Pub Date : 2023-12-06DOI: 10.1007/s13394-023-00479-5
Lovejoy Comfort Gweshe, Karin Brodie
Many researchers have tried to understand why some learners engage in and others disengage from mathematics by exploring learners’ mathematical identities. Significant others (i.e., teachers, peers and family members) offer learners’ different opportunities for mathematical identity support, but no study has explored their collective role in supporting or constraining learners’ identities. In this paper, we explore how relationships between high school learners and different groups of significant others shaped learners’ narrated mathematical identities. Fifty Grade 10 learners responded to a mathematical identity questionnaire. After analysing the results of the questionnaire, six learners were purposively selected for a semi-structured interview, and the interview data were analysed thematically. Identities are described as robust-leaning, mixed or fragile-leaning, depending on learners’ narrated confidence, persistence, beliefs and sense of belonging to or exclusion from mathematics communities. Relationships with teachers, peers and family members are described as robust-enhancing or fragile-enhancing, depending on the kind of identity encouraged by the relationships. The findings show that many learners narrated fragile-leaning identities, and all the learners showed some robustness and fragility in their identities. The more groups of significant others a learner developed robust-enhancing relationships with, the more likely the learner narrated a robust-leaning identity. We argue that understanding learners’ identities requires understanding their relationships with the three different groups of significant others as a collective.
{"title":"Learners’ mathematical identities: exploring relationships between high school learners and significant others","authors":"Lovejoy Comfort Gweshe, Karin Brodie","doi":"10.1007/s13394-023-00479-5","DOIUrl":"https://doi.org/10.1007/s13394-023-00479-5","url":null,"abstract":"<p>Many researchers have tried to understand why some learners engage in and others disengage from mathematics by exploring learners’ mathematical identities. Significant others (i.e., teachers, peers and family members) offer learners’ different opportunities for mathematical identity support, but no study has explored their collective role in supporting or constraining learners’ identities. In this paper, we explore how relationships between high school learners and different groups of significant others shaped learners’ narrated mathematical identities. Fifty Grade 10 learners responded to a mathematical identity questionnaire. After analysing the results of the questionnaire, six learners were purposively selected for a semi-structured interview, and the interview data were analysed thematically. Identities are described as robust-leaning, mixed or fragile-leaning, depending on learners’ narrated confidence, persistence, beliefs and sense of belonging to or exclusion from mathematics communities. Relationships with teachers, peers and family members are described as robust-enhancing or fragile-enhancing, depending on the kind of identity encouraged by the relationships. The findings show that many learners narrated fragile-leaning identities, and all the learners showed some robustness and fragility in their identities. The more groups of significant others a learner developed robust-enhancing relationships with, the more likely the learner narrated a robust-leaning identity. We argue that understanding learners’ identities requires understanding their relationships with the three different groups of significant others as a collective.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":"66 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545748","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 : 2023-11-15DOI: 10.1007/s13394-023-00478-6
Yusuke Uegatani, Hiroki Otani, Shintaro Shirakawa, Ryo Ito
Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term difficulty in mathematics education research. We start this paper by arguing that a constructivist perspective, which has often been adopted in researches on mathematical task design, can deal with difficulties in solving a mathematical problem, but it cannot theoretically deal with those in understanding a mathematical concept. Therefore, we need the alternative philosophy of Robert Brandom’s inferentialism to capture students’ real difficulties in conceptual learning. From an inferentialist perspective, we introduce the idea of illusionary and real difficulties. The former is defined as what students cannot do, but they are not conscious of what they should do, while the latter is defined as what students cannot do despite their consciousness of what they should do. Through an eighth grade classroom episode, we argue that it is important in mathematics education research to focus not only on illusionary difficulties but also on the transition from illusionary to real difficulties. Researchers are encouraged to design a learning environment in which students become conscious of what they cannot do and to observe their mathematics learning in such an environment.
