Pub Date : 2022-11-22DOI: 10.22342/jme.v13i3.pp415-436
Mutiawati, R. Johar, M. Ramli, Mailizar
This study aims to determine the mathematical model of student learning behavior. The model is built by analogizing the spread of learning behavior with infectious diseases, which is called the SEIR model. The survey was conducted through filling out a questionnaire on the learning behavior of junior high school students with a population of 1,143 students. The results of the simulation model show that the peak of students' vulnerability to changes in learning behavior increases rapidly in the first two days and will be stable when passing the 150th day. The results of the simulation of the SEIR mathematical model with an incubation period of 365 days found that student learning behavior in Non-Boarding Schools will be stable in on day 198, while in Boarding Schools it will be stable on day 201. Infection cases in Boarding Schools fell to 0 on day 25 while in Non-Boarding Schools decreased on day 21, meaning that infections occurring in Boarding Schools were slower and more resistant long, meaning that the influence of the social environment is very significant on student learning behavior. This study also serves as material for policy formulation for the Aceh Provincial Government regarding the junior high school curriculum.
{"title":"Mathematical model of student learning behavior with the effect of learning motivation and student social interaction","authors":"Mutiawati, R. Johar, M. Ramli, Mailizar","doi":"10.22342/jme.v13i3.pp415-436","DOIUrl":"https://doi.org/10.22342/jme.v13i3.pp415-436","url":null,"abstract":"This study aims to determine the mathematical model of student learning behavior. The model is built by analogizing the spread of learning behavior with infectious diseases, which is called the SEIR model. The survey was conducted through filling out a questionnaire on the learning behavior of junior high school students with a population of 1,143 students. The results of the simulation model show that the peak of students' vulnerability to changes in learning behavior increases rapidly in the first two days and will be stable when passing the 150th day. The results of the simulation of the SEIR mathematical model with an incubation period of 365 days found that student learning behavior in Non-Boarding Schools will be stable in on day 198, while in Boarding Schools it will be stable on day 201. Infection cases in Boarding Schools fell to 0 on day 25 while in Non-Boarding Schools decreased on day 21, meaning that infections occurring in Boarding Schools were slower and more resistant long, meaning that the influence of the social environment is very significant on student learning behavior. This study also serves as material for policy formulation for the Aceh Provincial Government regarding the junior high school curriculum.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72595506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-22DOI: 10.22342/jme.v13i4.pp631-660
M. Fathurrohman, H. Nindiasari, Ilmiyati Rahayu
This paper reported the design and development of a conventional and digital mathematical board game for use by students in learning arithmetic. At the time of research, there is no significant indication that a mathematical board game is available in scientific and published patent documentation. The availability of mathematical board games for students’ drills and practice in arithmetic, especially in mathematical statement construction, would benefit them, as this competency is an essential life skill. This research was conducted through the design and development research method with the procedure of users’ need analysis, researcher as developer capability analysis, product design, product development, field testing in its natural setting environment, and the prototype. The board game prototype was developed in both conventional printed and digital versions. The field testing for the conventional printed version was conducted at secondary school classes with 34 and 36 students, respectively, while for the digital by selected participants. The field testing shows that the developed mathematical board game can work as expected in its natural setting environment.
