Atomisation

Atomisation is my process for planning lessons. I don’t want to build it up too much, but it has been a game-changer in terms of how quickly my students get to grips with new ideas.

Diagnosis

1. How do you break down new ideas?
2. What challenges do you face?

Evidence

I watched a teacher deliver a worked example on the Sine Rule:

His explanation was clear. He took students through the required steps – labelling the sides, setting up the formula, entering the numbers into the calculator, etc. Along the way, he checked students’ understanding of prior knowledge, such as how to rearrange a formula and round their answers.

This all sounds like good stuff.

But there were three problems:

1. The worked example took ages. I timed it at 6 minutes 23 seconds.
2. Students were confused. Some told the teacher they didn’t get it, and others sat there in silence with pained expressions on their faces.
3. Very few students could answer the Your Turn correctly

I hypothesise that things went wrong because the teacher did not Atomise.

Solution steps

Warning, warning…

What follows is my attempt to distil a complex, intricate theory into something you can read in 30 minutes and apply in your classroom tomorrow.

I am indebted to the work of Kris Boulton, the UK’s leading expert on Atomisation. He would no doubt shudder and possibly vomit at the liberties and simplifications I make here. So, for the authentic take on Atomisation, I wholeheartedly recommend you check out Kris’ work, starting with my conversation with him here.

What is Atomisation?

I define Atomisation as follows:

Atomisation is the breaking routines down into their smallest constituent parts (atoms) that can be assessed or taught separately from the routine itself

If you are into Rosenshine’s Principles of Instruction, then Atomisation is Principle #2: Present new material in small steps but taken to the extreme.

Examples of Atomisation

To start, here are three procedures (or, in keeping with the language of Atomisation, what I will now call routines) that I have atomised. None of these routines have been perfectly atomised. But they all worked in the sense that all students could answer the We Do question and the Consolidation practice that followed. Having concrete examples early on of where we are trying to get to should help the following theory make more sense.

In each case, the routine is on the left, and the Atoms are on the right.

Example 1: Expanding double brackets

This routine consists of three atoms, each corresponding to a line of working.

Students have met Atoms 2 and 3 before, so they have a *. Anything students have met before will be assessed during the Atomisation phase.

Atom 1 is new, so it does not have a *. Anything students have not met before will be taught during the Atomisation phase. Crucially, they will be taught this Atom in isolation before it is used during the I Do.

Each Atom has a letter after it. This refers to the type of Atom. Here is the full list:

1. Category (Cat)
2. Comparative (Com)
3. Fact (F)
4. Transformation (T)
5. Routine (R)

As we will see below, once you know the Atom type, you know the best way to teach it to students.

Notice, in this example, that there is only one new atom, so that is all we need to teach students before we put all the atoms together in the I Do that follows the Atomisation phase.

Example 2: Adding fractions

In this example, we have more atoms. Generally, the more steps in a routine, the more atoms. Notice also that there is not a 1-to-1 correspondence between the number of lines of working.

Notice in this example that there is only one new Atom to teach students before we put the routine together in the I Do.

Example 3: Solving quadratic equations using the quadratic formula

Here, we have lots more atoms.

We also have several Atoms that are new to students and hence need teaching. These will be taught one at a time, and in isolation from the routine itself.

Why Atomise?

From what we have seen so far, Atomisation may seem complex and unnecessary. Most lessons I watch do not have this phase. The teacher either:

1. Dives straight into the I Do,
2. Assesses prerequisite knowledge first, but then bundles together new Atoms in the I Do.

This almost always causes problems. The problems may become apparent during the I Do if the teacher asks the students questions, during the We Do when they check students’ understanding, or during the Consolidation phase when it becomes clear that student understanding is not as secure as the teacher believed. But the problems always come.

Let’s return to the example from above:

Think how many Atoms of knowledge students need to follow the I Do:

1. Recall the sine rule
2. Decide under what conditions to use the sine rule
3. Label the triangle
4. Substitute values into the formula
5. Rearrange the formula
6. Enter values into the calculator
7. Find inverse sine
8. Round answers

Some of these Atoms are new, some of them students had met before.

