**EFFECT OF CONCEPT MAPPING STRATEGY ON STUDENTS’ ACHIEVEMENT IN SENIOR SECONDARY SCHOOL MATHEMATICS**

**CHAPTER ONE**

**BACKGROUND TO**

THE STUDY

THE STUDY

The sciences of map-making which is referred to as

cartography dates back to about 10,000BC (Hellemans and Bunch, 1988). A

cartographic map is a constructed bounded representation that corresponds to

perceived reality. Therefore, once, one’s experience has been mapped, that

region has become a known region and not an unknown region.

cartography dates back to about 10,000BC (Hellemans and Bunch, 1988). A

cartographic map is a constructed bounded representation that corresponds to

perceived reality. Therefore, once, one’s experience has been mapped, that

region has become a known region and not an unknown region.

Thus, to

map has always meant to know (wander see, 1990). The process gives insight into

how concepts are mapped. Two critical changes must take place if a map is to

fulfill its role as an instrument of human communication (Dent, 1985). In the

first place, the mapmaker must encode the meaning, using appropriate graph

conventions. Therefore, only potentially meaningful and contextually

appropriate information should be included in a map. Secondly, the map-reader

must perform detection, recognition, discrimination and estimation tasks in

order to extract the meaning, which was encoded (Gulk, 1976). The

interpretation process of mapping involves complex cognitive changes that go along

with both intellectual and visual components.

map has always meant to know (wander see, 1990). The process gives insight into

how concepts are mapped. Two critical changes must take place if a map is to

fulfill its role as an instrument of human communication (Dent, 1985). In the

first place, the mapmaker must encode the meaning, using appropriate graph

conventions. Therefore, only potentially meaningful and contextually

appropriate information should be included in a map. Secondly, the map-reader

must perform detection, recognition, discrimination and estimation tasks in

order to extract the meaning, which was encoded (Gulk, 1976). The

interpretation process of mapping involves complex cognitive changes that go along

with both intellectual and visual components.

These components may serve to challenge one’s

assumption to viz:

assumption to viz:

1.

Recognize new

patterns.

Recognize new

patterns.

2.

Make new

connections and

Make new

connections and

3.

Visualize the

unknown.

Visualize the

unknown.

To these effects, the

real word of experience yields the raw data of perception, which is changed by

the may-reader. He then, extracts the relevant meaning and uses it for problem

solving and decision making (Cuff and Mattson, 1982).

real word of experience yields the raw data of perception, which is changed by

the may-reader. He then, extracts the relevant meaning and uses it for problem

solving and decision making (Cuff and Mattson, 1982).

All maps

contain errors but the accuracy of any map is highly dependent upon the quality

and quantity of the data collected by the mapmaker about the reality to be

mapped. In this case, his prior knowledge influences his selection and

generalization about the data collected, his aesthetic sense and artistry also

affect the final product (Arthur, 1980). This is indeed a signal innovation in

human thought. Lawrence Martins, an Emeritus professor of cartography eulogized

this process. He said, the act of mapping was as profound as the invention of

number. The combination of the reduction of reality and the construction of an

analogical space is an attainment in abstract thinking of a very high order

indeed, for, it enables one to discover structures that would remain unknown if

not mapped (Arthur, 1982).

contain errors but the accuracy of any map is highly dependent upon the quality

and quantity of the data collected by the mapmaker about the reality to be

mapped. In this case, his prior knowledge influences his selection and

generalization about the data collected, his aesthetic sense and artistry also

affect the final product (Arthur, 1980). This is indeed a signal innovation in

human thought. Lawrence Martins, an Emeritus professor of cartography eulogized

this process. He said, the act of mapping was as profound as the invention of

number. The combination of the reduction of reality and the construction of an

analogical space is an attainment in abstract thinking of a very high order

indeed, for, it enables one to discover structures that would remain unknown if

not mapped (Arthur, 1982).

Concept

mapping was developed from a work by Novak (1972) and his graduate students at

cornel university (Rowell, 1978). The technique was originally intended as a

vehicle for exploring meaningful learning acquired through audio-tutorial

instruction in elementary school science. Also, as a research and evaluation

tool in science education in order to represent learner’s prior, relevant

knowledge (Novak, 1990). As a Meta learning technique, it was based on the

Ausubel (1968) theory of meaningful learning. It has direct relationship with

some theoretical principles, such as prior knowledge, subsumption, progressive

differentiation, cognitive bridging and integrative reconciliation.

mapping was developed from a work by Novak (1972) and his graduate students at

cornel university (Rowell, 1978). The technique was originally intended as a

vehicle for exploring meaningful learning acquired through audio-tutorial

instruction in elementary school science. Also, as a research and evaluation

tool in science education in order to represent learner’s prior, relevant

knowledge (Novak, 1990). As a Meta learning technique, it was based on the

Ausubel (1968) theory of meaningful learning. It has direct relationship with

some theoretical principles, such as prior knowledge, subsumption, progressive

differentiation, cognitive bridging and integrative reconciliation.

