2. CI 754X Fall 2000Mara Alagic1 What does successful teaching involve? Mara Alagic

3. CI 754X Fall 2000Mara Alagic2 What does successful teaching involve? 4 KNOWLEDGE of material 4 SKILLS in delivering material 4 ATTITUDES that foster learning 4 … 4…4… 4...

4. CI 754X Fall 2000Mara Alagic3 Mathematics Teaching Practices Supported by Research 4 Learning cycle approach 4 Concept development 4 Discrepant events 4 Cooperative learning 4 Concept Mapping 4 Analogies and Metaphors 4 Wait Time

5. CI 754X Fall 2000Mara Alagic4 Learning Cycle with Concept Development 4 Engage 4 Explore 4 Explain 4 Elaborate 4 Evaluate 4 Concrete (manipulative, experience) 4 Visual (pictorial, graphic) 4 Abstract (symbolic, iconic)

6. CI 754X Fall 2000Mara Alagic5 Learning Cycle with Concept Development (2) 4 Learning (Piaget): –access prior knowledge –assimilation and/or disequilibrium –accommodation –organization 4 Knowledge (Jerome Bruner) on –physical level –pictorial level –symbolic level

7. CI 754X Fall 2000Mara Alagic6 Discrepant Events Examples: – … –... –X X X X X M X X X X X X X X X X X X X

8. CI 754X Fall 2000Mara Alagic7 Cooperative learning 4 Assign groups 4 Agree on rules 4 Change roles

9. CI 754X Fall 2000Mara Alagic8 Concept Mapping (1) 4 Identify the relevant concept 4 Put them in order, from general to specific 4 Connect the terms with appropriate linking words 4 Inspiration - software

10. CI 754X Fall 2000Mara Alagic9 Concept Mapping (2) 4 Exploration of what is already known 4 Road-mapping a learning route 4 Extracting meaning from … (textbook, article, lesson, …) 4 Evaluating the effectiveness of a teaching unit 4 Evaluating student learning

11. CI 754X Fall 2000Mara Alagic10 Analogies and Metaphors 4   +  =    ; 2+1=3 4 A teacher is …. 4 1+2+3+ … + 30 and “a rainbow”

12. CI 754X Fall 2000Mara Alagic11 Effects of Wait Time (1) 4 Length of student responses increases 4 Number of appropriate responses increases 4 Failure to respond decreases 4 Confidence of students increases 4 Creative thinking increases 4 Number of student questions increases 4 More students contribute 4 Variety of responses increases

13. CI 754X Fall 2000Mara Alagic12 Effects of Wait Time (2) 4 Teacher-centered discussions decrease AND student-to-student interactions about activities increase 4 Teachers –repeated themselves less –asked fewer low level questions –asked more probing questions –asked more application questions 4 Teachers reported an increase in anxiety as they began to try to extend their wait time

14. CI 754X Fall 2000Mara Alagic13 Effects of Wait Time (3) 4 What do you think … (wait time)… 4 What do you think that … (wait time)… 4 What if … (wait time)…

15. CI 754X Fall 2000Mara Alagic14 Think About... 4 … 4 general praise at the end of class 4 neutral praise 4 think - share - pair -

16. CI 754X Fall 2000Mara Alagic15 Five Basic Elements of Teaching and Learning 4 Activating prior knowledge 4 Acquiring knowledge 4 Understanding knowledge 4 Using knowledge 4 Reflecting on knowledge

17. CI 754X Fall 2000Mara Alagic16 “We learn by doing if we reflect on what we’ve done.” - John Dewey

18. CI 754X Fall 2000Mara Alagic17 What did we learn last week?... 4...

19. CI 754X Fall 2000Mara Alagic18 What did we learn last week?... 4 Frustration with software: –Where do you think your students would have most trouble with? –Would it be same for everyone? –What does the nature of the learner has to do with the above?

20. CI 754X Fall 2000Mara Alagic19 What did we learn last week?... 4 a graphing design problem made of parabolas (Lisa) 4 Penta Problem 4 Number Daisy Problem