One of the most fundamental subjects of primary school mathematics, the
concept of fraction plays a key role in students' educational background.
Students experience difficulties and misconceptions regarding this concept.
Therefore, it is of great importance to understand this subject well and to use
different teaching methods and techniques. Various methods can be used in
learning mathematics, such as invention method, computer-assisted
teaching, problem solving, creative drama and discussion. Argumentation
method is a scientific discussion of a claim on a subject by providing data,
warrant and backing, and by revealing the rebuttal and the invalidity of the
claim. Students gain more skills by interacting with teachers or collaborating
with their peers, and that they possess skills that have not been obtained
before or that are too difficult to achieve on their own. Therefore, the
argumentation method was chosen for its effect on the development of
primary school students’ fraction calculation strategies. Having a case study
design, this study was conducted with 28 primary school fourth-grade
students and 10 open-ended questions prepared by the researchers were used
during interviews. The results suggested that primary school students were
able to develop fraction calculation strategies through the argumentation
method. In general, inventing strategies, using representations, number
sense, addition and subtraction, using unit fractions and proportional
reasoning were used as fraction calculation strategies. It recommended to
use the argumentation method in other critical subjects of mathematics as
well.
This study aimed to describe the process of thinking by prospective teachers of mathematics in making arguments. It was a qualitative research involving the mathematics students of STKIP PGRI Jombang as the subject of the study. Test and task-based semi structural interview were conducted for data collection. The result showed that 163 of 260 mathematics students argued using inductive and deductive warrants. The process of thinking by the prospective teachers of mathematics in making arguments had begun since they constructed their very first idea by figuring out some objects to make a conclusion. However, they also found a rebuttal from that conclusion, though they did not further describe what such rebuttal was. Therefore, they decided to construct the second ideas in order to verify the first ones through some pieces of definition.
The purpose of this study is to find out the critical thinking skills indicators and aspects of prospective elementary school teachers in mathematics-science integration lectures on electrical circuits and mathematical logic lesson. This research uses random sampling technique in which 30 first semester students were chosen randomly from one of university in Padang region West Sumatera Indonesia. This research uses Research and Development (R & D). The critical thinking skills are seen from processes, observations, and tests. The process of critical thinking skills of prospective elementary school teachers on the average of critical thinking skills indicator is 84% in strategies and tactics, 80% in advanced clarification and 83% in elementary clarification, basic support, and inference. The result of observing the critical thinking skills of prospective elementary school teachers on the average of each lectures is significantly increased to be 81.9%. The results of pre-test and post-test were increased significantly. It is shown from N-gain of 0.7 to be medium category.
The purpose of this research was to study the procedure of think pair share, the type of cooperative learning models, which can be implemented in mathematics instruction in Manokwari, West Papua Indonesia. This study was conducted at Senior High School in Manokwari (SMA Negeri 1), Manokwari West Papua Indonesia. The research was carried out using research and development methods. The Think Pair Share learning model was modified to get the procedure of implementation in accordance with the characteristics of students studying mathematics in Manokwari, West Papua. The results of the research showed that there were two principals in the application of the think pair share model in mathematics instruction in Manokwari West Papua, selection of group members and the determination of the number of group members. Students individually start thinking of finding answers to the assignment submitted. Group members must consist of students who already know each other well, but should not to have a similar level of knowledge, while the number of group members must start from two students.
This document discusses the implementation of the think-pair-share (TPS) cooperative learning model in mathematics instruction in Manokwari, West Papua, Indonesia. It finds that initially some student pairs did not cooperate well and discussions were not fully conducive. However, modifications were made so that students were paired with others of different knowledge levels, and subsequent lessons saw improved discussion and participation from all students. The study aims to modify the TPS procedure to better suit mathematics instruction and students in Manokwari.
Despite its central place in the mathematics curriculum the notion of mathematical proof has failed to permeate the curriculum at all scholastic levels. While the concept of mathematical proof can serve as a vehicle for inculcating mathematical thinking, studies have revealed that students experience serious difficulties with proving that include (a) not knowing how to begin the proving process, (b) the proclivity to use empirical verifications for tasks that call for axiomatic methods of proving, and (c) resorting to rote memorization of uncoordinated fragments of proof facts. While several studies have been conducted with the aim of addressing students’ fragile grasp of mathematical proof the majority of such studies have been based on activities that involve students reflecting and expressing their level of convincement in arguments supplied by the researchers, thereby compromising the voice of the informants. Further, research focus has been on the front instead of the back of mathematics. Hence, there is a dearth in research studies into students’ thinking processes around mathematical proof that are grounded in students’ own proof attempts. Therefore current investigations should aim at identifying critical elements of students’ knowledge of the notion of proof that are informed by students’ actual individual proof construction attempts.
A Framework To Foster Problem-Solving In STEM And Computing EducationDereck Downing
The document presents a framework for fostering problem-solving skills across STEM and computing education. The framework was developed based on a literature review of prominent problem-solving approaches in each discipline. It aims to provide a common set of idealized problem-solving processes and methods from across STEM and computing that teachers can draw from to help students solve interdisciplinary, authentic problems. The framework is not intended to prescribe specific procedures but rather to offer a "toolbox" of epistemological approaches that students can select, customize and apply based on the context. The authors argue this integrated framework can support both teaching practices and educational research on developing problem-solving competencies.
Monitoring The Status Of Students' Journey Towards Science And Mathematics Li...noblex1
A major focus of the current mathematics and science education reforms is on developing "literacy;" that is, helping students to understand and use the languages and ideas of mathematics and science in reasoning, communicating, and solving problems. In many ways, these standards documents are far more voluminous and complex than any scope and sequence in place in school systems today. But these documents are meant to be used as frameworks which provide guidance in education reform - they are not the definitive sources articulating to teachers how education reform must occur in their classrooms.
Our plan in this discussion is to lay out the components of mathematics and science literacy as set down in the major reform documents and then, using selected how-to articles, to show how strategies and activities tried by math and science teachers have been used, or can be used, to promote math and science literacy among students. For pragmatic reasons only, our discussions often focus either on mathematics or science reform recommendations and examples. In doing this, we do not mean to imply that the elements of literacy in these disciplines are somehow separate or different. In fact, the separate discussions show how both the mathematics and science education communities, coming from different directions at different points in time, independently arrived at similar positions and many of the same recommendations regarding the ideas of literacy.
In support of this discussion of the components of literacy, we also provide samples of resources, materials, and services that teachers might find useful in promoting mathematics and science literacy in their classrooms. The how-to articles are meant to be quick-reads that can be applied or adapted to classrooms directly. These articles are included to make it easier to decide which ones might be of special interest. Other articles and documents are intended as sources of a more general background. These documents provide some of the research bases and rationales behind some of the reform recommendations. Finally, we have included other references and information on databases which are not directly cited in the discussion but might prove valuable as additional sources of classroom ideas.
During the last decade, the mathematics education community appeared to lack clear focus and a sense of direction. Although many conferences were held, papers written, and reports produced, there was not a general consensus regarding which direction mathematics education should head.
The Standards offer an organization of important mathematical topics and abilities by grade-level groups (Kindergarten - grade 4, grades 5 - 8, and grades 9 - 12). Throughout the Standards the emphasis is: "knowing" mathematics is "doing" mathematics.
