandem and are often intertwined. To use an algorithm well, students have to have a strong foundation in understanding of numbers and place value. They need a strong foundation in understanding of what it means to add, subtract, multiply or divide before introducing an algorithm.
SOM claims it is a myth that inquiry learning is the best approach.
The argument given is very thin in that the view of inquiry based learning is interpreted as an approach that offers no support or guidance to students. Inquiry with support and scaffolding for student success is of benefit to students. There is little evidence to suggest that inquiry methods with support and scaffolding are inferior to explicit instruction methods.
Further myths claimed by SOM include:
• Teaching algorithms is harmful
• Productive Struggle is important
• Growth mindset increases achievement
• Executive training function is important
• Timed assessments cause maths anxiety
The emergence of SOM as a contempory contributor to the discourse of mathematics education should be treated with caution especially when picked up by politicians, policy makers and the media. Their inclination to support SOM is probably because of its focus on procedural fluency (which is easily measured) rather than sense making, reasoning, or problem solving for which is harder to gather “hard data” as evidence of this occurs over time and in application outside of the school setting. (Becoming numerate!)
We should focus on the common ground:
Timed assessments: - be wary of timed assessments when used ineffectively in providing useless data, creating high stakes assessment practices, used to compare students, or used as a means of withholding something, e.g. morning tea break.
Explicit instruction: defined as “an instructional design and delivery approach characterized as unambiguous, structured, systematic and scaffolded.” This approach can equally be applied to inquiry, problem based learning or other student-centred approaches. However to add to the definition should be “responsive and flexible to individual learning needs.”
It is imperative that as educators we do our due diligence with all new ideas, examining each critically and always ask ourselves why?
We need to make sure we go beyond asking ourselves;
What do I need to teach? (the curriculum)
How am I going to teach it (which resource am I going to use?)
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I would like to add a phrase, "Courses for Horses" in other words there is no one instruction that will fit the needs of all students. We as Teachers/Educators need to be aware of this and adjust our teaching strategies to meet the needs of all students in our classrooms.
Consider the learning styles or the students:
- Visual (Spatial): Prefer maps, diagrams, graphs, charts, and patterns to understand information.
- Auditory (Aural): Learn best through listening, discussions, lectures, and speaking.
- Reading/Writing (Verbal): Consume information best through text-based input and output, such as reading notes and writing.
- Kinesthetic (Physical): Learn through experience, hands-on practice, simulations, and movement.
"I can remember being asked to demonstrate how I would teach simple line graphs to a Year 10 group of girls in a private girls school.
I explained to the class that we were going to start the "maths lesson" outside on the tennis courst, where I had prepared a number line including negative numbers.
Once outside I asked some of the girls to stand on a number on the number line and then proceeded to give them an equation such as: y = 2x + 3
The students standing on the various numberline points had to look at the number between their feet and do the calculation: 2(-2) +3 =-1, 2(0) + 3 = 3, 2(3) + 3 = 9 etc.
Once the calculations had been completed with assistance from others especially for the negative numbers I instructed. "When I say "go" if your total is negative step that many steps backwards, if positive then step those many steps forward. Go
What have we made? A straight line!
After a number of these activities including a quadratic equation or two we then went inside and discussed what we found. This included drawing the graphs of the various equations.
At the debrief, with the schools teachers I was asked,
"Did you notice the girl at the back right who answer, or tried to answer all the questions?
"Yes, I did"
"She has never answer a question in maths before"
"Lets disregard the fact that I am a Male teacher in an all girls school, and consider if she is a Visual/Kinesthetic Learner?"
This is just one example how a changed teaching style can empower and involve a student who may have been "turned off" for most of the time.
One size(approach) does not fit all
