Introduction

• 1. Introduction

• Resource: my model of a Learning Episode

• 2. The benefits of online courses

• 3. Getting the most out of the course

• 4. Where are you at?

What I used to do

• 1. What my students' practice used to look like

• 2. Dodgy differentiation decisions

• 3. What do my students attend to?

• Research: Patterns of variation in teaching the colour of light to Primary 3 students

• 4. Students cannot form expectations

• Research: Variation and mathematical structure

• Research: Errors Committed with High Confidence Are Hypercorrected

• 5. There's not a lot to discuss

• 6. A correct answer means thinking stops

• 7. The interesting maths is at the end

• 8. The importance of structured practice

What I do now

• 1. An example of Intelligent Practice

• Activity: Product of prime factors (image)

• Activity: Product of prime factors (pdf)

• 2. Analysing the product of prime factors sequence

• Link: Product of prime factors (on website)

• 3. What do I mean by Intelligent Practice?

• 4. Where does Intelligent Practice fit in?

• 5. Purposeful Practice versus Intelligent Practice

• 6. Mathematical thinking

• 7. A tour of the site

• Variation Theory

Key features

• 1. Different features of Intelligent Practice sequences

• Activity: Volume with Pythagoras (image)

• Activity: Volume with Pythagoras (pdf)

• 2. Confronting the obvious

• Link: Volume with Pythagoras (website)

• Activity: Rounding to multiples of (image)

• Activity: Rounding to multiples of (pdf)

• 3. Confronting the unusual

• Link: Rounding to the nearest multiple of (website)

• Activity: Angles in isosceles triangles (image)

• Activity: Angles in isosceles triangles (pdf)

• 4. An opportunity to generalise

• Link: Angles in isosceles triangles (website)

• Activity: Factorise into a single bracket (image)

• Activity: Factorise into a single bracket (pdf)

• 5. Non-examples

• Link: Factorise into a single bracket (website)

• Activity: nth term of linear sequences (image)

• Activity: nth term of linear sequences (pdf)

• 6. Interleaving high-value concepts

• Link: nth term rule of linear sequences (website)

Reflect, Expect, Check, Explain

• 1. Reflect, Expect, Check, Explain to support mathematical thinking

• Resource: The double pause of questioning

• 2. Reflect

• Activity: Fractions of an amount - reverse (image)

• Activity: Fractions of an amount - reverse (pdf)

• Link: Fractions of an amount - reverse (website)

• 3. Expect

• 4. Check

• 5. Explain

• Research: Self-explaining: The dual processes of generating inferences and repairing mental models

• Research: The Self-Explanation Effect When Learning Mathematics: A Meta-Analysis

• Research: Inducing Self-Explanation: a Meta-Analysis

• Learning from Research: Worked-Out Examples: A Study on Individual Differences

• Research: Self-explanations: How students study and use examples in learning to solve problems

• Podcast: Ollie Lovell interviews Alexander Renkl

Model the first relationship

• 1. Reflect

• Resource: my process for running Intelligent Practice questions in the classroom

• 2. Expect

• 3. Check

• 4. Explain

• 5. Model the first relationship summary

• 6. Division with fractions practice

• 7. Division with fractions analysis

• Activity: Division with fractions (image)

• Activity: Division with fractions (pdf)

• Link: Division with fractions (website)

Student prompts

• 1. Mental addition practice

• Activity: Mental addition (image)

• Activity: Mental addition (pdf)

• 2. Mental addition anaylsis

• Link: Mental addition (website)

• 3. Sample Space Diagrams practice

• Activity: Sample space diagrams (image 1)

• Activity: Sample space diagrams (image 2)

• Activity: Sample space diagrams (pdf)

• 4. Sample Space Diagrams analysis

• Link: Sample space diagrams (website)

• 5. A question...

• 6. Student prompts

• Resource: Student prompts for Reflect, Expect. Check, Explain

• Resource: RECE Student Prompt Sheet from George Stone

What do the students write down?

• 1. Plans and elevations practice

• Activity: Plans and elevations (image)

• Activity: Plans and elevations (pdf)

• 2. Plans and elevations analysis

• Link: Plans and elevations (website)

• 3. Box plots practice

• Activity: Box plots (image 1)

• Activity: Box plots (image 2)

• Activity: Box plots (pdf)

• 4. Box plots analysis

• Link: Box plots (website)

• 5. A question...

• 6. Writing it down ideas

• 7. Too much writing

• Resource: writing template

• Resource: Intelligent Practice (example) by Nathan Day

• Resource: Intelligent Practice (blank) by Nathan Day

• Resource: Introducing RECE from @ah_haMaths

The 4-2 approach

• 1. Function machine practice

• Activity: Function machines (image)

• Activity: Function machines (pdf)

• 2. Function machines analysis

• Link: Function machines (website)

• 3. Factorising practice

• Activity: Factorise by grouping (image)

• Activity: Factorise by grouping (pdf)

• 4. Factorising analysis

• Link: Factorise by grouping (website)

• 5. A question...

• 6. Silent work

• Research: Cortical Tracking of Speech-in-Noise Develops from Childhood to Adulthood

• 7. Paired discussions

• Resource: Paired discussion prompts

• 8. The 4-2 approach

• 9. What do I do?