{"title":"A conventional and digital mathematical board game design and development for use by students in learning arithmetic","authors":"M. Fathurrohman, H. Nindiasari, Ilmiyati Rahayu","doi":"10.22342/jme.v13i4.pp631-660","DOIUrl":"https://doi.org/10.22342/jme.v13i4.pp631-660","url":null,"abstract":"This paper reported the design and development of a conventional and digital mathematical board game for use by students in learning arithmetic. At the time of research, there is no significant indication that a mathematical board game is available in scientific and published patent documentation. The availability of mathematical board games for students’ drills and practice in arithmetic, especially in mathematical statement construction, would benefit them, as this competency is an essential life skill. This research was conducted through the design and development research method with the procedure of users’ need analysis, researcher as developer capability analysis, product design, product development, field testing in its natural setting environment, and the prototype. The board game prototype was developed in both conventional printed and digital versions. The field testing for the conventional printed version was conducted at secondary school classes with 34 and 36 students, respectively, while for the digital by selected participants. The field testing shows that the developed mathematical board game can work as expected in its natural setting environment.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73674132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-22DOI: 10.22342/jme.v13i3.pp437-464
Junarti, M. Zainudin, A. Utami
The algebraic structure is one of the axiomatic mathematical materials that consists of definitions and theorems. Learning algebraic structure will facilitate the development of logical reasoning, hence facilitating the study of other aspects of axiomatic mathematics. Even with this, several researchers say a lack of algebraic structure sense is a source of difficulty in acquiring algebraic structures. This study aims to examine a pattern of sequences of problem-solving paths in algebra, which is an illustration of learners' algebraic structure sense so that it can be utilized to enhance the ability to solve problems involving algebraic structure. This study employed a qualitative descriptive approach. Students who have received abstract algebra courses were chosen to serve as subjects. The instruments include tests based on algebraic structure sense, questionnaires, and interviews. This study reveals the sequence of paths used by students in the structure sense process for group materials, i.e., path of construction–analogy (constructing known mathematical properties or objects, then analogizing unknown mathematical properties or objects), path of analogy–abstraction (analogizing an unknown mathematical property or object with consideration of the initial knowledge, then abstracting a new definition), path of abstraction-construction (abstracting the definition of the extraction of a known mathematical structure or object, then constructing a new mathematical structure or object), and path of formal-construction (constructing the structure of known and unknown mathematical properties or objects through the logical deduction of a familiar definition). In general, the student's structure sense path for solving problems of group material begins with construction, followed by analogy, abstraction, and formal construction. Based on these findings, it is suggested that there is a way for lecturers to observe how students develop algebraic concepts, particularly group material, so that they can employ the appropriate strategy while teaching group concepts in the future.
{"title":"The sequence of algebraic problem-solving paths: Evidence from structure sense of Indonesian student","authors":"Junarti, M. Zainudin, A. Utami","doi":"10.22342/jme.v13i3.pp437-464","DOIUrl":"https://doi.org/10.22342/jme.v13i3.pp437-464","url":null,"abstract":"The algebraic structure is one of the axiomatic mathematical materials that consists of definitions and theorems. Learning algebraic structure will facilitate the development of logical reasoning, hence facilitating the study of other aspects of axiomatic mathematics. Even with this, several researchers say a lack of algebraic structure sense is a source of difficulty in acquiring algebraic structures. This study aims to examine a pattern of sequences of problem-solving paths in algebra, which is an illustration of learners' algebraic structure sense so that it can be utilized to enhance the ability to solve problems involving algebraic structure. This study employed a qualitative descriptive approach. Students who have received abstract algebra courses were chosen to serve as subjects. The instruments include tests based on algebraic structure sense, questionnaires, and interviews. This study reveals the sequence of paths used by students in the structure sense process for group materials, i.e., path of construction–analogy (constructing known mathematical properties or objects, then analogizing unknown mathematical properties or objects), path of analogy–abstraction (analogizing an unknown mathematical property or object with consideration of the initial knowledge, then abstracting a new definition), path of abstraction-construction (abstracting the definition of the extraction of a known mathematical structure or object, then constructing a new mathematical structure or object), and path of formal-construction (constructing the structure of known and unknown mathematical properties or objects through the logical deduction of a familiar definition). In general, the student's structure sense path for solving problems of group material begins with construction, followed by analogy, abstraction, and formal construction. Based on these findings, it is suggested that there is a way for lecturers to observe how students develop algebraic concepts, particularly group material, so that they can employ the appropriate strategy while teaching group concepts in the future.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84557222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-21DOI: 10.22342/jme.v13i3.pp383-392
A. Rafiepour, Afsaneh Moradalizadeh
In this study, the mathematics of carpet will be introduced by presenting the lifestyle of two expert carpet-weavers from Kerman, Iran, who work for many years in carpet-weaving activities through an explanation of carpet weavers’ culture. This explanation reveals that carpet weavers can do mathematics and solve related real-world problems without academic education in mathematics according to their needs through practical activities. The main purpose of this study is to investigate the mathematical ideas in the art of carpet weavers, and the ethnography approach is used as a methodological framework. Our findings showed that there are many mathematical concepts in the carpet weaving process, such as mirror axes, parallel and diagonal lines, geometric shapes, ratio, and measurement which can be used as context for developing enrich and meaningful mathematical tasks.
