Refining Our Focus: From Transition Support to Conceptual Coherence in Maths Inquiry
It's common in the journey of teacher inquiry to realise that your initial question, while vital, needs sharpening to target the most impactful levers for change. I recently took a close look at my inquiry into supporting students transitioning from primary (Phase 3) to secondary (Phase 4, Year 9) mathematics, and felt a strong pull to refine it.
My original question was:
“How can I change my teaching practice to ensure that students transitioning from primary to secondary school feel supported in their mathematical learning, particularly in adapting to the expectations of Phase 3 of the new refresh Maths curriculum?”
While this question addresses a crucial student need feeling supported it’s very broad and focuses heavily on the emotional/pastoral aspect of transition. It makes it hard to pinpoint a specific, measurable pedagogical change.
Why the Shift?
The need for a slight, yet powerful, change arose from realising that the most significant barrier to student success during this transition isn't just a feeling of being unsupported; it's often a mathematical disconnect.
I’ve moved my inquiry to:
“How can Year 8 Maths instruction be strategically designed to ensure conceptual coherence and build representational fluency across the Phase 3 to Phase 4 (Y9) transition?”
Here are the key reasons why I felt this refinement was necessary:
1. Focusing on the 'What' and 'How' of Mathematics
The original question was about feeling supported. The refined question is about pedagogical strategy and mathematical depth. By focusing on designing instruction, I can investigate and implement specific teaching techniques that directly impact learning outcomes. It shifts the emphasis from a general well-being focus to a specific, high-leverage instructional change.
2. Conceptual Coherence as the Anchor
The new Maths curriculum refresh emphasises a progressive, connected learning journey. The term conceptual coherence is central to this.
What it is: Conceptual coherence means that mathematical ideas are not taught as isolated "tricks" or procedures. Instead, they are presented as a connected web of ideas. Students understand why a procedure works because they grasp the underlying concept.
In the transition: A lack of coherence means students might know how to find a fraction of a number (Phase 3 skill) but struggle to connect this to finding a percentage or solving a ratio problem (Phase 4 concepts) because the underlying concept of proportional reasoning wasn’t explicitly and consistently developed. My new inquiry targets building these bridges.
3. Representational Fluency is a High-Impact Skill
Transitioning to secondary school often involves moving from concrete, hands-on Phase 3 learning to more abstract, symbolic Phase 4 mathematics. Students need to be able to move fluidly between different ways of seeing a concept. This is representational fluency.
Example: A student who can solve 3x + 5 = 14 needs to be able to:
Represent the problem algebraically (3x + 5 = 14)
Represent it visually using a bar model or algebra tiles
Represent it verbally (three times a number plus five is fourteen)
Represent it graphically (a line y=3x+5 and y=14)
By focusing on building this fluency in Year 8, we proactively equip students with the tools to handle the increasing complexity and abstraction of Year 9 and beyond. It’s a direct strategy to support their mathematical adaptation, rather than just focusing on their feeling of being supported.