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