**INTRODUCTION**

Concept

mapping is a teaching and learning strategy that establishes a bridge between

how people learn knowledge and sensible learning, students need to have

sufficient foundation and a critical thinking about concept mapping and the

relations between different concepts. Concept mapping promises to be useful in

enhancing meaningful learning and students’ conceptual understanding in science

and mathematics. Students can develop their knowledge of mathematics; one way

of achieving this may be through the adoption of student-centered,

activity-based and minds-on approaches that cater for individual needs and

differences, learning styles, interests and abilities. One such

student-centered, inquiry-based approach to organize learning is concept

mapping.

mapping is a teaching and learning strategy that establishes a bridge between

how people learn knowledge and sensible learning, students need to have

sufficient foundation and a critical thinking about concept mapping and the

relations between different concepts. Concept mapping promises to be useful in

enhancing meaningful learning and students’ conceptual understanding in science

and mathematics. Students can develop their knowledge of mathematics; one way

of achieving this may be through the adoption of student-centered,

activity-based and minds-on approaches that cater for individual needs and

differences, learning styles, interests and abilities. One such

student-centered, inquiry-based approach to organize learning is concept

mapping.

Concept

mapping is a metacognitive learning strategy used in measuring individual’s

knowledge structure and organization in a specific domain of knowledge.

Concepts are a procedure that is used to measure the structure and organization

of an individual’s knowledge. Concept Mapping can also be explained as the

spatial representations of concepts and the interrelationships that are

intended to represent the knowledge structures that humans store in their

minds. Concept mapping as a method to visualize the structure of knowledge as a

means of representing frameworks for the interrelationships between concepts an

as an instructional and assessment tool to facilitate meaningful learning.

mapping is a metacognitive learning strategy used in measuring individual’s

knowledge structure and organization in a specific domain of knowledge.

Concepts are a procedure that is used to measure the structure and organization

of an individual’s knowledge. Concept Mapping can also be explained as the

spatial representations of concepts and the interrelationships that are

intended to represent the knowledge structures that humans store in their

minds. Concept mapping as a method to visualize the structure of knowledge as a

means of representing frameworks for the interrelationships between concepts an

as an instructional and assessment tool to facilitate meaningful learning.

Concept

maps as originally developed in assimilation theory of cognitive learning which

focuses on individual and how they integrate new learning into existing

conceptual frameworks by making explicit, conscious connections between

concepts as a way to integrate information into memory. Concept maps are built

by placing terms which represent the concepts to be mapped in structures called

nodes. The nodes, which are linked together into propositions, show how

students connect or link concepts. The propositions are represented by arrows

to connect individual concepts together. The directionality of the link is

indicated by arrow. The conceptualization of the materials by the students is

indicated by the directionality and the connecting proposition. The

proposition, thus illustrates the contextual relationship of the concepts to

each other.

maps as originally developed in assimilation theory of cognitive learning which

focuses on individual and how they integrate new learning into existing

conceptual frameworks by making explicit, conscious connections between

concepts as a way to integrate information into memory. Concept maps are built

by placing terms which represent the concepts to be mapped in structures called

nodes. The nodes, which are linked together into propositions, show how

students connect or link concepts. The propositions are represented by arrows

to connect individual concepts together. The directionality of the link is

indicated by arrow. The conceptualization of the materials by the students is

indicated by the directionality and the connecting proposition. The

proposition, thus illustrates the contextual relationship of the concepts to

each other.

The basic

premises of concept maps has been representation of knowledge in a hierarchy

form, several types of structures have been proposed, such hierarchy as, cyclic

chain, spider-maps, and networks that could be used to mentally represent the

knowledge embedded in one’s long-term memory, since the knowledge expressed in

the maps is mostly semantic. Concept maps are sometimes called semantic

networks.

premises of concept maps has been representation of knowledge in a hierarchy

form, several types of structures have been proposed, such hierarchy as, cyclic

chain, spider-maps, and networks that could be used to mentally represent the

knowledge embedded in one’s long-term memory, since the knowledge expressed in

the maps is mostly semantic. Concept maps are sometimes called semantic

networks.

