New textbooks Real-life context Student-centered Creative thinking
Typical Korean Math Teacher Orchestration of lessons Complete practice Coherent explanation Efficient imprinting Systematic instruction
Systematic instruction There is a pattern in their lessons Teacher initiates and leads learning Focuses primarily on procedures Gives priority to efficient delivery o f content Conclusion ? Introduction Development
Coherent explanation Learn by imitation Fundamental Guide to Math an obligation to make students Learn the intended content Within a given time limit Kind Easy Intuitive Insightful Model
Complete practice Long period of time to establish fundamental Hard for students to understand in the beginning Duty Persuade and cheer up students to practice as much as possible
Efficient Imprinting Last 3-5 minute-long imprinting provides students with efficient condensation of the intended learning content in a lesson
What students should keep in mind
How to memorize definitions, algorithms, etc
Why some specific knowledge is prior to others
Special order, context, map, relationship, etc
“ Good” mathematics teaching Enculturation Focused on process Conceptual understanding Guide to invention Positive attitude Rich context Meaningful Appropriate provocative Participation Student-centred Various contribution
How many pentagons are on the whole soccer ball? How many hexagons are on the whole soccer ball?
S1: So what is your answer? Mine is 12. S2: Regular pentagon? 12. I counted the regular hexagon first. It ’ s 19. S3: So did I, but in my case, it ’ s different, it ’ s 20. S1: How did you count? S2: Well, I started at this face, let ’ s count again , one, two, … , twenty. Oh, it ’ s strange, what ’ s happening here! [Pragmatic] Conversation (1) 1
S 4 : I think 20 is correct because there were no mistakes before. Maybe you ’ ve missed one. S 2 : I need to count once again. By the way, all of you got 20? S1, S 5 : Yeah. S1 : Why don ’ t you count by following different direction s ? I t might be helpful. Conversation (2) 2
S 5 : [speaking to S1] Directions? Why do we consider directions? S 2 : If we collect lots of evidence, then we can believe a lot. Is it correct? S1 : In addition to that, there would not be mistakes if we insist on direction while counting. S 5 : Oh! That ’ s a good idea. Then we had better investigate how many directions are there .