1. Philosophy of Teaching and Learning? COL Alex Heidenberg Ideas from Lowman, Bain, & Sousa

2. “Would your class have been different if there was a different group of students?” unknown 2 Why?

3. Student Types (Learners) R.D. Mann Compliant Student Anxious-Dependent Student Discouraged Student Independent Heroes Sniper Attention Seeking Student Silent Joseph Lowman, Mastering the Techniques of Teaching

4. Compliant Student  Good student  Tell them what to do – teacher dependent  Learn what instructor wants (19-2)  Speak to agree with instructor Anxious Dependents  Excessive concern with grades (20-1)  Frazzled; complain about “trick” questions  Low self-esteem Discouraged workers  Worked hard in the past, but burned out  Little control of learning (19-2) 4

5. Independent  High performers  High participators  Make friends with the instructor (5-16) Heroes  Try to impress early, show interest and knowledge (15-6)  Fail to deliver Snipers  Hostile, little hope that they will be recognized.  Cynical (5-16) Attention Seekers  Social butterflies (social needs trump intellectual) (7-14)  Organize group study (6-15) Silent (8-13)  Afraid instructor will not think highly of them  Hard to classify 5

6. 6 How We Learn Bain- Ch. 2  Knowledge is Constructed, not received;  Questions are Crucial – help construct knowledge;  Mental Models Change Slowly;

7. 7 How We Learn A Private Universe A Private Universe Video

8. 8 How We Learn Bain- Ch. 2  Knowledge is Constructed, not Learned;  Questions are Crucial – help construct knowledge;  Mental Models Change Slowly;  Caring is Crucial: WGAD;  What Motivates/Discourages Students? (Jul 23 rd )

9. Tappers vs. Listeners 9

10. 1.Happy Birthday 2.The Star Spangled Banner 3.We Will, We Will Rock You – Queen 4.I will Survive – Gloria Gaynor 5.Do-Re-Me - Sound of Music 6.Amazing Grace 7.It’s a Small World After All – Disney 8.The Sun Will Come Out Tomorrow – Annie 9.I’m a Little Tea Pot 10.Hail to the Chief 10

11. Tappers vs. Listeners 1.Happy Birthday 2.The Star Spangled Banner 3.We Will, We Will Rock You – Queen 4.I Will Survive – Gloria Gaynor 5.Do-Re-Me - Sound of Music 6.Amazing Grace 7.It’s a Small World After All – Disney 8.The Sun Will Come Out Tomorrow – Annie 9.I’m a Little Tea Pot 10.Hail to the Chief 11 The Curse of Knowledge

12. Helping Student’s Learn 12 Knowledge Comprehension Application Analysis Synthesis Eval Remembering Understanding Applying Analyzing Evaluating Creating Bloom’s Taxonomy 1971 Revised Bloom’s Taxonomy 2001

13. Revised Bloom’s Taxonomy Creating – Combine, Plan, Compose, Actualize Evaluating – Rank, Assess, Conclude, Action Analyzing – Order, Explain, Differentiate, Achieve Applying – Classify, Experiment, Calculate, Construct Understanding – Summarize, Interpret, Predict, Execute Remembering – List, Describe, Tabulate, Appropriate Use 13

14. Bloom’s Taxonomy 14 Bloom’s LevelIncreasing Level of Difficulty Increasing Complexity CREATE Rewrite the story from the point of view of the dog. Rewrite the story from the points of view of the dog and of the cat. EVALUATE Compare the two main characters in the story. Which would you rather have as a friend and why? Compare the four main characters in the story. Which would you rather have as a friend and why? ANALYZE What were the similarities and differences between this story and the one we read about the Civil War hero? What were the similarities and differences between this story, the one we read about the Civil War hero, and the one about the Great Depression? APPLY Think of another situation that could have caused the main character to behave that way. Think of at least three other situations that could have caused the main character to behave that way. UNDERSTAND Write a paragraph that describes the childhood of any one of the main character. Write a paragraph that describes the childhood of each of the four main characters. REMEMBER Name the major characters in this story. Name the major characters and the four locations in this story.

15. If p is a polynomial, then Create Evaluate Analyze Apply Understand Remember

16. Create Evaluate Analyze Apply Understand Remember

17. Create Evaluate Analyze Apply Understand Remember

18. Sketch the graph of the following function and determine and Create Evaluate Analyze Apply Understand Remember

19. Sketch the graph of a function f that satisfies all of the following conditions: 19 Create Evaluate Analyze Apply Understand Remember

20. Students Learn Best (Critical Thinking): Bain Pg. 85-86. Consciously raising the questions, what do we know? How do we know?; Clearly and explicitly aware of gaps in information; Discrimination between observation and inference; Probing for assumptions; Test one’s own line of reasoning for internal consistency. 20

21. Closing Thoughts Mathematical Problem Solving is the art of transforming representations until the solution is visible. One of the core skills of a mathematician is to simultaneously hold different representations of a (mathematical) object in his or her mind and to choose the one that is most useful in a given context. Bernhard Kutzler 21