Motivation in learning mathematics
In the last fifty years, researchers had curiosity with the effect of motivation. They studied students’ motivation and learned a great deal about the effect of motivational practices on school learning. It pointed to more simple aspects, such as achievement motivation, intrinsic motivation, and goal orientation as well as the effect of teacher practices which promote motivational beliefs. To be able to talk further about motivation in learning mathematics, it is essential to know what motivation actually means. Motivation is defined as an internal state that arouses, directs, and maintains behaviour (Woolfolk, 2008). But simply stated motivation is a reason of students’ thinking in a given situation. In Self-Determination Theory, motivation is distinguished between different types based on different reasons or goals – intrinsic and extrinsic motivation. Intrinsic motivation refers to doing something because it is certainly interesting or enjoyable. While extrinsic motivation refers to doing something because it leads to a separable outcome (Ryan &Deci, 2000). The examples of intrinsic motivation are personal interest in a satisfaction, subject, or pleasure in learning tasks. Whereas the examples of external motivation are awards, parent and teacher praise, and value.
Researchers found that although students have achievement, ability, and perceived competence which support the desire in learning mathematics, in fact intrinsic motivation comes to decrease developmentally (Lepper, Corpus, &Iyengar, 2005). This is one of motivational problem toward achievement, ability, and perceived competence of student learning. Also, researchers tend to internalize the activity’s initially external regulation in which people tend to take the regulation and integrate it with their sense of self (Ryan &Deci, 2000). It is likely that students must feel comfortable with mathematics, must be challenged to achieve, and must expect to succeed before the development of intrinsic motivation can begin. Therefore, this kind of problem has to be overcome, it is important to investigate role motivational practices on school learning. The question is whether students who have a good motivation can produce a good student achievement too? To answer this question, I will try to describe some researches which can help me to find the answer. First, I will describe the effect of motivational practices, then the second is whatstudents’ motivation affects, and the last is how motivation can be improved. As people tend to think that students who have a good motivation will lead into a good achievement too, this research aims to trace whether the opinion is true or not.
The effect of motivational practices
Motivational beliefs act as favourable contexts of learning and also refer to the students’ opinion of the efficiency or effectiveness of learning and teaching methods (Boekarts, 2002). Motivational beliefs refer to the opinions, judgments, and value which include objects, events, or subject-matter domain. For example, there is a student who cannot see what the possibly learn from doing homework while another student think that doing homework is a good activity to practice subject-matter in home.
Beliefs are likely inner control which can be divided into two parts, self-efficacy beliefs and outcome expectations. Self-efficacy beliefs are beliefs that hold student’s ability by themselves related to specific domain, such as “I believe I can do this type of mathematics problem.” Outcome expectations are beliefs about the achievement or failure in specific domain, such as “I have not answered this question before and I do not have any idea about it. I am certainly blank in my mind.”
The research has indicated that motivational beliefs are the result from direct learning experiences.There is shown from the need to take consideration subject-area specific characteristic, because of the differential role of each motivational factor.This role derived from the activation of strategies in different areas, especially in mathematics. Mathematics is still perceived as a “threatening” area; one that requires the effective application of deep cognitive strategies. This cognitive engagement presupposes the development of educational practices that lower negative thinking and feeling about evaluation foster the usefulness and instrumentality of mathematics as a subject area. Successful performance in language is a very effortful process in elementary school, and seems to rely more on confidence beliefs and the use of regulatory strategies (Metallidou&Vlachou, 2007). This issue means whether students conceptualize motivation differently in various content areas, such as mathematics self-efficacy involves confidence in one’s numeric skills.
Unfavourablemotivational beliefs impede learning
Unfavourablemotivational beliefs impede the learning process because they direct the learners’ attention away from the learning activity itself, another focus instead of the previous problem is student’s low ability. Although childrens’ understanding of causality changes because of age, their beliefs about the cause of their success and failure are very resistant to change. Students who state they will never be able to finish the task successfully is an alert that they no longer perceive a relation between their actions and a positive outcome. Helping student to re-construct the relation by creating learning situations where they can experience success and get a good achievement in class. However, it is not sufficient that they get the correct solution. They also need to understand why the plan solution was correct and what they can do to enhance their ability. It seems that the students’ attention have to be drawn explicitly to the relation between their actions and the outcome.
