Pub Date : 2023-06-09DOI: 10.22342/jme.v14i3.pp449-468
Z. H. Putra, Yesi Martha Afrillia, Dahnilsyah, H. Tjoe
Mathematical proofs play a paramount role in developing 21st-century skills, and the use of technology in mathematics learning has widely paved the way in the instruction of mathematical proofs. In mathematics education, GeoGebra has a significant role as a dynamic mathematics software in supporting students' learning process. This study aims to use GeoGebra in supporting prospective elementary teachers' mathematical proofs of the volume of 3-D shapes. This research used a case study method with 23 first-year prospective elementary teachers as participants from a public university in Riau, Indonesia. The data were gathered by means of students' work recordings in the GeoGebra classroom and video recordings from their interactions in the course of small group and classroom discussions. The videos were transcribed using verbatim, and then the mathematical proofs were analyzed using praxeological analysis. The findings show that prospective elementary teachers still had challenges to connect the construction of the volume of 3-D shapes using GeoGebra to its informal mathematical proofs. However, GeoGebra provides an opportunity to learn informal mathematical proofs for prospective elementary teachers.
{"title":"Prospective elementary teachers’ informal mathematical proof using GeoGebra: The case of 3D shapes","authors":"Z. H. Putra, Yesi Martha Afrillia, Dahnilsyah, H. Tjoe","doi":"10.22342/jme.v14i3.pp449-468","DOIUrl":"https://doi.org/10.22342/jme.v14i3.pp449-468","url":null,"abstract":"Mathematical proofs play a paramount role in developing 21st-century skills, and the use of technology in mathematics learning has widely paved the way in the instruction of mathematical proofs. In mathematics education, GeoGebra has a significant role as a dynamic mathematics software in supporting students' learning process. This study aims to use GeoGebra in supporting prospective elementary teachers' mathematical proofs of the volume of 3-D shapes. This research used a case study method with 23 first-year prospective elementary teachers as participants from a public university in Riau, Indonesia. The data were gathered by means of students' work recordings in the GeoGebra classroom and video recordings from their interactions in the course of small group and classroom discussions. The videos were transcribed using verbatim, and then the mathematical proofs were analyzed using praxeological analysis. The findings show that prospective elementary teachers still had challenges to connect the construction of the volume of 3-D shapes using GeoGebra to its informal mathematical proofs. However, GeoGebra provides an opportunity to learn informal mathematical proofs for prospective elementary teachers.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90879769","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 : 2023-06-09DOI: 10.22342/jme.v14i3.pp483-502
Edith Lindenbauer, Eva-Maria Infanger, Z. Lavicza
Digital task design is an important issue when integrating technology into mathematics education. However, existing frameworks often are not fine-grained enough for supporting teachers in designing tasks or they only focus on geometric topics. In this paper, we share a case study as the first cycle of our design-based research study that aims to extend and adapt the well-known Dynamic Geometry Task Analysis framework for analyzing further digital materials. The adapted framework is named Digital Task Analysis (DTA) model and can be utilized to analyze, modify, and design digital materials from other mathematical topics. The model focuses on supporting teachers in integrating two essential aspects within digital materials, namely creating cognitively stimulating tasks and exploiting added value of technology. In this paper, we present the first analyses of three cases representing digital materials including visualizations addressing lower secondary mathematics following the DTA model. The results show that the presented DTA model is suitable to analyze such digital materials and has the potential to support teachers in designing, assessing, and modifying digital tasks that support learners in focusing their attention on mathematically relevant aspects of digital resources, and in deepening their awareness of how to formulate targeted tasks for learners.