The teacher did not assess any Atoms students had met before, nor did he teach any new atoms separately. Instead, everything got chucked into the I Do melting pot.

What happened:

1. The I Do took ages. Of course, it did because the teacher was trying to teach students each new atom, check their understanding of atoms they had met before, and show them how they all fit together.
2. The students were confused. Again, of course, they were because they were trying to retrieve atoms they had met before, learn new atoms, and understand how all these atoms fit together. Cognitive overload was in full force.
3. Most students could not answer the Your Turn question. They may have fumbled through the I Do, with one or two struggling to get the teacher’s desired answer with lots of scaffolding. But when asked to solve a similar question on their own, the true fragility of their foundations was revealed.
4. Everyone felt pretty rubbish. The students’ confidence was rocked, and the teacher felt frustrated. Why didn’t his students understand?

We can do better than this.

During the I Do, we want everything my students see to be familiar, so their limited attention is focused on how familiar things fit together in an unfamiliar way. This gives students the best chance of understanding. Atomisation is most effective way to achieve this.

So, let’s learn how to atomise.

Where does Atomisation fit into a lesson?

In a previous section, I shared three possible lesson structures:

Lesson Structure #1

Lesson Structure #2

Lesson Structure #3

Atomisation comes after I have conveyed the purpose of what we are doing and before the I Do. Successful Atomisation sets up the teacher-led I Do that follows. It allows us to deliver a clear and concise explanation without needing to check for understanding, giving our students the best chance of attending to the sequence that the atoms fit together.

As we will see in the final section, it is sensible to atomise before each I Do, as opposed to one all-encompassing atomisation phase at the lesson’s start.

Step 1: Choose a good example

To make Atomisation effective, we need a good starting example to model during our I Do. If you are anything like me, the choice of that example gets relatively little thought when planning a lesson.

Here are some guiding principles.

1. Avoid repeating elements within a worked example

a) Avoid repeating elements in the question

Look at this equation:

During the I Do, the teacher will say something like:

Our first step is to add 2 to both sides of the equation.

But what 2 are we talking about? Sure, we will gesture, but the potential for ambiguity and confusion is not worth the risk.

Or how about this percentages question with the repeated 5:

Finally, look at this choice of I Do on rounding decimals:

Again, we have a proliferation of 5s. This confused the students when it came to the We Do:

b) Avoid repeating elements in the answer

Here is an innocent-looking sequence:

But look at the answer:

Does the fact that the sequence goes up in 4s determine the coefficient of n or the constant term?

Finally, look at this question a teacher used:

Everything seemed fine until a student worked out the answer (132º), and said:

Ah yes, it is the same because of opposite angles.

No, no, no!

2. Focus initially on the core concept and don’t weave in anything else

Weaving in prior content to the current concept is a good idea to reap the benefits of spacing. BUT – and it is a big but – the time to do this is not during the I Do.

At this stage, students’ knowledge of the concept is at its weakest. Therefore, they must dedicate all their attention to the new idea and nothing else.

In addition, if we weave in prior knowledge into the I Do and students struggle, we don’t know why. Is the issue a lack of understanding of the new content or a lack of understanding of the prior knowledge?

Here is an extreme example of this for introducing how to calculate the area of a rectangle:

Here is a more subtle one:

Students could not dedicate attention to the relationships between the angles because all their attention was taken up processing the arithmetic:

So, focus on the core concept for the I Do, and keep the numbers simple.

3. Start with general examples, not “easy” examples

However, keeping the numbers simple does not necessarily mean keeping the question simple.

Most teachers start with an easy initial example for the I Do and then expose students to more complex examples during the Consolidation phase. There are three issues with this:

1. Students could get them right for the wrong reasons (ie they take dodgy mental shortcuts)
2. Useful secrets are hidden
3. You have to teach a different method for more challenging examples

This is all very abstract, so let’s look at some examples to make things more concrete.

