Implementing my Refined Inquiry - some examples of resources/tasks and Activities I've included in my teaching and planning

 

Implementing the Refined Inquiry: Coherence and Fluency in Year 8 Maths

I believe moving from a general transition concern to the specific pedagogical targets of conceptual coherence and representational fluency makes my inquiry actionable and its impact measurable.

Here are examples of resources, activities, and a structured approach to data collection to support your inquiry.

Part 1: Resources and Activities for Intervention

The core of this intervention is the consistent and explicit use of the CPA (Concrete-Pictorial-Abstract) approach, focusing heavily on the "P" (Pictorial/Representational) stage to build fluency.

1. Conceptual Coherence: Proportional Reasoning

Coherence Goal: To explicitly link the Phase 3 concept of fractions/percentages to the Phase 4 concepts of ratio and algebraic equations.

2. Representational Fluency: Linear Functions/Algebra

Fluency Goal: To enable students to fluently translate a single relationship (e.g., a linear pattern) between four key representations: Verbal, Table, Graph, Symbol (Equation).

Reflections and Tweaks made

 

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.

Causal Chain 2025

This Causal Chain visualises the Theory of Change guiding my 2025 Inquiry. It connects my core question, supporting Year 8 transition into Phase 3 Maths, to three measurable student outcomes. A key pedagogical insight this year was the need to implement explicit "Think-Aloud" modelling in mathematics, a teaching practice I found was habitual in literacy but absent in my maths instruction. This intervention successfully led to students making a crucial learning step: the consistent use of precise mathematical vocabulary. The chain concludes by defining the desired measurable outcomes and the final criteria for success in generalised mathematics achievement.

Using Baseline Data to Track Maths Progress

As part of my student achievement challenge—to raise maths achievement for my Year 7 and 8 learners and ensure they are well-prepared for high school—I have collected a range of data to build a clear profile of where each learner is currently at. This data will serve as baseline evidence to compare against end-of-year achievement and measure the impact of targeted teaching strategies.

1. Formative Assessment Tasks (Term 1 & 2)

In-class activities, such as number knowledge quizzes, problem-solving tasks, and exit tickets from the Maths No Problem programme, have helped me identify gaps in students’ understanding of core number strategies. These formative tools give insight into students’ confidence and fluency in:

• Place value understanding

• Basic facts recall

• Applying the correct operations in multi-step problems

At the end of the year, I will repeat similar formative tasks (modified for progression) to measure growth in confidence, accuracy, and reasoning.

2. Diagnostic Testing and Observations

I used initial PAT Maths data and school-wide numeracy assessments to identify students below, at, and above expected curriculum levels. Combined with observational notes taken during collaborative problem-solving, these data points give a rich picture of both cognitive and affective aspects of learning (e.g. persistence, use of strategies, peer collaboration).

End-of-year diagnostic tools will allow me to directly compare shifts in these achievement levels, and determine whether more students are working confidently at or above curriculum expectations.

3. Student Work Samples

Work samples from maths books and Maths No Problem workbooks have been collected across the term. These samples illustrate:

• How well students unpack and solve word problems

• Their ability to explain their thinking (written and oral)

• Growth in using visual strategies like bar models

These will be compared against samples from Term 4, looking specifically at whether students can independently solve complex problems and show their thinking clearly and accurately.

4. Student Voice and Reflections

Students have completed goal-setting and reflection tasks about their learning in maths. This qualitative data gives insight into their self-perception, confidence, and attitudes toward maths. By gathering similar reflections at the end of the year, I can track whether students feel more capable and prepared for high school maths expectations.

Summary:
All of this data—standardised tests, observations, work samples, and student voice—forms a robust baseline that allows me to measure not just academic growth, but also shifts in confidence, engagement, and readiness for high school. The aim is to ensure that by the end of the year, more students are operating confidently at expected levels, and feel prepared for the increased challenge of secondary school maths.

Professional Readings

Professional Readings that helped me formed my Hypotheses:

1. "Visible Learning for Mathematics" – Hattie, Fisher & Frey (2017)

Key Insight:
This book emphasises what works best to improve student learning in maths, based on meta-analyses of thousands of studies. It highlights that one of the most impactful strategies is when teachers make learning intentions and success criteria visible to students, and actively teach students how to monitor their own progress.

How it helped form a hypothesis:
Based on this, I hypothesised that students in my class were struggling not just because of the complexity of the Maths No Problem programme, but also because they weren’t always clear about what success looked like. This supported my decision to integrate more co-constructed success criteria and verbal scaffolding, especially when unpacking word problems.

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2. "Mathematics for Young Children: An Active Thinking Approach" – Bobis, Mulligan & Lowrie (2013)

Key Insight:
This text explores how conceptual understanding in number develops through structured visual models and pattern recognition. It argues that children need repeated, explicit opportunities to see how numbers relate to each other—not just to compute answers.

How it helped form a hypothesis:
From this, I began to question whether students were being asked to solve complex problems too early, without first developing flexible number sense. This reading validated the need to "peel back" the Maths No Problem questions and revisit basic strategies—helping to ensure students had the mental models needed before tackling more abstract reasoning.

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3. NZC Resource: "Teaching Primary Mathematics" – Ministry of Education (TKI)

Key Insight:
The New Zealand Curriculum and associated resources on TKI stress the importance of culturally responsive teaching, cross-strand integration, and using rich tasks that connect maths to real-world experiences. It also promotes differentiated instruction that meets students at their learning level.

How it helped form a hypothesis:
I reflected that while Maths No Problem is a strong programme, it may not always connect to the lived experiences of my students or align with the contexts that engage them most. This led to the hypothesis that integrating strand content and hands-on, relevant tasks earlier in the year would boost both understanding and motivation—especially for learners who find abstract number work challenging.

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Additional Sources That Influenced My Thinking:

• Student voice and reflections – helped me see that students often felt “shut down” when faced with unfamiliar problem contexts.

• Classroom observation notes – showed that some students were highly capable with number when strand or real-life applications were introduced.

• Colleague collaboration and PLD discussions – reinforced the idea that structured scaffolding and vocabulary unpacking were critical for student success with problem solving.