Improving Student Performance in Developmental Mathematics Courses

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Improving Student Performance in Developmental
Mathematics Courses

• Wade Ellis, Jr.
• West Valley College in Saratoga, California
• wellis_at_ti.com

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Outline

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

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Introduction

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

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Adult Learners

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

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Introduction (contd)

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

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Introduction (contd)

• Uri Treisman (specific to mathematics)
• Adaptive Reasoning
• Strategic Competence
• Conceptual Understanding
• Productive Disposition
• Procedural Fluency

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Dos and Donts

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

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Learning Skills
Learning as a Process that can be improved

• Examples of Learning Skills
• Validating results
• Using prior knowledge
• Constructing examples
• Abstracting
• Generalizing
• Persisting
• Accepting responsibility

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Instruction Design Blooms Taxonomy of Learning

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

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Blooms Taxonomy of Learning

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

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Instruction DesignCreating Learning Materials

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

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

• Preparation
• Learning Activity
• Reflection

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1. Preparation

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

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2. Learning Activity

• Plan
• Key Questions/Critical Thinking Questions
  (Inquiry Questions encouraging Reflection)
• Examples and Models
• Application
• Problem Solving

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3. Reflection

• Self-Assessment
• Extension

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The Contour Map

• Contour Map

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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
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• 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.

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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?  
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Comments and Questions

• wellis_at_ti.com

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Additional Information

• Basic Skills as a Foundation for Student Success
  in California Community Collegeshttp//cccbsi.org
  /publications (choose Literature Review)
• Basic Skills Handbook
• http//cccbsi.org/publications (choose Basic
  Skills Handbook)
• 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.
• Dan Apple, and others (2009). Electronic Faculty
  Guidebook. Lisle, Illinois Pacific Crest.
  http//www.pcrest.com/PC/FGB/4th/index.htm
• Contour Map
• http//curvebank.calstatela.edu/contour81/contour
  81.htm