An Educational Enquiry into the use of Concept Mapping and Multimedia to Enhance the Understanding of Mathematics By Fionnuala Flanagan ITTE Conference.

PiagetPiaget

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 4.0Flash 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 ConceptsMathematical Concepts

SetsArea & VolumeTrogonometry

Concept MappingConcept 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 MapConcept Map

Food

Energy Nutrients

liquid solid

provides

can be can be

provides

Purpose of the StudyPurpose 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 StudyObjective of the Study

Students confidenceAppreciation of MathematicsEnjoyment of MathematicsUnderstanding of MathematicsDevelop problem-solving skills

ResearchResearch

Junior Certificate Mathematics Syllabus

Multimedia as an aid to learning

Concept mapping as a learning tool

Problem-solving skills in Mathematics

Junior Certificate Mathematics SyllabusJunior 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

MultimediaMultimedia

ControlSelf-pacedActively engaged-constructing knowledgeLearning is enhanced- visuals

sound

text

motion

Concept mappingConcept mapping

Promotes-Higher Order thinkingDevelops-problem-solving skillsEffective - collaborative environmentMisconceptions

Problem-solvingProblem-solving

Improved- a) methodology

b) work environment

Collaborative learning environment

Methodology & Action Methodology & Action ResearchResearch

“ 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 Methodology & Action ResearchResearch

“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 ResearchAction 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?

ImplementationImplementation

Transition YearPre- & Post DAT’s TestHomogenous pairsJunior Certificate Mathematics QuestionAction research Cycles-Two

Evaluation & ConclusionsEvaluation & Conclusions

Evaluation -Concept MappingEvaluation -MultimediaAnalysis-Learning stylesAnalysis- 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

SENSING / INTUITIVEMale v Female

0

1

2

3

4

5

6

11 9 7 5 3 1 1 3 5 7 9 11

T E S T S C OR E<< MORE SENSI NG MORE

I NTUI T I VE >>

SENSING / INTUITIVE SCORESHonours v Ordinary

0

1

2

3

4

5

6

11 9 7 5 3 1 1 3 5 7 9 11

T E S T S C OR E

<< MORE SENSI NG MORE I NTUI T I VE >>

VISUAL / VERBALMale v Female

0

1

2

3

4

5

6

11 9 7 5 3 1 1 3 5 7 9 11

T E S T S C OR E S<< MORE VI SUAL MORE VERBAL >>

VISUAL / VERBALHonours v Ordinary

0

1

2

3

4

5

6

11 9 7 5 3 1 1 3 5 7 9 11

T E S T S C OR E

<< MORE VI SUAL MORE VERBAL >>

SEQUENTIAL / GLOBALMale v Female

0

1

2

3

4

5

6

11 9 7 5 3 1 1 3 5 7 9 11

T E S T S C OR E S<< MORE

SEQUENTI AL

MORE GLOBAL >>

SEQUENTIAL / GLOBALHonours v Ordinary

0

1

2

3

4

5

6

1 1 9 7 5 3 1 1 3 5 7 9 1 1

T E ST SC OR E<< MORE

SE QUE NT IAL

MORE GLOBAL >>

ACTIVE / REFLECTIVE SCORES - Male v Female

0

1

2

3

4

5

6

7

8

9

11 9 7 5 3 1 1 3 5 7 9 11

T E S T S C OR E

ALL STUDENTS

MALE STUDENTS

FEMALESTUDENTS

<< MORE ACTI VE MORE REFLECTI VE>>

ACTIVE REFLECTIVE SCORES - Honours v Ordinary Level

0

1

2

3

4

5

6

7

8

9

1 1 9 7 5 3 1 1 3 5 7 9 1 1

T E ST SC OR E

ALLSTUDENTSHONOURSLEVELORDINARYLEVEL

<< MORE ACTI VE MORE REFLECTI VE>>

ConclusionsConclusions

Concept Mapping- visual toolAnimation – educational toolLearning Styles- all styles catered for.DAT’s- improvement in Mechanical &

Abstract Reasoning, and Space Relations Mathematical skills & ability- improved.

ConclusionsConclusions

1. Winter (1989)- six main principles for conduct of Action research

2. Reflexivity

3. Dialectics

4. Collaborative resource

5. Risk

6. Theory practice & transformation

TheoryTheory

“..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.”

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)