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
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.
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.
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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