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Source of Image:Maths4life, Improving learning in mathematics: challenges and strategies by Malcolm SwanRetrieved online from http://www.maths4life.org/content.asp?CategoryID=1068 3
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What is a Blind Spot?Jot down the first thing that comes to mind.Turn to a partner and discuss your thought.What ideas are out there? 5
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Try out your “Blind Spot” Participants were provided with an index card marked as below: A O X 6
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Try out your “Blind Spot” Hold your card in your left hand, with the X on the right side Cover your right eye with your right hand, and focus on the X Move the card slowly toward your face until the O disappears (but A remains) Now, flip the card horizontally and repeat, covering your left eye and still focusing on the X 7
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Expert Blind Spots An expert blind spot occurs when someone skilled in an area overestimates the ease of learning its formalisms or jargon or underestimates learners’ informal understanding of its key ideas. As a result, too little attention is paid to linking formal …understanding to informal reasoning…. Bransford, Brown and Hocking, How Students Learn, p. 355 8
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An Example: Multiplication 3 X 4 = 12 3 X 7 = 21 7 X 5 = 35Memorizing these facts is not really any different than memorizing what is below: Carl Dennis lives on Allen Brian Avenue Carl Gary lives on Brian Allen Avenue Gary Edward lives on Carl Edward Avenue Sousa, page 43
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Another Example Which of these problems is most difficult for a beginning algebra student? 1. Solve for x: x*6 + 66 = 81.9 OR 2. Starting with some number, if I multiply it by 6 and then add 66, I get 81.9. What number did I start with? OR 10
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Another Example 3. When Ted got home from his waiter job, he multiplied his hourly wage by the 6 hours he worked that day. Then he added the $66 he made in tips and found he had earned $81.90. How much does Ted make per hour? 11
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And the Answer is…. Most math teachers (from pre-service to higher ed) believe #3 is most difficult. The research showed that student responses were 1. 43% correct 2. 62% correct 3. 66% correct Koedinger and Nathan, 2004 12
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At Your Tables: Share a time when you were part of an EBS moment, either as the teacher or as the student. What more effective strategies might have been used? Why would it be helpful to know about EBS?
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Teaching StylesDimension OptionsInformation Concrete vs AbstractPresentation Visual vs VerbalOrganization Deductive vs InductiveParticipation Active vs PassivePerspective Sequential vs Global Felder/Silverman, p. 675
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What About in STEM Fields?Dimension OptionsInformation Concrete vs AbstractPresentation Visual vs VerbalOrganization Deductive vs InductiveParticipation Active vs PassivePerspective Sequential vs Global Felder/Silverman, p. 675
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What About in STEM Fields?Dimension OptionsInformation Concrete vs AbstractPresentation Visual vs VerbalOrganization Deductive vs InductiveParticipation Active vs PassivePerspective Sequential vs Global Landis, page 126
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Visual vs Verbal?? Really? Visual is NOT just something you show; it must involve charts, graphs, diagrams. (Writing on a board is generally verbal, not visual.) Visual Example: Expansion of (a + b)2 http://illuminations.nctm.org/ActivityDetail.a 17
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Inductive Vs DeductiveInductive ReasoningInductive reasoning is based on observation. Peopleusing inductive reasoning find a pattern in acollection of specific observations and draw ageneral conclusion based on that pattern.Deductive ReasoningDeductive reasoning is based on laws or generalprinciples. People using deductive reasoning applya general principle to a specific example. 18
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Inductive Vs Deductive“Induction is the natural human learningstyle .”“Deduction is the natural human teachingstyle , at least for technical subjects at the collegelevel. Stating the governing principles andworking down to the applications is an efficientand elegant way to organize and present materialthat is already understood .” Felder/Silverman, p. 677
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Classical Deductive ApproachDef: The point-slope form of a line is acommon and useful form of the equation of aline. If a line passes through the point ( x 0 ,y 0 ) and has a slope of m, then the equationof the line can be written 20
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Classical Deductive Approach1. Use this formula to find the equation of the line through the point (2,3) with slope -4.2. Find the equation of the line through the points (1,3) and (-1, 4).3. Oops, out of time, do the word problems for homework! 21
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An Inductive ExampleIn late summer, the outsidetemperature in degreesFahrenheit can bepredicted based on howfast the crickets arechirping! # Chirps °F 40 50Some summer interns 60 55working for a biology 100 65teacher recorded this data: 160 80 22
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An Inductive Example:What questions can weask and answer aboutthis situation? 23
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Rehearsal Find one or two other participants who teach similar content/courses. Together, identify a content piece that you might typically present in a deductive way. Sketch out a plan for teaching that same idea using induction followed by deductive practice. 24
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