A Case study approach to increasing teachers’ mathematics knowledge for teaching and strategies for building students’ maths self-efficacy

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A Case study approach to increasing teachers
mathematics knowledge for teaching and strategies
for building students maths self-efficacy
Southern Right Delta (S??'09) Gordons Bay, South
Africa, December 3, 2009

• T. Stevens, G. Harris, Z. Aguirre-Munoz, and L.
  Cobbs

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Support provided by the National Science
Foundation Math Science Partnerships Program
under Award No. 0831420.

• The opinions expressed in this presentation are
  those of the WTMSMP personnel and associates and
  do not necessarily reflect those of NSF.

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Math Science Partnerships

• Reduce the number of teachers who are teaching
  outside of their field.
• Encourage more students to take advanced
  coursework.
• Increase challenging curricula in schools.

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West Texas Middle School Math Partnership

• Develop a deep understanding of elementary
  mathematics in middle level math teachers.
• Develop teachers self-efficacy to improve the
  mathematics self-efficacy of their students.
• Develop teachers self-efficacy to teach
  mathematics to diverse student populations.

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Purpose

• Evaluate the use of a case study approach
  employed in a workshop as a strategy to increase
  teachers conceptual knowledge for teaching and
  understanding of self-efficacy.
• Do teacher participants possess the same learning
  preferences?
• Do teacher participants learning preferences vary
  depending upon the content taught?

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The case utilized in this study was designed to
elicit teachers content knowledge and their
ability to identify student misconceptions as
well as engage them in critical reflection. In
this way, this case offered an opportunity to
explore and develop teachers sensitivity to
student difficulty and needs (with respect to
content and self-efficacy) as well as an ability
to provide pedagogically sensitive and
mathematically precise feedback to the student.
Incorporated into a 2 hour workshop at a regional
meeting of the Mathematics Association of
America.
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Procedure

• Workshop participants were
• presented with the case study to discuss
  mathematical issues.
• shown a video describing self-efficacy and its
  sources.
• provided with the workshop manual.
• asked to review the case study to identify issues
  related to self-efficacy.

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Case Study Approach

• Authentic
• Allows for a variety of viewpoints and potential
  outcomes
• Fosters high levels of critical thinking and
  reflection
• Promotes process skills that complement content
  knowledge

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Q Methodology
Q Methodology is a research method used to study
peoples subjectivity that is, their
viewpoint.
Refers to a selected population of n different
tests (or essays, pictures, traits or other
measurable material), each of which is measured
or scaled by m Individuals.
Correlates individuals across a sample of
variables.
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Q Methodology

• Determination of all possible statements that
  could be said about the learning strategies used
  in the workshop.
• Development of the Q set.
• Selection of the P set.
• Q sorting.

• Factor analysis.
• Varimax rotation.
• PQmethod.

• Qualitative

• Quantitative

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Q Set

• Lecture done by workshop faculty
• Projected PowerPoint slides
• PowerPoint slides handout
• Large group activity (e.g., index card)
• Small group discussion
• Case study provided
• Specific examples provided by others
• Specific examples provided by faculty
• General comments made by others
• Formal question and answer period
• Informal discussion with workshop participants
• Informal discussion with workshop faculty

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Factors Conceptual Knowledge

• Autonomy
• Factor 1 participant led activities preferred
• Factor 2 instructor led activities preferred
• Factor 3 participant and instructor preferred
• All agreed the case study was beneficial.
• No demographic differences observed across
  factors.

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Factors Self-Efficacy

• Degree of content application
• Factor 1 preferred activities that required
  basic knowledge. (10.33 avg. public school
  teaching)
• Factor 2 preferred activities that required
  applied knowledge. (no public school teaching)
• Factor 3 preferred a blend of basic and applied
  activities with limited peer interaction.
• Factor 1, comprised of mostly public school
  teachers, did not prefer the case study.

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Conclusions

• Do teacher participants possess the same learning
  preferences?
• Participants did not prefer the same learning
  strategies, but agreed the case study was helpful
  in learning math concepts.
• Do teacher participants learning preferences vary
  depending upon the content taught?
• Public school teachers did not prefer the case
  study approach when studying self-efficacy.

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Conclusions

• Q methodology was useful in evaluating workshop
  effectiveness when
• time was limited.
• longitudinal analysis was not feasible.
• sample size was small.
• If systemic, sustainable change in mathematics
  education is to be achieved, researchers must
  work to understand what aspects of professional
  development are responsible for increases in
  targeted variables from subjective as well as
  objective sources.