{"title":"Real and illusionary difficulties in conceptual learning in mathematics: comparison between constructivist and inferentialist perspectives","authors":"Yusuke Uegatani, Hiroki Otani, Shintaro Shirakawa, Ryo Ito","doi":"10.1007/s13394-023-00478-6","DOIUrl":"https://doi.org/10.1007/s13394-023-00478-6","url":null,"abstract":"<p>Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term <i>difficulty</i> in mathematics education research. We start this paper by arguing that a constructivist perspective, which has often been adopted in researches on mathematical task design, can deal with difficulties in solving a mathematical problem, but it cannot theoretically deal with those in understanding a mathematical concept. Therefore, we need the alternative philosophy of Robert Brandom’s inferentialism to capture students’ real difficulties in conceptual learning. From an inferentialist perspective, we introduce the idea of illusionary and real difficulties. The former is defined as what students cannot do, but they are not conscious of what they should do, while the latter is defined as what students cannot do despite their consciousness of what they should do. Through an eighth grade classroom episode, we argue that it is important in mathematics education research to focus not only on illusionary difficulties but also on the transition from illusionary to real difficulties. Researchers are encouraged to design a learning environment in which students become conscious of what they cannot do and to observe their mathematics learning in such an environment.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":"40 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138541044","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 : 2023-11-14DOI: 10.1007/s13394-023-00477-7
Margaret Marshman, Peter K. Dunn
{"title":"Improving statistical thinking","authors":"Margaret Marshman, Peter K. Dunn","doi":"10.1007/s13394-023-00477-7","DOIUrl":"https://doi.org/10.1007/s13394-023-00477-7","url":null,"abstract":"","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":"21 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134991234","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 : 2023-10-17DOI: 10.1007/s13394-023-00472-y
Sashi Sharma
Abstract There are challenges making connections between language use and mathematics in mathematics education. A lack of connections between the two domains can have negative consequences on student learning and performance. The challenges in statistics classrooms, where language and contexts are important as a medium of instruction, have received little scrutiny. This article reports on collaborative research carried out in three largely Pasifika-dominated year 12 classes. Specifically, we explored the language resources and strategies that appear to enhance the statistical understanding of Pasifika students. Findings from the teacher reflection aspect of the study indicated that some strategies to incorporate student language and communicative resources in their learning worked better than others. Teachers may need to re-evaluate their teaching practices, especially if part of their population is learning English as a second language.
{"title":"Promoting statistical thinking in year 12 multilingual classrooms: a collaborative study","authors":"Sashi Sharma","doi":"10.1007/s13394-023-00472-y","DOIUrl":"https://doi.org/10.1007/s13394-023-00472-y","url":null,"abstract":"Abstract There are challenges making connections between language use and mathematics in mathematics education. A lack of connections between the two domains can have negative consequences on student learning and performance. The challenges in statistics classrooms, where language and contexts are important as a medium of instruction, have received little scrutiny. This article reports on collaborative research carried out in three largely Pasifika-dominated year 12 classes. Specifically, we explored the language resources and strategies that appear to enhance the statistical understanding of Pasifika students. Findings from the teacher reflection aspect of the study indicated that some strategies to incorporate student language and communicative resources in their learning worked better than others. Teachers may need to re-evaluate their teaching practices, especially if part of their population is learning English as a second language.","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":"948 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994936","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 : 2023-10-06DOI: 10.1007/s13394-023-00476-8
Qiaoping Zhang, Hui Min Chia, Francesca Morselli
{"title":"Exploring the impact of distance teaching on mathematics educational values in Hong Kong: a study of in-service teachers’ perspectives","authors":"Qiaoping Zhang, Hui Min Chia, Francesca Morselli","doi":"10.1007/s13394-023-00476-8","DOIUrl":"https://doi.org/10.1007/s13394-023-00476-8","url":null,"abstract":"","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":"214 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350483","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 : 2023-09-18DOI: 10.1007/s13394-023-00471-z
Miglena Asenova
Abstract In Mathematics Education (ME), research dealing with topic-specific (TS) issues (e.g., what levels of development exist in learning fractions) produces usually local results and is considered less fashionable and attractive for innovative research projects than research dealing with context-specific (CS) issues that have more general and abstract scopes (e.g., what is mathematical instruction? what is the field of ME?) and produces middle-range or grand theories. TS- and CS-research run along separate tracks with little or no crossover, at least from the beginning of the socio-political-turn in ME, but connecting them could help to single out hidden variables in CS-research. This paper shows that TS-research creates specific mathematical objects that allow us to reduce the distance between these two lines of research. Mathematical objects specific to ME research are shown to be both a technical link between the two lines of research because they allow topic-specificity to access more abstract and general realms of research, as well as factor at stake when aspects related to the social, political, and ethical implications of the ontological creativity of TS-research are discussed in a critical postmodern approach. Discussing its impact on textbooks, teacher-training, teaching practices, further TS-research-practices, as well as on the researcher’s epistemological empowerment and on the self-referentiality of ME research, TS-research moves from the periphery to the heart of CS-research.