Source: https://ebookschoice.com/monitoring-the-status-of-students-journey-towards-science-and-mathematics-literacy/
Problem-based learning is generally done with face-to-face interaction. This learning process, however, has not provided a lot of time for learners to find limitless and timeless information and learning resources. It still depends on the teacher as a source of information. Students are very dependent on the presence of lecturers during face-to-face interaction. This research aims to develop a Problem-based Blended Learning (PB2L) model to support student to improve their creative thinking skills. The method used in this research was R&D with ASSURE development model. Product validation was done through an expert’s assessment by using the expert’s validation sheet. The practicality of the product is tested with limited trials with college lecturers and some students with questionnaires and interviews. Product effectiveness was seen by implementing limited development testing to a particular class with a one group pretest-posttest design and the result was analyzed by using a Paired-Samples T-Test. The result of this research is a Problem-based Blended Learning (PB2L) valid, practical and effectively improves students' creative thinking abilities. The effectiveness of the learning model was also proven on the basis of Paired-Samples T-Test of students’ pretest and posttest with sig. (2-tailed) 0.000. This learning gives students the opportunity to think systematically by beginning by criticizing the interesting contextual problems and ending with meaningful reflection with adequate learning resources both in face-to-face and online interaction.
This study aimed to describe the process of thinking by prospective teachers of mathematics in making arguments. It was a qualitative research involving the mathematics students of STKIP PGRI Jombang as the subject of the study. Test and task-based semi structural interview were conducted for data collection. The result showed that 163 of 260 mathematics students argued using inductive and deductive warrants. The process of thinking by the prospective teachers of mathematics in making arguments had begun since they constructed their very first idea by figuring out some objects to make a conclusion. However, they also found a rebuttal from that conclusion, though they did not further describe what such rebuttal was. Therefore, they decided to construct the second ideas in order to verify the first ones through some pieces of definition.
The purpose of this study is to find out the critical thinking skills indicators and aspects of prospective elementary school teachers in mathematics-science integration lectures on electrical circuits and mathematical logic lesson. This research uses random sampling technique in which 30 first semester students were chosen randomly from one of university in Padang region West Sumatera Indonesia. This research uses Research and Development (R & D). The critical thinking skills are seen from processes, observations, and tests. The process of critical thinking skills of prospective elementary school teachers on the average of critical thinking skills indicator is 84% in strategies and tactics, 80% in advanced clarification and 83% in elementary clarification, basic support, and inference. The result of observing the critical thinking skills of prospective elementary school teachers on the average of each lectures is significantly increased to be 81.9%. The results of pre-test and post-test were increased significantly. It is shown from N-gain of 0.7 to be medium category.
The purpose of this research was to study the procedure of think pair share, the type of cooperative learning models, which can be implemented in mathematics instruction in Manokwari, West Papua Indonesia. This study was conducted at Senior High School in Manokwari (SMA Negeri 1), Manokwari West Papua Indonesia. The research was carried out using research and development methods. The Think Pair Share learning model was modified to get the procedure of implementation in accordance with the characteristics of students studying mathematics in Manokwari, West Papua. The results of the research showed that there were two principals in the application of the think pair share model in mathematics instruction in Manokwari West Papua, selection of group members and the determination of the number of group members. Students individually start thinking of finding answers to the assignment submitted. Group members must consist of students who already know each other well, but should not to have a similar level of knowledge, while the number of group members must start from two students.
This document discusses the implementation of the think-pair-share (TPS) cooperative learning model in mathematics instruction in Manokwari, West Papua, Indonesia. It finds that initially some student pairs did not cooperate well and discussions were not fully conducive. However, modifications were made so that students were paired with others of different knowledge levels, and subsequent lessons saw improved discussion and participation from all students. The study aims to modify the TPS procedure to better suit mathematics instruction and students in Manokwari.
Despite its central place in the mathematics curriculum the notion of mathematical proof has failed to permeate the curriculum at all scholastic levels. While the concept of mathematical proof can serve as a vehicle for inculcating mathematical thinking, studies have revealed that students experience serious difficulties with proving that include (a) not knowing how to begin the proving process, (b) the proclivity to use empirical verifications for tasks that call for axiomatic methods of proving, and (c) resorting to rote memorization of uncoordinated fragments of proof facts. While several studies have been conducted with the aim of addressing students’ fragile grasp of mathematical proof the majority of such studies have been based on activities that involve students reflecting and expressing their level of convincement in arguments supplied by the researchers, thereby compromising the voice of the informants. Further, research focus has been on the front instead of the back of mathematics. Hence, there is a dearth in research studies into students’ thinking processes around mathematical proof that are grounded in students’ own proof attempts. Therefore current investigations should aim at identifying critical elements of students’ knowledge of the notion of proof that are informed by students’ actual individual proof construction attempts.
A Framework To Foster Problem-Solving In STEM And Computing EducationDereck Downing
The document presents a framework for fostering problem-solving skills across STEM and computing education. The framework was developed based on a literature review of prominent problem-solving approaches in each discipline. It aims to provide a common set of idealized problem-solving processes and methods from across STEM and computing that teachers can draw from to help students solve interdisciplinary, authentic problems. The framework is not intended to prescribe specific procedures but rather to offer a "toolbox" of epistemological approaches that students can select, customize and apply based on the context. The authors argue this integrated framework can support both teaching practices and educational research on developing problem-solving competencies.
Monitoring The Status Of Students' Journey Towards Science And Mathematics Li...noblex1
A major focus of the current mathematics and science education reforms is on developing "literacy;" that is, helping students to understand and use the languages and ideas of mathematics and science in reasoning, communicating, and solving problems. In many ways, these standards documents are far more voluminous and complex than any scope and sequence in place in school systems today. But these documents are meant to be used as frameworks which provide guidance in education reform - they are not the definitive sources articulating to teachers how education reform must occur in their classrooms.
Our plan in this discussion is to lay out the components of mathematics and science literacy as set down in the major reform documents and then, using selected how-to articles, to show how strategies and activities tried by math and science teachers have been used, or can be used, to promote math and science literacy among students. For pragmatic reasons only, our discussions often focus either on mathematics or science reform recommendations and examples. In doing this, we do not mean to imply that the elements of literacy in these disciplines are somehow separate or different. In fact, the separate discussions show how both the mathematics and science education communities, coming from different directions at different points in time, independently arrived at similar positions and many of the same recommendations regarding the ideas of literacy.
In support of this discussion of the components of literacy, we also provide samples of resources, materials, and services that teachers might find useful in promoting mathematics and science literacy in their classrooms. The how-to articles are meant to be quick-reads that can be applied or adapted to classrooms directly. These articles are included to make it easier to decide which ones might be of special interest. Other articles and documents are intended as sources of a more general background. These documents provide some of the research bases and rationales behind some of the reform recommendations. Finally, we have included other references and information on databases which are not directly cited in the discussion but might prove valuable as additional sources of classroom ideas.
During the last decade, the mathematics education community appeared to lack clear focus and a sense of direction. Although many conferences were held, papers written, and reports produced, there was not a general consensus regarding which direction mathematics education should head.
The Standards offer an organization of important mathematical topics and abilities by grade-level groups (Kindergarten - grade 4, grades 5 - 8, and grades 9 - 12). Throughout the Standards the emphasis is: "knowing" mathematics is "doing" mathematics.
Source: https://ebookschoice.com/monitoring-the-status-of-students-journey-towards-science-and-mathematics-literacy/
Problem-based learning is generally done with face-to-face interaction. This learning process, however, has not provided a lot of time for learners to find limitless and timeless information and learning resources. It still depends on the teacher as a source of information. Students are very dependent on the presence of lecturers during face-to-face interaction. This research aims to develop a Problem-based Blended Learning (PB2L) model to support student to improve their creative thinking skills. The method used in this research was R&D with ASSURE development model. Product validation was done through an expert’s assessment by using the expert’s validation sheet. The practicality of the product is tested with limited trials with college lecturers and some students with questionnaires and interviews. Product effectiveness was seen by implementing limited development testing to a particular class with a one group pretest-posttest design and the result was analyzed by using a Paired-Samples T-Test. The result of this research is a Problem-based Blended Learning (PB2L) valid, practical and effectively improves students' creative thinking abilities. The effectiveness of the learning model was also proven on the basis of Paired-Samples T-Test of students’ pretest and posttest with sig. (2-tailed) 0.000. This learning gives students the opportunity to think systematically by beginning by criticizing the interesting contextual problems and ending with meaningful reflection with adequate learning resources both in face-to-face and online interaction.