Students who have established unfavourable motivational beliefs are not interested in such process-oriented feedback (Boekarts, 2002). It looks like students do not care about the correct way, they only want to know whether the answer is correct or not. So, if it is happened, students have to be reminded and given the emphasis in the right process. Such process-oriented feedback gives them a feeling of progress and it will stimulate them gradually to reflect their achievement.
Favourablemotivational beliefs facilitate learning
On the contrary, students are interested in doing activities because they need to learn about the subject to achieve something they want – favourable motivational belief. Students who value the learning activity are less dependent on encouragement or reward. For example, a student who likes mathematics because he thinks mathematics is easy. Then, in the future, he wants to be a space engineer. Another example, a student who does not like mathematics but still struggles with it because he remembers his dad’s words that mathematics is important. An activity is generally considered to be intrinsically motivating if external reward is not necessary for students to initiate and continue that activity. Favourable motivational beliefs are attached to the activity itself. Students who are intrinsically motivated will report that they do not have to invest a big effort.
However, not all students are intrinsically motivated because students are less motivated to learn. It is important to be aware of classroom situations and how the learning process is to facilitate students to interact with or even inhibit the motivation of students (Boekarts, 2002). To overcome this problem, students have to be addressed to find the relevant and interesting thing for themselves. For instance, finding out what their current interests and future career goals are. I think these ideas will catch students’ attention and curiosity enhancing performance and achievement of students in learning process also. Further, it allows them to adapt learning activities to their own psychological need which gives them a sense of freedom and the right to self-determination.
Student beliefs about goal orientation
Students who are ego-oriented learn less than students who are mastery-oriented (Boekarts, 2002). The way students orient themselves to learn is a strong indicator to show their achievement and work performance. Ego-oriented students are typically involved in learning tasks in order to demonstrate success (ego-oriented approach) or to hide the failure (to avoid ego-orientation) using learning strategies that are less effective than mastery-oriented students. For mastery-oriented, students usually learn they want to master new skills. This means that the process of mastery-oriented students’ motivation is different from ego-oriented students.
Such problems among students should be solved immediately, because they must know not only an important result but also the strategy of the solution. They must believe in this statement ‘process is more important than the correct result’. In the means of giving feedback in a relation to seek a right solution, encourages students to exchange ideas to other students about the strategies they used and allow them to learn from their mistakes. This is a very difficult job because of ego-oriented students become upset when they have to reflect on their mistakes. But the problem could be solved with some comments from teachers while guiding their cooperation so that progress and their efforts will be visible. Mastery-orientation will be developed when students have a pride in finding the solution process and have found the error.
Goal setting and appraisal
In recent years, achievement goal setting and also appraisal have become a dominant perspective for understanding differences in the level and quality of students’ engagement in school (Kaplan, Gheen, &Midgley, 2002). This achievement goal seems to suggest that the emphasis on mastery and performance goals in the classroom is related to students’ patterns of learning and behavior. Mastery goals refer to a focus on learning improvement and mastering skills, whereas performance goals refer to a focus on social comparison and demonstration of competence. These two goals come from the effect of motivational practices.
What affects students’ motivation?
Several things affect students’ motivation, such as student beliefs about learning, teacher and students’ interaction, and curriculum content stood up as significant predictors of motivation to learn. The explanation of all students’ motivation affects are described below.
Student beliefs about learning
Learning mathematics can develop students’ ability to think in quantitative terms but also can improve skills such as analysis and problem solving. People believe that mathematics is a subject that is difficult and unattractive. But, through technical assistance and some ways with innovative approaches in teaching mathematics, I believe that mathematics can have an attraction and sharpen students’ creativity as well. To be able to talk to students how important mathematics is having understanding of students’ beliefs in learning mathematics so as to find ways to improve students’ performance and achievement in mathematics (Tahir, 2009). He stated that there were significant differences between students’ beliefs based on institutions and mathematics grade and there were no significant differences among beliefs based on gender, secondary education, and major. The data in this research was taken from three different higher institutions in the East Coast of Malaysia. Students were randomly selected using the convenience sampling method. A total of 376 students (100 male and 276 female) participated. They answered a questionnaire in which contains of 17 statements pertaining to students’ beliefs towards learning mathematics. These items were measured using a 5-point, Likert-scale type format with the following anchors: 1 = strongly agree, 2 = agree, 3 = neutral, 4 = disagree, and 5 =strongly disagree.
