This study considered the use of practical work as one of the strategies that can be used to teach and learn the concepts of fractions in primary school mathematics. The classroom teacher's perception of practical work was investigated and the results confirmed the assumption that most educators use minimal or no practical work when teaching students fractions. The researcher conducted an experiment with students to find out if they saw any value in doing practical work.
Data collected from students confirmed that hands-on work had value in learning fraction concepts, especially adding fractions. The data have important implications for the teaching and learning of fractions, especially for fraction addition, teacher training in practical work and also for further research.
OVERVIEW OF THE STUDY
- INTRODUCTION
- MOTIVATION
- WHAT IS PRACTICAL WORK?
- WHY DO PRACTICAL WORK?
- RESEARCH PROBLEM
- RELEVANCE OF THE STUDY
- KEY RESEARCH QUESTIONS
- AIMS OF THE STUDY
- STRUCTURE OF THE DISSERTATION
- CONCLUSION
The practical work was supposed to be able to provide solutions to students' challenges in understanding the addition of fractions. How does engaging students in practical work affect their learning about addition of fractions? In this research, 6th grade students were taught to add fractions using fraction circles and diagrams.
The first section of the study focused on adding fractions with the same denominator and used fraction circles. This chapter introduced the motivation of the study and elaborated on the reasons why practical work is considered as a method that can facilitate the understanding of addition of fractions.
LITERATURE REVIEW
- INTRODUCTION
- THE NATURE OF MATHEMATICS
- LEARNING OF MATHEMATICS
- LEARNING OF FRACTIONS
- WHY IS LEARNING OF ADDITION OF FRACTIONS CHALLENGING ? .1 PROBLEM WITH TERMINOLOGY
- MULTIPLE REPRESENTATIONS OF FRACTIONS
- LEARNERS MISCONCEPTIONS ON ADDITION OF FRACTIONS
- TEACHING APPROACHES
- CONCLUSION
Kieren (1976) proposed that the concept of fractions consists of four interrelated sub-constructs: ratio, operator, quotient and measure. In most cases, the cause of problems arose from the fact that learners were applying their knowledge of whole numbers to the arithmetic of fractions (Lamon, 1999). In the MALATI (2004) project, it is noted that the traditional Least Common Divisor (LCD) way of adding fractions does not promote understanding of equivalent fractions.
Literature reviewed suggested that it is very important to expose learners to diverse interpretations of the concept of fractions. The literature reviewed also placed practical work at the center of meaningful understanding of adding fractions.
THEORETICAL FRAMEWORK
- INTRODUCTION
- CONSTRUCTIVISM DEFINED
- HISTORICAL PERSPECTIVE
- CONSTRUCTING MEANING
- CURRICULUM
- UNDERSTANDING MATHEMATICS
- ROLE OF THE EDUCATOR
- MATHEMATICS CLASSROOM
- CONSTRUCTIVIST’S VIEW ON ASSESSMENT
- TYPES OF ASSESSMENT
- FORMAL ASSESSMENT
- CONCLUSION
Principle two states that the function of cognition is adaptive and serves the organization of the experiential world, not ontological reality. Aspects of constructivist theory can be found among the works of Socrates, Plato, and Aristotle, all of whom speak to the formation of knowledge. Pestalozzi maintained that the educational process should be based on the natural development of the child and its sensory influences.
Piaget believes that it is through learners' own efforts that they will truly understand. Cobb (1994) contrasts the approach of delivering mathematics as 'content' to the technique of promoting the emergence of mathematical ideas from the collective practices of the classroom community. The constructivist theory or model of learning considers that knowledge is not always transferred directly from teaching to learner in a form that can be immediately understood.
For these students, learning mathematics assumes more the character of obedience than of understanding. The above does not totally reject memory at the expense of understanding: it is true that some of the basic concepts must be remembered to facilitate understanding. It is therefore clear that a good memory is an essential part of learning and understanding mathematics.
In the constructivist view, the educator's responsibility is to design activities that will make students actively participate in their learning (Orton & Frobisher, 1996). In the mathematics classroom, posters and concrete objects on display are useful; they can spark interest in students and help them understand the topic. The organization of the classroom directly affects both the nature of the interaction and the style of teaching, and in addition it must match the behavioral goals of the educators.
RESEARCH METHODOLOGY
- INTRODUCTION
- METHODOLOGY AND RESEARCH DESIGN
- DEALING WITH VALIDITY AND RELIABILITY
- THE PARTICIPANTS
- THE EDUCATOR
- LEARNERS
- THE EXPERIMENT
- SAMPLING
- RESEARCH INSTRUMENTS
- NATURALISTIC AND PARTICIPATION OBSERVATION
- INTERVIEWS
- TIME FRAME
- ANALYSIS
- CONCLUSION
I used interviews to obtain data about students' views on the use of practical work. Throughout the process, the students' context, experiences, attitudes, views and opinions were taken into account. The qualitative nature of the study meant that it was both descriptive and explanatory.
