This study investigates 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 under achievement in geometric construction in Senior Secondary Schools, a 3 year progressive educational program in Nigeria. A purpose sample comprising 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 Subject and Methodology" (SASM), to find out the students' attitude to mathematics and learning geometry collaboratively through the internet, 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 computers connected to the internet 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 and regression analysis. Results revealed that attitude to intructional methodology appeared to play a minimal role in achievement of geometric construction in mathematics. In spite of divergent earlier findings on impact of instructional methodology and attitude on achievement, this study revealed constructivist approach as a better approach in teaching as it had a positive impact on achievement, which also revealed web-based learning as slightly, it is therefore not conclusive. Implication of these findings calls for further studies on collaborative web-based learning, in teaching geometric construction in Nigerian Schools. A further study is recommended for rural and public school settings as against the urban and private school settings used. It is also recommended that web-based learning be applied to other areas of mathematics where students perform poorly and research into blocking unwanted sites during teaching involving the web.
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Keywords: Achievement, Attitude, Collaborative web-based learning, Constructivist Theory
Leading societies of the world 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 mathematics is a core subject taught at both the Junior and Senior Secondary levels of Education in Nigeria, (NPE, 2004); and which students must at least get a minimum credit pass to qualify for admission in any Nigerian Tertiary institution, students continue to perform poorly in this subject, 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 achievement 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 A.)
Psychologists define 'attitude' as any strong belief or feeling or any approval or disapproval toward people and situations. We favor the things we think are good and helpful, and oppose the things we think are bad and harmful (Kiamanesh, 2001). A study of German and Japanese high school science students revealed the Germans has a better attitude towards their subject but poorer achievement when compared to Japanese students who have poorer attitude but better achievement( Bruce et al, 2000). In support of this is the study of senior high students in Australia, Cyprus and United States of America where it was found that there is no permanent relationship between science achievement and attitude but the relationship varies from country to country (Papanastasiou, 2004). However the poor achievement in Nigeria students in Physics and Mathematics is attributable to negative attitude towards the subject (Ajayi, 1999; Seleshi, 2001).
A nation that desires growth should be concerned about students' achievement in school, which may be attributed to such factors as lack of qualified teachers, ill preparation by students, wrong attitude to specific subjects, insufficient teaching and learning resources in schools, environmental factors, parents socio-economic status, and many other factors.
Summers (2006) observed that one of the main reasons for difficulties of learning mathematics is teachers' method of making students memorize formulas, solving questions using the method and example the teacher has proffered, instead of helping them internalize mathematical knowledge. This was corroborated by Peterson, (1973); de Villiers, (1986); Van Engen, (1973); Chung, (2004).
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Web based instruction one of the important learning tool provides learner with rich style of learning and offers access to a wide variety of resources, such as open source materials that can be adopted for learning (Erdogan et al, 2008). The web based instruction may be delivered through the internet or computers networked together in a laboratory, however learner involvement is crucial for learning to reach its climax (Collins, 1998; Horton, 2000). According to Shany et al , 2002) we must examine the way in which this new technology fits into the need of individual students, and if this is not done, adverse effect is likely to occur. Learner expectations towards web based education significantly affect learning outcomes (Sanders et al, 2001; Alomyan et al, 2004). Most web-based courses provide formal and informal discussion forums, in the form of chat rooms and discussion seminars respectively. However, discussions are not necessarily integrated with other activities that students undertake. One of the reasons for this is that there is often a lack of a sound conceptual framework guiding the design of the courses. In order to develop collaborative spaces that maximize educational benefits, the design of the entire course (or program) needs to be taken into account so that individual and social learning opportunities complement each other. Students' perception of the usefulness of a web-learning is dependent on how fruitful and productive their collaborative interactions have been. (Puntambekar, 1999; Giannoukos et al, 2008).
It is believed that learning is particularly effective when collaborating students encounter conflicts, engage in argumentation and manage through negotiation to produce a shared solution (Veerman et al, 1999; Gokhale 1995).The opportunities to have access to open source materials on the web, which the learner can use to support the traditional mode of teaching, teachers can as well leverage on this open source to improve on their pedagogy. Learners at their own convenience can look into the web-instruction and construct their own knowledge either on their own or with the assistance of other people they feel connected to or are free to associate with. Collaboration either between learner and learner, teacher and teacher, or learner and teacher will be worth the while to investigate in web-instruction. Computer supported collaborative learning (CSCL) offers promising innovations and tools for restructuring teaching-learning processes to prepare students for the future. In a collaborative learning environment, learners are challenged both socially and emotionally since they listen to the different arguments of the individual from various perspectives and eventually come to a unique conceptual framework.
