An Educational Enquiry into the use of Concept Mapping and Multimedia to Enhance the Understanding of Mathematics : 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
Piaget : 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.
Flash 4.0 : 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.
Mathematical Concepts : Mathematical Concepts Sets
Area & Volume
Trogonometry
Concept Mapping : 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.”
Concept Map : Concept Map Food Energy Nutrients liquid solid provides can be can be provides
Purpose of the Study : 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.
Objective of the Study : Objective of the Study Students confidence
Appreciation of Mathematics
Enjoyment of Mathematics
Understanding of Mathematics
Develop problem-solving skills
Research : Research Junior Certificate Mathematics Syllabus
Multimedia as an aid to learning
Concept mapping as a learning tool
Problem-solving skills in Mathematics
Junior Certificate Mathematics Syllabus : 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
Multimedia : Multimedia Control
Self-paced
Actively engaged-constructing knowledge
Learning is enhanced- visuals
sound
text
motion
Concept mapping : Concept mapping Promotes-Higher Order thinking
Develops-problem-solving skills
Effective - collaborative environment
Misconceptions
Problem-solving : Problem-solving Improved- a) methodology
b) work environment
Collaborative learning environment
Methodology & Action Research : 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)
Methodology & Action Research : 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)
Action Research : 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?
Implementation : Implementation Transition Year
Pre- & Post DAT’s Test
Homogenous pairs
Junior Certificate Mathematics Question
Action research Cycles-Two
Evaluation & Conclusions : Evaluation & Conclusions Evaluation -Concept Mapping
Evaluation -Multimedia
Analysis-Learning styles
Analysis- Differential Aptitude tests.
Evaluation : 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.
Evaluation : Evaluation Learning styles
Active & Reflective learners
Sensing & Intuitive learners
Visual & Verbal learners
Sequential & Global learners Differential AptitudeTests
DAT’s- assess students aptitudes
Pre- & Post-Test
Mathematical ability asessed: Numerical Ability, Mechanical Reasonong, Abstract Reasoning, Space Relations
Conclusions : Conclusions Concept Mapping- visual tool
Animation – educational tool
Learning Styles- all styles catered for.
DAT’s- improvement in Mechanical & Abstract Reasoning, and Space Relations
Mathematical skills & ability- improved.
Conclusions : Conclusions Winter (1989)- six main principles for conduct of Action research
Reflexivity
Dialectics
Collaborative resource
Risk
Theory practice & transformation
Theory : Theory “..to improve the educational system we must look beyond classroom constraints to address cognitive and psychological issues that cause “good”students 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.”
Slide30 : 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 weren’t working,” they replied. “ So we had to change our methods.” The information showed that the kids were bright. If things weren’t 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)