ED ET 755 - Research Synthesis Assignmentknsmith620
Kayla Smith conducted research on learning strategies for students in distance education. She reviewed numerous scholarly articles and research studies on the topic. The research showed that effective strategies include developing motivation, metacognition, and resource management skills. Students must aim to engage deeply with content and interact with instructors and peers to promote meaningful learning from their own experiences.
This research is aimed to know students‟ concept understanding profile on heat and temperature. This research is descriptive research using a qualitative approach. Subjects of this research are 10th-grade students in Surakarta in the academic year of 2016/ 2017. They represent high, medium, and low categorized school. Subject selection is based on the average score of physics at the latest four years. This research uses the question of extended response test through essay question. Before having given to the subjects, essay questions are validated by the experts. Based on the research result and the data analysis, students‟ concept understanding on heat and temperature as follows: (1) The average percentage of students‟ concept understanding at high categorized school is 60,66%, at medium categorized school is 51,47%, and at low categorized school is 48,83%, (2) Most students have misconception on basic concept of heat and temperature such as heat capacity, thermal conductivity, and expansion concept.
Higher order thinking skills (HOTS) are an important element in facing the challenges of the 21 st-century. Difficulty in solving problems systematically, facing challenges in an organized manner, and being unable to design original solutions are due to the low HOTS that students have. HOTS ability can improve students who low-level thinking skills in several ways, for example, through learning integrated with media, practice, and assessment or HOTS-based cognitive assessment. The purpose of this study was to develop and implement a HOTS-based cognitive assessment to assess students' HOTS abilities. The device development model used is an adaptation of the analysis, design, development, implementation, and evaluation (ADDIE) model. The research sample consisted of 30 students in class 11 of the Governance and Office Automation Competency Program of Vocational High School 1 Kudus. The result is that 11 students have the HOTS ability with very good criteria, 17 well criteria, and 2 enough criteria. This study suggests that a test instrument for further research is to measure students' HOTS ability. The Experts conclude that HOTS-based cognitive assessment can be used as an approach to improve students' HOTS to actively think selectively and supported by logical argumentation.
This document describes best practices in technical education used at Mount Zion College of Engineering & Technology. It discusses how the college uses Bloom's revised taxonomy as a framework to develop specific, measurable learning objectives aligned with cognitive levels and knowledge dimensions. Teachers create lesson plans and learning activities mapped to the taxonomy to systematically facilitate student learning. Assessment is also designed based on the taxonomy to evaluate if students achieved the objectives. The methods section provides an example mapping of an objective, activities, and assessment to the taxonomy table to illustrate how it ensures proper alignment of the educational components.
This exploratory study was aimed at evaluating a module on the basis of the constructivist learning strategies to enhance the students’ motivation in Statistics learning. The design and development followed the Universal Design of Learning principles. The design included flexible instructional materials, techniques, and strategies for differentiating instruction which benefited the students of English Education Department taking the Statistics course. The study used a survey covering of 33 students. The students’ and teacher’ responses to questionnaires revealed that the students’ motivation and satisfaction increased toward the Statistics course in which Universal Design of Learning using various means of representation, action, and engagement was applied. It also suggested that the module was effective and that the Universal Design of Learning Model from the learners’ viewpoint put more emphasis on instruction. Its content was suitable in designing and developing module on Statistics in the higher educational context in Indonesia. The study results are expected to reveal information on how to further improve the Statistics teaching and learning quality. The implications of the research are provided along with suggestions.
The document summarizes a study that investigated the views of primary teachers and pre-service teachers on the misconceptions primary school students have about fractions. The teachers stated that students most often had difficulties representing fractions with models, understanding the concepts of the numerator and denominator, ranking fractions, solving problems, reading and writing fractions, distinguishing fraction types and converting between them, and placing fractions on a number line. They reported misconceptions with these concepts, such as thinking the numerator and denominator are separate numbers rather than parts of a whole. The study aimed to help teachers address common student misconceptions to improve fractional understanding.
There is overwhelming evidence that students face serious challenges in learning mathematical proof. Studies have found that students possess a superficial understanding of mathematical proof. With the aim of contributing to efforts intended to develop a comprehensive conception of mathematical proof, literature search was conducted to identify areas where research could be directed in order to increase proof understanding among students. To accomplish this goal, literature on modes of reasoning involved in proof construction, ideas on the classification of activities that constitute a proof path, and categories of proof understanding are exemplified using mathematical content drawn from Real Analysis. These exemplifications were used to illustrate the connections between modes of reasoning and levels of proof understanding. With regard to students’ fragile grasp of mathematical proof this critique of literature has revealed that many previous studies have given prominence to proof validations while there is lack of crucial interplay between structural and inductive modes of reasoning during proving by students. Hence, it is suggested in this paper that current research could also focus on mechanisms that promote an analytic conceptions of mathematical proof that are comprehensive enough to allow students to engage in more robust proof constructions.
Smith's curriculum theory and practice article review glenda pereyglenda75
The document discusses Mark K. Smith's analysis of curriculum theory and practice. Smith outlines four approaches to conceptualizing curriculum: as a body of knowledge, as product, as process, and as praxis. He describes the key aspects of each approach and their limitations. Overall, Smith argues that curriculum is contextual and influenced by social and environmental factors. An ideal approach would integrate aspects of the different theories to provide a holistic education that is responsive to student and societal needs.
The affective aspects must be owned by students in a lesson, where the
affective aspects will have a relationship with the cognitive aspects of a
student, therefore this study aimed to determine whether there is a
relationship between students 'mathematical dispositions and students'
mathematics learning outcomes. Using a mixed method and a sequential
explanatory plan, the research was undertaken by first collecting quantitative
data and then continuing to collect qualitative data. Where, the sample count
in this study was 413 students from junior secondary schools 18 in Jambi
City, Indonesia who used a total sampling technique. Data were then
analyzed with the help of SPSS 21 application to find descriptive statistics in
the form of mean, min, max, and category as well as inferential statistics
using Pearson Product Moment. The results obtained in this study dominate
both the mathematical disposition of pupils and the learning outcomes of
pupils in mathematics. This was reinforced by the existence of a relationship
between mathematical disposition and student learning outcomes in
mathematics which is indicated by the obtained sig <0.05. This means that
the mathematical disposition of students which includes the affective aspect
of students has a relationship with the cognitive aspect, by having a good
affective aspect, the cognitive aspects of the student are also good.
The previous research result showed that the learning model based on the investigation could increase the students’ critical thinking skills. The aim of this research was to measure the effectiveness of the using of problem-based learning model to increase the students’ critical thinking skills. The research design was quasi-experiment by using post-test only design. The population of this research was the eleventh grade students of science which contained 124 students of SMAN 6 and SMAN 7 Kupang that were chosen randomly. The treatment that was given in this research was problem-based learning model for the experiment class and conventional model for the control class whereas the given materials were the reaction rate. The instrument that was used in this research previously validated by two experts of theory and material. The result of this research showed that the students who studied in experiment class had different critical thinking skills better that the students who studied using conventional model.