{"title":"Using mathematical ideas from carpet and carpet-weavers as a context for designing mathematics tasks","authors":"A. Rafiepour, Afsaneh Moradalizadeh","doi":"10.22342/jme.v13i3.pp383-392","DOIUrl":"https://doi.org/10.22342/jme.v13i3.pp383-392","url":null,"abstract":"In this study, the mathematics of carpet will be introduced by presenting the lifestyle of two expert carpet-weavers from Kerman, Iran, who work for many years in carpet-weaving activities through an explanation of carpet weavers’ culture. This explanation reveals that carpet weavers can do mathematics and solve related real-world problems without academic education in mathematics according to their needs through practical activities. The main purpose of this study is to investigate the mathematical ideas in the art of carpet weavers, and the ethnography approach is used as a methodological framework. Our findings showed that there are many mathematical concepts in the carpet weaving process, such as mirror axes, parallel and diagonal lines, geometric shapes, ratio, and measurement which can be used as context for developing enrich and meaningful mathematical tasks.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76354734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-21DOI: 10.22342/jme.v13i3.pp393-414
C. Matitaputty, T. Nusantara, E. Hidayanto, Sukoriyanto
Permutations and combinations are generally taught by requiring students to memorize formulas and solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams in textbooks, while lacking the conceptual understanding required to deal with problems in the real world. Therefore, this study aimed to examine in-service mathematics teachers' pedagogical content knowledge (PCK) to determine students’ mistakes in solving permutations and combinations problem and their teaching strategies to eliminate these errors. Data were collected by distributing vignettes, CoRe, and PaP-eRs to thirteen mathematics teachers from ten provinces in Indonesia after they finished an online professional teacher education program to determine their PCK in teaching permutations and combinations. The data collected were analyzed qualitatively using a content analysis approach to obtain categories inductively. The result showed that PCK of in-service mathematics in teaching permutations and combinations was observed by identifying student mistakes conceptually and procedurally, even though some could not determine their mistakes in permutations. On the other hand, the knowledge of instructional strategies can engage all students in active learning, but most of them only give general answers. Furthermore, an in-depth understanding of permutations and combinations topic is needed to support the development of teachers’ pedagogic competencies sustainably. The contribution of this research will be of interest to curriculum development and mathematics educators.
{"title":"Examining the pedagogical content knowledge of in-service mathematics teachers on the permutations and combinations in the context of student mistakes","authors":"C. Matitaputty, T. Nusantara, E. Hidayanto, Sukoriyanto","doi":"10.22342/jme.v13i3.pp393-414","DOIUrl":"https://doi.org/10.22342/jme.v13i3.pp393-414","url":null,"abstract":"Permutations and combinations are generally taught by requiring students to memorize formulas and solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams in textbooks, while lacking the conceptual understanding required to deal with problems in the real world. Therefore, this study aimed to examine in-service mathematics teachers' pedagogical content knowledge (PCK) to determine students’ mistakes in solving permutations and combinations problem and their teaching strategies to eliminate these errors. Data were collected by distributing vignettes, CoRe, and PaP-eRs to thirteen mathematics teachers from ten provinces in Indonesia after they finished an online professional teacher education program to determine their PCK in teaching permutations and combinations. The data collected were analyzed qualitatively using a content analysis approach to obtain categories inductively. The result showed that PCK of in-service mathematics in teaching permutations and combinations was observed by identifying student mistakes conceptually and procedurally, even though some could not determine their mistakes in permutations. On the other hand, the knowledge of instructional strategies can engage all students in active learning, but most of them only give general answers. Furthermore, an in-depth understanding of permutations and combinations topic is needed to support the development of teachers’ pedagogic competencies sustainably. The contribution of this research will be of interest to curriculum development and mathematics educators.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81733833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-10DOI: 10.22342/jme.v13i2.pp357-382