{"title":"Developing the Digital Task Analysis (DTA) framework to enable the assessment and redesign of digital resources in mathematics education","authors":"Edith Lindenbauer, Eva-Maria Infanger, Z. Lavicza","doi":"10.22342/jme.v14i3.pp483-502","DOIUrl":"https://doi.org/10.22342/jme.v14i3.pp483-502","url":null,"abstract":"Digital task design is an important issue when integrating technology into mathematics education. However, existing frameworks often are not fine-grained enough for supporting teachers in designing tasks or they only focus on geometric topics. In this paper, we share a case study as the first cycle of our design-based research study that aims to extend and adapt the well-known Dynamic Geometry Task Analysis framework for analyzing further digital materials. The adapted framework is named Digital Task Analysis (DTA) model and can be utilized to analyze, modify, and design digital materials from other mathematical topics. The model focuses on supporting teachers in integrating two essential aspects within digital materials, namely creating cognitively stimulating tasks and exploiting added value of technology. In this paper, we present the first analyses of three cases representing digital materials including visualizations addressing lower secondary mathematics following the DTA model. The results show that the presented DTA model is suitable to analyze such digital materials and has the potential to support teachers in designing, assessing, and modifying digital tasks that support learners in focusing their attention on mathematically relevant aspects of digital resources, and in deepening their awareness of how to formulate targeted tasks for learners.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81334266","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 : 2023-06-09DOI: 10.22342/jme.v14i3.pp469-482
J. Cervantes-Barraza, Armando Aroca Araujo
The design of mathematical tasks has taken the replacement on the research agenda of Mathematics Education. In this article, we provide principles of design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program. The research context involved the design, the development, and the analysis of written and oral prospective mathematics teacher (PMT) in an initial training course. The methodology implemented was descriptive-interpretative and implicated the design of mathematical tasks by the PMTs based on the adaptation of the HiCuA analytical framework. Regarding to the analysis of the data collected, categories of mathematical task types were constructed because of a thematic analysis carried out with the purpose of characterizing the tasks designed by the prospective teacher. The findings of the study provide information on the design principles implemented by prospective teacher in the context of Reasoning and Ethnomathematics. Likewise, it was identified that promoting reasoning and Ethnomathematics through interactive mathematical task designs supports students by developing skills such as: justifying, criticizing, and reasoning the conclusions presented by others.
{"title":"Design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program","authors":"J. Cervantes-Barraza, Armando Aroca Araujo","doi":"10.22342/jme.v14i3.pp469-482","DOIUrl":"https://doi.org/10.22342/jme.v14i3.pp469-482","url":null,"abstract":"The design of mathematical tasks has taken the replacement on the research agenda of Mathematics Education. In this article, we provide principles of design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program. The research context involved the design, the development, and the analysis of written and oral prospective mathematics teacher (PMT) in an initial training course. The methodology implemented was descriptive-interpretative and implicated the design of mathematical tasks by the PMTs based on the adaptation of the HiCuA analytical framework. Regarding to the analysis of the data collected, categories of mathematical task types were constructed because of a thematic analysis carried out with the purpose of characterizing the tasks designed by the prospective teacher. The findings of the study provide information on the design principles implemented by prospective teacher in the context of Reasoning and Ethnomathematics. Likewise, it was identified that promoting reasoning and Ethnomathematics through interactive mathematical task designs supports students by developing skills such as: justifying, criticizing, and reasoning the conclusions presented by others.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77725549","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 : 2023-06-09DOI: 10.22342/jme.v14i3.pp415-448
D. Hamdani, Purwanto, Sukoriyanto, Lathiful Anwar
Failure to deduce false suppositions in proof by contradiction is still considered “more difficult” than proving the conditional to in proof by contraposition. This study aims to identify the types of proof construction failures based on the action steps of proof by contradiction, then offer a framework of construction failure hypothesis specifically used in proof by contradiction. The research data were collected and analyzed from the work of students who have agreed to be research participants, a total of 83 students. The results of the analysis of student work successfully identified four types of failures, namely formulating suppositions, constructing and manipulating suppositions, identifying contradictions, and disproving suppositions. These four types of failures then became the material for the development of the hypothesis framework of a failure to construct proof by contradiction, which consists of 17 hypothesis nodes divided into three main hypotheses, namely: operational (action), affective (emotional), and foundational (logical reasoning). The failure hypothesis framework justifies that the sources of the failure of proof construction in proof by contradiction are understanding of the act of producing a proof by contradiction, emotionality towards the coherence of the construction steps, disproving suppositions, beliefs, use of appropriate definitions-theorems and axioms, and cognitive tension in proof by contradiction; and formal logic of the act of producing a proof by contradiction, as well as differences in the underlying logic with other acts.
