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Abstract: This study investigated the effects of students' attitude, teaching and learning methodology on achievement in mathematical geometric construction. The study was carried out as a result of continuous poor performance in geometric construction in Senior Secondary Schools, a 3 year progressive educational program in Nigeria. A purpose sample comprised of 35 Male and 27 Female students from two intact classes of different private secondary schools in the Lagos Mainland Local Government Area of Lagos State was used for the study. A 28 (twenty-eight) - item questionnaire titled, "Survey of Attitude to Mathematics" (SAM), to find out the students' attitude to mathematics generally and geometric construction in particular, and A 3- item word- problem type, teacher made Mathematics Achievement Test in Geometric Construction (MATGC) instruments were used to conduct the study. An experimental group was taught using computer and based on constructivist theory of learning for a period of 12 contact hours over a period of 4 weeks. The responses of the questionnaires were subjected to descriptive analyses while the MATGC scores were subjected to t-test, Pearson correlation coefficient and regression analysis. Results revealed that attitude appeared to play a minimal role in achievement of geometric construction in mathematics. In spite of divergent earlier findings on impact of instructional methodology on achievement and attitude, this study revealed the constructivist approach as a better approach in teaching as it had a positive impact on achievement and attitude towards the topic. The study further revealed that male students performed better than female students. Implication of all these findings calls for review of mathematics curriculum by inclusion of Assisted Delivery Method in teaching geometric construction in schools. A further study is recommended for rural and public school settings as against the urban and private school settings. It is also recommended that an ADM approach be applied to other areas of mathematics where students perform poorly.
Keywords: Attitude, Computer, Constructivist Theory
Education, such a vital force and major player in a nation's economy, liberates the mind and opens up wide opportunity to whoever acquires it. An educated citizenry can use available technological developments to his/her advantage. Today the power of a nation is determined not by its share size of economic wealth but by its technological prowess. "The eminence, safety, and well-being of nations have been entwined for centuries with the ability of their people to deal with sophisticated quantitative ideas. Leading societies have commanded strong mathematical skills to keep them on the leading edge in science, medicine, and technology (National Mathematics Advisory Panel. Foundations for Success, 2008).
Despite the fact that some people don't have much penchant for mathematics and see it as an extremely difficult subject, it is a necessity in all facets of society. Two main reasons for difficulties of learning mathematics are the abstract structure of mathematics and teachers' efforts to make students memorize the subject instead of helping them internalize mathematical knowledge (Summers, 2006). In addition, math teaching methods may have a positive impact on students' understanding and performance in this subject area.
Information Communication Technology (ICT) an area that has pervaded every facet of human life with the mastery of computer applications giving a competitive edge to individuals in the school as well as job markets. ICT can be used to leverage instructional methods in the schools. According to Chung (2004) who noted that mmethods of teaching mathematics are founded upon and directly affected by the educator's investigations of learning. Teachers must investigate and use best teaching practices to impact student learning. Computer-based instructions will no doubt be a useful method to introduce mathematical concepts most especially those viewed as difficult topics.
Performance is a function of attitude and ability. To acquire skills, be it cognitive, affective or otherwise one must be mentally and emotionally prepared. A wrong attitude could turn a brilliant student who is capable of making As into an average students who achieves only Bs and Cs.
Despite the fact that mathematics is a core subject taught at both the Junior and Senior Secondary levels of Education in Nigeria, students continue to perform poorly in this subject (NPE, 2004); a subject described as the 'queen of the sciences' by the noted German mathematician Carl Friedrich Gauss.
The Chief Examiners' reports (Nigeria) of the West African Senior School Certificate Examination all said that student's performance in mathematics continues to be poor, but laid emphasis on geometric construction as one of the areas where students performed poorly (May/June 1998, Nov/Dec 1998, Nov/Dec 2003 and Nov/Dec 2004, Table 1.).
