EFFECTS OF LOGICAL AND CREATIVE PROBLEM-SOLVING ON ATTENTIVENESS AND PERFORMANCE IN MATHEMATICS AMONG SENIOR SECONDARY SCHOOL STUDENTS, SABON-GARI KADUNA STATE, NIGERIA.
This study investigated the effects of analytic and creative problem-solving on Interest and Performance in Mathematics among Senior Secondary School Students, Sabon-Gari Kaduna State, Nigeria. The objectives of this study were therefore, to determine the differences between Analytic and Creative Problem Solving on performance of Students in Mathematics, and to determine the effects of academic performance of students taught mathematics, using Analytic Problem-Solving and those taught with lecture method, the study also set out to investigate whether there was difference between the performance of students taught mathematics using Creative Problem-Solving and those taught with lecture method, it also investigate the performance of male and female students using Analytic and Creative Problem-Solving, so as to determine students interest before and after taught mathematics using Analytic and Creative Problem-Solving. Three Senior Secondary Schools in Sabon-Gari Local Govt of Kaduna State were randomly selected using stratified random sampling process was assigned by balloting to each experimental group and the other schools were for control group, the population collected was 130 students out of the total population of 2142 ( Two thousand one hundred and forty two)students, using Krejcie & Morgan (1970). Both experimental groups received treatment. Three instruments were designed for data collection but were pilot tested to ascertain their reliability. The validity of the instruments was checked by experts from Department of Science Education Mathematics Section A.B.U Zaria and C.O.E Zaria. The instruments were administered to two groups. Descriptive Statistics (mean, and standard Deviation) and inferential statistics (t-test and Kruskal-Wallis test) were used for data analysis. The level of significance for acceptance or rejection of hypothesis was set at 0.05. The results indicated that students taught using Analytic Problem-Solving Performance Test (APT) and Creative Problem-Solving Performance Test (CPT) had significantly higher in mathematics scores then those who was taught with conventional lecture method. It revealed that the teaching of Analytic and Creative Problem-Solving will enabled the students to retain more knowledge on mathematics, than those in the control group. Also the experimental groups taught mathematics using Analytic and Creative Problem-Solving demonstrated favorable and positive interest toward mathematics. Major recommendations from the study are that the teaching of analytic and creative problem-solving senior secondary school should be conducted in a manner that students will effectively understand and learn the approach taught. It should respect the views and ideas of the students since students‟ participation plays greater role in learners‟ performance The fact that higher mean was recorded in students‟ performance through the use of Analytic and Creative problem-solving, calls for teachers to acquaint themselves with the characteristics of this teaching method with a view to enhancing students’ performance and outcomes in learning. This could be done through seminars, conferences and workshops to be organized by State government and professional bodies.
In today’s technology-driven society, greater demands have been placed on individuals to interpret and use mathematics to make sense of information and complex situations. Rising learners ―performances/achievement in mathematics has become a matter of increased focus in recent years. Improving the quality of teaching mathematics may likely raise students‟ achievement in mathematics. Current technology and scientific advancement being experienced worldwide requires that Nigerian learners must be taught to go beyond low level comprehension and mere memorization of facts and formula, if they are to become problem solvers of the future. Trainee teachers therefore should be adequately equipped during initial teachers training to be able to develop in their pupils or learners higher-level thinking skills, especially in mathematics.
Mathematics is the backbone of all scientific/technological investigations and all activities of human developments. It is the only language and culture common to all studies (Golfing, 2005; Musa, 2006). Mathematical knowledge has much to offer in solving problems of mankind in everyday living. All professionals, according to Musa (2006) use mathematics in one-way or the other. Examples include: the driver on the steering uses basic knowledge of numeracy in changing gears; the cook in the kitchen uses the concept of measurement in preparing food and soup to know the quantity of what is required for each; the trader in the market tries to know the profit and loss made. Such trader must have knowledge of basic arithmetic. The farmer uses mathematical knowledge for farm mechanization for optimization of output and minimization of cost production where the concept of production, economic differentiation and integration of variables are greatly
utilized. It is in recognition of this that our curriculum planners include mathematics as one of the major and compulsory subjects in the school (F.M.E 2006). Mathematics is the body of knowledge centered on such concepts as quantity, structure and space as well as the academic discipline that studies them. Benjamin (2007) describes mathematics as the science of pattern and relationship which can be expressed in symbols. It embraces many important ideas about number and space which involve problem- solving activities and a very powerful way of communication.