Berge, 1997; Stocks & Freddolino, 1998; Kurubacak, 2000; Manzanares, 2004 posit that there is a scarce of research into learner's expectation in the use of we- based instruction, while available literature revealed that web based-learning improve achievement (Smith et al, 2001; Johnson, 2001; Erdogan et al, 2008). Attitude to subject, method of delivery, environmental factors no doubt have impact on achievement either negatively or positively. According to many reports, rapid social and economic changes are taking place as western society approaches the 21st Century. Recent research on CSCL has indicated several positive effects: enhanced individual learning outcomes; and higher group achievement, especially with regard to knowledge (Lipponen et al, 1999).
An important issue in learning research is the construction of knowledge through negotiation. In developed countries such as the USA and EU investment into web based education has been on the increase ( Erdogan et al, 2008;) and educational institutions are forced to find new pedagogy to cope with the challenges of an emerging knowledge society, where computers will play an important role. The same cannot be said of Sub Saharan Africa which is still grapling with adoption of electronic learning of which collaborative web-based learning is a branch.(Lelliott et al, 2000; Gunja et al, 2007)
This study therefore investigates the effect of collaborative web-based learning on achievement in Nigerian secondary schools with internet facilities. The key question is "Is it possible to deploy collaborative web-based learning in Nigerian secondary schools?"
The study is guided by social constructivist theory of learning . Constructivism is basically a theory, based on observation and scientific study about how people learn. It says that people construct their own understanding and knowledge of the world, through experiencing things and reflecting on those experiences (Sherman, 1995). To do this, we must ask questions, explore, and assess what we know. A productive, constructivist classroom, then, consists of learner-centered and active instruction. In such a classroom, the teacher provides students with experiences that allow them to hypothesize, predict, manipulate objects, pose questions, research, investigate, imagine, and invent. The teacher's role is to facilitate this process. According to Thompson (1992), problem solving is central to teaching for constructivist mathematics teachers where purposeful activity stems from problem situations that require reasoning and creative thinking, gathering and applying information, discovering, inventing, communicating and testing ideas. Social constructivsit theory stressed the fundamental role of social interaction in the development of cognition (Vygotsky, 1978; Wertsch, 1985), the community plays a central role in the process of constructing knowledge. Learners who are refered to as Less knowledgeable others (LKO) can, with assistance from More Knowledge Others (MKO) who could be adults or fellow learners grasp concepts, handle tasks or ideas on their own through manipulating objects, posing questions, and investigation. The learner through asking questions gets to the point when she can handle the task by herself. This is the theory of Zone of Proximal Development (ZPD) according to Vygotsky. This is the point where the learner knows what she does not know before being helped to now handle the task.
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Geometric construction involves basic construction of angles such as 900, bisection of angle, 1200 these were found to be simple for students to construct on their own but difficulties are encountered with agles such as 750, 150O, 1050 i .e any angle requiring some manipulations as adding two angles or involving subtraction. The model for this study is therefore based on social constructivism finding relationship between attitude, web-based instructional method and achievement.
This study made use of survey and experimental designs, starting with a survey to determine students' attitude to mathematics generally and geometric construction in particular as well as the methodology, followed by four weeks tutorials to two intact classes, SS2 Students in Private Secondary Schools in Lagos State.
The sample size comprised of 62 students drawn from two purposive 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 one intact classes of one school and 29 students from other intact classes of another school.
The schools were assigned as experimental and control group respectively. The experimental school had all the facilities needed for a web-based learning, 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 further individual/collaborative work. The activities were carried out collaboratively with the assistance of the researcher. Students in both schools had a pretest. The pretest scripts were graded out of 30marks, mean score for the experimental class was 11.18. The mean was used as benchmarks to classify the students into More Knowledgeable Others (MKO) and Less Knowledgeable Others (LKO). Any student scoring above the mean was classified as MKO while student scoring below the mean was classified as LKO. The MKO and LKO were randomly mixed in the class to achieve a collaborative learning effect; and put in groups to learn. The aim of this randomization was to neutralize all extraneous variables such as sex, personality, age, race, parents' educational status, and poor nutrition, which may affect the findings of this research. 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 experimental group used an open source software, an internet based geometric construction tutorial (Page, 2008). The choice of this package is the simplicity with which it taught geometric construction, using animations and graphical illustration. while a teacher who had ealrier been tutored by the researcher used the traditional method to teach the control group.
