Tips for Teachers by Craig Barton

Book 14: Purposeful Practice and Problem-Solving

Here are the resources referenced in the Tips for Teachers guide to Purposeful Practice and Problem-Solving.

Want to know more?

  1. The ATM book, Practising Mathematics, is a good starting place
  2. Colin Foster’s work on Mathematical Etudes is also worth checking out
  3. Colin Foster is excellent on problem-solving. Check out my conversation with Colin, and this interview with Ben Gordon.

Endnotes

  1. Learning to think mathematically: Problem solving, metacognition and sense-making in mathematics by Alan Schoenfeld. Read an analysis of the paper here
  2. Why minimal guidance during instruction does not work by Paul A. Kirschner, John Sweller, Richard E. Clarke. Read an analysis of the paper here
  3. Read Peps Mccrea’s post on how routines redeploy attention here
  4. Cognitive endurance as human capital by Brown et al. Read an analysis of the paper here
  5. Practising Mathematics – Developing the Mathematician as Well as the Mathematics by Dave Hewitt and Tom Francome. You can purchase the book here
  6. You can visit the Maths4Everyone website here
  7. Mathematical etudes: embedding opportunities for developing procedural fluency within rich mathematical contexts by Colin Foster. Read an analysis of the paper here
  8. View Colin Foster’s full collection of mathematical etudes here
  9. In The Tips for Teachers guide to Independent Practice, I discussed research that suggests there is an inverse relationship between task interest and cognitive load. You can read an analysis of the paper here
  10. #082 Mark McCourt: the return! Teaching for mastery. You can listen to the conversation here
  11. You can read more about planning Learning Episodes here
  12. You can check out Nathan Day’s website here
  13. I write about Book-to-Board: Quick Check, and lots of other related techniques, in The Tips for Teachers guide to Mini-Whiteboards
  14. You can find Jonathan Hall’s Completion Tables here
  15. You can find Nathan Day’s Completion Tables here
  16. You can find the Fill in the Gaps Completion Tables on my Variation Theory website with this direct link
  17. Learning about Functions through Learner-Generated Examples by Martha O. Dinkelman and Laurie O. Cavey. Read an analysis of the paper here
  18. See Dan Rose’s original tweet here
  19. Stimulating students to construct boundary examples by Anne Watson and John Mason. Read an analysis of the paper here
  20. I wrote a book all about variation theory called Reflect, Expect, Check, Explain
  21. You can find all my Venn Diagrams on my MathsVenns website here
  22. You can find all Jonathan Hall’s Venn Diagrams here
  23. You can get printable blank Venn Diagram templates here
  24. You can view the Open Middle website here
  25. View the Open-Middle website here
  26. View the Open-Middle Problems built for Desmos here
  27. You can read the Cognitive Load in Solving Mathematics Problems paper by Udita Gupta and Robert Z. Zheng here
  28. Colin Foster writes about his definition of problem-solving here
  29. You can read more about planning Learning Episodes here
  30. #183 How to help students remember things with Nick Soderstrom. Listen to the episode here
  31. A randomised control trial of interleaved maths practice by Roher et al. Read an analysis of the paper here
  32. Spacing and Interleaving Effects Require Distinct Theoretical Bases by Chen, Pass and Sweller. Read an analysis of the paper here
  33. When doing group work, make clear the group is responsible with Sammy Kempner. Watch the video here
  34. I wrote about this, and much more, in The Tips for Teachers guide to the Do Now
  35. You can find my SSDD Problems website here
  36. Why SSDD Problems Are Such An Effective Tool To Teach Problem Solving At KS3 & KS4. Read the blog here.
  37. Listen to Craig Latimir discuss No Number Problems with me here
  38. You can find Tanner Math’s wordy problems here
  39. The first problem goes by the name of Hannah’s sweets. You can read BBC News’ coverage here
  40. Mathematical Problem Solving by Alan H. Schoenfeld. You can buy the book here
  41. Problem-solving in the mathematics curriculum by Colin Foster. Read an analysis of the paper here
  42. I discuss the technique, and many more, in The Tips for Teachers guide to Turn and Talk
  43. Check out the Eedi collection of stretch and challenge problems. Click on any question in a quiz and scroll to the bottom of the page
  44. You can access the NRICH short problem collection here
  45. You can find the collection of UKMT past papers here
  46. You can access the LUMEN curriculum here
  47. You can read more about planning Learning Episodes here
  48. I have books on each of these lesson phases in my Tips for Teachers guide to series