Teaching Concepts through Examples and Non-Examples

Kris Boulton returns to the podcast to discuss atomisation and how it can lead to unstoppable learning for our students. You can access the show-notes here: mrbartonmaths.com/blog/atomisation-kris-boulton

Timestamps:

1. Atomization in mathematics education, with a focus on expertise-induced blindness and its impact on students' understanding. (10:57)
2. Breaking down complex processes into simpler steps. (15:12)
3. Teaching methods using a taxonomy of seven concepts (categories, comparative, transformation, fact, and process). (19:40)
4. Categorical concepts, comparatives, and transformations in mathematics. (23:43)
5. Identifying and teaching mathematical "atoms" for better instruction. (29:38)
6. Teaching math concepts by breaking them down into smaller, familiar "atoms" to help students understand and build upon them. (38:18)
7. Simplifying math expressions using factoring and atomization. (44:09)
8. Teaching math concepts by breaking them down into smaller, more manageable "atoms" to help students understand and build confidence. (49:48)
9. Categorical concepts in math education, with a focus on non-examples. (53:43)
10. Importance of examples in teaching, with a focus on the limitations of language in conveying concepts. (57:31)
11. Teaching concepts using examples and definitions. (1:03:31)
12. Using correlated features in math teaching. (1:08:50)
13. Teaching quadratics with examples and caveats. (1:13:28)
14. Using examples to teach concepts, including minimally different and maximally different examples. (1:19:20)
15. Teaching language learners using negative examples first. (1:27:01)
16. Teaching math concepts using examples and testing sequences. (1:31:20)
17. Decisions and categorization in math education. (1:35:10)
18. Using language to make math problems easier. (1:39:51)
19. Differentiating between cognitive routines and transformations in math. (1:45:04)
20. Teaching math concepts using different methods. (1:48:25)
21. Teaching math concepts to children using a step-by-step approach. (1:54:18)
22. Using mini whiteboards for testing sequences in math class. (1:59:19)
23. Teaching strategies, emphasizing the importance of interactive learning and using whiteboards. (2:02:36)
24. Using simplified symbols vs. expert-level symbols in math education. (2:07:59)
25. Using continuous conversion in math lessons. (2:12:00)
26. Teaching math concepts using cognitive routines. (2:20:02)
27. Teaching math concepts to students using explicit and implicit methods. (2:25:28)
28. Teaching strategies, including non-examples, identifying concepts, and managing classroom noise. (2:32:03)
29. Math education, examples, and training. (2:35:28)
30. Improving math education with technology and hybrid learning models. (2:39:19)
31. Teaching methods and classroom management. (2:43:42)
32. Teaching math to mixed-ability students, emphasizing the importance of exploration and unveiling mathematical concepts. (2:50:08)
33. Teaching math to high school students, focusing on approach for different learners. (2:53:42)
34. Teaching probability with creative problem-solving strategies. (2:57:47)
35. Breaking down complex math concepts into smaller parts for better understanding. (3:01:57)
36. Sequencing examples in teaching, emphasizing clarity and brevity. (3:06:53)
37. Using "atomization" to teach math concepts more efficiently. (3:11:09)