Since the introduction of mathematics in post-primary schools in Nigeria, Nigerian educators and the general public have made criticisms on the poor performance of students in mathematics (Obioma (1985), Adegboye, 1998). According to Ukeje (1997), the poor and alarming state of mathematics education in Nigeria’s Secondary School System needs no documentation. The mass failure and consistent poor performance of students in mathematics shown over decades now casts doubts on the country’s high attainment in the science and technology. Silby (2002) and Bature (2005) submit that among the factors responsible for the deteriorating performance of the students in mathematics at secondary school level are traceable to poor quality of teaching. Higher level mathematics requires all students to be proficient problem solvers, but as stated previously students struggle with mathematical problem solving. Based on this conceptualization of solving word problems, the mathematical equations are sometimes hidden within multifarious, complex word usage. Sometimes the numerals and numeric operations are difficult to identify due to unforeseen or unique language structures, especially in the most advanced word problems. This results in high levels of challenge for many students in the area of mathematics. Harbor, (2002) has attributed poor using teaching approaches in classroom by teachers as one of the root course of the undesirable poor interest and performances in mathematics. (Kurumeh, Jimin & Mohammed 2010) which are capable of alleviating poor performance of students in the subject. Yet, mathematics teachers are failing to use these approaches either due to logistic or lack of the provision of essentials needed for teaching. Available records have shown that researchers have discovered a series of teaching approaches like team teaching (Achor, Imo, & Jimin, 2011).
Problem-Solving historically, this notion was first put forth in (Kohler, 1925). However, Polya is often credited with the use of novelty as a component of his definition. For example, Polya (1945 & 1962) described mathematical problem solving approach as finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown. Teachers providing just enough information to establish background/intent of the problem, and learners clarifying, interpreting, and attempting to construct one or more solution processes (Cobb, Wood, Yackel, Nicholls, Wheatley, Trigatti, & Perlwitz, 1991). Many writers have attempted to clarify what is meant by a problem-solving approach to teaching mathematics as the emphasis has shifted from teaching problem solving to teaching through problem solving (Lester, Masingila, Mau, Lambdin, dos Santos & Raymond, 1994). According to Lester et al. (1994), teaching mathematics topics through a problem-solving approach is characterized by the teacher ―helping learners construct a deeper understanding of mathematical ideas and processes by engaging them in doing mathematics: creating, conjecturing, exploring, testing, and verifying‖ Specific characteristics of a problem-solving approach include: Interactions between learners/learners and teachers/ learners (Van Zoest, Jones, & Thornton, 1994). Mathematical dialogue and consensus between learners (Van Zoest et al., 1994). Teachers guiding, coaching, asking insightful questions and sharing in the process of solving problems (Lester et al., 1994). Teacher knowing when it is appropriate to intervene, and when to step back and let the pupils (learners) make their own way (Lester et al., 1994). This list of characteristics on teaching mathematics through a problem-solving approach involves the learner actively learning mathematics by doing, with teacher passively playing the supportive role of teaching by assisting the learner to construct his/her new mathematical knowledge and understanding. It also involves learners learning in cooperative and collaborative small groups. This type of learning supports constructivism and social-constructivism knowing and learning theories.
A problem-solving approach (a learner-centered approach) involves teaching mathematics topics through inquiry-oriented environments that are characterized by the teacher ―helping learners construct a deeper understanding of mathematical ideas and processes by engaging them in doing mathematics: creating, conjecturing, exploring, testing, and verifying‖ (Lester et al., 1994,). A problem-solving approach can be used to encourage learners to make generalizations about rules and concepts, a process that is central to mathematics (Evan & Lappin, 1994). It also shows an engagement in learning that may lead to the development of higher-order cognitive skills that are rarely developed by learners in more direct/conventional instruction, drill-and-practice classroom activities. A problem-solving approach to teaching mathematics defines the role of the teacher as a facilitator of learning rather than a transmitter of knowledge and the learner, as a manager and director of their own learning. Successful problem solving requires knowledge of mathematical content, knowledge of problem-solving approach, effective self-monitoring, and a productive disposition to pose and solve problems. Teaching problem solving requires even more of teachers, since they must be able to foster such knowledge and attitudes in their students. Looking more closely at problem solving, the conceptual definition of problem solving in mathematics is complex. Possibly the most significant reason for this is because no formal conceptual definition has ever been agreed upon by experts in the field of mathematics education. Furthermore, Bay (2000) explains teaching via problem solving as a method by which mathematics teachers may provide more meaningful instruction. Advancing his argument, Bay (2000) further explains that Teaching via problem solving (teaching through a problem-solving) is teaching mathematics content in a problem-solving environment. Lester and Kehle (2003) suggested that reasoning and/or higher order thinking must occur during mathematical problem solving. Grugnetti and Jaquuet (2005) even suggested that a common definition of mathematical problem solving could not be provided. One term that is often associated with mathematical problem solving is novelty. In the process of solving problems, the students interact with one another and with instructional materials and eventually construct knowledge and acquire the processes of science.