This document provides an overview of applying case study approaches in management studies. It discusses the significance of case studies, how to analyze case studies, and key elements to include in strategic case study analyses. Specifically, it recommends analyzing a case study's history, identifying internal strengths and weaknesses, scanning the external environment, conducting a SWOT analysis, reviewing corporate and business level strategies, and understanding a company's structure and controls to produce recommendations. The goal is for learners to apply concepts by examining issues facing real organizations and developing analytical and problem-solving skills.
One objective of mathematics learning is to solve problem and to communicate idea to get a solution. Human life is inseparable from social activity, including cooperation. Similarly, in mathematics learning sometimes students need friends to discuss with in solving mathematics problem. Cooperative learning model can be an alternative to bridge the difficulty the students encounter. The objective of research was to identify the impact of Think Pair Share type of Cooperative learning model on mathematics learning in elementary school. This study was a descriptive qualitative research. The subject of research was the fifth graders of three elementary schools in Karangpandan Sub District. Techniques of collecting data used were observation, interview, and documentation. Observation was conducted to observe the learning process using Think Pair Share-type of cooperative learning, interview to find out the impression and the impact the students experience, and documentation to find out the group’s work. The conclusion of research showed that there are some impacts found in mathematics learning using Think Pair Share type of cooperative learning related to: (1) group establishment; (2) learning environment; (3) learning achievement; (4) student participation; (5) information exchange; and (6) interpersonal relation.
Assessing Multiplicative Thinking Using Rich TasksMaria Perkins
The document describes the development of a learning and assessment framework to evaluate students' multiplicative thinking skills in Years 4 to 8. Researchers designed rich assessment tasks and administered them to nearly 3,500 students. The tasks were based on an initial hypothetical learning trajectory identified from the literature. Student response data were used to refine the tasks, scoring rubrics, and a final learning and assessment framework consisting of nine levels of increasing complexity in multiplicative thinking. Sample assessment tasks, such as a multi-part "Butterfly House" problem, and corresponding scoring rubrics are provided as illustrations.
Argumentation skills as a form of communication has function to externalize ideas through scientific discourse is a very important in learning of science. As an integral part of the science, argumentation skills should be included as a component of learning science. The purpose of this study is to determine the effectiveness of argument driven inquiry-based module in enhancing the students’ argumentation skills. This study was conducted at one of the State Senior High School in Surakarta academic year 2016/2017. The pre-test and posttest research design with treatment and control class groups were used in the study. While the treatment group taught by using module based on argument-driven inquiry, the control group was taught by a module that commonly used at school. As the study concluded, using argument driven inquiry-based module in the learning process is effective to enhance the quality of students’ argumentation skills.
The document provides an introduction to the Common Core Georgia Performance Standards for mathematics. It discusses how the standards focus on applying mathematical concepts in authentic problems, problem solving, reasoning and representation. It emphasizes concentrating early learning on numbers, measurement and geometry with less emphasis on data analysis and algebra. The standards aim to present mathematics concepts clearly and specifically to improve focus and coherence.
The document provides an introduction to the Common Core Georgia Performance Standards for Mathematics. It discusses the focus of the Georgia mathematics curriculum on developing conceptual understanding through problem solving, representation, reasoning and communication. It emphasizes applying math concepts in authentic contexts. The standards are designed to increase coherence and focus from grade to grade to improve math achievement. They define what students should understand and be able to do at each grade level.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The study aimed at investigating the levels of geometrical thinking among students receiving blended learning in Jordan. The study sample consisted of (104) students/teachers of open education systems in Jordan for the 2015-2016 academic year. In order to answer the questions of study, the researcher developed a scale of geometric thinking, it is validity and reliability has been verified. The results of the study showed a low level of geometrical thinking among students receiving blended learning. The percentage of students in the first level (visual) (51%), the percentage of students in the second level (descriptive) (15%), and the percentage of students in the third level (logical) (3%). Also it showed differences in the levels of geometric thinking between males and females in favor of males, as well as differences in the level of geometrical thinking between students from the scientific stream and students from the literary stream in favor of scientific stream. In the light of the results of the study, the researcher recommends that pre-service teachers should be trained on programs contains geometrical thinking at open learning universities.
The role of entrepreneurship in addressing the issue of educated unemployment is well acknowledged, while its specific implications for health professions students remain inadequately explored. This study's main objective is to investigate entrepreneurship education's effect on entrepreneurial intention by considering entrepreneurial self-efficacy as a mediator in students majoring in medical laboratory technology. This quantitative research uses an exploratory approach involving 300 respondents determined through simple random sampling techniques and analyzed using partial least square structural equation model (PLS-SEM). The analysis revealed that entrepreneurship education directly impacts self-efficacy and entrepreneurial intention. Furthermore, entrepreneurial self-efficacy was identified to exert a positive mediating effect between these variables. However, the effect size between the relationships of the research variables is low. Nevertheless, higher education offering health majors can optimize entrepreneurship education by implementing practical learning and field experience to increase confidence and intention in entrepreneurial activities.
Recent studies claimed that the absence of a paradigm is a challenge to developing education for sustainable development and soft skills competencies. This integrative study examines stimulating these transferable and transversal competencies through constructivist approaches to teaching from the cognitive, social, radical, and critical perspectives. The study argues that the use of constructivist approaches to teaching can contribute to the achievement of education for sustainable development and soft skills competencies through the delegation of power from teachers/lecturers to students. This, in active and interactive classrooms, empowers students and builds their confidence to develop on the personal, academic, and professional levels. The use of the cognitive constructivist approach assists in developing competencies based on a clear understanding of the cognitive structures of students in a vibrant classroom environment. The use of the social constructivist approach assists in constructing individualized learning environment based on predetermined zones of proximal development in sociocultural contexts. The radical and critical constructivist approaches to teaching, through the rejection of conventional epistemologies, allow students the freedom to creatively address issues related to environmental, economic, and social sustainability. This becomes effective through the fostering of self and social awareness, challenging existing ideas, and provoking innovative thoughts that are necessary to shape a sustainable future.
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Similar to Development of primary school fourth-grade students’ fraction calculation strategies through the argumentation method
ED ET 755 - Research Synthesis Assignmentknsmith620
Kayla Smith conducted research on learning strategies for students in distance education. She reviewed numerous scholarly articles and research studies on the topic. The research showed that effective strategies include developing motivation, metacognition, and resource management skills. Students must aim to engage deeply with content and interact with instructors and peers to promote meaningful learning from their own experiences.
This research is aimed to know students‟ concept understanding profile on heat and temperature. This research is descriptive research using a qualitative approach. Subjects of this research are 10th-grade students in Surakarta in the academic year of 2016/ 2017. They represent high, medium, and low categorized school. Subject selection is based on the average score of physics at the latest four years. This research uses the question of extended response test through essay question. Before having given to the subjects, essay questions are validated by the experts. Based on the research result and the data analysis, students‟ concept understanding on heat and temperature as follows: (1) The average percentage of students‟ concept understanding at high categorized school is 60,66%, at medium categorized school is 51,47%, and at low categorized school is 48,83%, (2) Most students have misconception on basic concept of heat and temperature such as heat capacity, thermal conductivity, and expansion concept.
