There does not exist presently a universally accepted definition of PBL as researchers ascribe varieties of definitions and meanings to it. For example, Simon & Schifter (1991) describe PBL as an alternative pedagogy, a new paradigm of mathematics instruction, long in gestation which has begun to find the support necessary to contest the old traditional method of instruction. PBL is also a classroom strategy that organizes mathematics instructions around problem solving activities and affords students more opportunities to think critically, present their creative ideas and communicate with peers mathematically (Krulic & Rudnick, 1999; Hiebert et al., 1996, 1997; Kyeong Ha, 2003). Major (2001) defined PBL as an educational approach in which complex problems serve as the context and the stimulus for learning. The common denominator to the varieties of PBL definitions is that students actively construct their own knowledge of mathematics. The current study adopts this notion of PBL.
Problem-Based Learning (PBL) was first established as part of the education of physicians in medical school at McMaster University, Hamilton, Ontario, Canada in the 1960s. Developed by Howard Barrows, this strategy has grown into an instructional approach, which is finding success in elementary through high school throughout the state of Illinois Mathematics and Science Academy and beyond. PBL was originally developed out of the perceived need to
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produce graduates who were prepared to deal with the information explosion, and who could think critically and solve complex problems (Major, 2001). PBL is rooted in Dewey’s “learning by doing and experiencing” principle (Dewey, 1938 in Hiebert et al., 1996). Dewey advocated engaging the learner in everyday problems to facilitate learning. Hiebert et al. (1996) proposed alternative principle by building on John Dewey’s idea of “reflective inquiry” that curriculum and instruction be guided by the basic principle that students problematize their subjects.
Smith (1997) described Hiebert et al. submission as a relatively narrow view of school mathematics content. He remarked that while they are correct to argue that topics traditionally taught in routine and uninteresting ways can be problematized, their implicit view of content is inconsistent with the problematizing process itself. He stated further that if students are encouraged to engage in that process seriously and articulate what they find interesting and problematic, and do not expect to be assigned problems to solve, their interests would inevitably lead them to ponder a much richer and wider range of mathematical ideas. Problematizing, according to Hiebert et al. (1996) if pursued seriously, will burst the boundaries of the traditional school mathematics curriculum. To problematize is to “wonder why things are, to inquire, to search for solutions, and to resolve incongruities”. When students problematize mathematics, they become “engaged in genuine problem solving” and find, present and discuss “alternative solution methods”. Whether tasks become “problematic” and engaging, there emphasis depends more on how teachers and students treat them than on their source e.g. ‘‘real–life situations”. Hiebert et al. (1996) admitted that the principle in mathematics fits under the umbrella of problem solving, but their own interpretation differs from many problem-solving approaches.
Educational and Professional schools also began to feel many of the same needs as medical schools, so they began to adopt the approach as well, although in different forms, such as hybrid PBL, and traditional curricula and course-by course models; again the approach spread to institutions around the world (Boud & Feletti, 1991). A search for a change from the traditional method of teaching resulted in the National Council of Teachers of Mathematics (NCTM) adopting a veritable pragmatic alternative method for effective teaching and learning of mathematics, which incorporates the characteristics of PBL (NCTM, 2000). PBL is an active learning approach which enables students to become aware of and
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determine his/her problem solving ability and learning needs, to learn how to learn, to be able to make knowledge operative and to perform group works “in the face of real life problems” (Akinoglu &Tandogan, 2007). Hence, the current study sought to determine its effectiveness in the learning of Further Mathematics in Nigeria.
Literature reveals that studies have focused on the use of PBL model in primary education, secondary and post-secondary education by the 1980s (Duch, Gallagher, Kaptan, & Korkmaz, in Akinoglu & Tandogan, 2007). In the current study, PBL was used in secondary school education. The PBL approach is a learning model which centres on students, develops active learning, problem-solving skills and field knowledge, and is based on understanding and problem-solving (Major, 2001). The PBL model turns the student from a passive information recipient to an active, free self-learner and problem solver, and it slides the emphasis of educational programme from teaching to learning. This model enables students to learn new knowledge by facing him/her with the problems to be solved, instead of burdened contents (Ndlovu, 2008). The PBL teaching approach is at present not in vogue in the Nigerian educational system. Teachers in Nigeria, as in other countries in the world hold beliefs that the traditional method of teaching is ineffective and highly unproductive (Awodeyi, 2003) in teaching curricular contents. The students are exposed to the curriculum that is more theoretical than practical (Azuka, 2003) thereby resulting into teachers adopting instructional strategies that are largely traditional. Most times students find themselves memorising mathematics formulae for passing examinations. Students do not immediately realize the applications of what they are taught and find it difficult to conceptualise the topics being taught, not to talk of the applications (Mji, 2003).
An enabling environment for the implementation of the PBL approach is yet to be put on ground by Government and stakeholders in the Nigerian education. . This might be due, among other reasons, to acute shortage of teaching facilities, textbooks written with PBL focus, orientation, and teachers that are trained in the PBL pedagogical approach. Government has made some efforts to address the problem of ineffective teaching methods being used in our classrooms. One of such efforts is the Second Primary Education Project (PEP II) and Teaching and Learning Studies. Under PEP II, the Universal Basic Education Programme (UBEP) carried out a number of activities across the country to improve the quality of teaching and learning in primary schools. Two types of research activities were
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undertaken that would contribute to improvement in the content and management of teacher education and training. These are; (a) national surveys of teachers and teacher education programme, and (b) action research and development activities in classrooms and across school clusters (UBEC, 2002). Participatory method of approach was planned for the use of the project. PBL, however accommodates this method and still possesses other features that can enhance effective teaching and learning of Further Mathematics.