DATA COLLECTION AND ANALYSIS
"SASM", a forty -one item questionnaire was administered to both groups as pre treatment and post treatment, while "MATGC", a 3- item teacher made achievement test was admnistered to both groups as pre and post tests. This survey and experiment was used to prove the hypotheses . The survey had two major sections labeled A and B. Section A consisted of items that queried students for bio-data (age, gender, type of school, if repeating the class and category aof subject). Section B comprised 36 structured items which are designed to elicit information about students' value of subject and technology, Enjoyment of subject and technology, Student self confidence, Information Technology skills, IT awareness and Team Spirit. The questionnaire were opinion statements and four optional responses structured in the modified Likert scale format. The options include:
Strongly Agreed (SA)
Strongly disagree (SD)
The responses to SASM and the test papers were scored, organised and analyzed using the following steps.
METHOD OF DATA ANALYSIS
The data generated with the questionnaire and the MATGC scores were analyzed with inferential statistical tools which include
Standard deviation and
In this research, three research questions and four hypotheses were posed based on the model. 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 to mathematics will not significantly affect their achievement in geometric construction
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 achievement. 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: The Instructional methodology will not significantly affect students' attitude to geometric construction
Table 2a presents the t-test analysis of mathematics attitudinal scores of students before the commencement of treatment. The p-value of 0.477 in the table implies a significant value above 0.05; hence at 0.05 levels of significances the difference in the mean attitudinal scores across treatment groups is not statistically significant. The column for mean and standard deviation however shows a higher mean and lower standard deviation for the control group. This implies that based on the sample of the study, the control group had better attitude before treatment.
Table 2b presents the t-test analysis of mathematical attitudinal scores of students across the treatment groups after treatment. It also displayed a p-value of 0.533 which is greater than 0.05. This implies a non-significant difference in the mean attitudinal scores of students in experimental and control groups. The column for mean and standard deviation however presents a picture completely different from that in Table 2a; here the experimental group had a higher mean and lower standard deviation compared with their counterparts in the control group. The implication is that in both cases the difference in the mean is not significant in both the pre and post attitudinal scores. However, before the treatment, the control group performed better in the attitudinal rating. Before treatment and after treatment, the experimental group performed better. Therefore, the special treatment of computer usage in teaching geometric construction had some impacts (though not significant) on the attitude of the students to geometric construction.
HYPOTHESIS III- There is no statistically significant difference between achievement of web-based learning and traditional learning groups.
The pre-test as shown in table 3a 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 3b 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 3a and 3b above, the experimental group (web based 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 achievements of the two groups is not significant. It then follows that the impact of the computer assisted instruction is not noticeable.
HYPOTHESIS IV: There is no statistically significant difference between web-based teaching and traditional 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 web based and traditional 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. The Hypothesis is therefore upheld that there is no significance difference between the two groups in the combined dependent variables.
An inspection of the mean scores indicated that the web-based group performed better in both achievement scores in geometric construction examination and attitude to geometric construction than the traditional group. Below are the means and standard deviations.
The result of hypothesis I revealed no correlation between attitude to subject and performance which upheld (Bruce et al, 2000; Papanastastasiou, 2004), however the further weakening of correlation between attitude and performance after treatment may be attributable to the fact that experimental study are criticised to be artificial (Dennis et al, 2001). The students did not see any benefit the study was going to bring to them even after the reearcher had tried to explain the purpose of the research.
The web learners' attitudunal change to mathematics was positive after treatment though not statistically significant enough to generalise, the traditional method learners had a better attitude to the subject prior to treatment, however the mean attitudinal scores across treatment groups is not statistically significant,
According to hypothesis III, that there is no significant difference between achievement of web based and traditional, 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 achievement of both the control and experimental group. The web based approach however, according to hypothesis IV 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 web-based teaching as supported by (Nguyen et al, 2005; Salami, 2008) that students taught mathematics with computer technology achieved cognitively higher than those taught without computer technology. Students were seen navigating between the instructional site and social network sites.
CONCLUSIONS AND IMPLICATION OF FINDINGS
This research has been able to show that both the traditional method of instruction and the web-based method play an important role in teaching and learning .The study cannot be said to be conclusive as to the effect of web based learning in performance in mathematics, it is therefore suggested that further work be carried out. The implication of this for;
Teahers of Mathematics should blend the two approaches to teaching and learning i.e web based and traditional method.
Information Systems developers and researchers should address filtering of unwanted sites out of computers during learning on the internet, as students were seen visiting social network sites during the experiment
More studies are recommended on impact of technology on achievement, this will ensure students are able to understand concepts, be technologically developed to face the challenges of global development
A further study is recommended for rural and public school settings as against the urban and private school settings used for this study.