Problem

1. Problem • Students are not successful in developmental math courses.Students are not successful in subsequent math courses.Students don't know how to learn.

2. Observations • ■ Placement scores • ■ Completion, attrition rates • ■ Program requirements • ■ Student demographics • ■ Math in society and workplace

3. Placement Scores in the past: MAT090 level: ~70 % MAT095 level: ~15% ---------- Placement Scores Fall 2007: MAT090 level: ~55 % MAT095 level: ~30% 80% of 55% score < 40

4. Data: Fall 2003 – Spring 2006 • ■ Enrollments • MAT090 – 2nd highest • MAT095 – 3rd highest • ■ Success Rates • MAT090 – 34% (lowest) • MAT095 – 35% (2nd lowest) • MAT195 – 61% (3rd lowest)

7. Pass first time Repeat (may or may not pass)‏ Do not continue MAT090 ~40% 19% ~41% MAT095 ~43% 20% ~37% Data: Fall 2001 – Summer 2006 80% of MAT090 students ■ CPT scores in the 20 - 40 range ■ Skill level of grades 1- 4 ■ Success rate of 34%.

8. ■ Many programs had no “college level” math requirement ---------- ■ Most programs now require two “college level” math courses Program Requirements

9. ■ Median age was about 26 ---------- ■ Median age now about 20 Student Demographics

10. ■ Math formerly used by select few ---------- ■ Math now required for entry to many fields ■ Math literacy needed for informed citizens Math in Society and Workplace

11. MAT090/MAT095“dead horse” • ■ New vehicle required to meet • today's needs • ■ Goals of new sequence • ■ 100% Math recommendations

12. ■ Success in developmental math courses ■ Success in subsequent college level math courses ■ Quantitative reasoning outside the classroom GOAL: Students learn math

13. ■ Generic study skills and learning strategies ■ Math specific study skills and learning strategies ■ Lifelong learning in the community and workplace Goal: Students learn how to learn

14. 100% Math Recommendations • ■ More contact time • ■ Student study skills and • learning strategies • ■ Instructional approaches

15. New Sequence • ■ MAT091–Fundamentals of Math • ■ MAT092–Prealgebra • ■ MAT094–Fundamentals of • Algebra

16. New Sequence • ■ More instructional time for • math content • ■ Time for study skills and • math learning objectives • ■ Implementation of • recommended best practices

17. New SequenceData Collection • Instructors • ■ Classroom Practices Inventory • Summer 2008 -> December 2008 • Students • ■ Successful Students Strategies Sept. Pretest -> Dec. Posttest • ■ Exit Test Data • Test format to be determined

18. 100% Math #15 • … contact time should be sufficient to enable instructors to implement all aspects of effective instruction and active learning … including the integration of study skills into classroom activities.

19. New Sequence – Math Content • ■Math content comparison: • MAT090/095 <-> MAT091/092/094 • ■ Math content objectives: • MAT091 • MAT092 • MAT094

20. Developmental ■ Build on concepts previously learned. ■ Introduce and develop concepts never learned. ■ Replace misconceptions. ■ Prepare for future math. Math ContentDevelopmental ≠ Remedial

21. Math ContentMATHEMATICS LEARNING CUBE DIMENSIONS Cognitive Representational Content Musser, G.L. and Burger, W.F. Mathematics for Elementary Teachers, Macmillan (1994).

22. New Sequence – Successful Student Objectives ■ Generic study skills and learning strategies ■ Math specific study skills and learning strategies

23. STUDENT PROFILE-COMPOSITE

24. Math Success Objectives STRANDS SELF-AWARENESS • personal strengths/weaknesses/attitudes GENERIC STUDY SKILLS • classroom, homework, test preparation MATH LEARNING PROCESS • math models and multiple representation, problem solving, math language

25. MAT091/092/094Successful Student Objectives • ■ Study Skills Objectives • SS1 – SS14 • ■ Math Learning Objectives • ML1 – ML11

26. 100% Math #6 • Skills and understandings related to learning process should be integrated directly into course curriculum and classroom activities

