One of the principles of best practice is to recognise when something has gone wrong and correct it, and by doing this you ensure you learn from your mistakes.

That’s true in all aspects of life, including lesson creation. Sometimes, a lesson just doesn’t cut the mustard, but after careful analysis and revision, an outstanding teaching tool can be produced.

Long Division Was Our Achilles Heel At Third Space Learning

Whilst the difficulty of our lessons is adaptable based on the ability of the pupil taking it, our lesson on long division was found to be overly challenging to our pupils.

This led us to believe that changes were required.

A tricky topic at the best of times, teaching long division requires the ability to convey these difficult concepts in an easy to understand way, allowing the pupil to take time to access and master each step (which is part of our mastery approach) . This is something that our specialist maths tutors are trained to do, but we are constantly striving to improve what we do so we tackled the problem head on.

How Do We Judge The Success Of Our Lessons?

Throughout the year, quantitative analysis of the performance of our lessons is carried out, enabling us to see which ones are performing well and which aren’t. We are always analysing the data from our sessions to ensure that we have provide the best lessons to the over 1,400 schools using our platform which is a big job, but we love doing it!

The Data From A Third Space Learning Lesson
An extract of the data from our platform.

This excerpt from our data analysis shows:

• How many times it has been taught

• The title of each lesson

• How many times the taught lessons were finished

• How many times the taught lessons were skipped

• How many lessons are still in progress

Steps to Success Third Space Learning
This is how we monitor how well the lesson has gone.

This section of the data analysis follows on from the previous excerpt and shows us the percentage of the steps to success (S2S) that have been completed, and whether those steps to success are new content or reinforced knowledge.

P.S. Steps to success are the learning objectives we use internally within our platform to gauge pupil progress throughout the lesson.

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It also tells us the results for the post-lesson quiz questions, the average number of weeks taken to complete the lesson, and finally whether the learning objectives have been judged by the tutors to be good, too easy or too difficult.

In the case of the long division lesson, as the quantitative analysis highlighted it as an under performing lesson, screen reports of some of the lessons were also analysed.

Long Division Lesson Analysis

In this screen report, we can see that the pupil only achieved 2 of the 5 learning objectives, which indicates to the content creators that there may be problems with the lesson itself, especially as this isn’t an isolated case.

We’d Identified A Problem & Now It Was Time To Get To The Bottom Of It

The next step in our process was to move on to qualitative analysis. We did this by watching six recorded videos of that particular lesson to identify what features of the lesson were causing the problems, and we also included tutor and pupil feedback in this process.

Once the problem areas have been identified, our team of experienced content creators can go in and improve them.

For the lesson on long division, we identified the problem areas as being:

  1. Differentiation
  2. Language
  3. Visuals

After problems have been identified within a lesson and changes have been made as a result, its performance is monitored to see whether it is proving to be more successful than it was before, allowing the content creators to judge whether the improvements they made have had a positive or negative impact.

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So, How Did We Actually Improve Our Long Division Lesson?

The lesson on long division has been taught 2,968 times and has been carefully analysed to judge its effectiveness and appeal, looking at whether it provides a platform for effective, pupil-led learning.

With much thought and deliberation, a vastly improved version was created. Making changes to a lesson is not something we take lightly and we only do it when we know we can improve the lesson for the pupil using a pedagogical approach.

Let me show you how:

Differentiation – Introducing A New Way Of Teaching Long Division

There are a variety of methods that can be used to teach long division and choosing which one to learn should not only offer the pupil choice, but the ability to work with a method they are fully confident with.

Differentiation in maths lessons

As can be seen here, our old lesson presented the formal long division method (sometimes known as ‘bus stop’ method) as the only option. This raises an immediate issue, particularly if the pupil has not been taught this method.

How We Changed Things

Long Division Lesson After Changes

In our new lesson, two commonly taught methods, chunking and formal long division, are shown, giving the pupil the option to choose the method they would be studying in school, and allowing the pupil the autonomy to choose the method they are most comfortable with.