The results showed that a significant relationship means the difference between the beliefs of students based on institutions and mathematics classes and there was no significant difference meaning among students beliefs based on gender, secondary education, and major education. This would mean that students who come from the same institutions and the same math class also do different things in their beliefs in mathematics. This conclude that student appreciate the subject and hold positive beliefs in learning mathematics (Tahir, 2009).
Teacher and students’ interaction
Teacher support is one of the factors effecting motivation and student achievement. The discovery that the views of teachers in teacher-child relationship characterized by safety and the possibility of dependence, such as parent-child relationship. Relationship characterized by dependency seems to be one in which the child shows a search aid for teachers. On the other hand, security in teacher-child relationship is most clearly assessed with items that reflect the confidence and sense of student understanding. Security was described by behavioural indications of open communication and a sense that children’s needs for support and help to feel fulfilled (Pianta&Nimetz, 1991). So, teachers have a direct effect on students’ motivation to learn (Khamis, Dukmak, &Elhoweris, 2008). It indicates that almost all activities of the teachers which are done in the classroom have effects (negative effect or positive effect) on students’ motivation to learn mathematics. For instance, teaching style and patterns of interaction are two kinds of teacher activities that have to be structured in well-organised course.
Students’ perceptions of teacher caring correspond the cooperation (helping/friendly and understanding), whereas non-caring characteristics are included in opposition (dissatisfied and admonishing). For example, a caring teacher ‘‘makes class interesting’’, ‘‘pays attention’’, ‘‘listens’’, ‘‘trusts me’’, ‘‘acts as a friend’’, and ‘‘asks if I need help’’. Uncaring teacher examples include: ‘‘screams’’, ‘‘yells’’, ‘‘embarrasses’’, ‘‘insults’’, and ‘‘doesn’t try to help you’’ (Lapointe, Legault, &Batiste, 2005).
From several descriptions of the research above, the role of perceptions of teacher behaviour in students’ motivational beliefs play a significant role in average and talented young adolescents’ self-efficacy, intrinsic value, and test anxiety in learning mathematics. It is well documented that these motivational variables are important factors in student achievement.
Content of the curriculum to motivate students
Social-constructivist theory confirms the importance of community and interactive power on motivation, in which turn into effective teaching links in ways to promote involvement and delivery discussions, especially in ways that encourage active participation and equal. This means that the pedagogical approach also motivates students to be considered important from the perspective of responding to diverse student learning styles and preferences. The cases of various strategies motivate and engage students, for example, the use of assessment and feedback, including the provision of scaffold student choice and control in assessment practices on various topics, methods, and criteria. Behaviour provided student-centered approach which provokes a high level investigation and analysis, and approaches that stimulate students to use original content and imaginative learning activities.
There is a research using a six-item Likert-type scale that investigates the degree to which students like or dislike the school work and courses and task difficulty, and whether the subject-matter is interesting or boring (Khamis, Dukmak, &Elhoweris, 2008).They said that moderate positive correlations were found in curriculum content. The impact of curriculum content was evidenced on students’ motivation to learn. Students who reported that they like the subject-matter, school work course, and task were more likely to report higher level of motivation to learn toward student achievement.
How to improve students’ motivation
It is difficult to improve students’ motivation, but it is not possible to do it. Several researchers showed this by describing some ways to improve motivation of students.
The assessment process in the classroom can be an important role in improving motivation and student achievement. Teachers can help to improve student performance by sharing. Through student involvement in the assessment process, students learn to be responsible in their own learning. Feeling accountability and control can increase students’ intrinsic motivation to learn and to improve success. In addition, teachers have the opportunity to support student success by providing the application and assessment with good communication quality.
A teacher who develops useful assessments, provides corrective instruction, and gives students second chances to demonstrate success can improve their instruction and help students to learn. “When teachers’ classroom assessments become an integral part of the instructional process and a central ingredient in their efforts to help students learn, the benefits of assessment for both students and teachers will be boundless” (Guskey, 2003). In addition, by determining exactly what students have learned and not learned, assessment is useful for both teachers and students.
