Implementing Promising Practices - doing the Right Thing with the Right Stuff

1. Implementing Promising Practices - doing the Right Thing with the Right Stuff Rob Kimball Project Director The Right Stuff: Appropriate Mathematics for All Students (NSF)

5. Previously, on the Right Stuff…

6. The RIGHT Message

7. The RIGHT philosophy:How do you know when learning has taken place ? When changes in the student’s way of thinking and/or habits of mind are altered. What changes do we want to cause/observe in our students?

8. Undergraduate programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide, 2004 (p. 27)http://www.maa.org/CUPM/curr_guide.html The RIGHT Goals (CUPM Curr. Guide): Offer suitable courses . . . designed to • Engage students in a meaningful and positive intellectual experience; • Increase quantitative and logical reasoning abilities needed for informed citizenship / workplace; • Strengthen quantitative and mathematical abilities that will be useful to students in other disciplines; • Improve every student’s ability to communicate quantitative ideas orally and in writing; • Encourage students to take at least one additional course in the mathematical sciences.

9. Teachers who use promising practices: • Believe knowledge is constructed – not received.

10. Teachers who use promising practices: • Lead students to mental discourse and then help them resolve the issues: Elicit – Confront – Resolve – Assess

11. Teachers who use promising practices: • Ask the right questions until students learn to ask them themselves. If students can’t learn to judge the quality of their own work – they really haven’t learned.

12. Teachers who use promising practices: • Create a natural critical learning environment.

13. Finally: Mental Models Change Slowly

14. A business runs an advertisement in a local paper every Thursday. The ad is 1.75 inches (height) by 2.75 inches (width) and costs $300. However, next month, the business is celebrating 10 years of service and is prepared to spend at least twice as much for a larger advertisement. The advertising manager has the following restrictions placed on ads in the paper: all ads are measured in 1/32 of an inch the width of an ad is limited to 8/32 of an inch intervals the paper gives a 10% discount on ads that are priced over $500. In addition, the advertising manager wants the advertisement to stay as close as possible to the golden ratio - so that it looks good to the eye. Find the size of the ad that the manager should use and be prepared to support your conclusion. Teaching Hint: Have students write a two-Minute paper at the end of this class: Describe how your group solved this problem and any disagreements you had

15. How do we want students to attack this problem ?

16. Module 7 Hurricanes

17. Hurricanes – this will blow you away Module 7 This project is sponsored, in part, by a grant from the National Science Foundation: NSF DUE 06 32883. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

18. Goal of the Module Students will construct a graph and a regression model which shows the relationship between wind speed and the force of the wind. The students will analyze the math model that fits the data to make predictions from the model.

19. MAA CompetenciesProblem Solving ◘ solving problems presented in the context of real world situations with emphasis on model creation and interpretation ◘ creating, interpreting, and revising models and solutions of problems

20. MAA CompetenciesFunctions and Equations ◘ effectively using multiple perspectives (symbolic, numeric, graphic, and verbal) to explore elementary functions ◘ investigating linear, exponential, power, polynomial, logarithmic, and periodic functions, as appropriate

21. MAA CompetenciesData Analysis ◘ collecting (in scientific discovery or activities, or from the Internet, textbooks, or periodicals), displaying, summarizing, and interpreting data in various forms ◘ fitting an appropriate curve to a scatter plot and use the resulting function for prediction and analysis

22. CROSSROADS StandardsIntellectual Development I – 1 Problem Solving I – 2 Modeling I – 3 Reasoning I – 4 Connecting with other Disciplines I – 5 Using Technology I – 6 Developing Mathematical Power I – 7 Linking Multiple Representations

23. CROSSROADS StandardsContent C – 1 Number Sense C – 2 Symbolism and Algebra C – 3 Geometry and Measurement C – 4 Function Sense C – 5 Continuous and Discrete Models C – 6 Data Analysis, Statistics, Prob. C – 7 Deductive Proof

24. CROSSROADS StandardsPedagogy P – 1 Teaching with Technology P – 2 Active and Interactive Learning P – 3 Making Connections P – 4 Using Multiple Strategies P – 5 Experiencing Mathematics

25. Introduction Hurricanes make the news every fall. In recent years, the interest in hurricanes has escalated because of the devastation done by Katrina, and other powerful storms. This activity will attempt to quantify the damage winds are likely to cause.Video:http://www.sciencedaily.com/videos/2006/0503-hurricanes_inside_the_storm.htm

26. Preparing for the Module: QL skills • Atmospheric pressure is measured in force per unit area (click here to learn more).One atmosphere is 14.7 pounds per square inch. Convert one atmosphere to kilograms per square centimeter. (tns file) atmosphericpressure.pdf

27. Preparing for the Module: QL skills • If one atmosphere of pressure exerts 14.7 pounds per square inch, how much pressure is exerted over one square foot?

28. Preparing for the Module: QL skills 3. A man weighing 200 pounds wears size 12 shoes. The surface area of the shoes is approximately 100 square inches.A woman wearing high heals who weighs 120 pounds comes in contact with only 12 square inches of surface.Compute the psf exerted by each person.If each stepped on your back, which one would hurt more?If each stood on a 2x4” plank, which one is more likely to break it?

