Mathematics Lesson (Modelling)

Step 1: Identify a teaching moment

The children were not able to understand how to combine two or more parts to make a whole using the addition symbol when they started their tasks.

Step 2: Write it down

When children started their independent work, they hesitated when using the addition symbol and some asked, “Do we put the whole first?” or “Why are the numbers swapped now?”

Step 3: Continuously ask ‘why?’

Why does this matter?

Because it shows that the children do not understand the concept of aggregation

Why did the children not understand the concept?

Because I modelled the same concept in different ways. In one example, I used part-part-whole language with clear left-to-right structuring (e.g. “3 bears and 2 bears make 5 bears, 3 + 2 = 5”). In another example, I reversed the structure by showing the total first (e.g. “5 counters, made from 2 and 3”). Later, I used different representations—counters in one example, a bar model in another, and cubes in a third—without clearly linking or explaining the continuity between them.

Why did I present the same idea in different ways?

Because I was trying to show variation in representations, thinking this would strengthen conceptual understanding. However, I failed to maintain consistency in the structure of my language and positioning of numbers in number sentences. This inconsistency confused pupils rather than supporting their understanding.

Why didn’t I maintain consistency in language and structure?

Because I was improvising and didn’t rehearse or script the modelling beforehand. I focused on gathering a variety of resources, but I hadn’t thought carefully about how each example would link to the next or how I would ensure mathematical clarity in each case.

Why didn’t I rehearse or plan the exact modelling steps?

Because I underestimated how important precision is at this early stage of learning. I believed that as long as the general idea of ‘adding’ was modelled, the children would grasp it. I also wanted to appear flexible and responsive during the lesson, but this led to muddled delivery.

Why did I think flexibility would outweigh clarity?

Because I’m still developing confidence in teaching maths and haven’t yet embedded the idea that consistency in structure is key when introducing abstract representations to young learners. I mistook flexibility for effectiveness, without realising that conceptual security comes from seeing the same concept modelled clearly and repeatedly.

Step 4: Reflect

Explain

This lesson aimed to help Year 1 pupils understand that combining two or more parts to make a whole is called aggregation, and that this can be represented using the addition symbol (+). The key learning was the structure: part (addend) + part (addend) = whole (total). This is a fundamental concept in early mathematics, supporting children’s understanding of number composition and laying the foundation for more complex addition and reasoning. At this stage, it’s vital that pupils connect what they do physically with concrete objects to the abstract written form. Modelling plays a central role in bridging this gap, and must be delivered with clarity and precision. The aim was not just for children to produce stem sentences, but to develop a conceptual understanding of what the symbols represent. The lesson was designed to progress from practical combining using manipulatives, to drawing representations, and finally to abstract simple equations. For this to be successful, the modelling had to be consistent and structured, highlighting the connection between each stage. The ultimate goal was for children to see the addition symbol not just as something they write, but as a meaningful representation of a mathematical action.

Assess

Although the lesson had clear intentions, its impact was reduced by inconsistent modelling, which confused the children and disrupted the pace. I presented aggregation using several different representations, counters, cubes, and bar models, but failed to maintain consistency in how I structured and explained each example. For instance, in one case I modelled “3 + 2 = 5” from left to right, but in another, I described the total first, or swapped the addends’ positions without explanation or checking the children had understood the left to right notation. This inconsistency led to visible confusion, with pupils asking questions like, “Which number comes first?” and hesitating when creating their own number sentences. Rather than reinforcing learning through the structured use of variation, my modelling involved erratic variation, which caused cognitive overload. As a result, the lesson slowed as I tried to clarify misconceptions on the spot. However, my attempts to address the issue during the lesson added further complexity instead of resolving the confusion. The children were left unsure of what aggregation looked like.

Modify

To improve future lessons, I need to ensure that modelling is consistent, clear, and rehearsed. This means using the same structure and language each time, beginning with positioning the addends on the right first, and consistently using the stem sentence appropriate to the context (e.g. I can see 5 ducks, 3 are swimming and 2 are on the bank), and supporting this with another stem sentence “we can write this as 5 = 3 + 2″. While showing different representations can deepen understanding, this must be done gradually and with clear links drawn between them. I will also reduce improvisation during key teaching points and instead rehearse how I will introduce each example, especially when introducing abstract symbols. Rather than aiming to be flexible mid-lesson, I should focus on being deliberate and predictable, which is more supportive for the children’s learning at this stage. I’ll also include key questions on the lesson plan to ensure that my explanations remain focused and variation is appropriately structured.

Mathematics Lesson (Pace)

Step 1: Identify a teaching moment

The lesson pace became inappropriate. (Note the wording that the lesson pace “became” inappropriate rather than “was” inappropriate. This helps focus attention on the cause rather than treating the symptoms (e.g. “make sure the pace is better next time.”)

Step 2: Write it down

From the beginning of the lesson my explanation and demonstration of the process were rushed and poorly modelled, leading to widespread confusion amongst the children.

Step 3: Continuously ask ‘why?’

… because I prioritised lesson pacing over clarity. In my eagerness to cover the planned content within the allotted time, I sacrificed thorough modelling, leading to an inadequate explanation. I also underestimated the difficulty of the concept for some students and did not check for understanding before progressing.

This matters because students’ understanding is built on clear and accessible instruction, and poor modelling undermines their ability to comprehend mathematical concepts.

Why did I prioritise speed over clarity?

… because I was concerned about completing the lesson objectives within the given timeframe. There was a perceived pressure to adhere to the curriculum pacing guide, which led me to believe that moving quickly would ensure that all necessary content was covered. However, this approach was counterproductive, as it resulted in children not understanding.

Why did I assume that students would understand with minimal repetition?

… because my assumption was based on previous lessons where students grasped concepts with little need for reinforcement. I did not sufficiently consider that fractions, particularly improper fractions, pose additional cognitive challenges for many students, requiring more explicit instruction and scaffolding.

Why did I not check for understanding earlier?

… because I assumed that visible engagement, e.g. children nodding and appearing to follow, indicated they understood. I did not incorporate formative assessment techniques, such as questioning or think-pair-share activities, to gauge their understanding before moving forward.

Step 4: Reflect

Explain

During a maths lesson on converting improper fractions to mixed numbers, I aimed to ensure children understood the concept clearly and confidently, as it forms a foundation for more advanced fraction operations. However, in an effort to maintain lesson pacing, I modelled the process too quickly, assuming students would grasp it with minimal repetition.

Assess

This led to confusion, disengagement, and a lack of confidence among the children. After reflecting, I now realise the importance of balancing speed with clarity, incorporating structured modelling and formative assessments to check for understanding. My assumptions were based on the immediate reactions of the children and I neglected AfL strategies as I incorrectly assumed they were not needed. I was worried about how to question the children to gauge their understanding and this heavily influenced the decisions I made.

Modify

In the future, I must not let my assumptions interfere with the good practice of employing effective AfL strategies. I plan to prioritise deeper exploration of complex topics to support children’s learning effectively and ensure I have planned the key questions in advance so that I can ask them with confidence.