Also Selvarantham (1983), Nott (1987) and Eze, (2001) observed that a systematic approach to problem-solving encourages good learning habits, contributes to clarity in thinking, logical reasoning and promotes intellectual development. Problem-solving teaching is an instructional approach in which problems of scientific nature or problem related to the real world are carefully formulated and presented to students (Bichi, 2002). Bichi (2002) also observed that as students engage in solving problems, they acquire skills and confidence which aid their capacity to tackle future problem. Therefore, as dexterity in solving problem increases, they become more self-confident to tackle novel problems and this is expected to increase their self-esteem/self-efficacy. Thus, it seems students’ self-efficacy may increase as
they are exposed to problem-solving approach. Danjuma (2005) observed that problem-solving activities encourages the development of problem-solving skills such as logical reasoning ability, In general, when researchers use the term ―problem solving approach ‟ in mathematics they are referring to mathematical tasks that have the potential to provide intellectual challenges that can enhance learners‟ mathematical development and hence improve their performance in mathematics. Such tasks also promote learners‟ conceptual understanding, foster their ability to reason and communicate mathematically, capture their interests and curiosity (Van de Walle, 2007). Manipulative skills, self-confidence (self-efficacy) and creativity in learners which may enhance progressive performance.
Analytic problem-solving approach is the use of an appropriate process to break a problem down into the smaller pieces necessary to solve it, each piece becomes a smaller and easier problem to solve Morgan (1995), and also an Analytic thinker has the ability to get into the detail of a problem, evaluate all components and perspectives to understand it and determine what’s missing. Analytic thinker asks questions to fill in any gaps they see in order to foresee next steps. They have confidence in their ability and make assumptions and decision because of their constructive fact finding process. Although their assumption is credible and decision well supported, they may not move quickly enough to a solution if they do not have all the facts. Because their fact-finding process takes time, they not opinions unless specifically asked. Morgan (1995) observed,Problem solving is puzzled solving. Each smaller problem is a smaller piece of the puzzle to find and solve. Putting the pieces of the puzzle together involves understanding the relevant parts of the system. Once all the key pieces are found and understood, the puzzle as a whole “snaps” together, sometimes in a final flash of insight. The key word in the above definition is “appropriate.” If your problem solving process doesn’t fit the problem at hand, you can execute the process to the highest quality possible and still not solve the problem. This is the reason most people fail to solve difficult problems. They’re using an inappropriate approach without realizing it. The process doesn’t fit the problem. You can look high and low, and under every bush in plain sight, but unless you’re using an appropriate analytic approach you will never find enough pieces of the puzzle to solve a difficult problem. Even the most brilliant and heroic effort will lead to naught if you’re using a problem solving process that doesn’t fit the problem. Lack of a process that fit the problem is why the alchemists failed to turn lead into gold. It’s also why so many people and organizations, as well as entire social movements, are failing to turn opportunities into successes.
Creative Problem Solving (or CPS) is a broadly applicable process providing an organizing framework for specific creative and critical thinking techniques to help design and develop new and useful outcomes for meaningful and important challenges, concerns and opportunities (Isaksen, Dorval & Treffinger, 1994). CPS is an operational model for a particular kind of problem solving where creativity is applicable for the task at hand. Creative problem solver has the ability to envision several outcomes, make assumptions as to what needs to be done to achieve an outcome and is willing to take risks because they have confidence in their own judgment. Creative thinkers start from scratch and are not limited by steps or processes; instead they create unique path and new solutions. The limitation of creative problem solving is often that there is no limit to the creative process. If a problem has a deadline or budget constraint, creative thinkers may struggle because they have difficult focusing and can lose sight of more obvious solutions (Dorval, 1994).