Higher order thinking skills (HOTS) are an important element in facing the challenges of the 21 st-century. Difficulty in solving problems systematically, facing challenges in an organized manner, and being unable to design original solutions are due to the low HOTS that students have. HOTS ability can improve students who low-level thinking skills in several ways, for example, through learning integrated with media, practice, and assessment or HOTS-based cognitive assessment. The purpose of this study was to develop and implement a HOTS-based cognitive assessment to assess students' HOTS abilities. The device development model used is an adaptation of the analysis, design, development, implementation, and evaluation (ADDIE) model. The research sample consisted of 30 students in class 11 of the Governance and Office Automation Competency Program of Vocational High School 1 Kudus. The result is that 11 students have the HOTS ability with very good criteria, 17 well criteria, and 2 enough criteria. This study suggests that a test instrument for further research is to measure students' HOTS ability. The Experts conclude that HOTS-based cognitive assessment can be used as an approach to improve students' HOTS to actively think selectively and supported by logical argumentation.
This document describes best practices in technical education used at Mount Zion College of Engineering & Technology. It discusses how the college uses Bloom's revised taxonomy as a framework to develop specific, measurable learning objectives aligned with cognitive levels and knowledge dimensions. Teachers create lesson plans and learning activities mapped to the taxonomy to systematically facilitate student learning. Assessment is also designed based on the taxonomy to evaluate if students achieved the objectives. The methods section provides an example mapping of an objective, activities, and assessment to the taxonomy table to illustrate how it ensures proper alignment of the educational components.
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Smith's curriculum theory and practice article review glenda pereyglenda75
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The affective aspects must be owned by students in a lesson, where the
affective aspects will have a relationship with the cognitive aspects of a
student, therefore this study aimed to determine whether there is a
relationship between students 'mathematical dispositions and students'
mathematics learning outcomes. Using a mixed method and a sequential
explanatory plan, the research was undertaken by first collecting quantitative
data and then continuing to collect qualitative data. Where, the sample count
in this study was 413 students from junior secondary schools 18 in Jambi
City, Indonesia who used a total sampling technique. Data were then
analyzed with the help of SPSS 21 application to find descriptive statistics in
the form of mean, min, max, and category as well as inferential statistics
using Pearson Product Moment. The results obtained in this study dominate
both the mathematical disposition of pupils and the learning outcomes of
pupils in mathematics. This was reinforced by the existence of a relationship
between mathematical disposition and student learning outcomes in
mathematics which is indicated by the obtained sig <0.05. This means that
the mathematical disposition of students which includes the affective aspect
of students has a relationship with the cognitive aspect, by having a good
affective aspect, the cognitive aspects of the student are also good.
The previous research result showed that the learning model based on the investigation could increase the students’ critical thinking skills. The aim of this research was to measure the effectiveness of the using of problem-based learning model to increase the students’ critical thinking skills. The research design was quasi-experiment by using post-test only design. The population of this research was the eleventh grade students of science which contained 124 students of SMAN 6 and SMAN 7 Kupang that were chosen randomly. The treatment that was given in this research was problem-based learning model for the experiment class and conventional model for the control class whereas the given materials were the reaction rate. The instrument that was used in this research previously validated by two experts of theory and material. The result of this research showed that the students who studied in experiment class had different critical thinking skills better that the students who studied using conventional model.
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Assessing Multiplicative Thinking Using Rich TasksMaria Perkins
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Argumentation skills as a form of communication has function to externalize ideas through scientific discourse is a very important in learning of science. As an integral part of the science, argumentation skills should be included as a component of learning science. The purpose of this study is to determine the effectiveness of argument driven inquiry-based module in enhancing the students’ argumentation skills. This study was conducted at one of the State Senior High School in Surakarta academic year 2016/2017. The pre-test and posttest research design with treatment and control class groups were used in the study. While the treatment group taught by using module based on argument-driven inquiry, the control group was taught by a module that commonly used at school. As the study concluded, using argument driven inquiry-based module in the learning process is effective to enhance the quality of students’ argumentation skills.
The document provides an introduction to the Common Core Georgia Performance Standards for mathematics. It discusses how the standards focus on applying mathematical concepts in authentic problems, problem solving, reasoning and representation. It emphasizes concentrating early learning on numbers, measurement and geometry with less emphasis on data analysis and algebra. The standards aim to present mathematics concepts clearly and specifically to improve focus and coherence.
The document provides an introduction to the Common Core Georgia Performance Standards for Mathematics. It discusses the focus of the Georgia mathematics curriculum on developing conceptual understanding through problem solving, representation, reasoning and communication. It emphasizes applying math concepts in authentic contexts. The standards are designed to increase coherence and focus from grade to grade to improve math achievement. They define what students should understand and be able to do at each grade level.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The study aimed at investigating the levels of geometrical thinking among students receiving blended learning in Jordan. The study sample consisted of (104) students/teachers of open education systems in Jordan for the 2015-2016 academic year. In order to answer the questions of study, the researcher developed a scale of geometric thinking, it is validity and reliability has been verified. The results of the study showed a low level of geometrical thinking among students receiving blended learning. The percentage of students in the first level (visual) (51%), the percentage of students in the second level (descriptive) (15%), and the percentage of students in the third level (logical) (3%). Also it showed differences in the levels of geometric thinking between males and females in favor of males, as well as differences in the level of geometrical thinking between students from the scientific stream and students from the literary stream in favor of scientific stream. In the light of the results of the study, the researcher recommends that pre-service teachers should be trained on programs contains geometrical thinking at open learning universities.
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Recent studies claimed that the absence of a paradigm is a challenge to developing education for sustainable development and soft skills competencies. This integrative study examines stimulating these transferable and transversal competencies through constructivist approaches to teaching from the cognitive, social, radical, and critical perspectives. The study argues that the use of constructivist approaches to teaching can contribute to the achievement of education for sustainable development and soft skills competencies through the delegation of power from teachers/lecturers to students. This, in active and interactive classrooms, empowers students and builds their confidence to develop on the personal, academic, and professional levels. The use of the cognitive constructivist approach assists in developing competencies based on a clear understanding of the cognitive structures of students in a vibrant classroom environment. The use of the social constructivist approach assists in constructing individualized learning environment based on predetermined zones of proximal development in sociocultural contexts. The radical and critical constructivist approaches to teaching, through the rejection of conventional epistemologies, allow students the freedom to creatively address issues related to environmental, economic, and social sustainability. This becomes effective through the fostering of self and social awareness, challenging existing ideas, and provoking innovative thoughts that are necessary to shape a sustainable future.
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Development of primary school fourth-grade students’ fraction calculation strategies through the argumentation method
1. Journal of Education and Learning (EduLearn)
Vol. 16, No. 2, May 2022, pp. 262~272
ISSN: 2089-9823 DOI: 10.11591/edulearn.v16i2.20511 262
Journal homepage: http://edulearn.intelektual.org
Development of primary school fourth-grade students’ fraction
calculation strategies through the argumentation method
Adem Doğan, Havva Kevser Yıldırım Sır
Department of Basıc Education, Faculty of Education, Sutcu Imam University, Kahramanmaraş, Turkey
Article Info ABSTRACT
Article history:
Received Mar 4, 2022
Revised Apr 20, 2022
Accepted May 25, 2022
One of the most fundamental subjects of primary school mathematics, the
concept of fraction plays a key role in students' educational background.
Students experience difficulties and misconceptions regarding this concept.
Therefore, it is of great importance to understand this subject well and to use
different teaching methods and techniques. Various methods can be used in
learning mathematics, such as invention method, computer-assisted
teaching, problem solving, creative drama and discussion. Argumentation
method is a scientific discussion of a claim on a subject by providing data,
warrant and backing, and by revealing the rebuttal and the invalidity of the
claim. Students gain more skills by interacting with teachers or collaborating
with their peers, and that they possess skills that have not been obtained
before or that are too difficult to achieve on their own. Therefore, the
argumentation method was chosen for its effect on the development of
primary school students’ fraction calculation strategies. Having a case study
design, this study was conducted with 28 primary school fourth-grade
students and 10 open-ended questions prepared by the researchers were used
during interviews. The results suggested that primary school students were
able to develop fraction calculation strategies through the argumentation
method. In general, inventing strategies, using representations, number
sense, addition and subtraction, using unit fractions and proportional
reasoning were used as fraction calculation strategies. It recommended to
use the argumentation method in other critical subjects of mathematics as
well.