Each method is clearly represented by an example question, making it clear to the pupil what each term represents.

Language – Ensuring Our Tutors Were Communicating In A Way Pupils Would Understand

Long division is a complicated topic, made more so if confusing language is used, leading to misconceptions.

Long Division Language Element

In this slide, we see the sentence “13 goes into 43 three times”. The phrase ‘goes into’ is confusing, failing to outline the concept of a number being divided into many parts.

Added to this is that instead of dividing the number into 4 300, the pupil is told that 43 is being divided.

This confusing use of language meant that the pupil couldn’t understand what they were being taught and highlights that clear language is important when explaining a complicated theory.

How We Changed Things

In the new lesson, the realisation that the language itself could lead to misconceptions meant that explicit instructions were needed for the tutors.

Accompanying the lesson from the tutor’s view, there are tutor notes which now state that the column each digit is in should be treated as a noun. Instead of saying “how many 3s in 50”, tutors are instructed to say “how many 3’s in 5 tens.’

Long Division Lesson Language Improvements

This clearly reminds the pupil about the place value of each digit, as well as reinforcing the idea that they are dividing a group, not just a number – 5 tens not 50!

Each of our specialist maths tutors go through a specific 1-to-1 maths training to ensure that they can provide the high-quality, individualised primary maths tuition that has come to be expected of Third Space Learning. As well as our lessons, we are constantly improving the way we train our tutors, and if you want to learn more about this then take a look at how we take maths specialists from good to outstanding!

Visuals – Making The Lessons More Engaging For Pupils

Alongside the confusing language, the old lesson’s unappealing visuals led to further confusion. The pupil is shown a calculation and goes through it step by step, with additional calculations being done outside the main calculation, with no clear link between them.

Long Division Lesson Visuals Analysis

As well as this, the colours used do not help to show what each number represents, leading the pupil to be unclear as to each number’s purpose.

How We Changed Things

Long Division Lesson Visuals After Changes

Our new lesson can instantly be seen to be anything but boring. Not only are there visuals in the form of different colours (each representing a part of the calculation), a table and a picture, but more importantly, the calculation has been placed in the concept of a story.

This instantly makes it more appealing to the pupil, as they are presented another person’s problem and asked to help solve it (not to mention there are cookies!) Children find it easier to understand theory when it is given a real life context that relates to them.

Notably, the calculation itself has been set out in a number of ways, meaning the pupil can be guided carefully through the problem, fully understanding how each step has been worked out.

Our Long Division Lesson Improvements – What Is The Next Step?

Singapore Maths extols the idea of CPA – Concrete, Pictorial, Abstract – suggesting that all lessons should involve each of these three ideas. Long division is certainly an abstract concept, and the first lesson outlined the theory, but didn’t use enough visuals or set it out in a relatable situation that children would understand.

In contrast, the new lesson takes this abstract idea and makes it easy to understand through its clever use of visuals and its ability to set out a normal calculation within a contextualised, visual and concrete background.

Overall, the differences in quality between the old and new lessons are clear to see, and will certainly appeal to all types of pupils, making one of the most complicated maths topics easier to learn, as well as making it more enjoyable to teach.  

This lesson is due to be rolled out in our next update, and will be carefully monitored to see whether it provides clear, fulfilling and effective learning.

Whilst we are busy in the office constantly making the Third Space Learning experience better for you and your pupils, we understand that we are not in the room everyday seeing the results of our hard work. That is why we asked the lifeblood of schools, teachers, to tell us what they thought of the platform. Check out what they had to say in our Third Space School Report!

If you are interested in learning more about what we do, book an obligation free demo to discuss your schools needs with one of the team. On the call you will be able to review our curriculum to ensure it matches your needs, explore the online learning platform and ask any other questions you have about how Third Space Learning works.

Chris Xerri , Curriculum Designer , Third Space Learning

After nearly 10 years teaching in primary schools in England and abroad, Chris is now working at Third Space as a teaching and learning curriculum designer.