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

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

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

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

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

7. How We LearnA Private Universe A Private Universe Video

8. How We LearnBain- 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 23rd)

9. Tappers vs. Listeners

10. Tappers vs. Listeners • Happy Birthday • The Star Spangled Banner • We Will, We Will Rock You – Queen • I will Survive – Gloria Gaynor • Do-Re-Me - Sound of Music • Amazing Grace • It’s a Small World After All – Disney • The Sun Will Come Out Tomorrow – Annie • I’m a Little Tea Pot • Hail to the Chief

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

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

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

14. Bloom’s Taxonomy

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: 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.

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