On the Teaching and Learning of Fractions through a Conceptual Generalization Approach (original) (raw)
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On the teaching and learning of fractions trough a conceptual generalization approach
IEJME - Mathematics Education, ISSN 2468-4945, 2017
This paper deals with precursory (propaedeutic) learning of the concept of number in the elementary mathematical education. The authors’ objective is to suggest a method allowing for the increase of the effectiveness of interactive expansion of the concept of number by using a grade-appropriate learning framework for elementary mathematical education content. A theoretical background for the creation of this method is based on the description of various characteristics of precursory learning and interactive teaching of mathematics as well and the flexible differentiation approach. The paper especially emphasizes the possibilities of propaedeutic understanding of the concept of fraction and examine the effects of such approach in terms of student achievement in elementary mathematics education, on the basis of a methodological approach. Results obtained during the experimental research suggest that under the influence of the methodological approach of introducing fractions through propaedeutic learning, students achieve significantly better results in learning compared to students who have not used this method.
Exploring the Transition of the Learning Content of Fraction from Elementary to Secondary Level
United International Journal for Research & Technology, 2021
Mathematics learning is well understood to be the process that must be considered at every level of education through a very comprehensive manner. Looking through, there are three interconnected elements in mathematics learning: teachers, students and materials/contents that generate the outcome of this learning. This study sought to investigate the learning content in fractions that transcend from elementary to secondary level. It utilized the traditions of a descriptive phenomenological research approach using pure qualitative data to give answers to the prevailing research questions. The learning contents in fraction transcend from elementary to secondary level following the framework of the CPA Approach with the sequence, namely: 1) Concrete and action-based representation using manipulative skills; 2) Pictorial representations of concrete objects; and 3) Abstract Notations using Mathematical Symbols. The learning contents in fraction scaffold using strategies, namely: 1) conduct of diagnostic assessment among learners; 2) review of learner's previous knowledge; 3) use of real, touchable, manipulative and concrete objects; 3) Peer support or tutorial approach learning; 4) learner-made learning materials; 5) contextualizing and localizing learning modules; and 6) providing learning support facilities. The learning contents in fraction transcend from elementary to secondary level according to the framework and principles of CPA Approach. There are varied strategies that teachers use to scaffold the learning content in fraction that transcend from elementary to secondary level. Elementary and Secondary teachers may become attentive and observant about the principles of their teaching to ensure that different empirical approaches such as the CPA Approach may appropriately and accordingly apply in their instructional practices especially when teaching fraction to fulfil the needed skills of learners in preparation to the next level of learning contents in fraction and other mathematical concepts. Varied and purposeful scaffolding strategies provided in the proposed handbook may be utilized to apply CPA in teaching fraction. The proposed teacher's handbook entitled Concrete-Pictorial-Abstract Approach (CPA Approach) to Teach Fraction & Other Mathematical Concepts-A Teacher's Handbook may be utilize to enhance the teaching skills of mathematics teachers in elementary and secondary. Action research along the utilization of CPA Approach as intervention may be conducted.
Exploration of primary school teacher students’ understanding in fraction concept
Journal of Physics: Conference Series, 2019
Fraction is a very complex mathematical material which must be mastered by every teacher who teaches in elementary school. Fraction concept understanding is very prominent because it is a prerequisite for comprehension in advanced mathematical concepts. In contrast with the other mathematical subjects in general, the fraction concept is considered as difficult material because it has many definitions. It creates a sustainable pedagogical challenge among the mathematics education community. Therefore, it must be ensured that all students of primary school teacher (PGSD students) have understood the concept of fraction before they teach in school. This research was conducted to explore the comprehension of the fraction concept among PGSD students. This research was in a form of qualitative research by employing test questions related to the concept of fractions toward 23 PGSD students. In this research, comprehension related to the aspect was tested through an analysis of non-standard problem solving processes that were verified by interviews. The results of the analysis showed that none of the students were completely correct in solving the problem. The main cause of the occurrence of the many errors in respondents was because they experienced false convictions or misconception related to the concept of fraction. For further research, we believe that PGSD students would have a proper comprehension of the fraction concept if at the beginning of the learning they receive reinforcement related to the concept.
