1. Critical Thinking: Does It Mean What You Think?

2. On Conjugation ofCyclically-GeneratedBanach Spaces 3. Whats So Critical AboutThinking Anyway? 4. Oceans Fourteen Auditions 5. So What Exactly IS Critical Thinking? (And Can It Really Kill You?) 6. Dave Sobecki Miami University* Hamilton* Miami University is not in Florida. When itwas founded, Florida was a Spanish territory(1809). 7. I shall not today attempt further to definethe kinds of material I understand to beembraced within that shorthanddescription ["hard-core pornography"]; andperhaps I could never succeed inintelligibly doing so. But I know it when Isee it, and the motion picture involved inthis case is not that.Justice Potter Stewart, concurringopinion in Jacobellis v. Ohio 378 U.S. 184(1964), regarding possible obscenity inThe Lovers. 8. Critical Thinking as Defined by the National Council for Excellence in Critical Thinking, 1987A statement by Michael Scriven & Richard Paul {presented at the 8thAnnual International Conference on Critical Thinking and EducationReform, Summer 1987}.Critical thinking is the intellectually disciplined process of actively andskillfully conceptualizing, applying, analyzing, synthesizing, and/orevaluating information gathered from, or generatedby, observation, experience, reflection, reasoning, orcommunication, as a guide to belief and action. In its exemplaryform, it is based on universal intellectual values that transcend subjectmatter divisions:HUH?clarity, accuracy, precision, consistency, relevance, soundevidence, good reasons, depth, breadth, and fairness. 9. Dude, this class sucks.Dude, this textbook sucks. Math and science education is at acritical juncture in the United States. 10. Analyze information provided in detail, and in a scholarlyway Evaluate a situation and judge what is useful in solvingproblemsand drawing conclusions A method of exercising ones thinking ability in a way thatis crucialto intellectual and personal development A transition from childhood thinking to adult thinking A process that leads to further intellectual developmentand encourages students to become lifelong learners. 11. Definition By ContradictionDef: Critical thinking in mathThe OPPOSITE of memorization andmimicry. 12. And now, the big question: 13. The Obvious (and most common) Way:Critical thinking questions on HW/TestsBut can we expect our students to excel at criticalthinking questions if we dont train them to, you know,THINK CRITICALLY?The More Important Way: TEACHINGSTYLE 14. What do your students understand?What can they explain?ASK THEM! 15. What is a variable?Its a letter, like x.NO ITS NOTAble to vary 16. Able to vary 17. What is an equation?Its a thing you solve for x.NO ITS NOTStatementIs 3y2 7y +12 true? 18. What is solving an equation?Its getting x by itself on one side.NO ITS NOTUnderstanding vs. Doing 19. What is solving an equation?Its getting x by itself on one side.NO ITS NOTUnderstanding vs. Doing 20. What is a function?Its a formula, like f(x) = x2.NO ITS NOTRelationshipI solved the function. 21. What is a graph?You plot points and connect the dots.NO ITS NOTPicturing Data 22. Unemployment Rate by YearYear 92 93 94 95 96 97 98 99 00 01Rate (%) 7.5 6.9 6.1 5.6 5.4 4.9 4.5 4.2 4.0 4.7Year 02 03 04 05 06 07 08 09 10 11Rate (%) 5.8 6.0 5.5 5.1 4.6 4.6 5.8 9.3 9.6 8.9 23. Assessment is important too!(A) Write a verbal description of the inequality x> 3, and a verbal description of the inequality x> 5.(B) The expression 3 < x > 5 is a combinationof the two inequalities from part (A). Rewriteyour two verbal descriptions from part (A) withthe word and in between, then use the resultto describe why the expression 3 < x > 5 is silly. 24. Assessment is important too! 2 x +16 dx 25. Assessment is important too!(A) Find the value of the expression (3 + 8)2. Dont forget order of operations!(B) Find the value of 32 + 82. How does it compare to your answer from part (A)?(C) Rework parts (A) and (B) with any two nonzero numbers you choose.(D) What can you conclude about distributing an exponent? 26. Assessment is important too!Explain what it means to solve an equation inyour own words. 27. But Dave, what about online homework? Cancritical thinking play a role?Yes. Yes it can. 28. Comments? Questions?Suggestions? Dirty jokes?davesobecki@gmail.comfacebook.com/Teachingbackwards@teachbackwards