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

**CHAPTER ONE**

** BACKGROUND TO 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.

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.

These components may serve to challenge one’s assumption to viz:

- Recognize new patterns.
- Make new connections and
- 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).

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).

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.

** 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.

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.

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.

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.

**STATEMENT OF THE 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.

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

- How does concept mapping affect students’ achievement, performance and interest in senior secondary school students in Nigeria?
- Is the score reliability of concept map assessments affected by the selection of scoring method?
- Do concept map assessments provide valid information about student’s knowledge?
- Can concept map assessments be practically applied 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.

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.

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.

**RESEARCH QUESTIONS**

This study is to find answers to the following questions:

- 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?
- 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?
- 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?

**RESEARCH HYPOTHESIS 1**

Null hypothesis (H_{o}): 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?

H_{o} : N_{1} = N_{2} or N_{1}– N_{2}= 0

(H_{1}): 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 H_{o} if T_{cal} > T_{tab} otherwise accept H_{o}.

**RESEARCH HYPOTHESIS 2 **

Null hypothesis (H_{o}): 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?

H_{o} : N_{1} = N_{2} or N_{1}– N_{2} = 0

(H_{1}): 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 H_{o} if T_{cal} > T_{tab} otherwise accept H_{o}.

**RESEARCH** **HYPOTHESIS 3**

Null hypothesis (H_{o}): 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.

H_{o}: N_{1}= N_{2} or N_{1} – N_{2} =0

(H_{1}): is that there is statistical significant difference or relationship between concept mapping and traditional method of teaching.

Hypothesis: Reject H_{o} if T_{cal} > T_{tab} otherwise accept H_{o}.

** DELIMITATION (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.

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.

**SIGNIFICANCE OF 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.

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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