{"title":"Causes of proof construction failure in proof by contradiction","authors":"D. Hamdani, Purwanto, Sukoriyanto, Lathiful Anwar","doi":"10.22342/jme.v14i3.pp415-448","DOIUrl":"https://doi.org/10.22342/jme.v14i3.pp415-448","url":null,"abstract":"Failure to deduce false suppositions in proof by contradiction is still considered “more difficult” than proving the conditional to in proof by contraposition. This study aims to identify the types of proof construction failures based on the action steps of proof by contradiction, then offer a framework of construction failure hypothesis specifically used in proof by contradiction. The research data were collected and analyzed from the work of students who have agreed to be research participants, a total of 83 students. The results of the analysis of student work successfully identified four types of failures, namely formulating suppositions, constructing and manipulating suppositions, identifying contradictions, and disproving suppositions. These four types of failures then became the material for the development of the hypothesis framework of a failure to construct proof by contradiction, which consists of 17 hypothesis nodes divided into three main hypotheses, namely: operational (action), affective (emotional), and foundational (logical reasoning). The failure hypothesis framework justifies that the sources of the failure of proof construction in proof by contradiction are understanding of the act of producing a proof by contradiction, emotionality towards the coherence of the construction steps, disproving suppositions, beliefs, use of appropriate definitions-theorems and axioms, and cognitive tension in proof by contradiction; and formal logic of the act of producing a proof by contradiction, as well as differences in the underlying logic with other acts.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78540239","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 : 2023-04-18DOI: 10.22342/jme.v14i3.pp395-414
Anaís Veloso Silva, Floriano Viseu, Luís Menezes
Communication plays a key role in teaching and learning processes. Questions are a communicational act greatly used by teachers to structure their discourse, establish dynamics, and foster interaction between the different participants in the classroom. In view of these potentialities of questions in the classroom context, we have developed a teaching experiment with the aim of understand the role of the teacher's question in the learning of topics on functions. Considering the nature of this aim, a methodology of qualitative and interpretative nature was used. The data collection was based on the students’ written productions and on the audio and video recordings of a mathematics class of a Grade 10 educational group (in northern Portugal). Data analysis is based on content analysis techniques, crossing collected data and categories emerging from the literature. The study revealed that the teacher’s questions alternated between confirmation, focalization, and inquiry, with inquiry prevailing. Questions aimed at testing the student’s knowledge gave both the teacher and actual student important information. Questions that focused the student’s attention on a particular detail enabled the students to organize their reasoning and structure their answer. Questions that required the students to explain or justify their thoughts were those that proved to most contribute to the development of the student’s reasoning process.
{"title":"The role performed by the teacher’s question in the learning of quadratic function in an exploratory mathematics class","authors":"Anaís Veloso Silva, Floriano Viseu, Luís Menezes","doi":"10.22342/jme.v14i3.pp395-414","DOIUrl":"https://doi.org/10.22342/jme.v14i3.pp395-414","url":null,"abstract":"Communication plays a key role in teaching and learning processes. Questions are a communicational act greatly used by teachers to structure their discourse, establish dynamics, and foster interaction between the different participants in the classroom. In view of these potentialities of questions in the classroom context, we have developed a teaching experiment with the aim of understand the role of the teacher's question in the learning of topics on functions. Considering the nature of this aim, a methodology of qualitative and interpretative nature was used. The data collection was based on the students’ written productions and on the audio and video recordings of a mathematics class of a Grade 10 educational group (in northern Portugal). Data analysis is based on content analysis techniques, crossing collected data and categories emerging from the literature. The study revealed that the teacher’s questions alternated between confirmation, focalization, and inquiry, with inquiry prevailing. Questions aimed at testing the student’s knowledge gave both the teacher and actual student important information. Questions that focused the student’s attention on a particular detail enabled the students to organize their reasoning and structure their answer. Questions that required the students to explain or justify their thoughts were those that proved to most contribute to the development of the student’s reasoning process.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74413121","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 : 2023-04-17DOI: 10.22342/jme.v14i2.pp375-394
Y. M. Sari, S. Fiangga, Yulia Izza El Milla, Nicky Dwi Puspaningtyas
Proportional reasoning has been greatly influencing the development of students’ mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students’ proportional reasoning in solving the conservation of plane figures. The study used guided-unguided area conservation problems using a proportional reasoning level as the analysis framework. Data were collected from 4 primary school students in Sidoarjo, Indonesia, who were in fifth-grade class. The students' strategies used were identified to analyze the students' proportional reasoning in solving area conservation. Results show that the level of proportional reasoning varies from zero to two. Regarding the students' proportional reasoning levels, most of the students' strategies use visual clues and cute paste strategies. Only one student can reach the level of quantitative reasoning by using a formula to compare both area measurements. Interestingly, the problem of the conservation of plane figures failed to reveal students' formal proportional reasoning due to their insufficient knowledge of fractions, division, multiplication, and decimals. Some implications regarding students' proportional reasoning and interventions in the area conservation problem are discussed.