Keywords:
Argumentation method
Fraction calculation strategies
Fractions
Mathematics teaching
Primary school
This is an open access article under the CC BY-SA license.
Corresponding Author:
Adem Doğan
Department of Basic Education, Faculty of Education, Sutcu Imam University
Kahramanmaraş Sütçü İmam University, Faculty of Education, Avşar Campus, D Block, Onikisubat,
46100, Kahramanmaraş Turkey
Email: aademdogan@gmail.com
1. INTRODUCTION
Primary school mathematics is a course that prepares children for life and contributes greatly to their
development; therefore, the objectives of this course are comprehensive. The aim of this course in the
Primary School Mathematics Curriculum [1] is defined as “developing mathematical literacy skills and using
these skills effectively, expressing their reasoning processes with their own thoughts, being aware of their
friends’ thinking gaps as well as realizing and complementing the mistakes in the reasoning processes”.
Various methods such as problem solving, creative drama and discussion appropriate for constructivist
understanding can be used in learning mathematics to achieve these above-mentioned objectives.
Argumentation is considered as one of these methods. Argumentation is a scientific discussion of a claim on
a subject by providing data, warrant, and backing, and by revealing the rebuttal and the invalidity of the
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claim. Toulmin's model is the most leading one even though many models can be used within the scope of
the argumentation method. Toulmin's [2] argumentation model refers to the main components such as claim,
data, backing and warrant, while rebuttal and qualifier are secondary components.
Figure 1 presents Toulmin [2] outlines. Data refer to the observations, proofs, event-facts and
knowledge regarding the claim. These data include all the learning related to the situation that the individual
has learned in advance or given in the content. Claims are thoughts and ideas put forward about a subject or
event. Warrant provides a link between the claim and the data. It explains how the data support a given claim
and include principles, rules and generalizations. Backing refers to strengthening the credibility of the
warrants and claims through making the backings more acceptable. A qualifier is to limit the claim. It is also
considered as phrases that draw the borders within a certain scope and distinguish them from different events
and facts in terms of their qualities. Rebuttal specifies conditions when the claim is invalid [3].
Figure 1.Toulmin argumentation model [2]
Pilar and Jimenez [4] defined argumentation method as using reasoning skills by choosing among
different explanations as shown in Figure 2. Likewise, numerous researchers pointed out that the
argumentation method contributes to reasoning skills [5]–[8]. The argumentation method ensures to
understand a concept and pay attention while making sense of the concept and to build a bridge between prior
experiences and new knowledge [9]. Similarly, mathematics learning involves consistency with already
learned information, principles and newly learned ones [10]. Thus, it will be more effective and easier for
students to remember their prior knowledge and bring them into the learning environment to create a schema
for the new knowledge in their mind. Moreover, there will be interaction among students, and they will
achieve better results since they work in larger groups [11]. Pilar and Jimenez [4] stated that students gain
more skills by interacting with teachers or collaborating with their peers, and that they possess skills that
have not been obtained before or that are too difficult to achieve on their own.
Figure 2. Example of discussion items in the model [2]
When students argue with their friends and are exposed to different ideas, they may reflect on their
own ideas and those of others, helping them in eliminating their misconceptions and developing better
learning [12]. Students learn to express their own ideas through working collaboratively [9], and to criticize
and respect the ideas of their friends. Furthermore, their self-confidence develops and they become more
socialized. The argumentation method aids in overcoming students' misconceptions about a subject and
achieving satisfactory results in learning difficult subjects. Various studies revealed that learning fractions
can be especially challenging for students [13]–[17].
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In this regard, the use of the argumentation method in teaching fractions, which is amongst the
challenging topics in mathematics, may help students and teachers. One of the most significant reasons why
learning fractions is challenging for students is that they are different from whole numbers, and that fractions
seem more abstract compared to other mathematics subjects. Considering that primary school students are in
the concrete operational stage according to Ramos-Christian et al. [18], logical and concrete operations are
required as much as possible while learning fractions. Visuals, objects and discussion on the topic can be
used to make fractions concrete.
More aid can be obtained for discussing fractions and calculating strategies in fractions along with
developing operational strategies through the argumentation method. It is likely that the argumentation
method is troublesome for primary school students. However, given that one of the eight standards identified
for mathematics in the Common Core State Standards for Mathematics [19] is the arguments and the others
related to reasoning and criticism, it would be very appropriate for the students to gain these skills especially
in primary school age. The description of this standard implicates that primary school students can construct
arguments using concrete references such as drawings, objects and actions. These arguments can be logical
and true even if they are not generalizations or certainties.
In the primary school mathematics curriculum, The Ministry of National Education emphasized that
students’ reasoning skills should be developed, they should realize the thinking gaps of their own and their
friends, and that they should be able to fill these gaps [1]. Besides, it is of great importance for students to
actively participate in the learning process and learn by doing and experiencing. The argumentation method
covers all the components mentioned at this point. Therefore, it is remarkable to embody a subject that is
difficult for students like fractions, and to actively participate in the learning process. This way of learning
can also be probable with the argumentation method. This study is paramount in terms of revealing the
implementation of the argumentation method at primary school level and the students’ development of
fraction calculation strategies.
Argumentation method is generally used in science studies around the world and in Turkey
[20]–[35]. A limited number of studies were conducted on the use of argumentation method in the field of
mathematics. Thus, this study is expected to not only fill the gap in the relevant literature but also show that
the argumentation method can be used for both fractions and primary school students. In this context, the
research question was related to how the argumentation method affected the primary school students’ fraction
calculation strategies. This study attempts to analyze the impact of the argumentation method on the
development of primary school fourth-grade students’ fraction calculation strategies.
2. RESEARCH METHOD
2.1. Research design
This study employed a case study design, one of the qualitative research methods, since the aim is to
develop fraction calculation strategies through the argumentation method. The case study is an approach that
allows an in-depth analysis to seek answers to scientific questions [36].
2.2. Working group
Case studies are generally conducted with a group of participants who engage with each other [37].
In-depth information can be gathered and a description can be made on the selected group. Therefore, this
study was carried out with a class that interacted with each other. One of the random sampling methods,
purposive sampling was used while determining the working group. Purposive sampling requires researchers
to conduct an in-depth study depending on the goal of the study. The working group of the study consisted of
20 fourth-grade students learning at a primary school in the Eastern Mediterranean Region. The students
were coded as S1, S2, S3… in order to comply with ethical rules.
2.3. Data collection tools and data collection process
One-on-one interviews were conducted with the students during data collection process. Interview is
a data collection method that requires the interviewer to collect in-depth information through verbal
communication or mass media that transmits audio and video instantly, like telephone [38]. This interview
method provides the direct collection of data with the participants’ responses and hence eliminating doubts.
The researcher removes the question marks by asking the points that pop into his mind. In the present study,
the researchers gathered direct and in-depth information through interviewing with a class group. The study
deployed a worksheet developed by the researchers to develop primary school students’ fractional strategies.
The questions in the worksheet were submitted to two field experts for revision. Necessary corrections were
made in line with the feedback. The worksheet includes 10 open-ended questions prepared in line with the
primary school fourth-grade mathematics curriculum. Before proceeding with data collection, necessary
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permissions were obtained from the university and the Ministry of National Education, further the data were
collected by considering students’ academic program. Students were initially informed about the
argumentation method, and various examples were demonstrated in different fields. After observing that the
students fully understood this subject, data were collected through the use of the worksheet on the subject of
fractions.
