ABSTRACT
Mathematics is a subject which seeks to understand patterns that permeate both the world around us and the mind within us. The knowledge of mathematics as a tool for use in everyday life is important for individual and societal development. Students’ achievement in mathematics is important in Science and Technology which is important for industrial advancement of a country. There are many ways of thinking and the kind of thinking one learns in mathematics is an ability to handle abstraction and solve problems that require knowledge of mathematics. Mathematical creativity is essential for scientists. Creativity is one of the goals of teaching mathematics in schools. However, students’ performance in Kenya Certificate of Secondary Education mathematics examination has been relatively poor. This has been attributed to teacher centred teaching and learning approaches among other factors that have impacted negatively on mathematical creativity and achievement. This study investigated the Effects of Experiential Learning Approach on students’ mathematical creativity and achievement in Kericho East Sub-County. The topic Statistics I was taught to Form Two since it is one of the topics that is poorly performed according to Kenya National Examinations Council reports on KCSE. Solomon Four Non Equivalent Control Group Design under the quasi-experimental research was used. A random sample of four co-educational sub-county secondary schools was drawn from schools in Kericho East Sub-County. Each school provided one Form Two class. This translated to a total of 168 students. The experimental groups were taught Experiential Learning Approach (ELA) while the control groups were taught using the Conventional Teaching Methods (CTM). One experimental and one control group was pre tested. At the end of the treatment all the four groups were post tested using Mathematical Creativity Test (MCT) and Mathematics Achievement Test (MAT). The instruments were validated with the help of experts in the Department of Curriculum Instruction and Education Management of Egerton University and mathematics teachers from selected secondary schools. The MCT and MAT were pilot tested to estimate their reliability coefficient using Cronbach alpha for MCT and Kuder Richardson 21 method for MAT before they were used in the study. The reliability coefficient was 0.778 for the MCT and 0.978 for the MAT. Means, t-test and ANOVA were used in data analysis. All statistical tests were subjected to test of significance at alpha (α) level of 0.05. The results revealed that ELA had a significant effect on students’ mathematical creativity and achievement in mathematics. However, the effects of treatment on mathematical creativity and achievement with regard to gender was not significant. The findings of the study may to assist mathematics teachers to adjust their instructional strategies and also teacher trainers may use the information from the study to sensitise in-service and pre- service mathematics teachers on the importance of Experiential Learning approach in enhancing Mathematical Creativity and achievement in Mathematics. The findings may also be used as a basis for future research in Mathematics Education.
CHAPTER ONE
INTRODUCTION
Background Information of the Study
Mathematics is a science of deductive reasoning. It is much more than algebra, geometry, statistics and calculus. Primarily mathematics is a way of thinking and a way of organising a logical proof. As a way of thinking, it gives insight into the power of the human mind and forms a crucial discipline of learning programmes in school subjects everywhere in the world (Johnson & Rising, 1972;Wojciech, 2009). Mathematics introduces learners to concepts, skills and ways of thinking that are important in their everyday lives. It helps them understand the sense of numbers, patterns and shapes they see around them. As their mathematical confidence grows they look for patterns, use logical thinking and discover new connections, new solutions and different approaches to problems. According to Breakel and Mutunga (1992) mathematics is a way of thinking in which a person determines the validity of an idea or information.
Mathematics is also a tool for understanding other subjects. It is said that mathematics is the gate and key to science. According to the famous philosopher Immanuel Kant; “Science is exact only in so far as it employs mathematics” therefore, all scientific education that do not begin with mathematics is said to be defective at its foundation (Wojciech, 2009). Mathematics plays a very important role in building up modern civilisation by perfecting all science (African Curricullum Organisation, [ACO] 1979; Riley 2000). Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance and for personal decision making. Mathematics is fundamental to national development by providing tools for understanding science, engineering, technology and economics. It is essential in public decision making and for participation in the knowledge economy (Buschang, Chung & Kim 2011). Mathematics is a tool for use in all spheres of life and it is important for the existence of any individual and society (Aguele & Agwagah, 2007).
According to Baber (2011) Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of pleasure and wonder for all learners when they solve a problem for the first time, discover a more elegant solution or notice hidden connections. Learners who are functional in mathematics are able to think independently in applied and abstract ways and can reason, solve problems and assess risks.
Creativity has been proposed as one of the major components to be included in the education of the 21st century (Mann, 2005). Therefore, the contemporary curricula should emphasize the development of students creative thinking (Lamon, 2003). There is no commonly accepted definition of mathematical creativity (Mann, 2006). However a commonly agreed upon definition is that mathematical creativity is a novel way of thinking characterised by fluency, flexibility, originality and elaboration (Gill, Ben-Zvi & Apel, 2007; Leikin, Berman & Koichu, 2010; Kim, Cho & Ahn, 2003; Imai, 2000; Runco, 2008). Fluency is the number of responses a learner can give to a mathematical question, flexibility is the shift in categories in the responses to a given mathematical task, originality is the degree of uniqueness of responses and elaboration is the ability of a person to produce detailed steps (Leikin, 2009).
Mathematical creativity is an essential aspect in the development of mathematical talent (Mann, 2005). Mathematical creativity is also important for constructing mathematical knowledge in a more central way than merely producing learnt knowledge thus teaching of mathematics must focus on seeking solutions creatively, exploring patterns uniquely and formulating hypothesis (Jha, 2012). Despite its importance, mathematical creativity is often neglected in mathematics education. There is need therefore, to improve upon the instructional methods to produce creative thinkers thus the use of ELA.
Learners’ performance in mathematics at the national examinations in many countries has remained low (Colwell, 2000). According to Colwell (2000) performance of American students in International Mathematical Tests was low in comparison to other countries. However some countries like Singapore, Taiwan, South Korea and Japan were doing better in mathematics. In Kenyamathematics is a compulsory subject at the primary and secondary school level and it is a basic requirement for many careers and trainings (Aguele & Agwagah, 2007; Githua, 2002). However students’ examination results in mathematics in Kenya Certificate of Secondary Education (KCSE) have been relatively low. The trend of performance of candidates in paper I and II of mathematics between the years 2010 and 2014 are shown in Table 1...
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