Reasons for this amongst others were attributed to:
Poor grasp of the details needed for answering questions
Insufficient drillings and tutorials from teachers and
lack of sufficient individual assignments and project
The suggestions made for improvement were:
Students should form study groups and exchange ideas
Students' knowledge of the rudiments of English Language should be improved
More drills and tutorials should be given by teachers.
Sufficient individual assignment and project should be used to engage students.
Longitude and Latitude
Word problem on Inequalities
Formulating Algebraic Expression
Geometric Construction Bearings
Use of Four Figure table
"Table 1": Performance in topics examined at the SSCE Examination
The issues raised above and the fact that good knowledge of geometric constructions (The mathematics of the properties, measurement, and relationships of points, lines, angles, surfaces, and solids) are important foundations for students who will like to further their education in such areas as mathematics, engineering, physics and other disciplines under Science and Technology (S&T)- an area of Education the Federal Government of Nigeria is passionate about its role in national development. These are what necessitated this study.
Purpose of the study
The purpose of this study was to:
Investigate possible differences between the impact of traditional method of teaching geometric construction and the assisted discovery method
Demonstrate the importance of appropriate methodology in teaching/learning, especially in Mathematics.
Look for any relationships between performance and instructional methods
Investigate whether attitude and methodology impact students' performance in mathematical geometric construction
Suggest ways that can be used, to ensure improvement in teaching of geometric construction in mathematics.
Does attitude play a role in achievement in geometric construction in mathematics?
What are the impacts of the traditional method of teaching and the assisted discovery method on students' achievement in mathematics geometric construction?
Does Gender have any role in achievement in geometric construction in mathematics?
Students' attitude will not significantly affect their achievement in geometric
There is no statistically significant difference between performance of computer and blackboard groups
There is no statistically significant difference between male and female students in the combined dependent variables that make up the learning outcomes
Design of the Study
This study made use of both survey and experimental designs, starting with a survey to determine students' attitude to mathematics generally and geometric construction in particular, followed by four weeks tutorials to two intact classes
Population of the study
The population of the study comprised the SS2 Students in Private Secondary Schools in Lagos State. (Since Mathematics is compulsory)
Sample and Sampling Techniques
The sample size comprised of 62 students was used for the study. These students were drawn from two randomly selected Private Secondary Schools from a Local Government Area of Lagos State, one of the 36 states making up Nigeria. The students were selected from intact SS2 classes in the schools comprising of 35 male and 27 female. There were 33 students from Science intact classes of one school and 29 students from Social Science intact classes (Commercial) of another school. The SS2 students in these schools had a pretest. The pretest scripts were graded out of 30marks. The mean score for a Social Science class was 9.45 while for the science class it was 11.18. These means were used as benchmarks to classify the students into More Knowledgeable Others(MKO) and Less Knowledgeable Others(LKO). Any students scoring above the mean were classified as MKO while student scoring below the mean was classified as LKO.
The science class and social science classes were assigned as experimental and control group respectively. The reason for this was that the schools where the science sample was drawn had all the facilities needed for computer-based teaching, such resources as computers, internet access, constant power supply, and a conducive laboratory. Students could use the package at their free periods which afforded them the opportunity to do individual further work.
The MKO and LKO were randomly mixed in the class to achieve a collaborative learning effect; the aim of this randomization was to neutralize all extraneous variables such as sex, personality, age, race, parents' educational status, poor nutrition, etc. that may affect the findings of this research work. However such intervening variables as fixed mathematics curriculum, time available after classes, reduction in attention and assimilation which may be due to fatigue after normal school hours could not be controlled.
The research instruments used were:
Twenty-eight item questionnaire titled "Survey of Attitude to Mathematics" (SAM) to find out students' attitude toward mathematics generally and geometric construction in particular. And
A three-item word-problem type, teacher made Mathematics Achievement Test in Geometric Construction (MATGC) was administered as a pre test to control and experimental group for categorization of the MKO and LKO. The same test was administered to both the control and experimental group as a post test. The MATGC was drawn from past West African Examination Council (WAEC), Secondary School Certificate Examination (SSCE) questions (1998-2008). The choice of WAEC, SSCE questions was based on the fact that they are standardized test questions which had already undergone validity and reliability tests by WAEC. It is also the examination the students will take at the completion of their Senior Secondary Education.