Fractions are well known to be difficult concept to learn. This makes the difficulty faced by the students of Choggu Demonstration Junior High School in the Sagnerigu District of the Northern Region of Ghana with the concept of fractions not an exception in the teaching and learning of fraction. The research design used was Action research. The study employed a simple random sampling technique to select forty (40) students out of the ninety (90) JHS.1 students for the study. Unstructured interview, Pre-test and Post-test were the research instruments used for data collection. Ninety percent (90%) of the students did not make meaning from the numerals of fractions shown to them, the only numeral which was popular among the fractions shown was half (ie. ½). In order to encompass the major aspects of knowledge about fractions, Bruner`s theory of development strategy was the intervention used to assist the students to overcome the difficulty they have in fraction. In the pre-test, 92.5% of the students got marks less than half of the total marks of 50 and after the intervention 95% of the students got marks more than half of the total marks of 50 in the post-test. The statistical analysis of before and after intervention means and standard deviations (ie. 13.82, 7.05 and 31.43, 8.77) and eta squared value of 0.58 showed that the intervention activities has helped improve students' competence in understanding the concept of fractions.
New Researches in Education Sciences , 2024
Scholarly knowledge goes through many changes and transformations until it becomes knowledge that is learned. All these changes and transformations are within the scope of didactic transformation theory. In order to understand and improve the teaching of concepts, it is important to examine them and observe the roles of the actors in the process. The purpose of this study was to examine the teaching of the subject of fractions in the context of in-service Turkish secondary school mathematics teachers' perceptions. In this study, a descriptive research method based on a qualitative research approach was used. Data were collected by semi-structured interview technique. The research was conducted with the participation of 10 middle school mathematics teachers working in various middle schools. The interviews were analyzed using qualitative research methods using content analysis. The results of the study revealed that the interviewed teachers were aware of the importance of the subject of fractions and emphasized that they are frequently used in everyday life. Therefore, they indicated that they started to teach fractions by giving samples of everyday life, drawing shapes, and making use of visual presentations. In their opinion, students have more difficulties in four operations in fractions: equalizing denominators, determining denominators and nominators, ordering fractions from least to greatest or vice versa, problem solving with fractions and so on. To overcome these difficulties, the teachers expressed that they used some methods such as solving a lot of questions, embodying and re-teaching the subject.
International Journal of Scientific and Research Publications (IJSRP), 2019
This study was to determine the effect of applying realistic mathematical approaches to learning outcomes. This research is an experimental study with a quantitative approach, the method used is quasi experimental. The design of this study is nonequivalent control group. The subject of this research was third grade students of Artodung Pamekasan State Elementary School. The data collection technique is a test technique, the tests used in the form of pretest and posttest are in the form of multiple choices with the number of each of the 20 items. Test instruments were tested for validity and reliability before being used for research. After research, the results of the study were analyzed using the normality test, homogeneity test, and hypothesis testing. The results of the research conducted at Artodung Pamekasan State Elementary School obtained the results that there was an influence from the realistic mathematical approach to the mathematics learning outcomes of third grade students, this was evidenced by the increase in the average value of the experimental class learning outcomes greater than the control class 22.5> 16.06. Besides that, it is also proven by the results of-thitung <-t tabel at the 5% significance level located in the negative Ho rejection area, which is-2.195 <-1.68107. So it can be concluded that Ha is accepted and Ho is rejected.
