Consolidation

Consolidation is where students can practice the skills the teacher has just modelled. When the Consolidation phase of a lesson is well executed, it can help students develop both competence and confidence.

Diagnosis

1. What does the Consolidation phase of your lesson look like?
2. What challenges do you face?

Evidence

There are several ways I see the consolidation phase go wrong in many of the maths lessons I watch:

1. A poor choice of questions. Questions are grabbed from the internet or the departmental folder and used with little thought.
2. Students lack the knowledge to access the questions. A sure sign is when several hands immediately shoot into the air as soon as the consolidation phase begins.
3. Not enough time is given to consolidation. For a variety of reasons, getting to this stage of the lesson has taken so much time that only a few rushed minutes remain for students to practice.
4. Students don’t put in the required effort. Students choose this phase of the lesson to go off task and take a cognitive break.
5. The teachers does not effectively check for understanding. Answers are projected onto the board, students are told to tick the ones they got right, correct the ones they got wrong, and that is that.

This presents us with a problem because we know that providing students with an opportunity to consolidate is crucial to helping them learn.

Research suggests that students perform better in maths when their teacher spends more time on individual practice and assessment. This is because consolidation helps students develop automaticity. To quote Professor Daniel Willingham in Why Don’t Students Like School?: “It is virtually impossible to become proficient at a mental task without extended practice”.

If we do not allow students to master the basics of a procedure, they have little chance of applying that procedure to solve problems.

Solution steps

Part 1: Where does Consolidation fit into a Learning Episode?

In a previous section, I shared three possible structures for a Learning Episode.

Learning Episode structure #1

Learning Episode structure #2

Learning Episode structure #3

Consolidation comes after the We Do and before Purposeful Practice in each structure. Its purpose is to solidify the skills the teacher has modelled, preparing students to use those skills more complexly.

Part 2: What do good Consolidation exercises look like?

For the remainder of this section, we will discuss how to get the most out of Consolidation: how to ensure instructions are given clearly, students remain on task, circulation is effective, and when we review answers, we learn about the understanding of all our students. But first, we need some good questions.

Good sets of Consolidation questions need to strike the balance between:

1. Not being so similar that students can stop thinking once they have done one or two questions
2. Not being so different that students are unable to draw connections and begin to develop automaticity

As we have seen, when students work on easy tasks they find uninteresting, they may need to invest additional mental effort to stay on task. So, the task needs to appeal to students’ interests.

The sequence should progress in difficulty to challenge students as they become more proficient. However, the jumps in question difficulty should not be so great as to confuse constantly.

Every maths teacher will have their favourite sources. In no particular order, here are some of mine:

1. Corbett Maths textbook exercises

For example, this ordering decimals activity:

2. Maths4Everyone

For example, this substitution activity:

3. Dr Frost

For example, this activity on angles in parallel lines:

4. Dr Austin Maths

For example, this area of a trapezium activity:

5. MathsPad

For example, this activity to introduce area:

6. Median

For example, this decimal sequences activity:

7. Increasingly difficult questions

For example, this activity on factorising:

Notice the common features of each of these activities:

1. There are plenty of opportunities to consolidate
2. There is a good progression of difficulty

Maths teachers will know that there is an almost endless supply of content available on the internet for us to choose from. Whilst this is undoubtedly a good thing and a testament to the generosity of many members of our profession, there are two issues with this:

1. Search costs – lots of time is spent searching for resources
2. Quality assurance – it can be difficult to determine what is a quality resource without either experience or dedicating time to working through it thoroughly

For these reasons, I always recommend that heads of department and other experienced teachers curate a small number of Consolidation resources for each topic that has passed their quality-assurance test so that other teachers can spend time preparing for lessons.

Part 3: Maximising the participation ratio during Consolidation

Once we have chosen a good Consolidation exercise, the next step is to ensure as many students as possible are thinking during it. This is where we can follow the strategies outlined in the Maximising the participation ratio during independent practice section:

1. Give clear instructions
2. Plan the first 3 minutes
3. Circulate strategically
4. Give students a calculator
5. Use the 4-2 Approach
6. Get data from all students when going through answers

Part 4: How much Consolidation practice is needed?

This is the million-dollar question. The answer is influenced by factors such as the topic, the student, and their previous experience. But, in general, students may not need as much Consolidation practice as we might suspect. This is for two reasons:

1. As we have seen, the We Do provides an opportunity to provide consolidation practice at a whole class level.
2. As we will see, the high-value Purposeful Practice structures have consolidation built into them.

However, I always give students at least five minutes of silent, independent consolidation practice so they can get to grips a procedure at their own pace.

Implementation planning

Here are the ideas we have discussed:

Use these ideas to complete the prioritisation exercise here.