Background to the Problem

1. EFFECTS OF GUIDED-DISCOVERY LEARNING STRATEGY AND COGNITIVE STYLES ON SENIOR SCHOOL STUDENTS’ PERFORMANCE IN MATHEMATICS IN OSUN, NIGERIA An Oral Ph.D. Thesis Defence By AKANMU, Morenikeji Alex 98/25OC030 DEPARTMENT OF SCIENCE EDUCATION, UNIVERSITY OF ILORIN, ILORIN, NIGERIA SUPERVISOR: PROF. M. O FAJEMIDAGBA

2. Background to the Problem • Mathematics is the science of patterns and relationships. • Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. • As a vital tool for the understanding and application of science and technology, the discipline plays the vital role of a precursor and harbinger to the much needed technological and of course national development, which has become imperative in the developing nations of the world.

3. Statement of the Problem • Mathematics difficulties are persistent, and students who have difficulties may never catch up to their normally achieving peers (Jordan, 2010). • These difficulties, consequences of which are serious for everyday functioning and educational attainment, have been linked to learners’ self perceptions of mathematics ability and Poor teaching methods • It is against this background that the present researcher is interested in using guided discovery method of teaching mathematics compared with expository method in relation to cognitive styles - field-dependence field-independence construct, which has become a sort of general theory of perception, intellect, and personality (personal trait which reflect both differences in ability and personalities) and find out its effect on secondary school students mathematics achievement.

4. Purpose of the Study Specifically, this study investigated the: i difference in mean gain scores of senior school students in mathematics when taught using guided-discovery strategy and non-guided discovery learning strategy. ii. influence of cognitive styles on the performance of students in mathematics when taught using guided-discovery learning strategy. iii. influence of gender on the performance of students in mathematics when they are taught using guided-discovery learning strategy. iv. influence of scoring levels on the performance of students in mathematics when they are taught using guided-discovery learning strategy on the performance of students in mathematics.

5. Purpose of the Study v. the interaction effect between the treatment and cognitive style on the performance of students in mathematics. vi. the interaction effect between the treatment and gender on the performance of students in mathematics. vii. the interaction effect between the treatment and the students’ scoring levels on the performance of students in mathematics. viii. the interaction effect among the treatment, cognitive style, gender and students’ scoring levels on the performance of students in mathematics.

6. Research Questions The following research questions were raised in the study: 1. What is the difference between the mean gain scores of students in mathematics taught using guided–discovery learning strategy and non guided-discovery learning strategy? 2. Does cognitive style (Field-dependent and Field-independent) have influence on the performance of senior school students in mathematics when taught using guided-discovery learning strategy? 3. What is the influence of gender on senior school students performance in mathematics when taught using guided-discovery learning strategy? 4. Is there any difference in the senior school students performance in mathematics on the basis of their scoring levels when taught using guided –discovery learning strategy?

7. Research Questions The following research questions were raised in the study: 5. Is there any interaction effect between the treatment and cognitive style on the performance of students in mathematics? 6. Is there any interaction effect between the treatment and gender on the performance of students in mathematics? 7. Is there any interaction effect between the treatment and the students’ scoring levels on the performance of students in mathematics? 8. Is there any interaction effect among the treatment, cognitive style, gender and students’ scoring levels on the performance of students in mathematics?

8. Research Hypotheses The following null hypotheses were tested in this study: • HO1: There would be no significant difference in post-test mean scores of the senior school students taught using guided discovery method in mathematics and those taught using conventional method. • HO2: There would be no significant difference in the mean post-test scores of field-dependent and field-independent students when taught using guided discovery.

9. Research Hypotheses The following null hypotheses were tested in this study: • HO3: There would be no significant difference in the post-test mean scores of male and female students in mathematics when they are taught using guided discovery method. • HO4: There would be no significant difference in post-test mean scores of students with high, medium and low scoring level when they are taught using guided discovery method.

10. Research Hypotheses The following null hypotheses were tested in this study: HO5: There would be no significant interaction effect between the treatment the treatment and the cognitive style on the performance of students in mathematics. HO6: There would be no significant interaction between the treatment and gender on the performance of students in mathematics.

11. Research Hypotheses The following null hypotheses were tested in this study: HO7: There would be no significant interaction effect between the treatment and students’ scoring levels on the performance of students in mathematics. HO8: There would be no significant interaction effect among the treatment, cognitive style, gender and scoring levels of students on the performance of students in mathematics.