Method of Data Collection
The students were divided into two groups, a control and experimental group. The SAM was administered to both groups by the researcher with the assistance of the mathematics teachers of the classes used. The students were encouraged to answer all questions in the questionnaire while the benefits that will accrue from the research were clearly explained to them. Implication of not answering all questions in the questionnaire was also explained to them. The Students were given codes instead of using their names to hide their identity in order to encourage them to participate in the research. These codes were written on the individual Survey of Attitude to Mathematics (SAM).
Method of data collection for the MATGC:
The three-item tests were administered to the experimental and control group with the assistance of their class teachers. The involvement of the teacher was necessary if the student will take the research seriously and for meaningful data collection. The same identification code used for the SAM by an individual student was used for the MATGC. This enabled the researcher to match the papers of the students together. The pretest scripts were graded out of 30 marks using a marking guide which was developed and used for grading the test. The scores were analyzed in order to identify the More Knowledgeable Others (MKO) and Less Knowledgeable Others (LKO) in the experimental group. A score above the experimental group class mean (Mean=7.58) qualified a student for MKO category while a score less than the mean qualifies a student for LKO. The MKO and LKO were made to sit alternately in their respective classes to achieve the collaborative learning effect; the aim of this randomization was to neutralize all extraneous variables such as sex, personality, age, race, parents' educational status, poor nutrition etc that may affect the findings of this research work. However, such intervening variables as fixed mathematics curriculum, time available after classes, reduction in attention and assimilation which may be due to fatigue after normal school hours could not be controlled. The two groups of students (i.e. the experimental and control groups) were now taken through a four weeks teaching of one hour per day for every other day (i.e. Mondays, Wednesdays and Fridays). Classes were conducted after the close of the regular classes, which was designed to take care of not disrupting the normal mathematics classes and putting those taking part in the experiment at a disadvantage. The researcher took the experimental groups while the controlled groups were taken by their individual mathematics teacher who had been earlier taught how to use the lesson plan drawn up by the researcher. The total number of contact period came to three hours a week and a total of 12 hours for the entire period of teaching. Consent from school authority and parents had been previously sought. Students in the experimental group were taught using the ADM method, a collaborative-based group teaching using the computer. The ADM was an internet based geometric construction tutorial developed by John Page on http://www.mathopenref.com/. The choice of this package is the simplicity with which it taught geometric construction, using animations and graphical illustration. Students of the experimental group have access to computers and to the package at school during their free periods or if they have internet access at home thereby learning further on their own. The package is interactive, provides good visualization for the students, it is free for all users, fascinating and captivates the students' interest. It therefore provides good understanding for students. Students were now required to perform constructions involving angle 750, 150O, 1050 angles. Any angle which are not basic have to undergo some manipulations such as addition or subtraction. This was the major problems the students faced. At this point they were allowed to collaborate in addition the MKO were to assist the LKO to get to a point they could apply the concept and construct the various angles on their own.
The control groups who were taught by their respective teachers were taught using the blackboard, blackboard compass, and ruler as a medium of instruction. They were taught how to construct basic angles,, how to bisect angles, constructions involving angle 750, 150O, 1050,i .e angle which have to undergo some manipulations such as addition or subtraction. No collaboration was allowed in this group. Drills and assignments were given to both the experimental and control groups at the end of each contact period, while two group projects were given to both groups after the end of the contact periods.
The SAM and the MATGC were now administered to the control and experimental group as post treatment. The responses to SAM and the test papers were collected, scored and analyzed.
Method of Data Analysis
All data gathered were organized and analyzed using the following steps.