27. Portfolios • ■ Portfolio Content • ■ Portfolio Logistics • ■ Portfolio Assessment

28. Portfolio Content • ■ 15 worksheet activities • corresponding to objectives from • 6 study skills areas • ■ 3 worksheet activities • corresponding to objectives from • 3 math learning areas • ■ 2 written reflections

29. Portfolio Logistics • ■ Classroom file cabinet will contain • student folders • ■ Each student folder label will show • course number, section number • and student number • ■ Each student folder will include the • portfolio index page and completed • worksheets collected over the • semester

30. Portfolio Assessment • Evaluating student work: • ■ Worksheets graded by instructor • ■ Portfolio weighted 5-15% of • semester grade

31. Portfolio Assessment • Evaluating portfolio process: • ■ Portfolio Index Page for each • student • ■ Complete portfolio folder for • randomly selected students • --- submitted to portfolio committee • --- evaluated using portfolio rubric

32. Materials – August 2008 • ■ Sample course policies • ■ Pretests – math objectives • ■ Pretest/posttest – success objectives • ■ Practice Final Exams • ■ Portfolio rubric • ■ Electronic versions of all materials

33. 100% Math #6 • Skills and understandings related to learning process should be integrated directly into course curriculum and classroom activities

34. Success Activities • Discussion Before Activity • ■ Establish baseline • ■ Motivate • ■ Describe activity

35. Success Activities • Three criteria • ■ Introduce information • ■ Apply immediately to math • context or individual needs • ■ Use multiple learning • channels

36. Success Activities • Discussion After Activity • ■ Summarize information • ■ Describe how helpful • ■ Extend to other contexts

37. 100% Math #3 • Adjust instructional approach to accommodate different learning styles

38. Learning Styles Reading Writing Visualizing Hearing Speaking Manipulating

39. Learning Pyramid* Average Retention Rate after 24 Hours 5% 10% 20% 30% 50% 75% 90% * National Training Laboratories of Bethel, Maine Sousa, David A. How the Brain Learns, NASSP (1995).

40. 100% Math #1 Instructors should incorporate active learning approaches into their classroom methodology. Students learn best by active involvement, so it is important to allow students the opportunity to do hands-on work in every class.

41. Classroom Methodology Classroom Structures Lecture/Whole Group Small Group Individualized Self-paced Instructional Approaches Active Learning Multiple Learning Channels Multiple Representations

42. Instructional Approaches ■LEARN BY DOING(Active Learning) Act Observe Interpret Connect Apply ■LEARN THROUGH MULTIPLE LEARNING CHANNELS Manipulate Visualize Hear Speak Read Write ■LEARN THROUGH MULTIPLE REPRESENTATIONS Use concrete models to understand abstract ideas

43. Learn by DoingAction-Consequence-Reflection ■ Perform math actions on math objects ■ Observe math consequences ■ Reflect on meaning

44. Change in Mindset Replace … With … • introduce build • show observe explain explore practice interpret connect apply

45. Learn through Multiple Representations SEQUENTIAL PROCESS concrete -> connecting -> abstract level levels level example: REAL OBJECT --> VISUAL MODEL --> VERBAL DESCRIPTION --> SYMBOLIC FORM

46. Models Modelling and technology facilitate a deeper understanding of mathematics content. Physical models -> -> Symbolic Models Concrete -> -> Abstract

47. Models • ■ Everyday objects • ■ Math manipulatives • ■ Diagrams/sketches • ■ Overhead manipulatives • ■ Smart Notebook objects • ■ Virtual models • ■ Math models

48. Math Models • Rule of Three: • Geometric – Numeric – Algebraic • Graph - Table - Expression • Rule of Four: • Geometric – Numeric – Verbal - Algebraic • Graph - Table - Words - Expression • Rule of Five: • Concrete - Geometric – Numeric – Verbal – Algebraic • Physical Object -Graph - Table – Words - Expression

49. Math Language Structure • ■ Elements • words, symbols, diagrams, • graphic devices • ■ Syntax • conventions for combining • elements

50. Learning Math Language thinking //// xx ---> idea of four xx listening and speaking hearing "four" saying "four" reading and writing reading four,4, writing four,4,