Discuss relationships

• 1. Probability of a single event practice

• Activity: Probability of a single event (image 1)

• Activity: Probability of a single event (image 2)

• Activity: Probability of a single event (pdf)

• 2. Probability of a single event analysis

• Link: Probability of a single event (website)

• 3. Median from a frequency table practice

• Activity: Median from a frequency table (image 1)

• Activity: Median from a frequency table (image 2)

• Activity: Median from a frequency table (pdf)

• 4. Median from a frequency table analysis

• Link: Median from a frequency table (website)

• 5. A question...

• 6. Discuss relationships

• Resource: Discuss relationships prompts

Prompts for delving deeper

• 1. Combining ratio practice

• Activity: Combining ratio (image)

• Activity: Combining ratio (pdf)

• 2. Combining ratio analysis

• Link: Combining ratio (website)

• 3. Multiplying and dividing terms practice

• Activity: Multiplying and dividing terms (image)

• Activity: Multiplying and dividing terms (pdf)

• 4. Multiplying and dividing terms analysis

• Link: Multiplying and dividing terms (website)

• 5. A question...

• 6. Prompts for delving deeper

• Resource: Prompts for delving deeper

Have we solved the problems?

• 1. Dodgy differentiation decisions

• 2. What do students attend to?

• 3. Cannot form expectations

• 4. There's nothing to discuss

• 5. A correct answer means thinking stops

• 6. The interesting maths is at the end

• 7. Mathematical thinking

Fill in the gaps

• 1. Straight line graphs practice

• Activity: Fill in the gaps - straight line graphs (image 1)

• Activity: Fill in the gaps - straight line graphs (image 2)

• Activity: Fill in the gaps - straight line graphs (pdf)

• 2. Straight line graphs analysis

• Link: Straight line graphs - fill in the gaps (link)

• 3. Fill in the gaps top tip

• 4. Time practice

• Activity: Fill in the gaps - time (image 1)

• Activity: Fill in the gaps - time (image 2)

• Activity: Fill in the gaps - time (pdf)

• 5. Time analysis

• Link: Time - fill in the gaps (website)

• 6. Fractions of an amount practice

• Activity: Fill in the gaps - fractions of an amount (image)

• Activity: Fill in the gaps - fractions of an amount (pdf)

• 7. Fractions of an amount analysis

• Link: Fractions of an amount - fill in the gaps (website)

• 8. How to find Fill in the Gap activities

Atomisation

• 1. Coefficients and constants practice

• Activity: Coefficients and constants (image)

• Activity: Coefficients and constants (pdf)

• 2. Coefficients and constants analysis

• Link: Coefficients and constants (website)

• 3. Choosing the correct trigonometric ratio practice

• Activity: Trigonometry - which ratio (image)

• Activity: Trigonometry - which ratio (pdf)

• 4. Choosing the correct trigonometric ratio analysis

• Link: Trig - which ratio? (website)

• 5. Factorising into double brackets practice

• Activity: Multiples to, adds to... (image)

• Activity: Multiples to, adds to... (pdf)

• Activity: Factorising into double brackets (image)

• Activity: Factorising into double brackets (pdf)

• 6. Factorising into double brackets analysis

• Link: Multiples to, adds to... (website)

• Link: Factorising into double-brackets (website)

Fluency Practice

• 1. A question...

• 2. What is fluency?

• 3. The role of Fluency Practice

• 4. How do I make the decision?

• 5. What does Fluency Practice look like?

• 6. How much Fluency Practice do we need?

• 7. My favourite sources of Fluency Practice

• Link: Maths Bot

• Link: Corbett Maths

• Link: CIMT MEP materials

• Link: 10 ticks

• Link: Practice makes perfect

• Link: Maths4Everyone

• Link: Increasingly difficult questions

• Link: Maths HKO

Method Selection

• 1. A question...

• 2. Circles practice

• Activity: Circles (image)

• Activity: Circles (pdf)

• 3. Circle analysis

• Link: Circles (website)

• 4. Expanding brackets practice

• Activity: Expanding brackets (image)

• Activity: Expanding brackets (pdf)

• 5. Expanding brackets analysis

• Link: Expanding brackets (website)

• 6. Percentage change practice

• Activity: Fill in the gaps - percentage change (image)

• Activity: Fill in the gaps - percentage change (pdf)

• 7. Percentage change analysis

• Link: Percentage change - fill in the gaps (website)

Useful links - from others

• What is made possible to learn when using the variation theory of learning in teaching mathematics?

• Variation: analysing and designing tasks

• Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics

• Seeing an exercise as a single mathematical object: using variation to structure sense-making

• Variation theory in mathematics education

• NCETM CPD course on Variation

• Podcast: Anne Watson and John Mason

• Podcast: Anne Watson on the TES podcast

• Blog: How to “teach” remotely

• Variation Unplugged - with Anne Watson

• Noticing and Attention - with John Mason

Conclusion

• 1. Where to next?

• 2. My online courses

• Course certificate

• Course feedback

Useful links - from me

• My research paper collection

• Book: How I wish I'd taught maths

• Book: Reflect, Expect, Check, Explain

• Mr Barton Maths website

• Mr Barton Maths Podcast

• Diagnostic Questions

• Variation Theory

• SSDD Problems

• Maths Venns