ABSTRACT
The present study investigated the effect of instruction in meta-cognitive skills on mathematic self-efficacy belief, interest and achievement of low-achieving mathematics students in Kogi State, Nigeria. Three research questions and three hypotheses were generated to guide the study. The design of the study was a quasi-experimental non-randomized pretest-posttest-control-group design, involving one experimental group and one control group. The sample consisted of 129 SSII low-achieving mathematics students in four senior secondary schools. The instruments used for the study were a researcher- made Mathematics Achievement Test, Mathematics Self-efficacy Scale and Mathematics Interest Inventory which were validated by experts and used for data collection. Mean, standard deviation, and Analysis of Covariance (ANCOVA) were used to analyze the data collected. Major findings of the study show that (I) Instructing students in metacognitive skills significantly enhanced their self efficacy belief, interest and achievement in mathematics, (II) The gender of the students was not a significant factor on their mathematics achievement, self efficacy belief and interest, (III) There is no significant interaction effect of gender and instruction in metacognitive skills on the self –efficacy belief, interest and achievement of low – achieving students in mathematics. Based on these findings, conclusions were drawn and the educational implications were extensively discussed. Among the recommendations made were that teachers should develop in students the skills in applying metacognitive strategy in solving mathematical problems and that instruction in metacognitive skills should be conducted involving male and female students since both gender benefits from such.
CHAPTER ONE
INTRODUCTION
Background to the Study
Higher order cognitive skills, such as ability to elaborate, synthesize, analyzed, apply, and evaluate specific learning information are very necessary for one to achieve academic success and adjustment in life. With the increasing demand of an ever changing and challenging problem-ridden world, the least any learner ought acquire from school is the ability to utilize an efficient thinking and problem solving strategy to face the complex situation and challenges of everyday life (Onu,2005). Higher order cognitive skills help learners to think more effectively, manage conflict by themselves, engage in practical thought, experiment, and question their own basic assumptions (Brown, 1997).
Mathematics is a core subject in the schools. It has been described as the key that unlocks the mystery of the subjects that shape and enhance logical thinking with its calculative inference and deductions (Exam Ethics Project, 2002). Ikeriondu (2006), maintained that mathematics offers the experience needed to develop ways of dealing with problems, not only at school but in all aspects of life. Generally, mathematics is regardedas the key to success in the study of other sciences and science related disciplines (Iwuoha, 1986).
Most universities in Nigeria insist on at least a pass in mathematics for any course of study while a credit level pass is compulsory for any science related course (JAMB 2006, 2007, 2008). However, it has been observed to be a subject that scares many candidates. The truth is that mathematics is a subject for all because virtually everybody, be they traders or sportsmen or carpenters, tailors or even farmers, make use of aspects of mathematics in their daily activities (Ikeriondu, 2006). The study of mathematics permeates all fields of human endeavour and has found a place in sciences, architecture, engineering, industries, aeronautic /space science, navigation, survey, nuclear energy to mention but few (Osuagwu, Anemelu,& Onyezili, 2000).
The challenge for schools is how to relate mathematics concepts and theories to practical activities of daily life (Peter, 2000). Okeke, and Ochuba (1989), Nwoke (1995) and Nateinyin (1995) observed that, the teachers’ teaching method and mastery of the subject is the key determinant of students’ achievement. In spite of teachers’ efforts to improve students’ mathematics achievement in Nigeria especially in Kogi state, their learning outcomes have continued to be very low. Evidence from the secondary school continuous assessment records in Kogi state has shown a consistent failure rate in Mathematics for some years. (MOE Report, 2008) West Africa Examination Council (WAEC) Chief Examiner’s Report shows evidence of poor mathematics achievement. For instance, in 2006, only 177, 800, candidates representing 15% of the 1, 184,384, that sat for the examination obtained credits in five subjects including, Mathematics. Similarly in 2007, only a 25% of the total population of 1, 275,330 candidates that sat for May/June WAEC passed with credit in mathematics. According to the results announced by the West African Examination Council (WAEC Chief Examiner Report, 2008), a total of 325,754 candidates representing 25.54% of the population obtained credit and above in English language, Mathematics and three other subjects. Also, 37,635 other candidates (2.95%) of the total figure obtained five credits and above in 5 subjects, but without English and Mathematics. Of that number, the council said 165, 994, (13.02%) were male candidates while 159,760 (12.52%) were female candidates (WAEC Chief Exams Report 2006, 2007 and 2008). These are indications of low mathematics achievement, which may be due to poor teaching or lack of interest on the part of the candidates or the perceived phobia for the subject (Exams Ethics Project, 2002).