Example 1

Two-squared should be made illegal as a starting example when teaching powers. You can arrive at the correct answer of 4 by adding the numbers, multiplying the numbers, or using the correct method. Hence, you can get the correct answer for the wrong reasons. Three-squared is a tougher calculation, but it makes it crystal clear what process is taking place.

Example 2

The left-hand example has several issues when used as the initial example for expanding double brackets.

1. It is not crystal clear where the x-squared term comes from in the resulting answer. If students have loads of examples like those, they may realise that the answer always starts with an x-squared and not realise that multiplication is taking place.
2. The constant term is 5. Is this because the second term in the first bracket is 5? Again, the process of multiplication is hidden.
3. Students may end up seeing the example on the right as a different type of question and, hence, not see the questions between the two.

If you are careful with the numbers, starting with the example on the right makes it clear that multiplication is the operation to arrive at each of the terms in the expansion. Once students are comfortable with this, you can use the example on the left as a special case.

Example 3

After several examples like the one on the left, students stop thinking about the concept of the area of a triangle and instead go into autopilot, multiplying the two numbers they see and halving the answer. In fact, the example on the left has an additional problem: Students might think the area is just the height.

The right-hand example requires students to think hard about which two numbers are needed and then calculate them. If students are not secure with their times tables, the numbers may need simplifying.

Example 4

10% is often the default start when teaching a percentage of an amount. And what do teachers often say? To find 10%, we divide by 10. So, how do we divide by 20%? Divide by 20?

Instead, if we want to start with factors of 100%, 25% is a better starting point. Or, we can jump right in and start with 17% and teach the factors of 100% later as special cases.

Example 5

A cube has six identical faces. If this is our initial example when teaching surface area, the process of identifying each face and its dimensions is lost. It is better to start with a cuboid or a pyramid.

Example 6

When teaching enlargements from a point, teachers often start with the centre of enlargement at (0, 0). The issue here is that you have a convenient shortcut to work out the new coordinates—just multiply them by the scale factor. Hence, all thoughts about the actual concept of enlarging from a point go out of students’ minds.

It is better to start with a more general point and then introduce (0, 0) later as a special case.

To reiterate, we are not deliberating about making the examples more difficult than they need to be. It is still essential to keep the arithmetic simple so that as much of our students’ attention as possible is focused on the process. However, by starting with a carefully chosen “general” example, we better set our students up for future success.

4. If you do multiple examples, only vary one critical feature per example

Often it makes sense to model two examples to students’ during the I Do. In these cases, varying one critical feature between examples helps students make connections.

On the left, everything changes between the first and second examples. On the right, only the denominator of the second fraction changes, so students can track what impact that change has on each step of the solution.

Step 2: Break down the example into atoms

Once we have chosen the example to use during the I Do, the next step is to break that example down into Atoms.

The best way to do this is to take a piece of paper, write the example and the working out on the left-hand side:

Then ask yourself: What knowledge do students need to get from one line to the next?

Each piece of knowledge becomes an Atom:

This takes practice. As we shall see later, some Atoms are invisible in our working. But, the more you do this, the better you will become. Better still, do this with a colleague, both listing your atoms to the same example independently and then comparing the results.

Step 3: Star (*) any atoms that students have met before and plan questions to assess these

These Atoms are the prerequisite knowledge.

Research suggests that assessing these Atoms before we teach a new idea has two benefits:

1. Identifying gaps in student understanding. We can identify gaps in prerequisite knowledge and support students to fill them.
2. Improving student learning. As a result, students head into the I Do that follows with a secure foundation upon which we can help build new ideas.

I will add an additional benefit to assessing prerequisite knowledge: It frees us up to deliver a clear and concise teacher-led I Do. We do not need to break the flow of our explanation by checking for understanding of prerequisite knowledge because we have already done it. Our attention and our students’ attention can be on how our existing knowledge, which they are secure with, fits into the new idea we are teaching.