Results from observations, students' written responses to the tasks, and students' responses to the two sets of interviews were categorized and compared to determine whether the information gathered from different methods confirmed each other. The researcher was granted permission to conduct this study at one of the Combined Schools of Umhlali branch which is located in Ilembe District. This captured the students' attention and kept them focused on what was being done in the lesson.
This is the kind of experiment that the study undertook on learners' use of practical means of adding fractions, and it helped the researcher to document the phenomenon before and after change. As there were two sets of interviews from each category, the scripts were separated; one learner was selected for interview for learners' views on practical work and one for interview according to performance. Giensburg (cited in Mokapi, 2002) argues that this method is used by researchers in Mathematics Education to investigate learners' conceptions of mathematical knowledge.
A semi-structured interview was conducted to find out learners' views on the use of fraction circles and diagrams. The researcher was able to probe learners with more questions and picked up non-verbal cues that show learners' views and preferences. The literature consulted, observations during lessons, semi-structured interviews conducted with learners and learners' written responses from worksheets provided rich data that enabled us to draw conclusions.
PRESENTATION AND DISCUSSION OF DATA
- INTRODUCTION
- LEARNER ENGAGEMENT IN FOUR ACTIVITIES
- LEARNERS’ PERCEPTIONS OF PRACTICAL WORK (OBSERVATION)
- CONCLUSION
Fraction circles helped the learner understand that denominators should not be added, only the numerators are added. Teachers using algorithms can be encouraged to use fraction circles when teaching addition of fractions, as this reinforces the concept of equivalence for learners. In this situation fraction circles worked well because for each task a learner was asked to use fraction circles to compare with a.
In this case, using fraction circles made it easy for this child to understand what fraction simplification means. Teachers should be encouraged to use them so that students can understand the concept. Activity three was about adding fractions with different denominators, where one denominator is the factor of the other.
To collect information about the students' perception of practical work, the researcher observed the students' behavior. In this class, everyone, even the shy ones, communicated with others and showed through their facial expressions that they enjoyed what they were using, especially the fraction circles. L 1: In practical work we used fraction circles and drew diagrams to find answers to.
For them, it was about using fraction circles and diagrams to find the answers with fractions. Responses to preference for fraction circles or diagrams showed that most students preferred using fraction circles compared to diagrams. This was packaged in a way that fraction circles were easy to handle and they were labeled, they were intended to work well with denominators that are the same, and the main purpose of using them was to eradicate the misunderstanding of adding denominators.
CONCLUSION AND RECOMMENDATIONS
INTRODUCTION
CONCLUSIONS
- INCLUSION OF PRACTICAL WORK
- STARTING FROM WHAT LEARNERS KNOW
- USAGE OF DIALOGUE
If students' voices are to be heard, it is important that teachers include practical work in their lessons as one of the strategies that can help them learn addition of fractions. Teachers have to create their own activities because the textbooks they use do not provide activities that include practical work. Building on what the students know played a crucial role in introducing the series of lessons in which the students would engage.
In 6th grade they are actually supposed to do fractions that have different denominators where one is a multiple of the other. For example, in activity one there was a learner who got her addition of numerators correct but also added the denominators. The researcher recommends that dialogue be used between the teachers and learners throughout the lesson.
It develops trust between the two participants and, above all, it gives the teacher the opportunity to examine learners' conceptual understanding of mathematical concepts. During dialogue, the learners could tell exactly how they arrived at their final answers, and this provided clarity and enabled the researcher to identify misconceptions that learners had. The use of fraction circles and diagrams made it easy for learners to discover their own mistakes.
FURTHER RESEARCH
Knowing and teaching elementary mathematics: Teachers' understanding of basic mathematics in China and the United States. INTERVIEW QUESTIONS BASED ON PRACTICAL WORK I : What did you understand about doing practical work when learning fractions. L 1 : In practical work we used fraction circles and drew diagrams to find answers to the questions.
L 3 : It was when you asked us to use fraction pieces to complete our activities. It also investigates whether students learn and understand better when they learn how to add fractions through hands-on work. Students and classroom teachers are asked to help participate in this research project as it would benefit educational practitioners and interested educators and/or mathematics teachers, but participation is completely voluntary and has no influence or impact on evaluation or assessment. student in any study or course during schooling.
Participants can review and comment on all parts of the thesis representing this research before publication.
