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Research School Network: Improving maths teaching with cognitive load theory Zain Mahmood shares a case study to support reflection

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Improving maths teaching with cognitive load theory

Zain Mahmood shares a case study to support reflection

by Bradford Research School
on the

Headshot ZMA

Zain Mahmood

Teacher of Mathematics, Jebel Ali School

Read more aboutZain Mahmood

In my previous blog, I explored how understanding cognitive load theory can help teachers with the many decisions they have to make about planning, designing and delivering lessons. To help explore these ideas, we share the case study of Mr Mahmood.

Mr Mahmood aims to ensure his students grasp the properties of parallelograms. To achieve this, he prepares a comprehensive worksheet incorporating a blend of definitions, proofs, and practical problems related to parallelograms.

Preparation

Worksheet Development: Mr Mahmood creates a worksheet featuring 20 problems, encompassing defining parallelograms, proving certain properties, and solving complex application problems involving parallelograms in real-world contexts.

Brief Introduction Plan: He plans a concise 5‑minute lecture to swiftly cover the basic properties of parallelograms, including the definition, opposite sides being equal, opposite angles being equal, and diagonals bisecting each other.

Teacher Delivery

Introduction: Mr. Mahmood begins the lesson with his planned 5‑minute lecture. He quickly reviews the basic properties of parallelograms, presenting the definitions and properties on the board without detailed explanations or examples.

Worksheet Distribution: Immediately following the lecture, he distributes the comprehensive worksheet to the students.

Independent Practice


Student Instructions: Mr. Mahmood instructs the students to complete the worksheet independently within the next 40 minutes. He does not offer any examples or step-by-step guidance to support their independent work but does circulate around the class.

Student Struggles: As the students commence their work, Mr. Mahmood notices several issues:

Many students are confused by the definitions and proofs, unable to recall the properties mentioned in the brief lecture.

Some students struggle with the application problems, as they have not yet fully understood the basic properties and cannot transfer their knowledge to more complex scenarios.

A significant portion of the class feels overwhelmed by the number of problems and the variety of tasks, leading to cognitive overload and frustration.

Reflection questions

How might Mr. Mahmood’s lesson design contribute to cognitive overload for his students?
What strategies could he use to sequence the learning more effectively to reduce cognitive load?
What formative assessment strategies could Mr. Mahmood use to check students’ understanding to ensure they are ready for independent work?

Reflection

Mr. Mahmood realises that his resource preparation did not align well with cognitive load theory. The students experienced intrinsic cognitive load from the complex mix of definitions, proofs, and applications, extraneous cognitive load from the lack of step-by-step examples and guided practice, and germane cognitive load from attempting to integrate and apply new information simultaneously. This combination made the task overwhelming and hindered effective learning.


To better align with cognitive load theory, Mr. Mahmood could have:

Provided Step-by-Step Examples
: Included detailed, worked examples to demonstrate the properties and proofs of parallelograms before asking students to attempt problems on their own.

Gradually Increased Complexity: Started with simpler problems and gradually increased the complexity, allowing students to build confidence and competence incrementally.

Scaffolded Practice: Designed scaffolded practice sessions with immediate feedback to help students apply the properties correctly.

Organised Problem Sets: Ordered problems by increasing difficulty to help students progressively develop their skills without becoming overwhelmed.

Used Formative Assessment Before Independent Work: Implemented quick formative assessment strategies — such as mini-whiteboard responses, think-pair-share discussions, or a few diagnostic questions — to check students’ understanding before assigning independent work. This would ensure they are ready to tackle problems with success.

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