Exploring the Use of UbD in the Teaching of Mathematics

1. Exploring the Use of UbD in the Teaching of Mathematics DR. GLADYS C. NIVERA Mathematics Faculty, PNU

2. “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.

3. Begin with the end in mind.

4. Quoted from the 7 Habits of Highly Effective People (Coven, 2005): By beginning with the end in mind (the habit of vision), you get • A clear definition of desired results • A greater sense of meaning and purpose • Criteria for deciding what is or what is not important • Improved outcomes

5. The foremost strength of UbD is the commonsense nature of its principles and strategies. - John Brown (2005)

6. Designing a Course by Common Sense

7. SED 4: Principles and Strategies in Teaching Mathematics • Course Description: • Designed to prepare students in the teaching of mathematics to secondary students • Enhances students understanding of the nature of mathematics and the philosophy of teaching mathematics • Familiarizes students with various teaching methods and strategies • Provides students an opportunity to enhance their teaching skills and to plan and execute a lesson successfully.

9. What is an effective teacher? NCBTS 7 Domains: • Social regard for learning • The Learning Environment • Diversity of Learners • Curriculum • Planning, Assessing and Reporting • Community Linkages • Personal Growth and Professional Development

10. How to Assess the Students

11. Assessment Outputs

12. Common sense tells us to expand assessment tools and repertoires to create a photo album of student achievement rather than a snapshot. - Wiggins and McTighe

13. Everything is wrapped up in a portfolio.

14. Analytic Rubric for Student Teaching Portfolio 4 – Outstanding 3- Very Satisfactory 2 – Fair 1- Needs Improvement

15. Summary Sheet

16. Components of the Grade • Portfolio (40%) • Demonstration teaching (40%) • Oral report (10%) • Participation (10%)

17. Then we draw up the ‘syllabus’ or the relevant experiences and instruction that the students need to have in order to reach the desired outputs.

18. Some Activities That We Do • Debate and reflect on issues • Analyze the BEC document • Critique Films • Conduct Group Discussions • React to journal articles • Discuss and demonstrate different strategies • Perform Micro-teaching

19. Stages of the Backward Design

20. Work in Progress.. • Development of Math 1 and 2 Syllabi • Use of UbD in the design

21. Mathematics Unit on Measures of Central Tendency (Wiggins and McTighe, 2005) Essential Question: What is fair – and how can mathematics answer the question?

32. UbD’s Strengths (Brown, 2004) • It follows common sense. • It could curb the tendency in public education to teach to the test and to emphasize knowledge-recall learning.

33. Workshop Mechanics • Form groups of 5 • Decide which of the two units you would like to design Geometry (Volume and Surface Area) Statistics (Measures of Variation)

34. Workshop Mechanics • Fill up the template. • Modify the activities in the initial template as you see fit • You may use extra papers. • Be ready to share your design.

35. Geometry Unit – Stage I • Established Goals: • II. Math7C3b, 4b: Use models and formulas to find surface areas and volumes. II. Math9A: Construct models in 2D/3D; make perspective drawings.

36. Understandings • The adaptation of mathematical models and ideas to human problems requires careful judgment and sensitivity to impact. • Mapping three dimensions onto two (or two onto three) may introduce distortions. • Sometimes the best mathematical answer in not the best solution to real-world problems.

37. Essential Questions • How well can pure mathematics model messy, real-world situations? • When is the best mathematical answer not the best solution to a problem?

38. Students will know… • Formulas for calculating surface • area and volume • Cavalieri’s Principle

39. Students will be able to… • Students will be able to… Calculate surface area and volume for various 3-dimensional figures • Use Cavalieri’s Principle to compare volume

40. Stage 2 - Assessment Evidence Performance Tasks 1 • Packaging problem: What is the ideal container for shipping bulk quantities of M&M packages cost effectively to stores? (Note: The best mathematical answer is not the best solution to the problem.)

41. Performance Task 2 • As a consultant to the United Nations, propose the least controversial 2-dimensional map of the world. Explain your mathematical reasoning.

42. Other Evidences • Odd-numbered problems in full • Chapter Review, pp. 516-519 • Progress on self-test, p. 515 • Homework each third question in subchapter reviews and all explorations

43. Stage 3 Learning Plan Learning Activities: Investigate the relationship of surface areas and volume of various containers (e.g. tuna fish cans, cereal boxes, Pringles, candy packages) • Exploration 25, p. 509

44. Investigate different map projections to determine their mathematical accuracy (i.e. degree of distortion) • Read Chapter 10 in UCSMP Geometry • Exploration 22, p. 504 • Exploration 22, p. 482

45. Statistics – Stage I • Established Goals: Develop statistical literacy by analyzing, comparing, and solving for the measures of variability accurately.

46. Understandings… Student will understand that… • Statistical analysis often reveals patterns that prove useful or meaningful. • Statistics can conceal as well as reveal • Abstract ideas, such as individual differences and consistency, can be modeled statistically

47. Essential Questions • How do people and events differ? • What is a consistent performance - and how can mathematics help us answer the questions? • How well can statistics reveal patterns in usually messy, real-world data?

48. Students will know… • Formulas for calculating variability of a given set of data (e.g. range, standard deviation) • Interpretation of the results obtained by the measures of variability

49. Students will be able to… • Calculate the different measures of variability relative to a given set of data, grouped or ungrouped (e.g., range, S.D.) • Give the characteristics of a set of data using the measures of variability. • Make a valid interpretation regarding the variability of graphs and data.

50. Stage 2 – Assessment Evidence • Three students must be selected to represent the school in a quiz bee. The principal asks the teacher to randomly select three students from any of the classes since all classes have the same mean. Is this fair? If the policy of the school is to really randomly select the 3 representatives from any of the classes, in which class should the teacher get the representatives - the one with high or low variability? Explain your answer.