Sara Bagossi, Osama Swidan, F. Arzarello
Meaning-making in teaching-learning mathematical processes is a relevant issue analysed through different philosophical and educational frames. In particular, the use of digital tools in mathematics education affects the meaning-making processes. This paper discusses meaning-making from a phenomenological standpoint, in which interpretative activities are relevant. This approach requires a careful analysis of the semiotic resources’ evolution, including those related to the used digital tools. The paper aims to introduce an analytical tool, the Timeline. This tool is an elaboration on previous analysis tools, like the interaction flowchart and the semiotic bundle. Such a tool allows the analysis of relationship among interactions, semiotic resources, and meaning-making. In this paper, the Timeline is used to analyze two episodes from two different learning experiments where GeoGebra and augmented reality are used. High school students from Italy and Israel participated in this study. Video recording has been used to document the entire learning experiments. The analysis provides evidence that the Timeline enables investigating the relationship between students-teacher-artifacts interactions and meaning-making. Moreover, results may give teachers ideas for using digital tools to foster students’ meaning-making.
{"title":"Timeline tool for analyzing the relationship between students-teachers-artifacts interactions and meaning-making","authors":"Sara Bagossi, Osama Swidan, F. Arzarello","doi":"10.22342/jme.v13i2.pp357-382","DOIUrl":"https://doi.org/10.22342/jme.v13i2.pp357-382","url":null,"abstract":"Meaning-making in teaching-learning mathematical processes is a relevant issue analysed through different philosophical and educational frames. In particular, the use of digital tools in mathematics education affects the meaning-making processes. This paper discusses meaning-making from a\u0000 \u0000phenomenological standpoint, in which interpretative activities are relevant. This approach requires a careful analysis of the semiotic resources’ evolution, including those related to the used digital tools. The paper aims to introduce an analytical tool, the Timeline. This tool is an elaboration on previous analysis tools, like the interaction flowchart and the semiotic bundle. Such a tool allows the analysis of relationship among interactions, semiotic resources, and meaning-making. In this paper, the Timeline is used to analyze two episodes from two different learning experiments where GeoGebra and augmented reality are used. High school students from Italy and Israel participated in this study. Video recording has been used to document the entire learning experiments. The analysis provides evidence that the Timeline enables investigating the relationship between students-teacher-artifacts interactions and meaning-making. Moreover, results may give teachers ideas for using digital tools to foster students’ meaning-making.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82923572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-31DOI: 10.22342/jme.v13i2.pp337-356
S. M. Adeniji, P. Baker
This study explores the worked-example instruction (WEI) and the van Hiele teaching phases (VHTP) pedagogies to advance students’ acquisition of procedural and conceptual understanding of solving simultaneous equations. The quasi-experimental study involved two groups of high school students (age=15): 157 students in total with 72 in one group and 85 in the other. The study followed a pre-, post- and delay tests design. This study adapted two conceptual frameworks, the structure of the observed learning outcomes (SOLO) model and the Rasch model, and employed Rasch analysis and Statistical Package for Social Sciences (SPSS) as data analysis tools. The results indicated that both WEI and VHTP improved students’ procedural and conceptual understanding of solving simultaneous equations at the post-test; however, the WEI effects (on both procedural and conceptual understanding) were not sustained after the post-test while the VHTP had a lasting effect on only conceptual understanding. Furthermore, the VHTP group significantly outperformed the WEI group at the post-test and delay test in both conceptual and procedural understanding. These results indicated that the WEI is only beneficial at the initial stage of knowledge acquisition and VHTP is better at the initial and long-term. Practical implications of these results were discussed.
