Pub Date : 2023-12-08DOI: 10.1007/s10649-023-10276-3
Stijn Van Der Auwera, Bert De Smedt, Joke Torbeyns, Lieven Verschaffel
This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children’s subtraction by addition strategy use (SBA; e.g., 712 − 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied components of conceptual knowledge: children’s knowledge of the addition/subtraction complement principle (i.e., if a + b = c, then c − b = a and c − a = b) and their knowledge of different conceptual subtraction models (i.e., understanding that subtraction can be conceived not only as “taking away” but also as “determining the difference”). SBA occurrence was examined using a variability on demand task, in which children had to use multiple strategies to solve a subtraction. SBA frequency and strategy adaptivity were investigated with a task in which children could freely choose between SBA and direct subtraction (e.g., 712 − 346 = ?; 712 − 300 = 412, 412 − 40 = 372, and 372 − 6 = 366) to solve 15 subtractions. We measured both children’s knowledge of the addition/subtraction complement principle, and whether they understood subtraction also as “determining the difference.” SBA occurrence and frequency were not related to conceptual knowledge. However, strategy adaptivity was related to children’s knowledge of the addition/subtraction complement principle. Our findings highlight the importance of attention to conceptual knowledge when teaching multi-digit subtraction and expand the literature about the relation between procedural and conceptual knowledge.
{"title":"Children’s subtraction by addition strategy use and their subtraction-related conceptual knowledge","authors":"Stijn Van Der Auwera, Bert De Smedt, Joke Torbeyns, Lieven Verschaffel","doi":"10.1007/s10649-023-10276-3","DOIUrl":"https://doi.org/10.1007/s10649-023-10276-3","url":null,"abstract":"<p>This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children’s subtraction by addition strategy use (SBA; e.g., 712 − 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied components of conceptual knowledge: children’s knowledge of the addition/subtraction complement principle (i.e., if <i>a</i> + <i>b</i> = <i>c</i>, then <i>c</i> − <i>b</i> = <i>a</i> and <i>c</i> − <i>a</i> = <i>b</i>) and their knowledge of different conceptual subtraction models (i.e., understanding that subtraction can be conceived not only as “taking away” but also as “determining the difference”). SBA occurrence was examined using a variability on demand task, in which children had to use multiple strategies to solve a subtraction. SBA frequency and strategy adaptivity were investigated with a task in which children could freely choose between SBA and direct subtraction (e.g., 712 − 346 = ?; 712 − 300 = 412, 412 − 40 = 372, and 372 − 6 = 366) to solve 15 subtractions. We measured both children’s knowledge of the addition/subtraction complement principle, and whether they understood subtraction also as “determining the difference.” SBA occurrence and frequency were not related to conceptual knowledge. However, strategy adaptivity was related to children’s knowledge of the addition/subtraction complement principle. Our findings highlight the importance of attention to conceptual knowledge when teaching multi-digit subtraction and expand the literature about the relation between procedural and conceptual knowledge.</p>","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138562126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.1007/s10649-023-10262-9
Ling Zhang, Naiqing Song, Guowei Wu, Jinfa Cai
This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students’ behavior in these three stages of problem posing, especially focusing on investigating the influence of task situation format and mathematical maturity on students’ thinking. The study was conducted using a 2 × 2 mixed design: task situation format (with or without specific numerical information) × subject category (master’s students or sixth graders). Regarding the task situation format, students’ performance on tasks with numbers was found to be significantly better than that on tasks without numbers, which was reflected in the metrics of how well they understood the task and the complexity and clarity of the posed problems. In particular, students spent more fixation duration on understanding and processing the information in tasks without numbers; they had a longer fixation duration on parts involving presenting uncertain numerical information; in addition, the task situation format with or without numbers had an effect on students’ selection and processing of information related to the numbers, elements, and relationships rather than information regarding the context presented in the task. Regarding the subject category, we found that mathematical maturity did not predict the quantity of problems posed on either type of task. There was no significant main group difference found in the eye-movement metrics.