The Effects of Strategies Used on the Teaching Methods Toward Students’ Fraction
School of Education, Faculty of Social Science and Humanities, Universiti Teknologi Malaysia, 2018
Fraction is the first experience of primary school students in learning mathematical concepts that use symbols which formed the basis for studying various concepts began at the primary level such as decimal, rational numbers, ratios, parts and percentages. This study employs systematic review to investigate the effects of the teaching strategies used towards students’ fraction learning and to identify the strategies in teaching method that can be used to overcome difficulties in learning fractions and improve fraction skills among students. In this review, 30 journals that focused on the strategies in teaching method used by the researchers and scholars in order to improve fraction skills among students were selected. The review perceived teaching methods as divided into physical manipulative to help students in comparing, finding equivalence and performing operations in a fraction, and virtual manipulative such as interactive digital resources that help in the development of the conceptual understanding of fraction. Although both teachers and students find it challenging in teaching and learning of fractions in primary and secondary schools, the result shows that over than 70% of the research use virtual manipulative strategies to approach students’ fraction learning. Manipulatives strategies help students to develop conceptual understanding of mathematical ideas by representing the ideas in many ways. Through manipulatives learning, students get the opportunities to create their own learning experiences which could sufficiently convince their understanding of mathematical concepts, especially in fraction learning. The study concluded that both manipulatives approached either virtual or physical are beneficial to students learning in different ways.
HE EFFECTS OF TEACHING FRACTIONS BY USING CONCEPT MAP ON THE ACHIEVEMENT OF SİXTH GRADE STUDENTS
Uşak Üniversitesi Eğitim Araştırmaları Dergisi, 2016
The aim of this study is to investigate the effects of using concept maps on the mathematics classes achievement of students. The sample consists of 71 students, who are in two sixth grade classes at a Secondary School in Turkey. One of the sixth grade classes was used as the experimental group and the other one as the control group. The equality of the groups was determined by t-test analysis on a pre-test. The research was carried out over four weeks. The control group studied with conventional teaching methods and the experimental group studied with a teaching method including the use of concept map. Achievment Test was used us a data source and t-test was used to evaluate the hypothesis. Results showed there was a significant difference between the control and experimental group based on results of the achievement post test. The experimental group was more successful than the control group, p=.000 (p<.05). Based on this results we concluded the teaching the subject “fractions” through the use of concept map increase the knowledge of fractions.
Education and New Developments 2022 – Volume I, 2022
Proportional reasoning causes considerable difficulty for students. One reason for this is, that a lack of basic understanding of fractions in earlier years, causes difficulties in the middle years. Moreover, learning of fractions and proportion is a long-term process and students encounter it continuously from grade 1 to 9. It is also difficult to teach, and teachers' mathematical content knowledge plays a crucial role in students' learning of mathematics. The purpose of this study is to analyse the effects of teaching, and the influence of teachers' mathematical content knowledge about fractions and proportion on students learning in progression from grade 4 and 5 to grade 8. The method contains pre-and post-tests for 86 students, classroom observations, checking students' written solutions and interviews of 35 selected students after the post-test. The intervention includes construction of educational materials (EM), teachers participating in seminars-training related to EM and teacher's implementation of EM. The EM contains tasks for students and a teachers' guide with aims and goals for teaching and a theoretical background. Tools for analysis were a methodological design, Variation theory, and a theoretical approach, Mathematical Content Knowledge for Teaching. In focus of the analysis was students learning in progression, related to variation and crucial aspects of learning. Findings from this study shows that teachers' mathematical content knowledge and their ability to identify the objects of learning and apply this in teaching is very important for students' learning and progression in their learning. Most students showed an ability to learn, but their performance was intimately linked to teachers' perception of the crucial aspects in teaching, and variation. Moreover, anomalies in students' perceptions of basic concepts caused obstacles in their learning. Some anomalies seem to have followed students from middle School to grade 8. Finally, the study illustrated how anomalies arise if misconceptions are not noticed by teachers. The outcome of the study can explain more about crucial steps in teaching and learning of fraction and proportion. The study pay attention to challenges in mathematics teaching.
Successes and obstacles in the development of grade 6 learners’ conceptions of fractions
1999
This paper reports on the development of some Grade 6 learners' conceptions of fractions during a yearlong intervention programme consisting of specially designed materials and a particular approach to learning and teaching mathematics. We highlight some gains in understanding, but also difficulties encountered in implementing the programme and suggest possible reasons for these difficulties.