{"title":"Worked-examples instruction versus Van Hiele teaching phases: A demonstration of students’ procedural and conceptual understanding","authors":"S. M. Adeniji, P. Baker","doi":"10.22342/jme.v13i2.pp337-356","DOIUrl":"https://doi.org/10.22342/jme.v13i2.pp337-356","url":null,"abstract":"This study explores the worked-example instruction (WEI) and the van Hiele teaching phases (VHTP) pedagogies to advance students’ acquisition of procedural and conceptual understanding of solving simultaneous equations. The quasi-experimental study involved two groups of high school students (age=15): 157 students in total with 72 in one group and 85 in the other. The study followed a pre-, post- and delay tests design. This study adapted two conceptual frameworks, the structure of the observed learning outcomes (SOLO) model and the Rasch model, and employed Rasch analysis and Statistical Package for Social Sciences (SPSS) as data analysis tools. The results indicated that both WEI and VHTP improved students’ procedural and conceptual understanding of solving simultaneous equations at the post-test; however, the WEI effects (on both procedural and conceptual understanding) were not sustained after the post-test while the VHTP had a lasting effect on only conceptual understanding. Furthermore, the VHTP group significantly outperformed the WEI group at the post-test and delay test in both conceptual and procedural understanding. These results indicated that the WEI is only beneficial at the initial stage of knowledge acquisition and VHTP is better at the initial and long-term. Practical implications of these results were discussed.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80643178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-23DOI: 10.22342/jme.v13i2.pp323-336
P. Johnson, Felipe Almuna, Marta Silva
Based on the unpredictable effect of context familiarity when students solve real-world problems, this work aims to analyse how certain contexts can be used by pre-service mathematics teachers in the representation and real-world verification of a first-order mathematical model in the classroom in the subject of Ordinary Differential Equations. Specifically, this paper reports a classroom experience in which pre-service mathematics teachers compared the solution of a first-order ordinary differential equations (ODE) with a real-world experimental model. Using documentary records (i.e., students´ hand-written solutions and field notes) and a questionnaire on students´ perceptions on this classroom experience, qualitative results indicated that the pre-service mathematics teachers’ familiarity with an authentic context was a fundamental factor they chose a real-world model to represent the solution of a first-order ODE. Our analysis of the results highlights the importance of integrating familiar real-world contexts for pre-service mathematics teachers to model a first-order ODE, which is one of the fundamental principles of STEM disciplines.
{"title":"The role of problem context familiarity in modelling first-order ordinary differential equations","authors":"P. Johnson, Felipe Almuna, Marta Silva","doi":"10.22342/jme.v13i2.pp323-336","DOIUrl":"https://doi.org/10.22342/jme.v13i2.pp323-336","url":null,"abstract":"Based on the unpredictable effect of context familiarity when students solve real-world problems, this work aims to analyse how certain contexts can be used by pre-service mathematics teachers in the representation and real-world verification of a first-order mathematical model in the classroom in the subject of Ordinary Differential Equations. Specifically, this paper reports a classroom experience in which pre-service mathematics teachers compared the solution of a first-order ordinary differential equations (ODE) with a real-world experimental model. Using documentary records (i.e., students´ hand-written solutions and field notes) and a questionnaire on students´ perceptions on this classroom experience, qualitative results indicated that the pre-service mathematics teachers’ familiarity with an authentic context was a fundamental factor they chose a real-world model to represent the solution of a first-order ODE. Our analysis of the results highlights the importance of integrating familiar real-world contexts for pre-service mathematics teachers to model a first-order ODE, which is one of the fundamental principles of STEM disciplines.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83317791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-19DOI: 10.22342/jme.v13i2.pp307-322
Evrim Erbilgin, G. Macur
Solving arithmetic word problems has been a challenge for primary students due to difficulties in understanding the problem structure and relating the quantities in the problem to each other. This paper reports on an action research study to enhance students’ subtraction word problem-solving skills. The authors observed that their students had difficulties in representing the situations in word problems and solving the problems correctly. They designed, implemented, and analyzed an intervention to scaffold their students’ subtraction word problem-solving skills. As part of the intervention, a digital subtraction game was developed and used with second and third-grade students. The game involves three different representations: a discrete visual model, a bar model, and a number sentence. The students played the game and solved additional problems to strengthen their skills for representing and solving subtraction word problems. Twenty-four 2nd grade students in China and two 3rd grade students in Turkey participated in the study. Data sources included a pre-test, a post-test, student worksheets, and teachers’ filed notes. Data analysis showed an increase in students’ subtraction word problem-solving performance. They also effectively used a variety of representations to represent problem situations. The design and implementation processes of the intervention are discussed in the paper. We share suggestions for future implementation.
