Much of this blog post has been lifted directly from Clare Sealy’s blog at Third Space Learning: https://thirdspacelearning.com/blog/how-teach-primary-maths-deliberate-practice-in-education/
Clare’s words are the sections in grey boxes.
Third Space Learning’s Crib Sheet for staff CPD is an excellent summary of Clare’s series of blogs and can be found here:
I am completely indebted and extend my thanks to both Third Space Learning (@thirdspacetweet) and @ClareSealy for their contributions to to the emerging conversations about maths pedagogy and for allowing me to reproduce their work here.
You can find out more about Third Space Learning here: https://thirdspacelearning.com/
And you can find Clare’s own blog here: https://primarytimery.com/
Maths pedagogy, research and planning Session 2:
The Five Stages of Deliberate Practice
This blog post is a version of the workpack I used to introduce the teachers at my school to the 5 stages of deliberate practice. Where I hope to have contributed is in the area of assessment by suggesting some tools which teachers can use to assess the skills taught.
You can download an editable version of the workpack here: https://docs.google.com/document/d/17lBuqT-DuOztwOxsBtOd7xkmvvqo3ZyYy-jrpZy-ujA/edit?usp=sharing
This is the term used in cognitive science to describe how much capacity something takes up in the working memory. Cognitive overload is what happens if too many demands are placed on working memory at once
By breaking down a complex process such as adding fractions into separate, individual skills and then deliberately practising those until they are easy, cognitive overload is avoided.
The Curse of Knowledge:
What this means is that once you are really good at doing something, you approach it very differently to someone who is at the beginning of their learning.
Deliberate Practice: What the research says:
Wiemann (2007)The “curse of knowledge”:
Ericsson et al (2007):
Practice makes permanent – in Deliberate practice the feedback is an essential ingredient in order to make sure students are on the right track.
Deliberate practice involves two kinds of learning: improving the skills you already have and extending the reach and range of your skills.
The 5 Stages of Deliberate Practice
The 5 stages are:
- Isolate the skills
- Develop each skill individually
- Assess each skill individually
- Put the skills together in one task
- Practice through Retrieval Practice
Stage 1: Isolate the skills
Sports coaches are very good at this deliberate practice as this image of some football drills from @SSPlanner reminds us.
Stage 2: Develop each skill individually
Once that has been practiced, and pupils can get it right effortlessly, then and only then can we move onto the next skill: Finding common denominators.
2: “Finding common Denominators” is a skill which we need to break down even further:
In order to find ‘common denominators’, pupils need to be able to:
- find multiples of a number,
- find common multiples of two numbers and
- find the lowest common multiple of two numbers.
And all this before the next step of creating equivalent fractions.
So let’s isolate the skills involved in finding lowest common multiples and develop
those before proceeding further:
2a) Finding multiples of a number:
Firstly a sorting exercise:
Multiple or not multiple?
2b) Find common multiples of two numbers:
Circle the common multiples:
Here’s a plug for Times Tables Rock Stars!
2c) Find the lowest common multiple of two numbers:
Circle the lowest common multiple for the following pairs of numbers:
Once this is secure, we are ready for the next step.
3: Transforming fractions, using equivalent fractions.
Again we can break this step down into sub-steps
- Making equivalent fractions (listing fraction families)
- Making equivalent fractions given a target denominator
- Transforming two fractions into equivalent fractions with the same given denominator
- Deciding on the lowest common denominator and transforming two fractions appropriately.
Here is an example of an activity which could be used for part c) above:
Stage 3: Assess the skills
The next stage in the 5 stages of deliberate practice is to assess whether children have developed the sub-skill sufficiently securely enough to move on.
Techniques for assessing the individual skills:
Using multiple choice questions to get quick – whole class feedback on whether the pupils have understood a concept. These are great for teasing out misconceptions:
Diagnostic questions can also be used in homeworks, worksheets and exit tickets.