The best way to assess the * atoms is to have one question per slide.

Give the students, say, 10 seconds in silence to write their answers on their mini-whiteboards. When ready, hover the boards face-down, and show in 3, 2, 1…

Then we need to respond.

If 80%+ of students get the answer correct, confirm it, write it down, and proceed to the next question.

If we do not hit that 80% figure, we need to explain and then recheck for understanding with a carefully chosen follow-up question:

If students are still struggling, we need to spend longer explaining and rechecking, as there is no point in continuing with a new idea built upon these foundations.

Step 4: Teach any new atoms separately

Just as we don’t want to assess Atoms during the I Do, we also don’t want to teach new Atoms during the I Do. We want students’ attention to be on how familiar Atoms fit together.

Therefore, if an Atom is new to students, we will teach it independently and in isolation from the I Do built upon it.

Before we go any further, a key point. If your version of Atomisation consists of:

1. Choose a good example
2. Break down the example into Atoms
3. Assess any Atoms students have encountered before
4. Teach any new Atoms individually and before you combine them in the I Do

Then, you will reap 80% of the benefits. Doing those four things will put your students in a strong position to learn the new routine built upon those atoms. So start here and make this part of your regular practice.

What follows is a bonus. It gets pretty technical and requires a fair bit of thought. Don’t attempt this until you have successfully embedded everything so far in this section.

***

For those of you still with me, let’s take an Atomisation deep-dive…

Different types of atoms

There are five different types of Atoms:

1. Category (Cat)
2. Comparative (Com)
3. Fact (F)
4. Transformation (T)
5. Routine (R)

Once you know the Atom type, you know how best to teach it.

Category atoms (Cat)

If you ask the question: “Is this a ___?” and the answer is either Yes or No, then you have a Category Atom.

Technical language is always a Category Atom. Examples include:

• Is this…a prism?
• Is this… an equation of a straight line?
• Is this… an alternate angle?
• Is this… equation balanced?

Decisions are also Category Atoms. Examples include:

• Do I use Pythagoras to solve this problem?
• Is y the subject of the formula?
• Is this answer feasible?
• Is this the perpendicular height?

Decisions often get missed during the Atomisation process because they do not appear in the lines of work. As experts, we make such decisions without much thought, yet they can be stumbling blocks for our students.

The best way to teach Category atoms is via a sequence of related examples and non-examples.

To get into the weeds, we can improve our sequence or related examples and non-examples by using the following principles from research into Direct Instruction.

1. The wording principle. To make the sequence as clear as possible, we should use the same wording on all items (or wording as similar as possible).

2. The setup principle. Examples and non-examples selected for the initial teaching of a concept should share the greatest possible number of irrelevant features

3. The difference principle. To illustrate the limits or boundaries of a concept, we should show examples and non-examples that are similar to one another except in the critical feature and indicate that they are different.

4. The sameness principle. To show the range of variation of the concept, we should juxtapose examples of the concept that differ from one another as much as possible yet still illustrate the concept and indicate that they are the same

5. The testing principle. To test for acquisition, we should juxtapose new, untaught examples and non-examples in random order

Combining these principles, Kris Boulton suggests introducing Category Atoms to students using NPPPN. That is:

1. Start with a non-example
2. Vary one thing to generate a positive example
3. Show a maximally different positive example
4. Show another maximally different positive example
5. Vary one thing to generate a non-example

We present these to students one at a time, saying as little as possible, letting the examples do the talking.

Here is a sequence I put together to teach the Atom: What is a quadratic equation?

These examples are presented on the board one at a time. We can draw students’ attention to that critical change by rubbing out the feature we are changing.

Here is a sequence to teach students the Atom: Are these fractions in a form ready to be added?

Immediately after this sequence of related examples and non-examples, test students by showing them many examples without pausing for discussion or questions. We need a reliable check for understanding, so get all students to respond using mini-whiteboards or other voting devices such as cards or fingers.