The low-achieving mathematics students therefore, need special intervention if they must record success in dealing with mathematical problems. Low mathematics achievers are those students whose achievements are consistently very low and who, in spite of efforts to cope, may be quite slow, confused and lack confidence in themselves (Okebukola 1994). They are those whose achievements are consistently below average, and who may have numerous aversions associated with solving arithmetic related problems, (Montague, 1998). Such problems could be attributed to a number of environmental factors such as peer group influence, relationship with teachers, cultural factors and school factors (Obioma and Ohuche 1985, Okeke and Ochuba 1989).
Recent studies in Nigeria show that most learners do not have effective strategy that could facilitate learning, including the learning of mathematics (Eze, 2003). Instead, they adopt rote learning methods which have been found to be ineffective for learning complex task (Eze, 2007). Many studies have been carried out on the teaching strategies which were to be effective. They include the use of advance organizers, concept mapping, and group activity strategies (Okebukola, 1994; and Idowu, 2002). These methods seem to be inadequate for teaching Mathematics. Mathematics is a subject requiring problem solving and such strategies as metacognitive learning strategy that will transfer the responsibility of learning by developing in the learners self-regulating skills has been suggested to facilitate mathematics achievement (Schoenfeld, 2008; Flavell, 1987).
Rajagopal (2008) defined metacognition as a form of cognition, which involved active control of cognitive process. To Sandtrock (2001), metacognition could be seen as cognition about cognition or knowing about knowing. According to Kuhn (1995) metacognition refers to learners’ automatic awareness of their own knowledge and their ability to understand, control and manipulate their cognitive processes. Flavell (1979) described metacognition as one’s knowledge concerning one’s own cognitive processes and requires active monitoring and consequent regulation of the processes. These definitions emphasize the executive role of metacognition in overseeing and regulating cognitive process. Executive control processes are those processes responsible for the growth directed processing of information, the selection of actions, and the implementation and monitoring of task and cognitive processes (Flavell, 1979; 1985; 1987; 1999).
Metacognitive skills consist of those skills required for deliberate planning, monitoring, regulation and evaluation of cognitive process and its outcome (Eze, 2007). Metacognitive skills enable the learners to become aware, understand, monitor, control and manipulate their learning processes. These suggest that learners with appropriate metacognitive skills are able to organize, monitor and direct their own learning process (Eze, 2007). As students become more skilled in using metacognitive skills, they gain confidence and become more independent as learners. Independent approach leads students to assume ownership of the learning processes as they realize they can pursue their own intellectual needs and discover a lot of information at their pace. The task of the educator then is to acknowledge, cultivate, exploit and enhance the metacognitive capability of all learners (Brown, 2008; Alexandra, Fabricius, Fleming, Zwahr and Brown, 2003).
The use of metacognitive skills has been suggested to be essential for learning. The skills ensure that the learner will be able to construct meaning from information. To accomplish this, the learners must be able to think about their own thought processes, identify the learning strategies that work best for them and consciously manage them as they learn (Flavell, 1987). Good examples of metacognitive skills in mathematics include planning, checking, testing, reversing and evaluation (Ellis, 1999).
It has been suggested that students with good metacognitive training demonstrate good academic achievement compared to others who lack the skills. Students without metacognitive skills may benefit from metacognitive instruction to improve their metacognition and academic achievement (Everson and Tobias, 1998).
Metacogntive skills acquisition has also been suggested as an important means for enhancing learner’s self-efficacy (Pajares and Urdan 2006). This is because when the skills have been acquired through instructions, learners become more focused to approach learning tasks in a systematic manner. The acquisition of skills necessary for tackling problem is also believed to raise the learner’s self-efficacy for task accomplishment (Siegler, 1998). According to Santrock (2001), the mastery of metacognitive skills will develop student feelings of competency and arouse his/her attention in learning mathematics and other science related subjects in school.