The first major component in this operational model is called Understanding the Problem which includes a systematic effort to define, construct, or formulate a problem. Although many researchers have focused on problem finding as a process separate from problem solving, such a distinction may be arbitrary especially within the context of a flexible or descriptive approach. It is not necessarily the ―first‖ step in CPS, nor is it necessarily undertaken by all people in every CPS session. Rather than prescribing an essential problem finding process, Understanding the Problem involves active construction by the individual or group through analyzing the task at hand (including outcomes, people, context, and methodological options) to determine whether and when deliberate problem-structuring efforts are needed. The Understanding the Problem component of CPS includes the three stages of Mess-Finding, Data-Finding, and Problem-Finding. A mess is a broad statement of a goal or direction that can be constructed as broad, brief, and beneficial. The Mess generally describes the basic area of need or challenge on which the problem solver’s efforts will be focused, remaining broad enough to allow many perspectives to emerge as one (or a group) looks more closely at the situation. Data-Finding includes the generating and answering of questions to bring out key data (information, impressions, observations, feelings, etc.) to help the problem solver(s) focus more clearly on the most challenging aspects and concerns of the situation. Problem-Finding includes the seeking of a specified or targeted question (Problem statement) on which to focus subsequent effort. Effectively worded problem statements invite an open or wide-ranging search for many, varied and novel options. They are stated concisely and are free from specific limiting criteria.
1.2 Statement of the Research Problem
This study was conceived to determine if exposure to analytic and creative problem-solving approach could affect student’s performance/ interest or not. According to Ukeje (1997), the mass failure and consistent poor performance of students in mathematics shown over decades now casts doubts on the country’s high attainment in the science and technology. Since the introduction of mathematics in post-primary schools in Nigeria, Nigerian educators and the general public have made criticisms on the poor achievement of students in mathematics (Adegboye, 1998); Silby (2000) and Bature (2005) submit that among the factors responsible for the deteriorating performance of the students in mathematics at secondary school level are traceable to poor quality of teaching. Based on this conceptualization of solving word problems, the mathematical equations are sometimes hidden within multifarious, complex word usage. Especially in the most advanced word problems. This results in high levels of challenge for many students.
Given the fast pace of technological development in our global education economy, business and industry needs Analytic and Creative Problem Solvers to remain competitive. Public education is being asked to play an important role in preparing young people for the challenges of the work place by providing its students with analytic and creative problem solving skills. Both potential skills are developing to engage students in a series of mini lessons on analytic and creative approaches over a period of several weeks. However, the effectiveness of such an approach has not been established. Therefore, the purpose of this study was to determine Analytic and Creative responses would improve if students were exposed to Analytic and Creative Problem-Solvingon daily basis. This is expected as skills like manipulation, procedure, self-confidence, evaluation, communication and logical reasoning ability among others are related to Analytic and Creative skills. Thus, it seems that exposure to problem-solving could affect the Analytic and Creative subsequent achievement in Genetics. Since poor academic achievement in genetic according to Okebukola (2002), Ibraheem (2004) have been attributed to student’s poor manipulative skills, insufficient instructional materials, poor method of teaching employed, mathematical aspect and nature of the genetic concepts. As dexterity in problem-solving builds self-confidence, it may be an indication that exposure to problem-solving could affect analytic and creative learners. Researchers such as Danjuma (2005) have linked Analytic and Creative Problem-Solving has made achievement in science.
1.3 Objectives of the Study
The purpose of this study is to examine the effectiveness of explicit instruction in the Analytic and CreativeProblem Solving on Interest and Performance in Mathematics among Senior Secondary School Students. The study objectives are:
- To determine the difference between academic performances of students taught using Analytic and Creative Problem-Solving.
- To determine the effects of academic performance of students taught using Analytic
Problem-Solving and those taught using convention lecture method.
- To investigate whether the performance of students taught mathematics using Creative
Problem-Solving was better than those taught using convention lecture method.
- To determine the performance of male and female students taught using Analytic and
- To determine whether student’s interest before and after taught mathematics using Analytic and Creative Problem-Solving and those taught using conventional lecture method.
1.4 Research Questions:
1 What are the differences between the performances of students taught using Analytic and
- What are the effect of academic performance of students taught mathematics using Analytic Problem-Solving and those taught using lecture method?
- To what extent does the performance of the students taught mathematics using Creative Problem-Solving and those taught using lecture method?
- Are there difference between academic performances of male and female students taught using Analytic and Creative Problem-Solving?
- To what extent student’s response on interest determined before and after taught mathematics using Analytic and Creative Problem-Solving and those taught using conventional lecture method?
1.5 Null Hypotheses:
H01 There is no significant difference between performance of students taught using Analytic and Creative Problem-Solving.
H02 There is no significant difference between performance of students taught mathematics using Analytic Problem-Solving and those using taught using lecture method..
H03 There is no significant difference between the performance of students taught mathematics using Creative Problem-Solving and those taught using lecture method.
H04 There is no significant difference between the performance of male and female students taught using Analytic and Creative Problem-Solving.
H05 There is no significant difference between student’s responses on interest, before and after teaching mathematics using (1) Analytic method(2) Creative Problem-Solving and (3) conventional lecture method.