{"title":"Exploring students’ proportional reasoning in solving guided-unguided area conservation problem: A case of Indonesian students","authors":"Y. M. Sari, S. Fiangga, Yulia Izza El Milla, Nicky Dwi Puspaningtyas","doi":"10.22342/jme.v14i2.pp375-394","DOIUrl":"https://doi.org/10.22342/jme.v14i2.pp375-394","url":null,"abstract":"Proportional reasoning has been greatly influencing the development of students’ mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students’ proportional reasoning in solving the conservation of plane figures. The study used guided-unguided area conservation problems using a proportional reasoning level as the analysis framework. Data were collected from 4 primary school students in Sidoarjo, Indonesia, who were in fifth-grade class. The students' strategies used were identified to analyze the students' proportional reasoning in solving area conservation. Results show that the level of proportional reasoning varies from zero to two. Regarding the students' proportional reasoning levels, most of the students' strategies use visual clues and cute paste strategies. Only one student can reach the level of quantitative reasoning by using a formula to compare both area measurements. Interestingly, the problem of the conservation of plane figures failed to reveal students' formal proportional reasoning due to their insufficient knowledge of fractions, division, multiplication, and decimals. Some implications regarding students' proportional reasoning and interventions in the area conservation problem are discussed.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73802457","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 : 2023-04-16DOI: 10.22342/jme.v14i2.pp353-374
Nick W. Sibaen, Julie A. Buasen, Monica S. Alimondo
The abrupt migration of educational institutions into a more flexible mode of learning due to the COVID-19 pandemic has undoubtedly resulted in students' difficulties. Such difficulties specific to mathematics flexible learning are generalized in this quantitative study. Using Principal Component Analysis, seven (7) factors were identified as the emerging students’ difficulties. Further analyses reveal a moderate degree of seriousness for most of the components. However, the standard deviation suggests that the students' responses are spread across the measuring scale, indicating that the severity of difficulties experienced by other students is higher than moderate. Further comparison of such ratings shows that for students enrolled in advanced and major mathematics courses, difficulties emanating from inadequate learning materials and support, and difficulty in submitting requirements on time are more pronounced. These intertwined difficulties generally stem from the lack of planning and preparation, at the same time from the nature of mathematics as being complex, abstract, and notational. By considering these difficulties, adjustments may be prioritized by students and teachers in the hope of improving the current state of mathematics flexible learning. These improvements will eventually lead to sustainable and fully stable online academic programs that may be offered even after the pandemic.