{"title":"A subtraction game to scaffold primary students’ word problem solving skills","authors":"Evrim Erbilgin, G. Macur","doi":"10.22342/jme.v13i2.pp307-322","DOIUrl":"https://doi.org/10.22342/jme.v13i2.pp307-322","url":null,"abstract":"Solving arithmetic word problems has been a challenge for primary students due to difficulties in understanding the problem structure and relating the quantities in the problem to each other. This paper reports on an action research study to enhance students’ subtraction word problem-solving skills. The authors observed that their students had difficulties in representing the situations in word problems and solving the problems correctly. They designed, implemented, and analyzed an intervention to scaffold their students’ subtraction word problem-solving skills. As part of the intervention, a digital subtraction game was developed and used with second and third-grade students. The game involves three different representations: a discrete visual model, a bar model, and a number sentence. The students played the game and solved additional problems to strengthen their skills for representing and solving subtraction word problems. Twenty-four 2nd grade students in China and two 3rd grade students in Turkey participated in the study. Data sources included a pre-test, a post-test, student worksheets, and teachers’ filed notes. Data analysis showed an increase in students’ subtraction word problem-solving performance. They also effectively used a variety of representations to represent problem situations. The design and implementation processes of the intervention are discussed in the paper. We share suggestions for future implementation.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82719064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-17DOI: 10.22342/jme.v13i2.pp289-306
P. Vos, P. Frejd
Many students do not experience usefulness in mathematics. To address this problem, we offered them a mathematical tool, Sankey diagrams, which is a flow chart appearing in news media to visualize social, industrial or environmental processes. We carried out an Educational Design Research (EDR) to develop and evaluate lesson materials about contextualized Sankey diagrams. We tested these materials with a class of grade 8 students and evaluated these on the feasibility of students’ appropriation of the diagrams. In the lesson, we observed how students were able to read the Sankey diagrams, liked the societal processes visualized, yet did not fully grasp their mathematical properties. However, weeks later, the same students skillfully used Sankey diagrams in an unrelated project, which showed they needed time for their learning. Our contributions are that (1) grade 8 students can appropriate Sankey diagrams and use these in situations relevant to them, (2) design researchers should consider long-term learning effects beyond the experimental phase in EDR. We recommend educational designers to innovate curricula and introduce diagrams from news media to make students experience usefulness in school content.
{"title":"Grade 8 students appropriating Sankey diagrams: The first cycle in an educational design research","authors":"P. Vos, P. Frejd","doi":"10.22342/jme.v13i2.pp289-306","DOIUrl":"https://doi.org/10.22342/jme.v13i2.pp289-306","url":null,"abstract":"Many students do not experience usefulness in mathematics. To address this problem, we offered them a mathematical tool, Sankey diagrams, which is a flow chart appearing in news media to visualize social, industrial or environmental processes. We carried out an Educational Design Research (EDR) to develop and evaluate lesson materials about contextualized Sankey diagrams. We tested these materials with a class of grade 8 students and evaluated these on the feasibility of students’ appropriation of the diagrams. In the lesson, we observed how students were able to read the Sankey diagrams, liked the societal processes visualized, yet did not fully grasp their mathematical properties. However, weeks later, the same students skillfully used Sankey diagrams in an unrelated project, which showed they needed time for their learning. Our contributions are that (1) grade 8 students can appropriate Sankey diagrams and use these in situations relevant to them, (2) design researchers should consider long-term learning effects beyond the experimental phase in EDR. We recommend educational designers to innovate curricula and introduce diagrams from news media to make students experience usefulness in school content.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84280323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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