An Educational Enquiry into the use of Concept Mapping and Multimedia to Enhance the Understanding of Mathematics

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An Educational Enquiry into the use of Concept
Mapping and Multimedia to Enhance the
Understanding of Mathematics

• By
• Fionnuala Flanagan
• ITTE Conference
• Trinity College
• July 2002

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Piaget

• Cognitive theorist.
• Believed that a child learns by exploring
  manipulating and examining objects, which leads
  to understanding and theories Bee, H., 1995. The
  developing child.

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Flash 4.0

• Flash was developed by Macromedia in 1996
• Vector graphics editor and animation tool
• Standard fro creating high-impact vector based
  web sites
• Sound
• Interactivity
• Graphics
• Animations
• Multiple browsers and platforms.

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Mathematical Concepts

• Sets
• Area Volume
• Trogonometry

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Concept Mapping

• spatial representations of concepts and their
  interrelationships that are intended to represent
  the knowledge structures that humans store in
  their minds, Jonassen, Beissner, Yacci,
  (1993).
• Concept maps have been described as cognitive
  tools which facilitate higher-order thinking
  through deep reflective thinking which must take
  place for meaningful learning to occur (Norman,
  1993). This allows the learner to internalise new
  knowledge, which will help formulate concepts
  that the learner can actively use to solve
  problems.
• Okebukola et al., (1993) were of the belief that
  concept mapping and its results are predictive
  of problem solving performance.

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Concept Map
Food
provides
provides
Energy
Nutrients
can be
can be
liquid
solid
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Purpose of the Study

• This study set out to investigate the
  effectiveness of implementing a new methodology
  involving the introduction multimedia software,
  flash 4.0 and concept mapping into the classroom
  environment and to examine their potential for
  enhancing the understanding of Mathematics for
  Transition Year students. The focus topic, as
  decided by the students, was Area Volume.

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Objective of the Study

• Students confidence
• Appreciation of Mathematics
• Enjoyment of Mathematics
• Understanding of Mathematics
• Develop problem-solving skills

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Research

• Junior Certificate Mathematics Syllabus
• Multimedia as an aid to learning
• Concept mapping as a learning tool
• Problem-solving skills in Mathematics

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Junior Certificate Mathematics Syllabus

• 1966 until 2002- Department of Education and
  Science.
• Domain of the teacher.
• Lack of reviews of teaching practices.
• March 2002- Department in conjuction with the
  National Council for Curriculum and Assessment
  (NCCA)
• Action Research

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Multimedia

• Control
• Self-paced
• Actively engaged-constructing knowledge
• Learning is enhanced- visuals
• sound
• text
• motion

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Concept mapping

• Promotes-Higher Order thinking
• Develops-problem-solving skills
• Effective - collaborative environment
• Misconceptions

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Problem-solving

• Improved- a) methodology
• b) work environment
• Collaborative learning environment

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Methodology Action Research

• action research is systematic, critical and
  self-critical enquiry made public, which is
  carried out by practitioners and aims to inform
  (their) educational judgements and decisions in
  order to improve educational action. (Bassey,
  1995., Fineagan, 2001)

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Methodology Action Research

• How can I improve the process of education
  here? (McNiff, Lomax Whitehead, 1996)
• Action Research involves the practitioner at the
  center of the research investigating their own
  practice. (McNiff, Lomax Whitehead, 1996)

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Action Research

• What is your research focus?
• Why have you chosen this as a focus?
• What kind of evidence can you produce to show
  what is happening?
• What can you you do about what you find?
• What kind of evidence can you produce to show
  that what you are doing is having an impact?
• How will you evaluate that impact?
• How will you ensure that any judgements you might
  make are reasonably fair and accurate?
• What will you do then?

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Implementation

• Transition Year
• Pre- Post DATs Test
• Homogenous pairs
• Junior Certificate Mathematics Question
• Action research Cycles-Two

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Evaluation Conclusions

• Evaluation -Concept Mapping
• Evaluation -Multimedia
• Analysis-Learning styles
• Analysis- Differential Aptitude tests.

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Evaluation

• Concept Mapping
• Aided students in solving Mathematics problem
• Ordinary -clear, concise and logical.
• Honours-work was correct but not very clear
• Both groups- benefitted through learning in a
  collaborative environment.
• Concept mapping aided in structuring the steps
  taken to solve that Maths problem.
• Concept mapping helped them to establish where
  they made errors in solving the Maths question
• Aided in the transfer of the solution into
  animation format

• Multimedia
• Students enjoyed using Flash
• Ordinary level group- confidence improved
• Animation helped them to understand Area
  Volume.
• Animation assisted in making Mathematics clearer.

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Evaluation

• Learning styles
• Active Reflective learners
• Sensing Intuitive learners
• Visual Verbal learners
• Sequential Global learners

• Differential AptitudeTests
• DATs- assess students aptitudes
• Pre- Post-Test
• Mathematical ability asessed Numerical Ability,
  Mechanical Reasonong, Abstract Reasoning, Space
  Relations

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Conclusions

• Concept Mapping- visual tool
• Animation educational tool
• Learning Styles- all styles catered for.
• DATs- improvement in Mechanical Abstract
  Reasoning, and Space Relations
• Mathematical skills ability- improved.

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Conclusions

• Winter (1989)- six main principles for conduct of
  Action research
• Reflexivity
• Dialectics
• Collaborative resource
• Risk
• Theory practice transformation

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Theory

• ..to improve the educational system we must look
  beyond classroom constraints to address cognitive
  and psychological issues that cause
  goodstudents to perform poorly and that rewards
  some students but leaves other behind. By using
  concept mapping and multimedia in a collaborative
  learning environment, hidden strengths are
  discovered, synergistic communication can
  flourish, student learning skills are improved
  and learning performance is enhanced the
  teacher becomes catalyst and the student is
  empowered.

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PERCEPTION AND METHODOLOGY   CAUSE AND
EFFECT   One of the classic examples in the
field of self-fulfilling prophecies is of a
computer in England that was accidentally
programmed incorrectly. In academic terms, it
labeled a class of bright kids as dumb kids
and a class of supposedly dumb kids bright.
And that computer report was the primary
criterion that created the teachers paradigms
about their students at the beginning of the
year.   When the administration finally
discovered that mistake five and a half months
later, they decided to test the kids again
without telling anyone what had happened. And the
results were amazing. The bright kids had gone
down significantly in IQ test points. They had
been seen and treated as mentally limited,
uncooperative, and difficult to teach. The
teachers paradigms had become a self-fulfilling
prophecy.   But scores in the supposedly dumb
group had gone up. The teachers had treated them
as though they were bright, and their energy,
their hope, their optimism, their excitement had
reflected high individual expectations and worth
for those kids.   These teachers were asked what
it was like during the first few weeks of the
term. For some reason, our methods werent
working, they replied. So we had to change our
methods. The information showed that the kids
were bright. If things werent working well, they
figured it had to be the teaching methods. So
they worked on methods. They were proactive they
worked in their circle of influence. Apparent
learner disability was nothing more or less than
teacher inflexibility.   ( Covey, 1989)  
Treat a man as he is and he will remain as he
is. Treat a man as he can and should be and he
will become as he can and should be. ( Goethe
.)   (ibid)