1.6 Basic Assumption
The following were the basic assumptions for the study. In carrying out this study it was assumed that;
¡. The students used for the study have covered the Senior Secondary (SS2), Mathematics ` Curriculum that were familiar with four (4) topics in mathematics.
1.7 Significance of the Study
Mathematics is useful for day to day activities particularly in our homes and industries and also an important tool for science and technology development; hence the result is significant for the following reasons.
The study will help authors to advocate appropriate methods of teaching mathematics concept in their textbooks in subsequent editions. The findings will help in improving further education, since more students will be able to read course of their choices. The finding will be useful for further researchers in Analytic and Creative Problem-Solving.
Performance and interest as well as other theories of learning. The findings could be used to clarify, support or substantiate the existing learning theories expressed by other psychologist. It could contribute to the improvement of Mathematics teaching and learning at all levels of secondary schools. It could foster new approaches in curriculum and text development. It could help in actively involving the participation of students. Also, Mathematics being the backbone of science and technology is a prerequisite for almost all engineering and other technological courses. It is therefore anticipated that the findings of this study would be valuable to various bodies/stakeholder that are likely to benefit from the outcome/result of the study, and those who are engaged in scientific and technological policy formulation, implementation and development in the country like: teachers, students, universities and colleges, National educational organization and curriculum developers. In addition, the study will help teachers in the adaption of appropriate approach of teaching mathematics concepts Analytic and Creative problem-solving problem skills. Teachers responsible for the teaching of Mathematics to secondary school students might utilize the finding in the secondary school classroom by:
- Helping students to have conception shift in favor of mathematics valid concept.
- Taking into consideration, students prior knowledge and
- Developing inexpensive modules that would enhance teaching, learning and assessing understanding of mathematics concept. Furthermore, it is hoped that the study would encourage students to be actively involved in the construction of knowledge and to take charge of their own learning. Active participation of student might help them to develop self-confidence and positive interest toward Mathematics.
Additionally, institutions of higher learning where Mathematics teachers are trained would need to /incorporate the approaches to teaching learning. This would enable them produce more efficient teachers who would help student construct knowledge on their own. Bodies like
Mathematical Association of Nigeria (MAN) Statistics Association of Nigeria (SAN), National Education Research and Development Council (NERDC) that carry out researches discuss and disseminate research findings, might wish to consider the result of the research with a view to using the Analytic and Creative problem-solving to promote mathematics instruction in schools. Again, the findings of the study would be useful to mathematics textbooks publishers as it will assist them in selecting materials and activity questions base exercises to be incorporated in the text that would promote academic performance and change interest positively among students. Finally, poor attitude acquired at the foundation level could continue to hurt the students at every level of education. This trend if left to continue, will in no small measure affect adversely the growing needs to have trained scientist, technicians, economist and people in other fields of profession, since all depends in one way or the other upon Mathematics. The findings of this study is hoped to change negative interest towards mathematics concept among secondary school students.
1.8 Scope/Delimitation of the Study
This study examined the effect of Analytic and Creative Problem-Solving on Interest and
Performance in Mathematics among Secondary School Students, Sabon-Gari Local Govt
Kaduna State. Nigeria. It covered selected public Senior Secondary Schools in Sabon-Gari Local Government (SS2) that are under Sabon-Gari Educational Zone. The SS2 were used because they are the most appropriated sets. SS1 were newly admitted, while SS3 students were getting ready for their Senior Secondary Certificate Examination (SSCE). The study considers the effect of Analytic and Creative Problem-Solving approach on Interest and Performance in Mathematics among Secondary School Students. The topics taught were from syllabus of SS2 are as follows.
Also the concepts taught in mathematics during this study included Quadratic equation,
Simultaneous equation, Sets and Surds at the confine of the SS11 curriculum. These Concepts were chosen because knowledge of them establishes the foundational background leading to mathematics among Senior Secondary Schools. The concept is also part of the SS11 curriculum. These topics were selected for the purpose of this research because they involved concepts that required active participation by the students and teachers at SS11 level during the teaching and learning process, with the assumption that they may sound a bit abstract to students at the Senior Secondary School level. In addition, the Analytic and Creative problem-solving performance test was the instrument used consisting of 20 items with option A –D. Also the mathematics concept statement questionnaire was used to find out interest of student towards mathematics before and after the treatment.
EFFECTS OF LOGICAL AND CREATIVE PROBLEM-SOLVING ON ATTENTIVENESS AND PERFORMANCE IN MATHEMATICS AMONG SENIOR SECONDARY SCHOOL STUDENTS, SABON-GARI KADUNA STATE, NIGERIA.