12. Scope of the Study • This study was limited to Mathematics students in Senior Secondary Class I (SSI) and their Mathematics teachers. The choice of SSI students was considered appropriate because these students would not have been taught the topic. Two schools from Ejigbo Local Government Area of Osun State, Nigeria participated in the study. The schools were government-owned institutions operating co-educational system. The mathematics teachers in the selected schools were trained mathematics teachers with at least five years of teaching experience at the Senior Secondary Level. • The content Area for treatment were drawn from West African Examinations Council (WAEC) recommended syllabuses for mathematics on Set Theory because it was observed that there are always questions every year on this topic in WAEC SSCE (Ale, 1989).

13. Clarification of Major terms and Variables In this study, the following terms were operationally defined: • Teacher-Student Ratio • Mathematics Performance • Guided discovery method • Cognitive styles • Control Method • Field-dependent and Field-independent • Scoring Level: Low Scorer students, Medium Scorer students and High Scorer students

14. Significance of the Study It is expected that, school administrators, curriculum planners, teachers, students, parents and the public would find useful the results of this study: Create students with learning challenges that would enable them develop, understand and or find out to their effective learning through mental process. Teachers would be more sensitive to the goals of mathematics teaching. Hence, the appropriate choice of methods of teaching for improved performance or achievement in mathematics. Study might provide useful information to curriculum designers and the school administrators on appropriate curriculum materials, teaching strategies and instructional aids for schools. The findings of this study would acquaint federal and state ministries of education (Mathematics division) and educational agencies such as Mathematical Association of Nigeria (MAN) with the current structure in the mathematics classrooms in Nigeria.

15. Chapter Two: REVIEW OF RELATED LITERATURE The review of the related literatures covers the following areas • nature and objectives of the Senior Secondary General Mathematics Curriculum in Nigeria • theoretical framework of the study; • factors influencing Students’ Performance in General Mathematics; • influence of Teaching Strategies on Students’ academic performance in Mathematics; • influence of Gender on Students’ Performance in General Mathematics; • influence of Scoring Levels on Students’ Performance in General Mathematics; and 7. appraisal of the Literature Reviewed

16. CHAPTER THREE: RESEARCH METHODOLOGY Research design This study was a quasi-experimental research designed to determine the effects of cognitive styles and guided-discovery learning strategy as predictor of learners’ achievement in mathematics. The research design represents the major methodological thrust of the study, being a distinctive and specific approach which is best suited to answer the research questions. Therefore the pre-test and post-test control group design was considered appropriate for this study. The pre-test, post-test of 2 x 2 x 3 experimental design was employed. The experimental levels are as follows: Methods of teaching at 2 levels (guided- discovery and conventional), Gender occurring at 2 levels (male and female) with Performance (scoring ability) at 3 levels (high, medium and low scorers)

17. TREATED (EXPERIMENTAL) GROUP EXPOSED TO GUIDED DISCOVERY NON-TREATED (CONTROL) GROUP NOT EXPOSED TO GUIDED DISCOVERY Field Independent Field Independent Field Dependent Field Dependent M M M M L L L L L L L L M M M M M M M M F F F F H H H H H H H H Diagrammatic Representation of the Experimental Design

18. Diagrammatic Representation of the Experimental Design Sampling frame for the students that participated in the Experimental group • label No M F LS-M MS-M HS-M LS-F MS-F HS-F Field-dependent 29 16 13 0 1 150 1 12 Field-independent 61 30 31 3 24 3 3 25 3 Sampling frame for the students that participated in the control group Field Dependent 17 8 9 0 4 4 0 3 6 Field Independent 95 65 30 3 59 3 2 27 1

19. Sample and Sampling Technique • The target population consisted of all students in Senior Secondary School I in Ejigbo, Osun State offering Mathematics. The choice of SSI students was considered appropriate because these students had not been taught the topic. The sample consisted of 202 students from the two purposively selected Schools. The schools were labelled A and B with school A used as experimental and B as the control group respectively. The students in the schools selected were randomized into the two treatment groups’ with the use of standardized (adopted from past questions of the West African Examinations- 1988-2011) Group Embedded Figures Test (GEFT). • The students in each of the school selected were later stratified into the three scoring groups (Low, Medium and High) using the students’ post test scores in the Mathematics Achievement Test of Group Embedded Figures Test type into the high, medium and low scorers groups.

20. Research Instrument Group Embedded Figures Test (GEFT) type which had been applied most commonly was adopted for this study. There were two reasons for choosing GEFT in this study. The Mathematics Achievement Test contained twenty multiple choice questions also drawn from the West Africa Senior School Certificate Examinations Mathematics questions. Validation and Reliability of the Instruments Apart from the content validation being ensured, the test items were given to the researcher’s supervisor , internal-external examiner and two experienced senior secondary school mathematics teachers in two secondary schools in Ilorin.

