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)

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

8 ■ Many programs had no “college level” math requirement ■ M ost programs now require two “college level” math courses Program Requirements

9 Student Demographics ■ Median age was about ■ Median age now about 20

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

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

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

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

14 100% Math 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 Sequence Data Collection Instructors ■ Classroom Practices Inventory Summer > 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:Math content comparison MAT090/095 MAT091/092/094 ■ Math content objectives: MAT091 MAT092 MAT094

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

21 Math Content MATHEMATICS 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 MAT091/092/094 Successful 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 Doing Action-Consequence-Reflection ■ Perform math actions on math objects ■ Observe math consequences ■ Reflect on meaning

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

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

51 The Role of Technology ■ Create action/consequence scenarios ■ Ask good questions ■ Emphasize “sense” making

52 Technology As a Learning Tool User controls technology. User makes inquiries; technology responds. --> User asks questions, makes conjecture | Software provides information <-- User verifies or modifies conjecture Process repeats until ideas are clarified.

53 Technology As a Learning Tool  Student is actively involved in the learning process  Visual Models for: concepts symbols relationships algorithms formulas

Course Policy ■ Math content objectives ■ Study skills and math learning objectives ■ Portfolio content ■ Tentative schedule ■ Exit test ■ Grading policy to include math content grade, portfolio grade, (5-15%) and final exam grade

Summary Classroom activities should integrate successful student strategies with math content objectives in order to implement all aspects of effective instruction and active learning.

56 “Teaching is a long distance event. It is more than just today’s lesson, since students return tomorrow, the next day, and the next.... Your teaching is influential. It shapes and influences what students know today, tomorrow, and in years to come.” Skip Fennel NCTM Newsletter