Combining Discovery Learning and MasteryBased Teaching: A Unit on Logarithms and Exponents

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Combining Discovery Learning and Mastery-Based
TeachingA Unit on Logarithms and Exponents

• Dianna Spence
• Gregg Velatini
• North Georgia College and State University
• October 20, 2006
• Georgia Mathematics Conference

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Background

• Setting
• Introductory college math classes
• Comparable to secondary math courses
• Issues
• Broad range of topics, but minimal depth
• Students working many problems demonstrating
  partial understanding, but none with full
  understanding
• Students trying to build understanding of
  advanced topics with mediocre grasp of basic
  concepts

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New Instructional Approach

• More guided discovery learning exercises
• More time spent on core concepts
• More meaningful foundation
• Students work more at own pace
• Mastery-based approach
• Content differentiated into core material (C
  level) and two more levels (B and A level)
• Students demonstrate mastery of basics before
  proceeding to next level
• Student pace and level varies

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Implementation Proficiencies

• Proficiency replacement for Quiz
• C, B, and A level proficiencies available
• One proficiency per set of related objectives
• Proficiency not passed until student scores 90
  or higher on it (credit only for passing)

• Students who do not pass a proficiency take
  another version of same proficiency after making
  corrections to the initial one
• Student must pass all C level proficiencies
  before attempting any B or A levels in each
  section
• Time at end of most class periods for students to
  take proficiencies pace varies by student

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Course Organization

• Class Time
• Discovery exercises
• Group problem solving
• Brief lecture and discussion sessions
• Proficiencies
• Homework
• Listed by objective level (A, B, or C)
• Written submission required to re-take a
  proficiency

• Course Schedule
• Deadlines for self-paced proficiencies imposed
  through scheduled unit tests
• Grading
• Proficiencies a designated percentage of overall
  grade
• Content on tests mapped to A, B, and C level
  proficiencies and weighted accordingly

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Implementation Details

• Spence
• Proficiencies
• In class only
• Students identified when ready
• Pacing
• Set schedule, but enforced only by tests
• Magnified student lack of discipline
• Grading
• Passing scores on proficiencies scaled (e.g., low
  to high C)

• Velatini
• Proficiencies
• Take-home allowed
• Distributed to all students together
• Pacing
• More flexible
• Grading
• Any passing score on proficiency given same level
  of credit

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Results I (Spence)
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Results II (Spence)

• Participating having attempted at least 75
  of C level proficiencies

Students who only completed C-level proficiencies
often made A or B on test anyway
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Results I (Velatini)
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Results II (Velatini)
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Student FeedbackCourse Evaluations (Spence)
I really like the idea of having the proficiency
exams instead of the quizzes. It put the
responsibility of our grade on us. It also helped
me to learn better because I felt like I was
learning at my own pace.
The proficiency evaluations really helped prepare
me for tests and learn without the pressure of
quizzes. The proficiencies really helped me
actually grasp the material.
This method forced students to take
responsibility for their grades and made them be
productive. I was very fond of it. Keep using
proficiency evaluations. It really is an
excellent system for preparedness.
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Student FeedbackCourse Evaluations (Spence)
The proficiency system, though great in theory,
needs refinement. Earlier in the semester, when
given a heavier load, I felt pushed for time and
got few done past the C levels. Once the load was
pushed down, it was easier to complete all of
them.
What aspects of this class detracted from your
learning? The proficiency exams. The free form
unregulated environment severely affected my
performance.
I really dont like the idea of proficiencies
because I always feel behind and stressed.
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Student FeedbackCourse Evaluations (Velatini)
The proficiencies were the most help to me
because we did them until we got them right
Keep doing proficiencies and not quizzes.
I love the proficiency sheet.
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Student FeedbackCourse Evaluations (Velatini)
Completely disorganized way of teaching
It would be easier for me to learn if it was a
little more structured
Sometimes I felt overwhelmed with proficiencies...
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Other Student Feedback

• Students were initially distrustful.
• In class where the proficiencies were only used
  for one unit, students were unhappy to return to
  the more traditional methods.

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Issues

• Not enough guided discovery exercises
• Too many proficiencies, too little time
• Student absences
• Student self-discipline and motivation
• Proficiencies substituting for homework
• No solid metrics for effectiveness

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Possible Resolution

• Not enough guided discovery exercises
• Collaborative effort to develop bank of materials
• Too many proficiencies, too little time
• Fewer, more consolidated proficiencies
• Restructured, easier to grade proficiencies
• Student absences
• Find make-up system for missed proficiencies

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Possible Resolution

• Student self-discipline and motivation
• Set student expectations for advantages and
  responsibilities
• Enforce schedule for initial proficiency attempt
• Proficiencies substituting for homework
• Include system for checking/enforcing HW
• No solid metrics for effectiveness
• Track student progress with comparable assessments

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Questions
Presentation and course materials available
at http//radar.ngcsu.edu/djspence/gctm