Beyond the "Miracles" of Math: Backward Planning and Teaching Mathematics

Transcript

1. BEYOND THE “MIRACLES” OF MATH: BACKWARDS PLANNING AND TEACHING MATHEMATICS Teaching Presentation at Gettysburg College—27 February 2013! Jeremy Price, PhD—University of California, Berkeley! http://www.gocomics.com/calvinandhobbes/2011/03/09
2. Orientation Big Ideas Backward Design Essential Questions Common Pitfalls Gaining Confidence
3. Identifying Big Ideas A big idea is a concept, theme, or issue that gives meaning and connection to discrete facts and skills.! ! Wiggins & McTighe, 2005, p. 5! http://flic.kr/p/de5dUt
4. Powers of Ten What are the Big Ideas and Big Questions evoked by this video?
5. Reversing The Design of Instruction We advocate the reverse of habit: starting with the end (the desired results) and then identifying the evidence necessary to determine the results have been achieved (assessments). With the results and assessments clearly specified, the designer determines the necessary (enabling) knowledge and skill, and only then, the teaching needed to equip students to perform.! ! Wiggins & McTighe, 2005, p. 338! http://flic.kr/p/3MiCy4
6. Understanding Backward Design 1. Identify Desired Results! 2. Determine Acceptable Evidence! 3. Plan learning experiences and instruction! http://flic.kr/p/7vMZs1
7. Identify Desired Results “Would you tell me, please, which way I ought to go from here?” “That depends a good deal on where you want to get to,” said the Cat. “I don’t much care where,” said Alice. “Then it doesn’t matter which way you go,” said the Cat. Essential Questions • What questions will foster inquiry, understanding, and transfer? Understandings • Big Ideas • Specific Understandings • Predictable Misunderstandings • Key Knowledge and Abilities Established Goals • Standards • Objectives • Learning Outcomes
8. Determine Acceptable Evidence Performance Tasks •  Authentic demonstrations of desired understandings •  Criteria for evaluating performances Other Evidence •  Other kinds of demonstrations of desired results •  Student reflection and self-assessment http://flic.kr/p/8Box52
9. Plan Learning Experiences and Instruction http://flic.kr/p/a4vKzM (Wiggins & McTighe, 2005, p. 22) •  Where is the unit going? What is expected? W •  Hook and Hold students H •  Equip students, Experience key ideas, and Explore issues E •  Rethink and Revise R •  Evaluate work and implications E •  Tailored to individual needs, interests, and abilities T •  Organized O
10. What Are Essential Questions? 1.  Genuine and relevant inquiry into big ideas and core content! 2.  Provocative to sustain thought, discussion, inquiry, and new understanding and more questions.! 3.  Require considerations of alternatives, evidence, and justifications.! 4.  Stimulate vital, ongoing rethinking of big ideas, assumptions, prior lessons.! 5.  Spark connections with prior learning and personal experiences.! 6.  Naturally recur, creating opportunities for transfer to other situations.! Overarching Topical • Go beyond particular topics and skills • General, transferable understandings • Help students come to a particular understanding • (Provisionally) resolved Characteristics! Granularity! http://flic.kr/p/z6Ebx
11. Returning to Your Big Ideas and Questions Which big questions or big ideas can be considered! essential questions? http://flic.kr/p/d3UADU
12. Curricular Priorities Worth Being Familiar With Important to Know and Do Enduring Understanding Understand the place value system (5.NBT) ~~~~~~~~~~~~~~~~~~~~ Work with radicals and integer components (8.EE) ~~~~~~~~~~~~~~~~~~~~ Reason quantitatively and use units to solve problems (N-Q) Explain patterns in number of zeros and in the placement of the decimal point (5.NBT) ~~~~~~~~~~~~~~~~~~~~ Use a single digit times an integer power of 10 to estimate quantities (8.EE) ~~~~~~~~~~~~~~~~~~~~ Use units, define appropriate quantities, choose appropriate level of accuracy (N-Q) ????
13. Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Common Core State Standards for Mathematics
14. Essential Questions as a Bridge to Standards How do your questions connect with the standards?! Can we generate new questions to connect the Powers of Ten video with the standards?! http://flic.kr/p/aAXs9N
15. The New Powers of Ten
16. Twin Sins of Traditional Design Coverage! Activity- Oriented! http://flic.kr/p/5HwWZg http://flic.kr/p/8bUFch “hands-on without being minds-on”
17. Math Miracles
18. Against Answer Getting The American teacher looks at a problem they’re going to use in a lesson and ask themselves, how can I teach my kids to get the answer to this problem? The Japanese teacher asks, what’s the mathematics they’re supposed to learn working on this problem? How can I get them to learn that mathematics? Phil Darrow, Against ‘Answer-Getting’ http://vimeo.com/30924981 http://flic.kr/p/DGy17
19. Backward Design Requires Practice Many educators have observed that backward design is common sense. Yet when they first start to apply it, they discover it feels unnatural. Working this way may seem a bit awkward and time-consuming until you get the hang of it. But the effort is worth it—just as the learning curve on good software is worth it. http://flic.kr/p/7FdBxt
20. Adding Backward Design To Your Teaching Toolkit http://flic.kr/p/4E9q5o
21. Jeremy Price, PhD Postdoctoral Scholar University of California, Berkeley The Learning Design Group, Lawrence Hall of Science jeremy.price@berkeley.edu