2.4. Data analysis
In qualitative research, the data obtained from interviews, observations and documents are first
coded and then synthesized by considering the coding, and the findings are presented [36]. Unlike
quantitative research, not statistical analysis but description is mostly used in qualitative studies. Content
analysis is one of the analysis methods used in qualitative research. The data are analyzed in depth and in
detail, thus revealing new themes and codes. The data were gathered under the categories of "invented
strategies, fraction representations, using number sense, addition and subtraction, proportional reasoning,
using unit fractions". The data were stored directly and without any additions and transferred into the
program to ensure the validity and reliability of the study. The consistency between intercoders was also
checked for reliability. After the researchers completed the coding process, two more researchers who were
experts in the field participated in the coding process and the results were compared by examining the
consistency between intercoders. The consistency between the coders was calculated through using Miles and
Huberman's formula [38] (reliability=agreement/agreement+disagreement X 100). The consistency was
identified as 0.84, which is satisfactory since the result is close to or over 90% [36]. In addition, member
checking was performed for exploring the credibility of the study. The papers were returned to participants to
check for accuracy. Moreover, each phase of the study was explained to the students in detail for contributing
to the credibility.
The researchers were unbiased and objective at all phases to ensure internal validity. They tried to
increase the internal validity by taking notes and giving instructions to the students when necessary. Last but
not least, experts’ views were taken into account regarding the appropriateness of the questions. External
validity is mostly related to the generalizability of the study results. It is inappropriate to make
generalizations in qualitative studies, since qualitative research is conducted on a social event, and it is
challenging to repeat the same social event for the same person, place and time [36]. All phases of the study
were explained in detail to confirm external validity. Descriptions were made clear for having other
researchers work with a group of participants with a similar subject and similar characteristics.
Toulmin's model focuses on documents with well-formed explicit arguments. To adapt to the
informal arguments made in usability issue discussions, we started by using Toulmin's model directly to code
the two problems. Based on our observations, we have made the following adjustments in order to reveal
what kind of mistakes students make in fraction learning. First, in our initial analysis, we found it extremely
difficult to demarcate Warrant and Support in issue discussions. We have made adjustments to avoid
ambiguity. From these two components, we evaluated all statements of students that act as a bridge between
concrete facts as explanations with warrant. Second, to accommodate the concise, informal style of argument
in issue discussions, we have removed rejection as an argument component and instead set the point of view
of any comment in the discussion as support or against with the original claim. Finally, we excluded the
qualifier due to its low representation in our issue discussion data. These changes resulted in the components
coding scheme used in content analysis.
It has been taken with the decision of Kahramanmaraş Sütçü İmam University Social and Human
Sciences Ethics Committee dated 09.09.2021 and numbered 56553-44/8 that there is no obstacle in the
implementation of the research. In addition, application permissions were obtained with the decision of
Kahramanmaraş Provincial Directorate of National Education dated 15.09.2021 and numbered E-35776031-
605.01-32015728.
3. RESULTS
This section presents findings on examining the development of primary school fourth-grade
students’ fraction calculation strategies through the argumentation method. Table 1 displays 28 students’
scores related to the argumentation components. Students were required to write 5 components for each of
the 10 questions on the worksheet. The maximum score that can be obtained from the worksheet is 50 with a
total of 50 components, each of which is 1 point. S5 was found to have the highest score with 40, while S2
had the lowest score with 0. The most frequently repeated score is 7 with 7 repetitions. The reason why the
students failed in writing the components may be because activities and lectures based on the argumentation
method are not included in primary school instruction.
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Table 1. The scores students got from the argumentation components
Student codes Scores Percentage (%)
S05 40 100
S17 24 60
S14 22 55
S08 22 55
S01 21 52,5
S12 19 47,5
S10 18 45
S07 17 42,5
S27 15 37,5
S26 14 35
S11 13 32,5
S09 13 32,5
S22 12 30
S19 11 27,5
S15 10 25
S16 9 22,5
S17 7 17,5
S18 7 17,5
S19 7 17,5
S20 7 17,5
S21 7 17,5
S22 7 17,5
S23 7 17,5
S24 6 15
S25 5 12,5
S26 2 5
S27 2 5
S28 0 0
Table 2 depicts the fraction calculation strategies and their use frequency by the students. The
students were identified to mostly use the fraction representation strategy. All students used this strategy at
least 2 times except for S18 and S16. This may be due to students’ use of area model in fractions. The least
used strategy was determined as using unit fractions. As is seen in Table 2, S4, S23 and S24 preferred this
strategy. The reason why students used this strategy less often may be because they have a passing
acquaintance with fractions. Upon examining Table 2, the majority of the students (except for S2, S8, S9,
S11, S12, S15, S18, S22, S23 and S28) invented a strategy in calculating and used the proportional reasoning
strategy (except for S2, S8, S18, S22, S23 and S28). Inventing strategies and using proportional reasoning
strategy indicate the effect of the argumentation method since reasoning, creativity and higher-level thinking
skills are used and developed effectively in the argumentation method.
Table 3 suggests that all of the students, except for S16 and S28, used the area model as a fraction
representation. Students were noted to mostly use area model for fraction representation. This may arise from
the fact that the fractions become more concrete with the use of area model. Besides, students frequently used
the set model (except for S8, S9, S14, S18, S20, S25 and S28), yet it is not a model that students can use a
lot. This may be because of the effectiveness of the argumentation method on the development of fraction
calculation strategies. Number line was identified as the least used model in representing fractions. As in
Table 3, almost half of the class (13 students) used this model as well. It may be wise to mention that the
argumentation method has an impact on the use of the number line model.
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Table 2. Strategies used by the students in calculating fractions
Strategies
Invented
strategy
Fraction
representation
Number
sense
Addition and
subtraction
Using unit
fractions
Proportional
reasoning
Total
S1 1 6 - 1 - 2 10
S2 - 2 - - - - 2
S3 2 7 - 1 - 2 12
S4 2 6 - 1 1 2 12
S5 2 9 - 1 - 2 14
S6 1 4 - 1 - 1 7
S7 3 5 - - - 2 10
S8 - 2 1 1 - - 4
S9 - 6 - 1 - 1 8
S10 2 6 - 2 - 2 12
S11 - 5 1 1 - 2 9
S12 - 4 1 3 - 2 10
S13 1 3 - - - 2 6
S14 3 8 - 2 - 2 15
S15 - 5 - - - 1 6
S16 1 1 - - - 2 2
S17 1 5 - 2 - 1 9
S18 - 1 1 2 - - 4
S19 1 5 - 2 - 2 10
S20 2 2 - - - 2 6
S21 1 2 - - - 1 4
S22 - 2 1 - - - 3
S23 - 2 - - 1 - 3
S24 1 2 - 1 1 1 6
S25 1 2 - - - 2 5
S26 1 3 - 2 - 1 7
S27 1 2 - 1 - 1 5
S28 - - - 1 - - 1
Total 27 107 5 26 3 36 194
Table 3. Number of models used in fraction representation
Students Area model Set model Number line model Total
S5 2 7 1 10
S3 2 4 1 7
S9 6 - 1 7
S10 5 1 1 7
S2 1 1 - 2
S6 1 2 - 3
S7 3 1 1 5
S8 1 - 1 2
S4 4 1 1 6
S1 4 1 1 6
S11 3 1 1 5
S12 2 1 1 4
S13 2 1 - 3
S14 7 - 1 8
S15 4 1 - 5
S16 - 1 - 1
S17 4 1 - 5
S18 1 - - 1
S19 3 1 1 5
S20 2 - - 2
S21 1 1 - 2
S22 1 1 1 3
S23 1 1 - 2
S24 1 1 - 2
S25 2 - - 2
S26 2 1 - 3
S27 1 1 - 2
S28 - - - 0
Total 66 31 13 110
Figure 3 displays that the student coded S7 solved the question by drawing the remaining three
cakes and the strawberry slices on them, since it was said that there were four cakes in the question. In this
regard, as the student can see the strawberry slices as a whole, it is easier to understand and solve the
question. As can be seen in Figure 4, S11 wrote the claim and data components while solving the question.