**STATEMENT OF THE**

PROBLEM

PROBLEM

Concept

mapping however, is an effective teaching strategy that has been extensively

used in mathematics and other subjects out of Nigeria. Since the use of concept

mapping had been found effective in enhancing students’ achievement in

mathematics and other related sciences subject in Nigeria, there is therefore

the need to investigate the effect of concept mapping in mathematics in

Nigeria.

mapping however, is an effective teaching strategy that has been extensively

used in mathematics and other subjects out of Nigeria. Since the use of concept

mapping had been found effective in enhancing students’ achievement in

mathematics and other related sciences subject in Nigeria, there is therefore

the need to investigate the effect of concept mapping in mathematics in

Nigeria.

The

problems investigated in this study, posed as a question is:

problems investigated in this study, posed as a question is:

Ø How does concept mapping affect students’

achievement, performance and interest in senior secondary school students in

Nigeria?

achievement, performance and interest in senior secondary school students in

Nigeria?

Ø Is the score reliability of concept map assessments

affected by the selection of scoring method?

affected by the selection of scoring method?

Ø Do concept map assessments provide valid information

about student’s knowledge?

about student’s knowledge?

Ø Can concept map assessments be practically applied

to classroom situations?

to classroom situations?

**PURPOSE OF THE STUDY**

The

purpose of the thesis (study) is to highlights, the imperatives of adopting

concept-mapping technique as a means of improving the performance of students

in mathematics, hence, it shall be focus on the learner rather than the

teacher. As the learners interact with their environment, they gain an

understanding of its features, construct their own conceptualization and find

solution to problems, mastering autonomy and independence.

purpose of the thesis (study) is to highlights, the imperatives of adopting

concept-mapping technique as a means of improving the performance of students

in mathematics, hence, it shall be focus on the learner rather than the

teacher. As the learners interact with their environment, they gain an

understanding of its features, construct their own conceptualization and find

solution to problems, mastering autonomy and independence.

In

constructivism, learning is the result of individual mental construction in

which learners match new against given information to establishing meaningful

connection. There should be development and improvement of new skill to enhance

meaningful study and renovation in mathematics.

constructivism, learning is the result of individual mental construction in

which learners match new against given information to establishing meaningful

connection. There should be development and improvement of new skill to enhance

meaningful study and renovation in mathematics.

It is

expected that student’s learning of mathematics through doing mathematics,

using realistic instructional techniques should enhance the inculcation of the

generic skill of inquiry, reasoning, conceptualizing, problem-solving and

communicating. To cap it all, the study is purposely for students to improve

their knowledge of mathematics and to develop and establish confidence and

positive attitudes toward mathematics.

expected that student’s learning of mathematics through doing mathematics,

using realistic instructional techniques should enhance the inculcation of the

generic skill of inquiry, reasoning, conceptualizing, problem-solving and

communicating. To cap it all, the study is purposely for students to improve

their knowledge of mathematics and to develop and establish confidence and

positive attitudes toward mathematics.

**RESEARCH QUESTIONS**

This study is to find answers to the

following questions:

following questions:

(a) Is there any difference between the pre-test

achievement scores of students exposed to the concept mapping strategy and

those exposed to the regular teaching method?

achievement scores of students exposed to the concept mapping strategy and

those exposed to the regular teaching method?

(b) Is there any difference between the post-test

achievement scores of students exposed to the concept mapping strategy and

those exposed to the regular teaching method?

achievement scores of students exposed to the concept mapping strategy and

those exposed to the regular teaching method?

(c) Is there any difference between the students’

analysis, synthesis and evaluation levels of cognition after being exposed to

the concept mapping strategy and the regular teaching methods?

analysis, synthesis and evaluation levels of cognition after being exposed to

the concept mapping strategy and the regular teaching methods?

**RESEARCH HYPOTHESIS**

1

1

Null hypothesis (Ho): the

null hypothesis is the decision that there is no statistical significant

difference or relationship between the pretest achievement scores of students

exposed to the concept mapping strategy and those exposed to the regular

teaching method?

null hypothesis is the decision that there is no statistical significant

difference or relationship between the pretest achievement scores of students

exposed to the concept mapping strategy and those exposed to the regular

teaching method?

Ho :

N1 = N2 or N1-

N2= 0

N1 = N2 or N1-

N2= 0

(H1):

is that there is statistical significant difference or relationship between the

pre-test achievement scores of students exposed to the concept mapping strategy

and those exposed to the regular teaching method?

is that there is statistical significant difference or relationship between the

pre-test achievement scores of students exposed to the concept mapping strategy

and those exposed to the regular teaching method?