{"title":"Understanding the cognitive processes of mathematical problem posing: evidence from eye movements","authors":"Ling Zhang, Naiqing Song, Guowei Wu, Jinfa Cai","doi":"10.1007/s10649-023-10262-9","DOIUrl":"https://doi.org/10.1007/s10649-023-10262-9","url":null,"abstract":"<p>This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students’ behavior in these three stages of problem posing, especially focusing on investigating the influence of task situation format and mathematical maturity on students’ thinking. The study was conducted using a 2 × 2 mixed design: task situation format (with or without specific numerical information) × subject category (master’s students or sixth graders). Regarding the task situation format, students’ performance on tasks with numbers was found to be significantly better than that on tasks without numbers, which was reflected in the metrics of how well they understood the task and the complexity and clarity of the posed problems. In particular, students spent more fixation duration on understanding and processing the information in tasks without numbers; they had a longer fixation duration on parts involving presenting uncertain numerical information; in addition, the task situation format with or without numbers had an effect on students’ selection and processing of information related to the numbers, elements, and relationships rather than information regarding the context presented in the task. Regarding the subject category, we found that mathematical maturity did not predict the quantity of problems posed on either type of task. There was no significant main group difference found in the eye-movement metrics.</p>","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-06DOI: 10.1007/s10649-023-10269-2
Snezana Lawrence
{"title":"Book Review: The new mathematics education of new Europe. Alexander Karp (Ed.) (2020) Eastern European mathematics education in the decades of change","authors":"Snezana Lawrence","doi":"10.1007/s10649-023-10269-2","DOIUrl":"https://doi.org/10.1007/s10649-023-10269-2","url":null,"abstract":"","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135635014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-24DOI: 10.1007/s10649-023-10272-7
Jodie Hunter, Roberta Hunter
{"title":"Correction to: Weaving together the threads of Indigenous knowledge and mathematics","authors":"Jodie Hunter, Roberta Hunter","doi":"10.1007/s10649-023-10272-7","DOIUrl":"https://doi.org/10.1007/s10649-023-10272-7","url":null,"abstract":"","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135268416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-21DOI: 10.1007/s10649-023-10270-9
David Wagner, Susanne Prediger, Michèle Artigue, Angelika Bikner-Ahsbahs, Gail Fitzsimons, Tamsin Meaney, Vilma Mesa, Demetra Pitta-Pantazi, Luis Radford, Michal Tabach
{"title":"The field of mathematics education research and its boundaries","authors":"David Wagner, Susanne Prediger, Michèle Artigue, Angelika Bikner-Ahsbahs, Gail Fitzsimons, Tamsin Meaney, Vilma Mesa, Demetra Pitta-Pantazi, Luis Radford, Michal Tabach","doi":"10.1007/s10649-023-10270-9","DOIUrl":"https://doi.org/10.1007/s10649-023-10270-9","url":null,"abstract":"","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135511742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-21DOI: 10.1007/s10649-023-10267-4
Dirk De Bock
{"title":"Book Review: One hundred years of mathematics education seen through the lens of ICMI. Fulvia Furinghetti & Livia Giacardi (Eds.) (2022). The International Commission on Mathematical Instruction, 1908–2008: People, Events, and Challenges in Mathematics Education","authors":"Dirk De Bock","doi":"10.1007/s10649-023-10267-4","DOIUrl":"https://doi.org/10.1007/s10649-023-10267-4","url":null,"abstract":"","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135512387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-13DOI: 10.1007/s10649-023-10266-5
David Pomeroy, Mahdis Azarmandi, Matiu Tai Ratima, Sara Tolbert, Kay-Lee Jones, Nathan Riki, Te Hurinui Karaka-Clarke
Abstract Decades of research has documented the consequences of allocating school students into a hierarchy of classes with narrow ranges of mathematics attainment, a process known as streaming, tracking, setting, or “ability” grouping. The purported benefits of streaming are inconsistent and disputed, but the harms are clear, in particular, (1) the limiting curriculum often available in low streams and (2) the loss of self-confidence that results from being positioned in a low stream. Building on this foundation, we discuss streaming in mathematics as tied to systemic racism in Aotearoa New Zealand, where the harmful effects of streaming fall most heavily on Māori and Pasifika students. Previous analyses of race and streaming have focused primarily on the racial composition of streamed classes, bias in stream allocation, and racialised teacher expectations in streamed settings. In contrast, we focus on the emotional consequences of streaming, arguing that streaming produces racialised emotions of shame and entitlement as unintended but predictable consequences. We illustrate the racialised production of entitlement and shame through collaborative storying, interweaving our own biographies with a re-analysis of student interviews from two prior studies.