{"title":"Principal components of students’ difficulties in mathematics in the purview of flexible learning","authors":"Nick W. Sibaen, Julie A. Buasen, Monica S. Alimondo","doi":"10.22342/jme.v14i2.pp353-374","DOIUrl":"https://doi.org/10.22342/jme.v14i2.pp353-374","url":null,"abstract":"The abrupt migration of educational institutions into a more flexible mode of learning due to the COVID-19 pandemic has undoubtedly resulted in students' difficulties. Such difficulties specific to mathematics flexible learning are generalized in this quantitative study. Using Principal Component Analysis, seven (7) factors were identified as the emerging students’ difficulties. Further analyses reveal a moderate degree of seriousness for most of the components. However, the standard deviation suggests that the students' responses are spread across the measuring scale, indicating that the severity of difficulties experienced by other students is higher than moderate. Further comparison of such ratings shows that for students enrolled in advanced and major mathematics courses, difficulties emanating from inadequate learning materials and support, and difficulty in submitting requirements on time are more pronounced. These intertwined difficulties generally stem from the lack of planning and preparation, at the same time from the nature of mathematics as being complex, abstract, and notational. By considering these difficulties, adjustments may be prioritized by students and teachers in the hope of improving the current state of mathematics flexible learning. These improvements will eventually lead to sustainable and fully stable online academic programs that may be offered even after the pandemic.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78066165","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 : 2023-04-11DOI: 10.22342/jme.v14i2.pp339-352
A. Rafiepour, Nooshin Faramarzpour
This study aims to investigate students' mathematical connection ability in solving the problem of mathematical and correlation between indicators of mathematical connection ability. This research is correlation research. The sample of the study is 35 girls’ students in the 9th grade in a middle school in Kerman province (south-east of Iran). Data collection is done by giving a test on mathematical connection skills. The variables in this study are indicators of mathematical connection ability, namely the connection between mathematical concepts, connections between mathematics and other sciences, and connections between mathematics and everyday life. Spearman's correlation coefficient was used to analyze the data after calculating the score and percentage of test answers. The findings showed that qualification of students in the indicator of the connection between mathematical concepts was good enough (69%), in the indicator of the connection between mathematics and other sciences was also good enough (66%), and the indicator of the connection between mathematics and everyday life was not enough (42%). Also, the results of Spearman's correlation coefficient showed that there is a significant relationship between both indicators of mathematical connection ability. Therefore, the connection between mathematics and everyday life of Students must be improved.
{"title":"Investigation of the mathematical connection’s ability of 9th grade students","authors":"A. Rafiepour, Nooshin Faramarzpour","doi":"10.22342/jme.v14i2.pp339-352","DOIUrl":"https://doi.org/10.22342/jme.v14i2.pp339-352","url":null,"abstract":"This study aims to investigate students' mathematical connection ability in solving the problem of mathematical and correlation between indicators of mathematical connection ability. This research is correlation research. The sample of the study is 35 girls’ students in the 9th grade in a middle school in Kerman province (south-east of Iran). Data collection is done by giving a test on mathematical connection skills. The variables in this study are indicators of mathematical connection ability, namely the connection between mathematical concepts, connections between mathematics and other sciences, and connections between mathematics and everyday life. Spearman's correlation coefficient was used to analyze the data after calculating the score and percentage of test answers. The findings showed that qualification of students in the indicator of the connection between mathematical concepts was good enough (69%), in the indicator of the connection between mathematics and other sciences was also good enough (66%), and the indicator of the connection between mathematics and everyday life was not enough (42%). Also, the results of Spearman's correlation coefficient showed that there is a significant relationship between both indicators of mathematical connection ability. Therefore, the connection between mathematics and everyday life of Students must be improved.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89940250","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 : 2023-04-09DOI: 10.22342/jme.v14i2.pp293-310
Kgaladi Maphutha, S. Maoto, Paul Mutodi
In this paper, we explored the type of mathematical connections Grade 11 learners make when solving two-dimensional (2D) trigonometric problems in an Activity-Based Learning (ABL) environment. We followed a qualitative case study design within an interpretive paradigm. Convenience sampling was used to select a whole class of 45 Grade 11 learners from one of the public non-fee-paying secondary schools in Capricorn District, Limpopo Province of South Africa. Group work presentations and classroom interactions were used to collect data. Data were analyzed using deductive thematic analysis guided by the mathematical connections’ framework. The findings indicated that learners managed to make procedural, meaning, reversibility, different representations, feature, and inclusion part whole as well as integrated connections as they worked on 2D trigonometric problems in an ABL environment. We established that learners did not make generalization part-whole connections. In addition, we found that some learners lacked mathematical connections skills and failed to solve the problems. Engaging learners in an ABL environment provided a fine-grained approach that allowed them to make mathematical connections. We, therefore, recommend that teachers should create an ABL environment to enable learners to make different types of mathematics connections during the teaching and learning of trigonometric concepts.