21. Research Instrument ...contd. Procedure for Data Collection After obtaining permission from the selected schools for the study and interaction established with mathematics teachers in the chosen schools, the first week was devoted to training the research assistant and educate the teachers of the schools on the task. Data Analysis Technique Hypotheses one, two and three were tested with independent (uncorrelated) sample t-test statistics while hypothesis four was tested using Analysis of Covariance (ANCOVA). Statistical Package for the Social Sciences (IBM SPSS 20.0 version) was used to analyzed the data while Duncan post hoc test was used to ascertain the homogeneous nature of the groups (where the significance level lied)

22. Hypothesis one HO1: There would be no significant difference in post-test mean scores of students taught using guided discovery and those taught without the use of guided discovery. Table 4. The t-Test Analysis showing difference in post-test mean scores of students taught using guided discovery and those taught without the use of guided discovery.

23. Table 4 reveals that the calculated t-value =9.389 with p-value of .000 ˂ 0.05 alpha level. Since the p-value is lesser than the alpha level of 0.05, the null hypothesis one was rejected and the alternative hypothesis that, there would be a significant difference in post-test mean scores of students taught using guided discovery and those taught without the use of guided discovery was upheld. To ascertain where the significant difference lies, the mean scores of the two groups were compared. The mean scores of the guided discovery (14.0667) is greater than the mean scores (10.7143) of the conventional method. Thus, it is favour of guided discovery learning.

24. Hypothesis Two HO2: There would be no significant difference in the mean post-test scores of field dependent and field independent students when taught using guided discovery method. Table 5: The t-Test Analysis showing difference in the mean post-test scores of field dependent (FD) and field independent(FID) students when taught using guided discovery method

25. Table 5 shows that the calculated t-value = 3.348 with p-value of .001 ˂ 0.05 alpha level. It implies that the null hypothesis two was rejected and the alternative hypothesis that, there would be a significant difference in the mean post-test scores of field dependent and field independent students when taught using guided discovery method is accepted. To further ascertain where lies the significant difference, the mean scores of the field dependent and field independent students were compared and it was found that it was in favour of the field independent students. The mean scores obtained for the field dependent is (15.2759) which is greater than the mean scores (13.4918) obtained in respect of the field dependent learners.

26. Hypothesis Three Ho3: There would be no significant difference in post-test mean scores of male and female students in mathematics when they are taught using guided discovery method Table 6: The t-Test Analysis showing difference in post-test mean scores of male and female students in mathematics when they are taught using guided discovery method

27. From Table 6, analysis reveals that the calculated t-value = .168 with p-value of .867 ˃ 0.05 alpha level. It implies that the null hypothesis three which state that there would be no significant difference in post-test mean scores of male and female students in mathematics when they are taught using guided discovery method was accepted . In other words, the performance of male and female students taught using guided discovery method shows no difference. Hence, the hypothesis is upheld. The mean scores obtained for male and female in field-dependent were 5.5667 and 5.0968 respectively. For the field-independent, 11.6250 and 12.3846 was obtained as mean scores for male and female in the group.

28. Hypothesis Four HO4: There would be no significant difference in post-test mean scores of students with high, medium and low scoring level when they are taught using guided discovery method Table 7: ANCOVA Analysis showing difference in the post-test mean scores of students with high, medium and low scoring level when they are taught using guided discovery method

29. Table 7 indicates the Analysis of Covariance containing the scoring level ability, mean squares, f-test value and the corresponding p-values. From the table, the calculated f-value is 8.413 with p-value equals .000 which is less than the alpha level of 0.05. this implies that the null hypothesis four is rejected and the alternative hypothesis which states that there would be a Significant difference in post-test mean scores of students with high, medium and low scoring level when they are taught using guided discovery method.

30. Hypothesis FiveHO5: There would be no significant interaction effect between the treatment and thecognitive style on the performance of students in mathematics.Table 11:ANCOVA Computation on Post-test Mean Scores of Students in the TreatmentGroup and Cognitive style Source

31. Table 11 showed that at F(1, 197) = 6.534, p < 0.005, the null hypothesis was rejected. Hence, there was significant interaction effect between the treatment and the cognitive style of the students. The profile plot is shown in figure 10.

32. Figure 10: Graph on the interaction effect between the treatment andthe students’ Cognitive Style

33. Hypothesis 6HO6: There would be no significant interaction between the treatment and gender on the performance of students in mathematics.Table 12: ANCOVA Computation on Post-test Mean Scores of Students in the Treatment Group and Gender

34. From table 12, there was no significant interaction effect between the treatment and students’ gender. This was because at F(1, 197) = .002, p > 0.05. therefore, the null hypothesis was not rejected. This is further corroborated in the profile plot as shown in figure 11 where the two lines appeared too close indicating that, there was no major difference even in the treatment condition.