Comparative atoms (Com)

An atom is a comparative if you witness change by observing before and after.

Examples include:

• Speed
• Gradient
• Density

We can employ the same principles above to teach Comparative atoms. We need a carefully sequenced set of examples with one key feature varying each time.

Two positive examples, followed by two negative examples, works well for Comparative Atoms.

Here is an example from the primary maths classroom to teach the Atom: What is one more? Again, these would be presented one at a time, with the change highlighted by either adding more or rubbing out.

Facts (F)

Facts are things students need to remember. Facts connect concepts together. Crucially, the concepts in the Fact Atom must be understood – they will be Category or Comparative Atoms.

Examples include:

Formula:

• Area of a triangle
• Quadratic formula

Theorems:

• Angle at the centre
• Pythagoras

Properties:

• Multiplication is commutative
• Angles in a triangle add to 180

I like to teach Fact Atoms using Call and Respond, specifically my Explain-Frame-Reframe structure:

• Explain: The formula for the area of a triangle is base multiplied by perpendicular height divided by two
• Frame: The formula for the area of a triangle is…
• Reframe: Base multiplied by perpendicular height divided by two is…

Transformations (T)

Transformations occur when an input is changed to an output in an obvious way. If it is not obvious, then the Atom is a Routine.

This table should help illustrate the difference:

Once again, we can employ the principles outlined in the Category atom sequence:

1. During the teacher demonstration, between one to three examples of the transformation are usually enough
2. Each new example should change just one thing you want to draw students’ attention to. Again, the key to this is rubbing out the change and only the change.
3. Where possible, let the examples do the talking
4. In the testing sequence, use minimal changes, but also build in some re-sets where lots of things change
5. Progress to ever-greater changes throughout the expansion sequence, which is essentially extension questions at the end of the testing sequence

Here are the three examples I use when teaching students the Atom: Break-up double brackets:

Then by the end of the testing sequence, you can give students examples like this, and typically they will get them correct:

Here is a video example from some work I was doing with 4 and 5-year-old students:

Routines (R)

The final Atom type is not really an Atom at all. As we saw above, Routines are like Transformations in that they change an input into an output, but this time, the change is not immediately obvious.

Because of this, we are unlikely to be able to teach Routines with two or three relatively quick examples presented with little teacher talk.

Instead, routines are taught using the I Do, We Do approach, which you can find in later sections.

Before we move on, I want to reiterate my earlier point. If all this stuff about labelling and teaching atoms in fancy ways feels too much, please don’t worry. If you choose a good example, break it down into atoms, assess the ones students have met before, teach the new ones (however you want), and then put them all together in the I Do, you will reap substantial rewards.

Step 5: Chain some atoms together

Recently, I saw an example of Atomisation not quite working, and I thought it was worth further exploration.

The lesson

The objective of the lesson was for students to be able to plot straight-line graphs from an equation by filling in a table of values like this one:

The atoms

The teacher had identified that his students needed to be secure with the following Atoms to complete this process successfully:

1. Reading algebraic expressions
2. Substituting into formulae
3. Multiplying with negative numbers
4. Adding and subtracting with negative numbers
5. Plotting coordinates on a set of axes

What happened

The teacher assessed each of the atoms with well-chosen questions, and students were able to answer them successfully. So, he moved on to the new routine – filling in a table of values – which used each of these atoms.

He asked his students to think of the value of y when x equals -3.

And his students couldn’t do it.

Suddenly, 2 x (-3) = 6, or (-6) + 2 = -8, despite no students making these mistakes some 30 seconds before.

Why had this happened?

In the coaching session, we discussed why. We hypothesised that the jump from answering questions on individual atoms to carrying out a process involving these atoms combined (interpreting algebraic expressions, substituting, multiplying negative numbers, and adding negative numbers) was too much for these students.