{"title":"Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment","authors":"Kgaladi Maphutha, S. Maoto, Paul Mutodi","doi":"10.22342/jme.v14i2.pp293-310","DOIUrl":"https://doi.org/10.22342/jme.v14i2.pp293-310","url":null,"abstract":"In this paper, we explored the type of mathematical connections Grade 11 learners make when solving two-dimensional (2D) trigonometric problems in an Activity-Based Learning (ABL) environment. We followed a qualitative case study design within an interpretive paradigm. Convenience sampling was used to select a whole class of 45 Grade 11 learners from one of the public non-fee-paying secondary schools in Capricorn District, Limpopo Province of South Africa. Group work presentations and classroom interactions were used to collect data. Data were analyzed using deductive thematic analysis guided by the mathematical connections’ framework. The findings indicated that learners managed to make procedural, meaning, reversibility, different representations, feature, and inclusion part whole as well as integrated connections as they worked on 2D trigonometric problems in an ABL environment. We established that learners did not make generalization part-whole connections. In addition, we found that some learners lacked mathematical connections skills and failed to solve the problems. Engaging learners in an ABL environment provided a fine-grained approach that allowed them to make mathematical connections. We, therefore, recommend that teachers should create an ABL environment to enable learners to make different types of mathematics connections during the teaching and learning of trigonometric concepts.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85169934","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 : 2023-04-09DOI: 10.22342/jme.v14i2.pp311-338
Aybegum Albay, Hatice Çetin
This is a comprehensive study aiming to examine pre-service primary school teachers’ (PPST) mathematical disposition levels in terms of various variables, and to explain the results thoroughly. It employed the explanatory sequential design among the mixed method research designs. The data were collected through Mathematics Dispositional Functions Inventory (MDFI) and semi-structured interviews. The participants consisted of 361 PPSTs in the quantitative phase, and six PPSTs in the qualitative phase. Quantitative data were analyzed with descriptive and inferential statistics, while qualitative data were analyzed with descriptive analysis. The PPSTs’ mathematical disposition levels did not differ significantly in terms of grade level, high school type, area of education at high school and ability area variables; however, their scores in the attitude toward mathematics lesson factor of MDFI differed significantly in terms of area of education at high school and ability area variables. There were significant, positive, and low-level relationships between PPSTs’ mathematical disposition levels and their levels of mathematics learning experience in primary, middle and high schools, and their perception level of mathematics teaching efficacy. The PPSTs’ scores in attitude toward mathematics lesson factor related to ability area were consistent with their statements in the interviews. The quantitative analysis results regarding mathematics learning experience levels and mathematics teaching efficacy perception levels, defined as continuous variables, overlapped with the qualitative analysis results.
{"title":"A mixed method research study on pre-service primary school teachers’ mathematical disposition","authors":"Aybegum Albay, Hatice Çetin","doi":"10.22342/jme.v14i2.pp311-338","DOIUrl":"https://doi.org/10.22342/jme.v14i2.pp311-338","url":null,"abstract":"This is a comprehensive study aiming to examine pre-service primary school teachers’ (PPST) mathematical disposition levels in terms of various variables, and to explain the results thoroughly. It employed the explanatory sequential design among the mixed method research designs. The data were collected through Mathematics Dispositional Functions Inventory (MDFI) and semi-structured interviews. The participants consisted of 361 PPSTs in the quantitative phase, and six PPSTs in the qualitative phase. Quantitative data were analyzed with descriptive and inferential statistics, while qualitative data were analyzed with descriptive analysis. The PPSTs’ mathematical disposition levels did not differ significantly in terms of grade level, high school type, area of education at high school and ability area variables; however, their scores in the attitude toward mathematics lesson factor of MDFI differed significantly in terms of area of education at high school and ability area variables. There were significant, positive, and low-level relationships between PPSTs’ mathematical disposition levels and their levels of mathematics learning experience in primary, middle and high schools, and their perception level of mathematics teaching efficacy. The PPSTs’ scores in attitude toward mathematics lesson factor related to ability area were consistent with their statements in the interviews. The quantitative analysis results regarding mathematics learning experience levels and mathematics teaching efficacy perception levels, defined as continuous variables, overlapped with the qualitative analysis results.","PeriodicalId":37090,"journal":{"name":"Journal on Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73801322","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：