Find out more about diagnostic questions here: https://diagnosticquestions.com/
It is important that the teacher acts on this data by:
a) re-teaching if there are misconceptions amongst the majority of students,
b) addressing the misconceptions which are present amongst a few students,
c) stretching students by requiring them to come up with reasons why the correct answer is right and why the incorrect ones are wrong and/or creating their own diagnostic questions on the subject.
This is an idea from @Doug_Lemov‘s Teach Like a Champion:
At the end of the learning cycle the students are given a sheet of paper with a small number of questions on (no more than 5). These questions are designed to assess whether the pupils have grasped the key concepts in that learning cycle.
These could be diagnostic questions or ‘normal’ questions.
An example for part 2 above might be:
Caution: Pupils getting the Exit Ticket correct have not necessarily put the learning into long-term memory – Retrieval Practice will still be necessary to cement the learning
These could be daily/weekly or fortnightly quizzes or tests which are low-stakes as they are more about giving you as the teacher a good picture of where the students are at than they are about ‘grading’ students.
Again, it is how the information you get is then used to inform future planning which is crucial. Do you need to reteach part of the sequence of skills to everyone? Is there a small number of students who are really struggling whilst the rest are moving on? How can you deal with this?
End of Term Assessments:
These are more formal assessments which take longer to administer but allow you to capture better data about the long-term retention of topics and skills from a wider domain.
They do not need to be high-stakes but should be done under ‘exam conditions’ so you get an accurate picture of where the students are at.
And again, it is crucial that this information is then used to inform your planning as above. The tests allow you to be self-reflective as a teacher – which bits did the kids learn, which bits did they not, how can I improve for the future?
Stage 4: Put the Skills Together
Once all the sub-skills have been mastered then it is time to put all the skills together and, in this case, add those fractions!
The example-problem pair can be used at this stage (as well as earlier) with intelligently varied practice to build up confidence and then onto purposeful practice and finally richer, open-ended tasks as the students become more proficient.
Stage 5: Retrieval Practice
It is essential that any skills taught must be brought back through retrieval practice in order to embed them in long-term memory.
You can download the workpack on Cognitive Load Theory and Retrieval Practice here:
or read it on my blog here:
This Approach Is Worth The Time It Takes
To see an example of how Clare Sealy has broken down teaching the time into small sub-steps, see her blog on how to teach the time for KS1 and KS2.
This next section is a suggestion for an activity to do with colleagues during departmental meetings:
Deliberate Practice – Your Turn
Agree with a partner what the overall skill or procedure is that you want the students to know, remember or be able to do? (does not have to be maths)
What is the most difficult question type you would like all students to be able to respond to correctly, by the end?
Individually at first, see how many separate skills you can break this process down into – go crazy, @Kris_Boulton has famously broken simultaneous equations down into 13 (or more) sub-skills.
[Hint: try to keep your list items written in terms of a behaviour that you would expect to see a pupil exhibit. Try ‘doing’ words like ‘solve, substitute, show, identify, add, find, decide, determine’. Avoid words like ‘know, understand’]
When you are done, confer with your partner and see if you missed any sub-skills out. The next step would be to try to come up with an activity for the pupils for each sub-skill which really isolates that sub-skill for deliberate practice.
List of Sources
“How I wish I’d Taught Maths” Part 4: Deliberate Practice:
“How to Teach Telling the Time to KS1 and KS2: https://thirdspacelearning.com/blog/how-to-teach-telling-time-ks1-ks2-activities/
Diagnostic Questions: https://diagnosticquestions.com/
Doug Lemov: Teach Like a Champion 2.0:
Doug on Exit Tickets: http://teachlikeachampion.com/tag/exit-ticket/
Kris Boulton: “My Best Planning”
Bruno Reddy: Times Tables Rock Stars: https://ttrockstars.com
Wiemann (2007): The “curse of knowledge”
Ericsson et al (2007): Deliberate Practice