{"title":"Is theoretical topic-specific research “old fashioned”? An epistemological inquiry about the ontological creativity of Mathematics Education Research","authors":"Miglena Asenova","doi":"10.1007/s13394-023-00471-z","DOIUrl":"https://doi.org/10.1007/s13394-023-00471-z","url":null,"abstract":"Abstract In Mathematics Education (ME), research dealing with topic-specific (TS) issues (e.g., what levels of development exist in learning fractions) produces usually local results and is considered less fashionable and attractive for innovative research projects than research dealing with context-specific (CS) issues that have more general and abstract scopes (e.g., what is mathematical instruction? what is the field of ME?) and produces middle-range or grand theories. TS- and CS-research run along separate tracks with little or no crossover, at least from the beginning of the socio-political-turn in ME, but connecting them could help to single out hidden variables in CS-research. This paper shows that TS-research creates specific mathematical objects that allow us to reduce the distance between these two lines of research. Mathematical objects specific to ME research are shown to be both a technical link between the two lines of research because they allow topic-specificity to access more abstract and general realms of research, as well as factor at stake when aspects related to the social, political, and ethical implications of the ontological creativity of TS-research are discussed in a critical postmodern approach. Discussing its impact on textbooks, teacher-training, teaching practices, further TS-research-practices, as well as on the researcher’s epistemological empowerment and on the self-referentiality of ME research, TS-research moves from the periphery to the heart of CS-research.","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":"171 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135203553","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 : 2023-09-16DOI: 10.1007/s13394-023-00473-x
Jane Watson, Noleine Fitzallen, Ben Kelly
Abstract Incorporating an evidence-based approach in STEM education using data collection and analysis strategies when learning about science concepts enhances primary students’ discipline knowledge and cognitive development. This paper reports on learning activities that use the nature of viscosity and the power of informal statistical inference to build students’ conceptual understanding of interpolation and extrapolation without imposing on them the demands of understanding the nonlinear mathematics used to explore the concepts at the tertiary level. An exploratory research strategy was adopted to investigate the way in which Year 5 students created and analysed graphical representations from data collected when performing viscosity experiments. The data representations produced by the students and their subsequent predictions were analysed using the Structure of Observed Learning Outcomes (SOLO) model as adapted specifically for graphical representations. The results illustrate that when provided with appropriate technological tools to scaffold student learning, in this case TinkerPlots ™, development of students’ appreciation of interpolation and extrapolation within meaningful data contexts across the STEM curriculum does not have to wait until the tertiary level.
{"title":"Interpolation and extrapolation in Year 5 STEM activities: exploring data about viscosity without advanced statistics","authors":"Jane Watson, Noleine Fitzallen, Ben Kelly","doi":"10.1007/s13394-023-00473-x","DOIUrl":"https://doi.org/10.1007/s13394-023-00473-x","url":null,"abstract":"Abstract Incorporating an evidence-based approach in STEM education using data collection and analysis strategies when learning about science concepts enhances primary students’ discipline knowledge and cognitive development. This paper reports on learning activities that use the nature of viscosity and the power of informal statistical inference to build students’ conceptual understanding of interpolation and extrapolation without imposing on them the demands of understanding the nonlinear mathematics used to explore the concepts at the tertiary level. An exploratory research strategy was adopted to investigate the way in which Year 5 students created and analysed graphical representations from data collected when performing viscosity experiments. The data representations produced by the students and their subsequent predictions were analysed using the Structure of Observed Learning Outcomes (SOLO) model as adapted specifically for graphical representations. The results illustrate that when provided with appropriate technological tools to scaffold student learning, in this case TinkerPlots ™, development of students’ appreciation of interpolation and extrapolation within meaningful data contexts across the STEM curriculum does not have to wait until the tertiary level.","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135308145","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 : 2023-09-07DOI: 10.1007/s13394-023-00470-0
Rosemary Callingham, Jane Watson
{"title":"Statistics education research at the school level in Australia and New Zealand: A 30-year journey","authors":"Rosemary Callingham, Jane Watson","doi":"10.1007/s13394-023-00470-0","DOIUrl":"https://doi.org/10.1007/s13394-023-00470-0","url":null,"abstract":"","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47580274","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 : 2023-09-06DOI: 10.1007/s13394-023-00475-9
Y. F. Zakariya, Yousef Wardat
{"title":"Job satisfaction of mathematics teachers: an empirical investigation to quantify the contributions of teacher self-efficacy and teacher motivation to teach","authors":"Y. F. Zakariya, Yousef Wardat","doi":"10.1007/s13394-023-00475-9","DOIUrl":"https://doi.org/10.1007/s13394-023-00475-9","url":null,"abstract":"","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42493140","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 : 2023-09-05DOI: 10.1007/s13394-023-00474-w
Jennifer D. Cribbs, Juliana Utley
{"title":"Mathematics identity instrument development for fifth through twelfth grade students","authors":"Jennifer D. Cribbs, Juliana Utley","doi":"10.1007/s13394-023-00474-w","DOIUrl":"https://doi.org/10.1007/s13394-023-00474-w","url":null,"abstract":"","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41980286","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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