Assessment should be no longer seen as just a tool to determine academic achievement. Various options exist in the assessment process can influence student motivation and achievement. When students and teachers enter into an assessment relationship, they became a team with a clear, mutual learning goals, and task-specific assessment tasks. As teachers began to implement new strategies by using assessment as an instructional tool, they will recognize the students’ ability to take control of their own success and accept responsibility for their own learning. This feeling of empowerment will inspire and motivate students toward greater achievement.
A self-paced program
One useful framework addresses the multiple dimensions of motivation and engagement that are relevant to academic outcomes in students’ lives. Contextualizing motivation and engagement in a multidimensional way communicates to students that there are many ways in which they can succeed from a motivation and engagement perspective (Martin, 2010). A self-paced program for students sustained motivation strengths and improve motivation weakness. It separates into positive motivation thoughts (self-belief, learning focus, and valuing of school), positive motivation behaviours (planning, study management, and persistence), negative motivation thoughts (anxiety, failure avoidance, and uncertain control), and negative motivation behaviours (self-sabotage and disengagement).There are many direct strategies that educators, parents, and students can use these strategies to enhance motivation and to maintain the strength of motivation.
Achievement goal theory has emerged as one of the most prominent theories of achievement motivation. It uses a goal framework achievement in the influence of classroom and school environments. Then, it will improve students’ academic motivation and achievement also. Considerable evidence suggests that elementary and secondary students show the most positive motivation and learning patterns when their school settings emphasize mastery, understanding, and improving skills and knowledge(Meece, Anderman, &Anderman, 2006).
The findings of environmental studies in the classroom have a number of interesting and important implications for both practice and further research (Opolot-Okurut, 2010). He said that from a practical standpoint, there are three clear implications of the discovery. First, teachers must be aware of the different aspects of their classroom environment. For example, a modified instrument, which is used in the classroom to assess aspects of teacher support, student involvement, task orientation, cooperation among students, and equity in the classroom environment. Students’ consideration of the environmental aspects of their classes differs in the two types of school and maybe between classes within the same school. But, in addition, there are several other aspects of classroom learning environment which is covered in other classroom environment instruments and are worth knowing. Second, teachers should give more emphasis on the dimensions assessed in order to increase student motivation to learn mathematics. Third, in general, teachers should pay more attention to their learning classroom environment and change them. It seems that it is suggesting the teachers wish to improve student motivation towards mathematics, in general, should emphasize the learning environment dimensions that have assessed.
This essay begins with the question whether students who have a good motivation will lead into a good achievement too? The answer is not directional answer, such as yes or no, but it depends on the point of view of some cases. These cases mean that the influence of student who has a good motivation is not always produce a good student achievement. It depends on several things, such as the effect of motivation itself toward students achievement, some affects that happened due to students’ motivation, and also keep the motivation existed then enhanced it.
Many people said that bad teaching kills motivation and that good teaching brings out the best in students of all ages. The principles that guide motivated learning are important to know to encourage students’ motivation to develop independent learning skills and also a good achievement for students. I try to describe the principles in such a way that gain insight into the reasons why students are or are not motivated to learn in the context of the classroom. However, these principles have to be adapted firstly to the local context so students can focus on their beliefs, opinions, and values and how these motivational beliefs affect learning. Knowledge of motivational beliefs will help them to create learning environments that are well suited to their psychological needs.
However, it should be clear about the fact that causality and improvement of students’ motivation are different each other. For example, from the explanation before, assessment is one of the media that can improve students’ motivation. Instead of it, assessment can be an affect to students’ motivation in the same time. It can be happened if the content of curriculum is applied an assessment in learning process. That is why the position of the studies is not always clear.
There are some general aspects that should be considered when describing the relation of all these studies. Because student achievement needs existence of motivation, there must be a relation between those two studies. But when I criticized it, I think those two studies not always have a clear relation. In fact, there are some studies that concern to the lack of theoretical guidance driving the conduct of the majority of studies. One of the research stated that the research on mathematics education has been primarily descriptive and inadequately conceptualized. Often motivation has been described to add a little thing to studies originally focused on others factors, such as mathematics achievement (Middleton &Spanias, 1999).
Overall, it seems that a good student achievement can be achieved if student has a good motivation too. Even though there are still existed unclearly relation among studies, the aim of the present study has been obtained positively. Simply I can say “A good motivation produce a good achievement also”.
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