Improving Student Performance in Developmental Mathematics Courses Wade Ellis, Jr. West Valley College in Saratoga, California

Outline Introduction Introduction Learning Skills (appropriate for a Math course) Learning Skills (appropriate for a Math course) Instructional Design Instructional Design Bloom’s Taxonomy (updated) Bloom’s Taxonomy (updated) Learning Process Methodology Learning Process Methodology An example of a lesson An example of a lesson Additional Information Additional Information Comments and Questions Comments and Questions

Introduction Basic Skills Initiative (BSI) in California Basic Skills Initiative (BSI) in California The Big Five/Social aspects of a course The Big Five/Social aspects of a course Come to class, Come to class, On time, On time, Pay attention Pay attention Take notes, and Take notes, and Do your homework Do your homework Context-base activities Context-base activities High expectations High expectations Frequent feedback (MyMathLab) Frequent feedback (MyMathLab) What we know about Adult Learners What we know about Adult Learners

Adult Learners Malcolm Knowles makes the following assumptions about the design of learning for adult learners [Andragogy ] 1. Adults need to know why they need to learn something, 2. Adults need to learn experientially, 3. Adults approach learning as problem-solving, and 4. Adults learn best when the topic is of immediate value.

Introduction (cont’d) Neuroscience research Neuroscience research Act/Observe-Reflect/Conjecture/Test Act/Observe-Reflect/Conjecture/Test (David Kolbe and James Zull) (David Kolbe and James Zull) Emotions make a difference in retention Emotions make a difference in retention What students think of themselves What students think of themselves Social persuasion (Albert Bandura) Social persuasion (Albert Bandura)

Introduction (cont’d) Uri Treisman (specific to mathematics) Uri Treisman (specific to mathematics) Adaptive Reasoning Adaptive Reasoning Strategic Competence Strategic Competence Conceptual Understanding Conceptual Understanding Productive Disposition Productive Disposition Procedural Fluency Procedural Fluency

Dos and Don’ts Don’t say “That’s easy.” when asked to talk about a problem. Don’t say “That’s easy.” when asked to talk about a problem. Do return tests the next class meeting. Do return tests the next class meeting. Don’t answer questions students can answer. Don’t answer questions students can answer. Do use lectures to wrap up learning. Do use lectures to wrap up learning. Don’t lecture the whole period. Don’t lecture the whole period. Don’t use green or red colored chalk or markers. Don’t use green or red colored chalk or markers. Do acknowledge good thinking. Do acknowledge good thinking. Don’t give partial credit. (Yes, you should.) Don’t give partial credit. (Yes, you should.) Do come to class early. Do come to class early. Do train your tutors not to pick-up a pencil. Do train your tutors not to pick-up a pencil. Do ask students to explain or verify. Do ask students to explain or verify.

Learning Skills Examples of Learning Skills Examples of Learning Skills Validating results Validating results Using prior knowledge Using prior knowledge Constructing examples Constructing examples Abstracting Abstracting Generalizing Generalizing Persisting Persisting Accepting responsibility Accepting responsibility Learning as a Process that can be improved

Instruction Design Bloom’s Taxonomy of Learning Information - remembering Information - remembering Knowledge - understanding Knowledge - understanding Application - applying Application - applying Problem Solving - analyzing Problem Solving - analyzing Evaluation- judging Evaluation- judging Research - creating Research - creating

Bloom’s Taxonomy of Learning Information - remembering Information - remembering Knowledge - understanding Knowledge - understanding Application - applying Application - applying Problem Solving - analyzing Problem Solving - analyzing Evaluation- judging Evaluation- judging Research - creating Research - creating

Instruction Design Creating Learning Materials Deciding on the behaviors you want the students to display as a result of the course Deciding on the behaviors you want the students to display as a result of the course Backward design Backward design Concept Map (at the beginning of the course) Concept Map (at the beginning of the course) Creating a Lesson Creating a Lesson Seeing the textbook as a resource, but not the course Seeing the textbook as a resource, but not the course Infusing a lessons with what we have learned Infusing a lessons with what we have learned

Variable Expressions Equations Functions Re-express Solve Graph Developmental Mathematics Analyze Interpret Verify

Learning Process Methodology 1. Preparation 2. Learning Activity 3. Reflection

1. Preparation Why? Why? Where does it fit in the knowledge framework? Where does it fit in the knowledge framework? Prerequisites Prerequisites Goals Goals Performance Criteria Performance Criteria Language/Vocabulary Language/Vocabulary Resources Resources

2. Learning Activity Plan Plan Key Questions/Critical Thinking Questions (Inquiry Questions encouraging Reflection) Key Questions/Critical Thinking Questions (Inquiry Questions encouraging Reflection) Examples and Models Examples and Models Application Application Problem Solving Problem Solving

3. Reflection Self-Assessment Self-Assessment Extension Extension

The Contour Map Contour Map Contour Map Contour Map Contour Map

1. Preparation Why? Understanding contour mapping will help you in reading such maps when you deciding on paths for power lines or hiking paths. Where does it fit in the knowledge framework? You can currently read road maps and hiking trail maps. The ability to understand topographic information superimposed on these maps can allow you to understand the placement of buildings or plan hikes more effectively. Prerequisites The ability to read street and road maps. An understanding of the coordinate plane. Goals The ability to interpret topographic maps. The ability to create a simple topographic map from data. Performance Criteria Reading topographic maps. Language/Vocabulary Slicing plane Level curve Contour Contour map Resources Contour map animation

2. Learning Activity Plan 1. Read the Critical Thinking Questions 2. Work with the Contour map program 4. Answer the Critical Thinking Questions 3. Interpret the Applications 4. Solve the Problems Examples and Models Contour Maps (see below) Key Questions/Critical Thinking Questions (Inquiry Questions) Why are the slicing planes the same distance apart? What does it mean when the contour lines are close together on the 2D contour map? How can you tell which peak is highest from the contour plot? Could the contour plot be of a set of valleys rather than a set of peaks? What does it mean when there is a large region at the top of a peak? Application Another topographic map to interpret (see below) Problem Solving Decide on the steepest ascent to the highest mountain or ridge. Interpret a temperature contour map.

3. Reflection Self-Assessment Can you determine the steepest part of a topographical map? Can you determine the saddle points of a topographical map? Can you determine where the lakes or plains are on a topographical map? Extension To what other measurements can contour maps be applied? Why would such maps be useful?

Comments and Questions

Additional Information (choose Literature Review) Basic Skills as a Foundation for Student Success in California Community Colleges (choose Literature Review) Basic Skills Handbook (choose Basic Skills Handbook) James Zull, ( 2002). The Art of Changing the Brain: Enriching the Practice of Teaching by Exploring the Biology of Learning,. James Zull, ( 2002). The Art of Changing the Brain: Enriching the Practice of Teaching by Exploring the Biology of Learning,. Knowles, M. (1984). Andragogy in Action. San Francisco: Jossey-Bass. Knowles, M. (1984). Andragogy in Action. San Francisco: Jossey-Bass. Dan Apple, and others (2009). Electronic Faculty Guidebook. Lisle, Illinois: Pacific Crest. Dan Apple, and others (2009). Electronic Faculty Guidebook. Lisle, Illinois: Pacific Crest. Contour Map Contour Maphttp://curvebank.calstatela.edu/contour81/contour81.htm