35. Figure 11:Graph on the interaction effect between the treatment and the students’ Gender

36. Hypothesis 7HO7: There would be no significant interaction effect between the treatment andstudents’ scoring levels on the performance of students in mathematics.Table 13:ANCOVA Computation on Post-test Mean Scores of Students in the Treatment Group and Scoring levels

37. Table 13 showed that the computed value of F(1,196) = .171, p < 0.05, the null hypothesis was rejected. Therefore, there was a significant interaction between the scoring levels of the students and the treatment. Figure 12 also revealed the difference that existed in the treatment condition.

38. Figure 12: Graph on the interaction effect between the treatment and the students’ Scoring levels

39. Hypothesis 8HO8: There would be no significant interaction effect among the treatment, cognitive style, gender and scoring levels of students on the performance of students in mathematics. From table 14, F(1, 183) = .221, p < 0.05, the was significant interaction effect among the treatment, cognitive style, gender and scorings of the students. No profile plot is shown as SPSS 20.00 can only plot graph for variables not exceeding three.

40. Table 14:ANCOVA Computation on Post-test Mean Scores of Students in theTreatment Group, Cognitive style, Gender and Scoring levels

41. Table 14 contd.

42. Summary of Major Findings The following are the summary of major findings in this study: 1. the experimental group taught using guided-discovery learning strategy had a significantly higher score than the control group taught using the non guided- discovery; 2. the post test mean scores of the field-independent students were significantly higher than the post test mean scores of the field-dependent students when taught using Guided-discovery learning strategy; 3. post test mean scores of male students was not significantly higher than that of the female students when taught using guided-discovery learning strategy; 4. higher scorers benefited most, followed by medium scorers and the low scorers benefitted least when taught using guided-discovery learning strategy. To further ascertain this with respect to where the difference lied, Duncan post-hoc test was carried out and the output of 15.1818 in table 8 subset 3 reveals that students with high scoring ability is most significant of all the groups.

43. Summary of Major Findings...contd 5. there was significant interaction effect between the treatment and the cognitive style of the students, F(1, 197) = 6.534, p < 0.05. 6. there was no significant interaction effect between the treatment and students’ gender. This was because at F(1, 197) = .002, p > 0.05. 7.there was a significant interaction between the scoring levels of the students and the treatment, F(1,196) = .171, p < 0.05. 8. the was significant interaction effect among the treatment, cognitive style, gender and scorings of the students, F(1, 183) = .221, p < 0.05.

44. Chapter Five: Discussion, Conclusion and Recommendations Discussion The findings of this study agreed and also varied with the findings existing studies Conclusion Results from this study have shown that there was a significant difference in the performance of Mathematics students taught using guided discovery method over the students taught using conventional method. The study has shown the potency of guided discovery method of teaching in improving student’s performance. Equally, the outcome of the study with respect to cognitive styles was in favour of the field independent students. Findings from the present study have also shown that gender has no role to play in the performance of the students. The findings of this study has also revealed that all scoring ability groups benefited from the method of teaching with high scoring ability as most significant of all the groups.

45. Recommendations n line with the findings of this study, the following are recommended: • Guided Discovery Learning was found helpful in learners’ ability to extract a simple figure from a complex one since it was more interactive. It is recommended that the teachers should make the teaching-learning of mathematics an interactive and activity – based one for the students. Teachers should use many methods while teaching mathematics, for instance set theory, so that all students could gain from the teaching irrespective of the ability levels of the students. • Mathematics teachers should be taught different methods of teaching. This can be made possible by organising seminars and workshops on pedagogy for the teachers. • Students could be rewarded for their performance in mathematics test with little gifts which are not expensive. This will ginger the low scorers to improve on their performance

46. Recommendations • Male and females should have roles to play in mathematics class since males are not superior to female in mathematics class as found out in this study. • Ministries of Education at both Federal and State levels should periodically asides regular workshops for teachers develop a mean of reviewing / assessing the impact of teaching methods.

47. Suggestions for Further Studies • Further study be carried out to involve other methods for teaching mathematics. • Other variables like attitude, school type and teachers qualification can be included alongside either with guided discovery or other identified methods of teaching. • Further study be conducted in other States of the Federation or geo-political zone. • A replication of a similar study be carried out to either corroborate or refute the findings of this study since knowledge and human behaviour are dynamic.

48. Thank you