The responses from the pre and post SAM were placed against the four- point Likert Scaling, Strongly Agree (SA=4), Agree (A=3), Strongly Disagree (SD=2) and Disagree (D=1) for positive statements while the points were reversed for negative statements i.e. (SA=1), (A=2), (SD=3) (D=4). Descriptive analyses was used for the SAM. There were no incomplete responses to any questionnaire since the filing of the questionnaire was closely monitored by the researcher to ensure all questions were answered by students.
The MATGC was scored out of 30 marks using a marking scheme. The pre and post scores from MATGC were subjected to Pearson Correlation coefficient analysis for variables that can be ranked and ordered, e.g performance and attitude, while t-test statistics was used for variables with no order such as relationship between attitude and instructional method while relationships amongst multiple variables such as attitude, performance and methodology were subjected to multivariate analysis of variance (MANOVA). Regression analysis was also used to find out the contribution of each of the independent variables to the dependent variables. All hypotheses were tested at 0.05 level of significance.
In this research, three research questions and four hypotheses were posed. The results of the pre-test and post-test of MATGC were analyzed using means, standard deviation (S.D), t-test statistics. All hypotheses were tested at 0.05 level of significance. A p- value (calculated value) < than 0.05 leads to rejection of the null hypothesis, otherwise it is accepted.
HYPOTHESIS I- Students' Attitude will not significantly affect their achievement in geometric construction
Table1a: The Pearson correlation between attitude and achievement before treatment
Pearson correlation ( r )
P - value
Pre - Achievement score
Pearson correlation ( r )
P - value
Table1b The Pearson Correlation between Attitude and Achievement after treatment
Post attitude score
Pearson correlation ( r )
P - value
Post - Achievement score
Pearson correlation ( r )
P - value
From Table 1a above, the Pearson-correlation coefficient between achievement score and the attitudinal score before treatment was positive but weak (r=.038). The p-value which is the significant value of correlation between the two variables (pre- achievement score and pre-attitudinal score) is r=0.684 which was greater than 0.05 showing that the correlation was not significant before treatment.
From Table 1b shows the Pearson-correlation coefficient between achievement score and the attitudinal score after treatment (r=.005), which was positive but weaker than before treatment, while the p-value which is the significant value of correlation between the two variables (post achievement score and post attitudinal score) was p=0.955. The values showed a further weakening of the relationship between attitude and performance. Since this is greater than 0.05 i.e p> 0.05, it follows that the correlation was not significant.
Therefore there was no significant relationship between the post achievement score and post attitudinal score. The attitude of students therefore did not significantly affect their achievement in geometric construction.
HYPOTHESIS II- There is no statistically significant difference between performance of computer and blackboard groups.
Table 2a: T-test analysis of pretest scores for control (Blackboard) and experimental groups
Table 2b: T-test analysis of post -test scores for control and experimental groups
The pre-test as shown in table 1a above, the mean of the experimental group (= 8.58) is higher than that of the control group ( = 6.17). The p-value which is the significant value shows that the difference is not significant (p>0.05). The hypothesis is therefore upheld for the pretest.
Table 2b presents the post-test scores and the t-test analysis which showed that the experimental group maintained the lead with a mean of 11.18 over the control group with a mean of 9.45. The t-test analysis shows that the significant value of 0.355 is also greater than 0.05. Again, the hypothesis is upheld in the post test scores.
In summary, from the tables 2a and 2b above, the experimental group (computer group) performed better in both the pre and post tests than the control group as evidenced by the means; but the difference in the mean performances of the two groups is not significant. It then follows that the impact of the computer assisted instruction is not noticeable.
HYPOTHESIS III: There is no statistically significant difference between male and female students in the combined dependent variables that make up the learning outcomes
Note: The variables that make up the learning outcomes in this study are
Students' achievement (scores) in geometric construction examination.
Students' attitude to geometric construction.
A one-way between groups Multivariate Analysis of Variance (MANOVA) was performed to investigate sex differences in learning outcomes (achievement and attitudes). Two dependent variables (Achievement in geometric construction examination and attitude to geometric construction) were involved. The independent variable was gender.
