3. Try a few more…(just to make you smile!) All teachers are educated. Dr. Butler is a teacher. Therefore… Dr. Butler loves cats. Bigs is a cat. Therefore…
4. Deductive thinking Process of thought that leads from one set of principles to another based on principles of logic. Allows thinkers to extract implications from what is already known Information rearranging process The process most dependent on formal learning
5. Inductive reasoning vs. deductive reasoning Inductive reasoning is often used more than deductive reasoning Inductive thinking is information extending, practical reasoning, seeing what in practice can be accomplished Deductive thinking is information rearranging, theoretical reasoning, seeing what in principal must be true Ex: What We Need VS What We Want VS
6. Information rearranging & deductive thinking skills Skills for deductive reasoning: Evaluation Skills: Assessing information, determining criteria, prioritizing, recognizing fallacies & verifying Analyzing information skills/problem-solving strategies: recognizing, classifying, identifying assumptions, identifying main ideas, & finding sequences Problem Solving: compare and contrast, principles of logic, inferential thinking, & identification of causal relationships Quick Test...
7. Spreadsheets for fun??? Well planned spreadsheet activities emphasize reasoning, problem solving, making connections, and communicating mathematical ideas (Holmes, 1997) Todd Funkhouser, teacher of Algebra 1 Rearrange information The Fun Factor Discussion – real world
8. Thinking about Thinking: Metacognition Metacognition is the awareness of our own thinking process Awareness – activities that foster awareness? Metacognition is the monitoring and guiding of one’s own thought processes; mind observing and correcting itself Example: Mr. Foster & The Lemmings
9. Learning from Lemmings Reflection on problems Describing solutions Scaffolding Teaching/helping peers Chance to create problems Challenges Deductive Reasoning Evaluations Cross Curricular Variety of Programs
10. Review of Heuristics General Problem Solving Strategies Problem solving process can be taught Metacognition can be taught Example: War of the Worlds Alien Project
11. Putting the problem at the center Student learning views are shifting from transmitting skills and knowledge to helping develop confidence, skills, and knowledge necessary to solve problems and become independent learners and thinkers. (21st Century!) Anchored Instruction – offers a framework for merging problem solving with content specific instruction Creates environment of sustained exploration Help novices adopt skills of experts with tools
12. Micro-contexts vs macro-contexts Micro-contexts focus attention on smaller subsets of a larger problem If learning about the environment, focus on pollution’s effects on one animal Macro-contexts allow exploration of a problem space for extended periods of time and from many perspectives Spend a vast amount of time researching and examining several animals Emphasis on the importance of creating an anchor or point of focus enables students to identify and define problems, and their perception of the problem
13. Major goal of Anchored Instruction Enable students to notice critical features of problem situations and to experience the changes in their understanding of the anchor as they view the situation from new points of view.
14. Greatest Advantages of Anchored instruction Use of complex, realistic contexts to provide meaning and reasons for why information is useful Grasp abstract ideas Allows teachers to direct the student’s attention to general problem solving Authentic activity: Factual Level, Degree of Reflection, For whom are the tasks authentic Focus on the relevant features of the problem they are solving
15. Problem-Based Learning Also known as Problem-Centered Learning Built around Real-World problem of interest Creates situation where students “do” instead of mastery of facts Pick problems that are contemporary, nontrivial, and real (not realistic) Examples?
16. Problem Based Learning Practice Life Skills: ability to make decisions raise awareness of complexity of real world issues acquiring body of knowledge developing capacity for self-directed learning generating the ability and desire to think deeply and holistically
17. Authenticity!! The more authentic the problem – the more closely the problem resembles life – the more learners respond!
18. Greenburg’s (1990) Good Problem Solving Characteristics Demands that students make a testable prediction Makes use of relatively inexpensive equipment Complex enough to elicit multiple problem-solving approaches from students Benefits from group efforts Problem solvers must view the problem as relevant (Added by Brooks & Brooks, 1999)
19. Ill-defined Problems Effective problems at the center of the curriculum are ill-defined These problems are ones that need more knowledge than is initially available Problems where there is no absolutely right way or fixed formula for conducting an investigation New information = change of ill-defined problems Element of risk Real as if in the adult world
20. Teachers and Problem Based Learning Still content experts but expertise is used to facilitate and guide Craft problems Specify content Decide process goals Create criteria to measure success Embed problem situations at certain points
21. Collaborative learning is best Problem-based learning is best suited for group work Gives students control over the process of learning new material and representing what they know
22. How to choose problems? Inspiration Pieces Film News story Favorite story Personal Experience Current social events Challenges of various occupations Student experience Example of Daily Warm Up Question Daily Warm Up Question:
23. Resources Pictures of Lemmings Game, Accessed June 27, 2010: http://en.wikipedia.org/wiki/Lemmings_(video_game) Clip Art from Microsoft Clip Art, Accessed June 27, 2010. Alien Picture from Brandon Bowers, 2009 Norton, P. & Karin Wiburg. Teaching with Technology. 2003. Picture of Dr. J. Butler, Accessed July 4, 2010:http://www.utb.edu/vpaa/coe/Pages/JaniceButler.aspx Picture of Bigs, Accessed July 4, 2010: http://butleratutb.pbworks.com/Hurricane-Alex