Drawing a picture while writing the data made it easier for the student to understand. The student drew 12
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stars for the rest of the set. The student's use of claim and data components may have helped him/her
understand and solve the question.
Figure 3. An example of area model Figure 4. An example of set model
Figure 5 demonstrates that the student coded S22 noted the claim and data components while
solving the question. Afterwards, the student drew the number line and assigned each unit as two meters.
Upon analyzing Figure 6, the student coded S10 invented the strategy of smashing the cookies instead of
dividing. First, the student divided three cookies from two pieces into a total of six pieces, then solved the
question by dividing the last cookie into six equal pieces.
Figure 5. An example of number line model Figure 6. An example of invented strategy
Figure 7 illustrates that the student coded S11 started to solve the question by writing down the data
and claim. Making operations by drawing a figure in the data section contributed to solving the question. As
is seen in Figure 8, S1 first wrote down the fractions that represent the portion of objects in the figures and
then solved the question by creating the problem statement.
Figure 7. An example of number sense strategy Figure 8. An example of addition and subtraction
strategy
4. DISCUSSION
This study attempts to develop the primary school students’ fraction calculation strategies through
the argumentation method. In this vein, the results revealed that the students’ fraction calculation strategies
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developed through the argumentation method. In line with the findings, the students were determined to
mostly use the fraction representation strategy. Among the fraction representation strategies, all but two
students were found to use the area model. Yet, the students did not prefer the number line-length model as
much as the other models. A similar result emerged in the study conducted by Duran [39] with pre-service
secondary mathematics teachers. The reason why students mostly prefer the area model may be because this
model is more concrete and visual compared to the others. Duran [39] concluded that the area model was
mostly used as it requires equal separation. At that point, we do not agree with Duran [39] since the set model
and the number line model also necessitate equal separation. Similarly, Doğan and Tertemiz [40] also noted
that the number line model was used less frequently than the area and set model. The results implicated that
the set model was frequently preferred by the students, except for few. In Doğan and Paydar's study [41], it
was found that the classroom teachers predominantly showed the area model while showing fractions.
Another study carried out by Cumhur and Korkmaz [42] suggested that pre-service primary school teachers
mostly used the number line model, while the set model less. This may result from the fact that their abstract
thinking and high-level thinking skills are developed by their age.
Duatepe et al. [43] outlined that the questions should be prepared by using different strategies
regardless of the traditional understanding in order to improve students' proportional reasoning skills. This
result is in line with those of the present study on the grounds that all but six of the students solved the
questions through using the proportional reasoning strategy.
The results also revealed that most of the students used the addition and subtraction strategy.
Contrary to popular belief, addition and subtraction in fractions are challenging for students. Because
students were determined to perceive fractions as natural numbers while using adding and subtracting
operations in fractions, and by considering the numerator and the denominator separately [44]. The present
study emphasized that the use of the argumentation method might be the reason why students did not make
similar mistakes while adding and subtracting in fractions.
Çekirdekçi et al. [44] defined number sense as the ability to solve problems encountered in daily
life, to name numbers and to include strategies such as estimation and mental calculation. Several studies
affirmed that number sense is quite low among primary school fourth-grade students [45], [46]. In this
regard, the finding of the study related to number sense is congruent with those of other studies.
Çekirdekçi et al. [45] interpreted the reason for the lower level of number sense as such: "The lower success
of students' number sense and the students’ tendency towards using rule-operation based methods may be the
result of the activities in the Mathematics Curriculum and textbooks used in our country."
Besides, fewer students were identified to use the unit fraction strategy. Divrik and Pilten [47]
concluded that the students could not easily determine the unit fraction, inasmuch as they did not have any
conceptual knowledge about the unit fraction. The findings of the study are similar to these findings.
Inventing a strategy requires creative thinking. The results demonstrated that most of the students
were able to invent a strategy. It is referring to the students’ creative thinking and the positive effect of the
argumentation method.
A scientific discussion, the argumentation method is generally used in science studies in the world
and Turkey [48]–[52]. A limited number of studies were conducted on the argumentation method in other
fields. Çelik et al. [53] examined the development of pre-service mathematics teachers' critical reading levels
through on-line argumentation method, and concluded that their critical reading levels increased
significantly. This paves the way for the fact that the argumentation method is effective when used in other
fields apart from natural sciences.
Uc and Benzer [54] investigated the effect of argumentation practices performed with writing
activities on the secondary school students’ creative writing and concept learning. The results revealed a
significant positive difference across students’ creative writing in the experimental group. Kara et al. [24],
Ecevit et al. [55], Karakaş and Sarıkaya [56] pinpointed the positive effect of the argumentation method at
primary school level. Further, they recommended disseminating the use of this method in primary schools.
5. CONCLUSION
The study involved such fraction calculation strategies as inventing strategies, using fraction
representation, number sense, addition and subtraction, using unit fraction and proportional reasoning. The
results of this study also highlighted that the students developed fraction calculation strategies through the
argumentation method, still they had difficulty in writing the argumentation components. This may arise
from the lack of using argumentation method at primary school level. Because the argumentation method at
primary school level can be high in terms of mental performance. It will require metacognitive performance
to think of many components together and to build bases for each of them.
Another result of the study suggested that participants rarely used the number sense. Number sense
is more strategically important at the primary school level. Many different notations and manipulatives must
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be used to develop number sense. One of them can be the argumentation method. Among the results of this
study, it is important that the argumentation method has a positive effect on the sense of number. My
argumentation method is widely used at secondary school level, as it enables children to develop different
perspectives, use different representations, and enable group work. It is seen that lowering this grade level to
primary school is also effective in students' mental abstract-concrete concept relations.
In consequence, this study maintained that the fourth-grade students' fraction calculation strategies
improved through the argumentation method. As the lessons, activities and plans based on the argumentation
method become widespread. The components of this method will be better understood by the students and
thus, it will become much more efficient. The argumentation method should be more preferred by teachers in
primary school lessons. Studies based on argumentation method should be increased in the field of
mathematics education as in science education. Argumentation method can also be included in order to
develop students' sense of number. More studies should be carried out through using argumentation method
at primary school level. Similar studies may examine the effect of argumentation method on a different
subject of fractions.
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BIOGRAPHIES OF AUTHORS
Adem Doğan received his undergraduate, graduate and doctorate degrees from
Gazi University. He taught Mathematics for 20 years at the Ministry of National Education.
Half of this period was spent providing mathematics and project consultancy to gifted
students. He works in fields such as mathematics education, gifted students, basic education,
classroom education, inclusive education. He is currently a faculty member at
Kahramanmaraş Sütçü Imam University Faculty of Education, teaching Mathematics in
Basic Education. He can be contacted at email: aademdogan@gmail.com.
Havva Kevser Yildirim Sir completed her undergraduate degree at Gazi
University. She is still doing her master's degree at Gazi University. She works as a
Research Assistant at Kahramanmaraş Sütçü İmam University. She can be contacted at
email: hvvkvsryldrm@gmail.com