The poor achievement of the control group in this study was an attestation of the inherent weakness of the traditional method of instruction as a means of enhancing learning in Further Mathematics. The traditional method of teaching is typical of Nigerian Further Mathematics classes and the poor performance of students may be because of over reliance on this method. The effectiveness of the PBL in this study lied in the fact that it stimulated students’ level and ways of thinking. The method allowed students to make decisions of their own. It helped students to develop their ability to frame and ask questions. The PBL method made students to be bold and convinced when a solution was appropriate or not. It agitated the minds of the students via their experience to be able to defend their discoveries; hence, the method stimulated their reasoning capability. The method encouraged discussion between and among the students. It promoted interpersonal relationships among the students. Within the group, students learned and gained various ideas. It encouraged teamwork among students. Criticism is allowed which made students to understand better.
The implication of the findings of this study to educational practice is that PBL as part of the current reform in (Further) Mathematics is likely to make students develop problem-solving
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skills for performing higher-level operations in an atmosphere of active inquiry-based constructivist instructional environments.
A major pre-occupation of (Further) Mathematics teachers in this 21st century has been shifting from traditional teaching approaches that emphasized rote learning to student- centred, minds- on, and activity-based approaches that promote meaningful learning. Adopting the PBL approach in (Further) Mathematics classes requires that teachers have a good knowledge of constructivist learning and the ways in which PBL can be used to promote the students’ thinking. This calls for new roles on the part of teachers thereby shifting from telling, dictating and drilling which are considered less motivating and incompatible with constructivism to learning and constructing meaning. Efforts should be made to integrate the philosophy of PBL into the pre-service teachers’ curriculum at the teacher-preparation institutions in Nigeria. 5.5 Conclusion
In the course of the present study, it can be asserted that the PBL as a constructivist instructional strategy is more amenable to the teaching of Further Mathematics. Effective teaching and learning of Further Mathematics could only be achieved through the introduction of various innovative strategies that are cognitively learner-centred, minds-on, hands-on, and peer-mediated like the PBL in this study. As shown in this study the PBL approach made students more creative, act purposefully, think rationally and relate effectively with their peers in the Further Mathematics classroom. The adoption of the PBL prompted teachers to know when and how to apply scaffolding during the course of classroom teaching. It also assisted teachers through diagnostic testing to ascertain the students’ level of preparedness before the introduction of PBL as an intervention strategy. The adoption of the PBL in the Further Mathematics classroom could assist low achievers and enhance their interest in Further Mathematics at the Senior Secondary School Certificate Examinations. The PBL could be adopted as a viable strategy for strengthening the students’ cognition at the levels of knowledge and application.
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The following recommendations are hereby made:
(1) The results from this study show that mathematics teachers need in-service training on modern instructional strategies including the PBL regularly to make them competent in preparing the 21st century students to face global challenges in their chosen disciplines. (2) Government should give greater emphasis to in-service education for teachers because no matter the efficiency of pre-service training, the constant change in society and resultant change in curriculum will necessitate continuous in-service training for Mathematics teachers. (3) The study has in no small dimension revealed that problem-based learning approach could improve the students’ cognition at the knowledge and application levels thereby improving their achievement in Further Mathematics.
(4) It could also positively influence the students’ belief about Further Mathematics. There is need for Mathematics teachers to be knowledgeable about problem-based learning approach before it can be introduced into the classrooms at all levels of education especially at the elementary and secondary levels.
(5) If the PBL approaches were to be adopted, significant changes would have to be effected in the classroom structure in the area of sitting arrangements, location and placement of all materials needed by the teacher. School time-table, curriculum, assessment orientations and a host of others would also have to be re-structured to favour PBL.
(6) Textbook writers and Publishers would also have to incorporate this new technique in their write-ups for the benefit of both the teachers and the students.
(7) The NERDC whose part of its mandates is to develop, review, and produce the school- based subject curricula should consider it expedient to review the broad based and highly loaded Further Mathematics curriculum for students’ active participation in class discussion and consequently improving their achievement.
(8) Professional bodies such as the Science Teachers’ Association of Nigeria (STAN), the Mathematics Association of Nigeria (MAN), and Nigeria Mathematical Society (NMS) would
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have to start thinking about how PBL approach could be integrated into their yearly Panel workshops and annual conferences as the case may be for thorough practical demonstration for all participants.