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

Improving Student Improving Student Performance Performance

in in Developmental Developmental Mathematics Mathematics

CoursesCoursesWade Ellis, Jr.Wade Ellis, Jr.

West Valley College in Saratoga, West Valley College in Saratoga, CaliforniaCalifornia

[email protected]@ti.com

OutlineOutline

IntroductionIntroduction Learning Skills (appropriate for a Math Learning Skills (appropriate for a Math

course)course) Instructional Design Instructional Design

Bloom’s Taxonomy (updated)Bloom’s Taxonomy (updated) Learning Process MethodologyLearning Process Methodology An example of a lessonAn example of a lesson

Additional InformationAdditional Information Comments and QuestionsComments and Questions

IntroductionIntroduction Basic Skills Initiative (BSI) in CaliforniaBasic Skills Initiative (BSI) in California

The Big Five/Social aspects of a courseThe Big Five/Social aspects of a course Come to class,Come to class, On time, On time, Pay attentionPay attention Take notes, and Take notes, and Do your homework Do your homework

Context-base activitiesContext-base activities High expectationsHigh expectations Frequent feedback (MyMathLab)Frequent feedback (MyMathLab)

What we know about Adult LearnersWhat we know about Adult Learners

Adult LearnersAdult Learners

Malcolm Knowles makes the following Malcolm Knowles makes the following assumptions about the design of learning assumptions about the design of learning for adult learners for adult learners [Andragogy[Andragogy] ]

1.1. Adults need to know why they need to Adults need to know why they need to learn something, learn something,

2.2. Adults need to learn experientially, Adults need to learn experientially, 3.3. Adults approach learning as problem-Adults approach learning as problem-

solving, and solving, and 4.4. Adults learn best when the topic is of Adults learn best when the topic is of

immediate value.immediate value.

Introduction (cont’d)Introduction (cont’d)

Neuroscience researchNeuroscience research Act/Observe-Reflect/Conjecture/TestAct/Observe-Reflect/Conjecture/Test

(David Kolbe and James Zull)(David Kolbe and James Zull) Emotions make a difference in retentionEmotions make a difference in retention

What students think of themselvesWhat students think of themselves Social persuasion (Albert Bandura)Social persuasion (Albert Bandura)

Introduction (cont’d)Introduction (cont’d)

Uri Treisman (specific to Uri Treisman (specific to mathematics)mathematics) Adaptive ReasoningAdaptive Reasoning Strategic CompetenceStrategic Competence Conceptual UnderstandingConceptual Understanding Productive DispositionProductive Disposition Procedural FluencyProcedural Fluency

Dos and Don’tsDos and Don’ts Don’t say “That’s easy.” when asked to talk Don’t say “That’s easy.” when asked to talk

about a problem.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 Don’t use green or red colored chalk or

markers.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 SkillsLearning Skills

Examples of Learning SkillsExamples of Learning Skills Validating resultsValidating results Using prior knowledgeUsing prior knowledge Constructing examplesConstructing examples AbstractingAbstracting GeneralizingGeneralizing PersistingPersisting Accepting responsibilityAccepting responsibility

Learning as a Process that can be Learning as a Process that can be improvedimproved

Instruction Design Instruction Design Bloom’s Taxonomy of LearningBloom’s Taxonomy of Learning

Information Information - remembering- remembering Knowledge Knowledge - understanding- understanding Application Application - applying- applying Problem Solving Problem Solving - analyzing- analyzing EvaluationEvaluation - judging- judging Research Research - creating - creating

Bloom’s Taxonomy of Bloom’s Taxonomy of LearningLearning

Information Information - remembering- remembering Knowledge Knowledge - understanding- understanding Application Application - applying- applying Problem Solving Problem Solving - analyzing- analyzing EvaluationEvaluation - judging- judging Research Research - creating - creating

Instruction DesignInstruction DesignCreating Learning MaterialsCreating Learning Materials

Deciding on the behaviors you want the Deciding on the behaviors you want the students to display as a result of the students to display as a result of the coursecourse Backward designBackward design

Concept Map (at the beginning of the Concept Map (at the beginning of the course)course)

Creating a LessonCreating a Lesson Seeing the textbook as a resource, but not Seeing the textbook as a resource, but not

the coursethe course Infusing a lessons with what we have learnedInfusing a lessons with what we have learned

Variable

ExpressionsEquations

Functions

Re-express

Solve

Graph

Developmental Mathematics

Analyze

Interpret

Verify

Learning Process Learning Process MethodologyMethodology

1.1. PreparationPreparation

2.2. Learning ActivityLearning Activity

3.3. ReflectionReflection

1. Preparation1. Preparation

Why?Why? Where does it fit in the knowledge Where does it fit in the knowledge

framework?framework? PrerequisitesPrerequisites GoalsGoals Performance CriteriaPerformance Criteria Language/VocabularyLanguage/Vocabulary ResourcesResources

2. Learning Activity2. Learning Activity

PlanPlan Key Questions/Critical Thinking Key Questions/Critical Thinking

Questions Questions (Inquiry Questions encouraging Reflection)(Inquiry Questions encouraging Reflection)

Examples and ModelsExamples and Models ApplicationApplication Problem SolvingProblem Solving

3. Reflection3. Reflection

Self-AssessmentSelf-Assessment ExtensionExtension

The Contour Map The Contour Map

Contour MapContour Map

1. PreparationWhy?

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 mapResources Contour map animation

2. Learning ActivityPlan

1. Read the Critical Thinking Questions2. Work with the Contour map program4. Answer the Critical Thinking Questions3. Interpret the Applications4. Solve the Problems

Examples and ModelsContour 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 QuestionsComments and Questions

[email protected]@ti.com

Additional InformationAdditional Information Basic Skills as a Foundation for Student Success in

California Community Collegeshttp://cccbsi.org/publications (choose Literature Review)http://cccbsi.org/publications (choose Literature Review)

Basic Skills Handbookhttp://cccbsi.org/publications (choose Basic Skills http://cccbsi.org/publications (choose Basic Skills Handbook)Handbook)

James Zull, ( 2002). James Zull, ( 2002). The Art of Changing the Brain: The Art of Changing the Brain: Enriching the Practice of Teaching by Exploring Enriching the Practice of Teaching by Exploring the Biology of Learningthe Biology of Learning,.,.

Knowles, M. (1984). Knowles, M. (1984). Andragogy in ActionAndragogy in Action. San . San Francisco: Jossey-Bass. Francisco: Jossey-Bass.

Dan Apple, and others (2009). Dan Apple, and others (2009). Electronic Faculty Electronic Faculty GuidebookGuidebook. Lisle, Illinois: Pacific Crest.. Lisle, Illinois: Pacific Crest. http://www.pcrest.com/PC/FGB/4th/index.htm

Contour MapContour Maphttp://curvebank.calstatela.edu/contour81/contour81.htmhttp://curvebank.calstatela.edu/contour81/contour81.htm