Reaching for the Ideal Course Through Student-Centered Course Redesign

1. Reaching for the Ideal Course Through Student-Centered Course Redesign NCAT’s Redesign Conference 2008 Gary Hagerty (Presenter) GaryHagerty@bhsu.edu Stan Smith (Co-Redesign Participant) StanleySmith@bhsu.edu

2. Results By following much of NCAT’s philosophies, we moved from a traditional 3 day a week lecture, to a student centered approach based around technology beginning in 2004. Resulting in a 40% cost reduction and more possible.

3. Results • Passing Rate = 83% • Increased test scores • Enrolling in Trig after college algebra • Increased from about 1% to about 6% • Increased grades in Trig • Increased acceptance and support outside the department

4. Results Passing rate Passing as defined as a “C” or better – (83% rate is defined as a “D” or better -- )

5. Results Test Results 1 CAAP results for students who completed the CAAP Test prior to beginning the Redesign versus most recent year. The subgroup of ACT scores of 20-24 were evaluated to remove as much outside influence as possible. (This group primarily enrolled only in College Algebra) NOTE: Using a normalcdf – this change is approximately increasing from the 49.5 percentile to the 61 percentile.

6. Results Test Results 2 A Brief look at CAAP results based on Grades in College Algebra. This examination was to look for grade inflation with the desire that the Null Hypothesis: The means of pre and post groups are equal to be upheld.

7. Results Outside Department Over the last 3 years I've noticed atrend intheincreasedgeneral level ofmathematical background and preparednessmystudents have, this has beenesp. noticeable in my geneticscourse with regard to algebra. Another interesting (andencouraging!) trend I've noticed over the past 2-3years hereiswhat seems to beagreateroverallappreciation formathematics as a field, anditsvalue and practical benefitsin the real world. This is avery interesting and welcometrendthat I hope continues here at BHSU. It seems whatever you guys are doing in themath programis having positive effects on many students.In fact , severalstudents over the past 2 years have specifically commented on the high quality of the several math classes, most notably algebra. Dr. Dan Bergey – Biology 11-2007

8. Results Outside Department Due to the revision of the College Algebra course by the Mathematics Department, I have observed that the students in my required mathematics courses for prospective elementary teachers have better procedural skills, more confidence in their mathematics ability, and improved problem solving competence. Dr. John Alsup – Math Education 12 - 2007

9. The Redesign Overview The redesign has been developed in three parts and readably fit into most formats of delivery. • The Big Picture • Theoretical • Historical • Connections • Real World Applications • Group Work • ALEKS • Traditional Algorithm development

10. The Redesign ALEKS • For the Small Picture, we have chosen to use technology to deliver Traditional Assignments. • Software Choice – ALEKS • Individualized • Programmed (mastery) Learning • Well Designed

11. The Redesign ALEKS Initial Assessment Using the initial assessment from ALEKS, we can advise students. Red – Indicates weak student who may want to consider enrolling in Intermediate Algebra for a refresher. As this group is often returning students who have been away from math for a while, they can also choose to put in extra effort and catch up. Yellow – Weak students, who should probably start in a review chapter in a traditional test. Green – Strong students, who can start at a typical first chapter in College Algebra.

12. The Redesign ALEKS Consider the traditional course. Predetermined Course Pace Content Time When looking at the traditional spread of students enrolled in a College Algebra Course (previous slide), one needs to question the traditional wisdom of a course designed around every starting on the same assignment and moving at the same speed

13. The Redesign ALEKS • After the first Assessment • Mastery Learning (Bloom) • Self-Efficacy • (Bandura)

14. The Redesign The Small Picture Ongoing Assessments keep Students in their Zone of Proximal Development

15. The Redesign The Small Picture • Intermediate Objectives allow for the instructor to control the primary curriculum so that all students are working in the same content at the same time. • Polynomials • Rational/Inverse/Composition • Logs and Exponents • Series and Sequences • Matrices

16. The Redesign The Small Picture By being Self Paced ALEKS Provides a path for recovery When needed (A student ends up in the Hospital for a week and another week at home in bed without being able to work. ALEKS allows us to individualize for this student and develop a plan to assist the student in gaining the necessary skills to successfully pass the course)

17. Stepping Aside ALEKS At this point, ALEKS can be used as a complete program. Western Missouri State U uses ALEKS as the sole delivery tool in remedial math courses with an 80% passing Rate and success in general education courses at the level of those who place directly into the general education courses.

18. Stepping Aside ALEKS At this point, ALEKS can be used as a supplemental program. Boise State and Louisiana Tech use ALEKS to support algebra and trig skills in Calculus Courses, obtaining a 15-20% increase in grades and continuation rates.

19. The Redesign The Big Picture • 1/3 Lecture • Based on • Theory • History • See Hagerty, Smith Goodwin, The unique effects of including history in College Algebra. MAA’s Convergence Journal http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1629#discussion • Usefulness

20. The Redesign The Big Picture

21. The Redesign The Big Picture • History • Too often, students leave school never realizing that knowledge is the answers to someone’s prior questions, produced or refined in response to puzzles, inquiry, testing, argument, and revision. To teach from questions means rhetorically asking, “If knowledge is made up from answers, then what were the questions that gave rise to textbook or teacher answers and current subject-matter knowledge answers?” • -- Understanding by Design • Wiggens and McTighe 1998

22. The Redesign The Big Picture • Usefulness Graph of absorption of a medication into the blood stream followed by elimination and metabolism of the medication. Graph is created by a piecewise rational function

23. The Redesign The Big Picture • Usefulness By translating the function on the last page and adding together translated functions we can look at the level of medication at any time period if the medication is take every four hours (red) or every two hours (blue). Green line represents the level where the medication is effective and yellow line represents where the level is toxic. Question: Is the purpose of mathematics to develop people can remember the quadratic formula or people who can understand the mathematical concepts when they present themselves?

24. The Redesign APPLICATION 1/3 Group Work Application Oriented

25. The Redesign APPLICATION Application were designed after discussing with others on Campus as to their needs: Business – Profit, Loss, Maximum sales. Financial Models, Prediction models. Science – Decay, Population Growth (Logistic model) Psychology, Kinesiology, Education – Behavior Change

26. The Redesign APPLICATION By creating applications with other departments in mind, we are working on tearing down the compartmentalization boxes.

27. The Redesign APPLICATION A Curve A represents a profit curve. Why do we want to find the x-intercepts? Will a business student recognize that the x-intercepts in this problem are what will be called “break even points” in business if we continue to teach algebra in isolation?

28. The Redesign A Student Perspective I did not like math in high school. I could never understand or remember any of the details to make the math work or to apply it to anything tangible. I intended to take College Algebra and be done with math forever. However, the way that college algebra was set up allowed me to master every part of the course and fill in my weak areas. I am now a mathematics major who is seriously looking into a career in cryptanalytics. I wouldn't be a math major today if I'd enrolled in a normal college algebra course. Peter Lemke class of 2009

29. Closing College Algebra needs to remain a Gateway Course Because: Modeling: Polynomial, exponential, logistic Tools for Understanding: Polynomials, Exponentials, Series and Sequences Rational and Logical Thought Processes Finding zeros Skills necessary for continuation: both within math and in other subjects.

30. Closing College Algebra needs to remain a Gateway Course But We must unlock the Gate for all.

31. Closing Tools Such as ALEKS and Redesign allows for the unlocking of the Gate and all can push it open!