29. Preparing for the Module: QL skills • According to USA Today, a wind speed of 39 miles per hour produces a force of 6.1 pounds per square foot.How much force would be exerted on a door (6 ft 8 inches by 32 inches) by a wind of 39 mph? Would you be able to hold the door against the wind ? <tns file>

30. Preliminary Thoughts and Opinions • Ask participants to share their experiences with hurricanes • Introduce the concepts of wind speed and air pressure (click here) • Elicit student opinion (individually and then as a group) on what happens to the force exerted by the wind as the wind speed increases. • Confront students with the graphic from the USA Today on wind speed and air pressure (click here).

31. Activity • Enter the data from the USA Today graphic into Excel or a graphing calculator • Construct a reasonable model to predict the force from the wind (psf) from wind speed (mph). <tns.file>

32. Questions • Read the graphic more carefully and find the formula used by Ahren. How does that model compare with your’s ? • You may ask students to do more research on Ahren’s model.

33. Applying the Model Based on your model, ►What would be the force of the wind in psf if the wind speed were 100 mph ? 200 mph ? ► If the force of the wind were 50 psf, what would the wind speed be ? 75 psf ? ► Make a table and calculate the change in the force of the wind for each increase of 5 mph in wind speed. Start the table at 40 mph. Describe the change in the rate of change of force.

35. More Difficult Questions Examine the information from the Atlantic Oceanographic and Meteorological Laboratory (click here). Is it feasible to find a model to predict the median damage of a hurricane based on its wind speed ? Explain. Is it feasible to find a model to predict the number of “extreme hurricane impacts” for any decade?Explain.

36. CONTENT Mathematics courses and programs in the first two years of college need to develop students’ quantitative and workplace skills and actively engage them in the mathematics they will encounter outside the class-room.  Faculty may need to teach content that is different from what they were taught, teach more than they were taught, and teach differently than the way they were taught.  Students should understand some of the big ideas of mathematics through a curriculum, a variety of problem-solving strategies, and significant projects that examine selected topics in depth.  Students should have opportunities to demonstrate their mathematical knowledge, as well as their creativity.  BEYOND CROSSROADS, CH 6

37. CONTENT Besides algebra, what other mathematics will students see in and use in their daily lives and in their profession? Statistics Probability Networks – Graph Theory Finance Geometry – of solids and shapes

38. Integrating Content Applications can often blend content from several areas. This helps to dispel the notion that mathematics is a collection of isolated topics.

39. CLASSROOM ASSESSMENT Collecting information from students to measure their learning aids instruction and guides the instructor. • feedback on lessons • assessing important concepts • improving the course

40. Teaching should be a reflective process

41. Teaching should be a process reflective Planning The teachers who are teaching a course meet together as a team, usually once a week. Previously, they had collaboratively constructed the syllabus and put together materials that would supplement the course.In the weekly meetings, meetings led by the “Lead Instructor”, the team follows the agenda, established by the LI. Topics include ideas for applications to introduce topics in the coming week, methods that have worked before, and challenges in the upcoming material.They have previously identified the “Learning Objectives” that are measured in tests, projects, and exams.The team works together to write departmental tests that all instructors use.Minutes of all meetings are kept, sent to the department head, and placed on the web.

42. Teaching should be a process reflective Implementing Teachers reflect on the ideas of others and on their own experiences and teach their class to the best of their ability.

43. Teaching should be a process reflective Evaluating Teachers often use various means of assessing student learning.Minute papers – to measure understanding, to measure student satisfaction, to assess methodologyQuick Quizzes – (online, paper, clickers) students take a quick quiz to measure the degree of learning / understandingDialogue – using good questioning, faculty create an environment where students have to communicate mathematicallyLearning Objectives – bench marks for the course – data is kept on all sections

44. Teaching should be a process reflective Documenting The minutes of all of the course team meetings are kept in one file with the most recent minutes placed on top. This gives a historical record of the dialogue and provides a rationale for changes that have been made. College algebra minutes at Wake Tech

45. Teaching should be a process reflective Redefining In addition to self-reflection, teachers may assess how well instruction met the established goals in a number of ways. Informal Discussion – teachers talk about their class with others Peer Review – teachers, usually teaching the same course, observe each other and offer constructive feedback Mentor – new faculty often are provided a mentor who reviews plans, observes classes, and assesses performance

46. Teaching should be a process reflective Our Goal This process of continuous improvement is also our method of checks and balances. Academic freedom is not about allowing teachers to do whatever they want. There are promising practices. There is appropriate technology. There are expectations with regard to content. Teachers, guided by their own strengths and experiences, should work together to achieve common goals. All teachers; guided by research, enabled by professional development, and supported by colleagues, can grow professionally.

47. Module 0The Rule of Four

48. Implementing the Rule of Four Module 0 This project is sponsored, in part, by a grant from the National Science Foundation: NSF DUE 06 32883. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

49. Goals of the Module This module will provide examples of how faculty should employ the rule of four in the teaching and learning of mathematics – especially with regard to college algebra.

50. Contents Part 1 Linear Models Fuel in a generator Part 2 Polynomial Models Price of a mile-high snack Gas mileage