There was a statistically significant difference between males and females on the combined dependent variable: F (2, 58) = 3.763, p = 0.029; with lambda = 0.885; Eta squared = 0.115. when the results for the dependent variables were considered separately using 0.05 alpha level of significance, the only difference to reach statistical significance was the achievement score after treatment: F(1,59) = 6.713, p = 0.012; eta squared = 0.102. An inspection of the mean scores indicated that males reported higher scores (mean = 13.154, SD = 7.00) than females (mean = 8.457, S.D = 7.01).
HYPOTHESIS IV: There is no statistically significant difference between computer and blackboard groups in the combined dependent variables that make up the learning outcomes.
Note: The variables that make up the learning outcomes in this study are;
Students' achievement scores in geometric construction examination.
Students' attitude to geometric construction
A one-way between groups Multivariate Analysis of Variance (MANOVA) was performed to investigate differences in learning outcome (achievement and attitudes). Two dependent variables (Achievement in geometric construction examination and Attitude to geometric construction) were involved. The independent variable was instructional methodology. There was no statistically significant difference between computer and blackboard groups on the combined dependent variables: F (2, 59) = 0.591, p=0.557; Wilks' lamda = 0.980, Eta squared = 0.020. When the results of the dependent variables were considered separately, none of the differences reached statistical significance. An inspection of the mean scores indicated that the computer group performed better in both achievement scores in geometric construction examination and attitude to geometric construction than the blackboard group. Below are the means and standard deviations. The Hypothesis is therefore upheld that there is no significance difference between the two groups in the combined dependent variables.
Achievement test in geometric construction
Attitude to geometric construction
The acceptance of this hypothesis provides answers to the research question, "Does Assisted Discovery Method of instruction affect students' achievement in geometric construction positively". The hypothesis may not be significant and does not uphold Rosen's (2007) study on "Different Learning Environments Provide Different Learning Experiences" where he stated that overall constructivist learning environments are more effective than traditional ones, but to the contrary to expectations, traditional settings did not differ from constructivist ones when traditionally-appropriate measures were used.
The results of this investigation were able to answer some of the research questions: What are the impact of the ADM and traditional method of teaching on students' achievement in mathematics geometric construction? According to hypothesis two, the mean and standard deviation of both the pre and post test was not statistically significant therefore there may not be any noticeable impact that instructional technology had on performance of both the control and experimental group. The ADM approach however, according to hypothesis four revealed a better approach in terms of improvement in both achievement and attitude of the experimental group. There was only a slight impact in attitudinal change after the intervention from the experimental group. The reason for this could be attributed to the interest students have in computer-based teaching as supported by earlier findings of (Salami 2008) that students taught mathematics with computer technology achieved cognitively higher than those taught without computer technology. Further research by Julia in (Salami 2008) stated "computer tutorials, training through World Wide Web etc can be a rewarding useful experience for students".
The Impact Gender played in attitude and performance to geometric construction study revealed that male (mean =13.154) as against female (mean=8.457) performed better in geometric construction than females. This may be topic specific as there are studies to show that mathematic performance is not gender specific.
This research has been able to show that both the traditional method of instruction and the computer based method plays an important role in teaching and learning .The implication for this is a need to:
Implication to Practice
Students' attitude is key to learning and teachers should do all possible to inculcate in students the right attitude.
ADM approach should be applied to other areas of mathematics where students perform poorly.
Implication to Policy
Improve on mathematics curriculum by putting more emphasis on use of Instructional aids in teaching and learning. The emphasis should be on the use and not which specific one as from this study the attitude of students to whether traditional or computer-based was not significant, but the impact of instructional method was noticeable in performance.
More teacher training development program in current instructional methodology
Female students should be given more encouragement in learning mathematics.
A further study is recommended for rural and public school settings as against the urban and private school settings used for this study.