The concept of self-efficacy is the focal point of Albert Banduras social cognitive theory. He defined self-efficacy as the judgment of personal capacity to perform a specific and prospective task (Bandura, 1997). Self –efficacy is a person’s judgment about being able to perform a particular activity. It is a student’s “I can’ or ‘I can not’ belief. Unlike self-esteem, which, reflects how students feel about their worth or value, self-efficacy shows how confident a student is about performing specific task (Joanne and Shui-fong, 2008). For example, high self-efficacy in mathematics does not necessary translate to high self-efficacy in spelling. Self-efficacy is specific to the task being attempted.
Perceived mathematics self-efficacy is concerned with students’ belief in their capabilities to exercise control over their own mathematical problem solving skills. Belief in personal self-efficacy affects choice of strategies, level of monitoring, quality of functioning, resilience to adversity and vulnerability to stress and depression (Bandura, 2000; Schunk, 1990; White, 1990). A growing body of research reveals that there is a positive, significant relationship between students’ self-efficacy beliefs and their academic achievement. For instance, people with low- self-efficacy towards mathematics are more likely to avoid it while those with high self-efficacy are not only more likely to attempt the task but also work harder and persist longer in the face of difficulties (Wang, 2008). Self-efficacy influences what activities students select; how much effort they put forth; how persistent they will be in pursuing their goals in the face of difficulties. Students with low- self-efficacy may not achieve at a level that is commensurate with their abilities. They may not have the skills to do well and may not therefore, try (Bandura 2001; Omroid, 2006). They may just lack interest in the subject.
Elliot, Kratochwill, Littlefield and Travers (2000) defined the term interest, as an enduring characteristic expressed by a relationship between a person and a particular activity or object. Ngwoke (2005) explained interest, as something with which one identifies one’s personal well-being. In this sense interest is a source of motivation. Deci and Ryan (1991) argued that since intrinsically motivated behaviour is a behaviour an individual undertakes out of interest, then clarifying the importance of interest would add to educator’s understanding of the impact of intrinsic motivation in learning.
According to Hurlock as cited in Ngwoke (2005), interests drive people to do what they are free to choose. When people see that something will benefit them, they become interested in it. Every interest satisfies a need. In activities like counting, subtraction, addition and multiplication in mathematics, interest leads one to know and learn more from the task. Interest adds enjoyment and makes the performance of activity or task more economical in terms of demand on limited cognitive resources. The interest students show in an activity or in an area of knowledge predicts how much they will attend to it (Papalia, Old and Feldman, 2002). Achievement, self-efficacy and interest are cognitive variables that may vary along gender attributes.
Gender as a psychological construct has been used to describe maleness and femaleness. Mboto and Bassey (2004) looked at gender as a term that describes the behaviour and attitude expected of an individual on the basis of being born either male or female. Evidence has shown that studies on gender as a factor in mathematics achievement have focused mainly on such variable as gender stereotype in training and assessment, and that very few studies have investigated how gender interacts with skills needed for mathematics achievement (Omirin, 2005). Betiku (2002) in a study reported that gender differences in the achievements of students (boys and girls) in Science, Technology and Mathematics (STM) show a line of difference in favour of boys. That is to say boys perform better in mathematics than girls while some other research studies show evidence of girls’ superiority over boys in mathematics (David, Lay, and Kay 1987). These findings show inconsistencies in the research findings on gender differences in mathematics achievement. This study may therefore, contribute significantly to the unresolved controversy on gender factor in mathematics achievement of the students.
In spite of various efforts by teachers, researchers, and governmental organizations to develop effective and efficient methods of teaching and learning mathematics in school in order to meet the science, technological and manpower needs of the nation (Nworgu, 1999), achievement in mathematics still fall below acceptable level as many students’ achievements are low despite the role mathematics plays in technological development. Low mathematics achievement relates to the issue of how Nigeria can position herself to achieve the scientific and technological requirement for survival in the 21st century. According to cognitive psychologists, efficient learners would actively self regulate their behaviour and pursue learning in an independent, active and deliberate manner (Zimmerman, 1990; Butter, and Winner, 1995; Flavell, 1985). They are effective in their management of the learning experiences (Schunk, and Zimmerman, 1994), motivated and become metacognitively active in the process of learning (Eze, 2007). Due to the high percentage of low achieving mathematics students in secondary schools in Kogi State (Ministry of Education Report, 2008), there is the need to determine the effect of instruction in metacognitive skills on mathematics self-efficacy belief, interest and achievement of low achieving students.