Hypothesis:

Reject Ho if Tcal > Ttab otherwise accept Ho.

Reject Ho if Tcal > Ttab otherwise accept Ho.

**RESEARCH HYPOTHESIS 2**

Null hypothesis (Ho): the

null hypothesis is the decision that there is no statistical significant

difference or relation between the post-test achievement scores of students

exposed to the concept mapping strategy and those to the regular teaching

method?

null hypothesis is the decision that there is no statistical significant

difference or relation between the post-test achievement scores of students

exposed to the concept mapping strategy and those to the regular teaching

method?

Ho :

N1 = N2 or N1-

N2 = 0

N1 = N2 or N1-

N2 = 0

(H1):

is that there is statistical significant difference or relationship between the

post-test achievement scores of students exposed to the concept mapping

strategy and those exposed to the regular teaching method?

is that there is statistical significant difference or relationship between the

post-test achievement scores of students exposed to the concept mapping

strategy and those exposed to the regular teaching method?

Hypothesis:

Reject Ho if Tcal > Ttab otherwise accept Ho.

Reject Ho if Tcal > Ttab otherwise accept Ho.

**RESEARCH**

**HYPOTHESIS 3**

Null hypothesis (Ho): the

null hypothesis is the decision that there is no statistical significant

difference or relationship between concept mapping and traditional method of

teaching in our secondary school setting.

null hypothesis is the decision that there is no statistical significant

difference or relationship between concept mapping and traditional method of

teaching in our secondary school setting.

Ho: N1=

N2 or N1 – N2

=0

N2 or N1 – N2

=0

(H1):

is that there is statistical significant difference or relationship between

concept mapping and traditional method of teaching.

is that there is statistical significant difference or relationship between

concept mapping and traditional method of teaching.

Hypothesis:

Reject Ho if Tcal > Ttab otherwise accept Ho.

Reject Ho if Tcal > Ttab otherwise accept Ho.

**DELIMITATION**

(SCOPE) OF THE RESEARCH

(SCOPE) OF THE RESEARCH

**Students build concept maps in homework assignment**

recurrently, so they can correct their understanding about concept maps. It is

expected that concept maps help students to over come difficulties by

integrating them into well-structured cognitive frameworks.

Thus, it can be concluded that concept

mapping involved students who use concept maps as a training method relating

new information to prior knowledge resulting in meaningful learning and

consequently higher achievement. Concept maps help the students to answering

the questions. However, concept mapping as a training method is not a solution

for all problems in learning mathematics, there are mathematics concepts that

are abstract, non-intuitive, needs rational thinking, and not directly

interrelated and cannot be taught by concept mapping as a training method.

mapping involved students who use concept maps as a training method relating

new information to prior knowledge resulting in meaningful learning and

consequently higher achievement. Concept maps help the students to answering

the questions. However, concept mapping as a training method is not a solution

for all problems in learning mathematics, there are mathematics concepts that

are abstract, non-intuitive, needs rational thinking, and not directly

interrelated and cannot be taught by concept mapping as a training method.

Ideas of concept mapping are of

non-arbitrary relations among concepts in the learners’ minds. Moreover, it

highlights the importance of mathematics instruction that emphasizes

identifying key concepts and stresses on teaching concepts and their

relationships. Concept mapping is most useful if it is used as a study tool

over the course of instruction.

non-arbitrary relations among concepts in the learners’ minds. Moreover, it

highlights the importance of mathematics instruction that emphasizes

identifying key concepts and stresses on teaching concepts and their

relationships. Concept mapping is most useful if it is used as a study tool

over the course of instruction.

**SIGNIFICANCE OF**

THE STUDY

THE STUDY

**The**

study is to investigate the effect of concept mapping strategy on achievement

in mathematics of 80 senior secondary year two Nigerian students.

Another

aim of the research effort presented here was to investigate the effect of

concept mapping on student’s achievement in higher order abilities in senior

secondary school mathematics.

aim of the research effort presented here was to investigate the effect of

concept mapping on student’s achievement in higher order abilities in senior

secondary school mathematics.

And this study aim to show either

there is low or high correlation between concept mapping scores and traditional

test scores of students’ abilities, it has been aims to know whether students

had a strong positive attitude toward the use of concept mapping despite the

lack of difference in performance on multiple choice assessment test between

the experimental and control groups.

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