We should have chained some of these atoms together before tackling the process—and I take full responsibility here, as I delivered CPD on atomisation the last time I visited the school.

So, following on from questions like 3 x (-5) and (-4) + 3, we should have included some questions that combined these two atoms and these two atoms alone, such as 2 x (-3) + 1. Students could then have focused on these two atoms without extra attention needing to be diverted towards thinking about the other atoms, such as interpreting expressions and substitution.

Once the chaining of those two atoms was secure, more atoms could be added to the chain until students completed the whole routine.

What I learned

The whole point of Atomisation is to help students thrive with a multi-step process. But my mistake was assuming that the leap from nailing individual atoms to being able to chain every atom together to complete the multi-step process was a small one. If there are several atoms, a more sensible approach is to teach or assess two or three atoms individually and then chain those together. Once students are secure with that chain, teach or assess more atoms and add those to the chain.

Obvious, maybe. But I certainly missed it!

Step 6: Teach the full routine

Once you have completed the assessment of Atoms students have met before, the teaching of new Atoms, and any necessary chaining, you are ready to teach the routine that is built upon these foundations.

To do so, we will use the I Do, We Do framework in the next two sections.

What about differentiation?

I often get asked whether Atomisation looks different for top sets versus bottom sets studying the same procedure. My answer is: No.

I would typically give students from all classes the same examples, and hence would have the same list of Atoms.

I would then assess any Atoms that students had met before.

I wouldn’t assume that just because a student was in the top set, they must remember a certain Atom. If they can, then great, the assessment takes a few seconds, and the studetns experience a moment of success. And if they can’t, then it is a good job I have assessed their understanding.

Likewise, I wouldn’t assume that a class could not remember a certain Atom because they are in a lower set. They may not, but I can support them. But they might surprise me, in which case I have saved time.

I would also teach each of the new atoms in the same way. As we have seen, the Atoms are so focussed, and the teaching is so quick, that differentiation is rarely needed.

Likewise, I would respond to the data in the same way. If 80%+ of students have the correct answer, I will move on. If fewer than 80% do, I will stop, intervene, and reassess.

The only thing that changes with Atomisation between a lower and a higher set is determined by that data. Typically, I have to do more explaining and reassessing with a lower-achieving class than another. But not always. And this is always determined by the data instead of my assumptions.

Atomisation is for everyone.

Atomise per worked example, not per lesson

One final point…

Here is a lesson structure I see a lot:

The teacher atomises at the start of the lesson. One of two things usually goes wrong when one or more of those atoms are only needed for later examples:

The teacher forgets to include something in the atomisation that is needed for one of the later I Dos, and only discovers this knowledge is lacking when they are in the middle of the explanation

This happened with a lesson I saw on standard form. The teacher atomised and assessed those atoms students needed for dealing with positive powers of 10 at the start of the lesson:

As a result, students could follow the I Do:

And nail the independent practice:

But later in the lesson, when the teacher moved onto negative powers, she did not do a prerequisite knowledge check, and instead jumped straight into the I Do:

To understand this, students need to be secure on negative powers of 10. But this had not been assessed. When I later checked students; understanding of this, it was not secure:

The solution is to Atomise before each I Do, checking if any new Atoms need teaching and if any of the Atoms from previous routines need reassessing. Hence, the lesson structures I introduced earlier:

Lesson Structure #1

Lesson Structure #2

Lesson Structure #3

Want to know more?

Kris Boulton is the main man when it comes to all things Atomisation. As he produces more content, I will link to it here:

1. Our podcast conversation

Implementation planning

Here are the ideas we have discussed:

1. Step 1: Choose a good example
2. Step 2: Break the example down into atoms
3. Step 3: Star (*) any atoms that students have met before and plan questions to assess these
4. Step 4: Teach any new atoms separately
5. Step 5: Chain some atoms together
6. Step 6: Teach the full routine
7. Atomise per worked example, not per lesson

Use these ideas to complete the prioritisation exercise here.