{"title":"Shame, entitlement, and the systemic racism of mathematics “ability” grouping in Aotearoa New Zealand","authors":"David Pomeroy, Mahdis Azarmandi, Matiu Tai Ratima, Sara Tolbert, Kay-Lee Jones, Nathan Riki, Te Hurinui Karaka-Clarke","doi":"10.1007/s10649-023-10266-5","DOIUrl":"https://doi.org/10.1007/s10649-023-10266-5","url":null,"abstract":"Abstract Decades of research has documented the consequences of allocating school students into a hierarchy of classes with narrow ranges of mathematics attainment, a process known as streaming, tracking, setting, or “ability” grouping. The purported benefits of streaming are inconsistent and disputed, but the harms are clear, in particular, (1) the limiting curriculum often available in low streams and (2) the loss of self-confidence that results from being positioned in a low stream. Building on this foundation, we discuss streaming in mathematics as tied to systemic racism in Aotearoa New Zealand, where the harmful effects of streaming fall most heavily on Māori and Pasifika students. Previous analyses of race and streaming have focused primarily on the racial composition of streamed classes, bias in stream allocation, and racialised teacher expectations in streamed settings. In contrast, we focus on the emotional consequences of streaming, arguing that streaming produces racialised emotions of shame and entitlement as unintended but predictable consequences. We illustrate the racialised production of entitlement and shame through collaborative storying, interweaving our own biographies with a re-analysis of student interviews from two prior studies.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1007/s10649-023-10265-6
Stanislaw Schukajlow, Janina Krawitz, Jonas Kanefke, Werner Blum, Katrin Rakoczy
Abstract Open mathematical modelling problems that can be solved with multiple methods and have multiple possible results are an important part of school curricula in mathematics and science. Solving open modelling problems in school should prepare students to apply their mathematical knowledge in their current and future lives. One characteristic of these problems is that information that is essential for solving the problems is missing. In the present study, we aimed to analyze students’ cognitive barriers while they solved open modelling problems, and we evaluated the effects of instructional prompts on their success in solving such problems. A quantitative experimental study ( N = 263) and a qualitative study ( N = 4) with secondary school students indicated that identifying unknown quantities and making numerical assumptions about these quantities are important cognitive barriers to solving open modelling problems. Task-specific instructional prompts helped students overcome these barriers and improved their solution rates. Students who were given instructional prompts included numerical assumptions in their solutions more often than students who were not given such prompts. These findings contribute to theories about solving open modelling problems by uncovering cognitive barriers and describing students’ cognitive processes as they solve these problems. In addition, the findings contribute to improving teaching practice by indicating the potential and limitations of task-specific instructional prompts that can be used to support students’ solution processes in the classroom.
{"title":"Open modelling problems: cognitive barriers and instructional prompts","authors":"Stanislaw Schukajlow, Janina Krawitz, Jonas Kanefke, Werner Blum, Katrin Rakoczy","doi":"10.1007/s10649-023-10265-6","DOIUrl":"https://doi.org/10.1007/s10649-023-10265-6","url":null,"abstract":"Abstract Open mathematical modelling problems that can be solved with multiple methods and have multiple possible results are an important part of school curricula in mathematics and science. Solving open modelling problems in school should prepare students to apply their mathematical knowledge in their current and future lives. One characteristic of these problems is that information that is essential for solving the problems is missing. In the present study, we aimed to analyze students’ cognitive barriers while they solved open modelling problems, and we evaluated the effects of instructional prompts on their success in solving such problems. A quantitative experimental study ( N = 263) and a qualitative study ( N = 4) with secondary school students indicated that identifying unknown quantities and making numerical assumptions about these quantities are important cognitive barriers to solving open modelling problems. Task-specific instructional prompts helped students overcome these barriers and improved their solution rates. Students who were given instructional prompts included numerical assumptions in their solutions more often than students who were not given such prompts. These findings contribute to theories about solving open modelling problems by uncovering cognitive barriers and describing students’ cognitive processes as they solve these problems. In addition, the findings contribute to improving teaching practice by indicating the potential and limitations of task-specific instructional prompts that can be used to support students’ solution processes in the classroom.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135199175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-20DOI: 10.1007/s10649-023-10268-3
Anthony Cotton
{"title":"Book review: A life in critical mathematics education. Ole Skovsmose (2023) Critical Mathematics Education. Springer","authors":"Anthony Cotton","doi":"10.1007/s10649-023-10268-3","DOIUrl":"https://doi.org/10.1007/s10649-023-10268-3","url":null,"abstract":"","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136313267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-20DOI: 10.1007/s10649-023-10264-7
Anna Tirpáková, Dalibor Gonda, Adriana Wiegerová, Hana Navrátilová
Abstract The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to the results of several researches, these changes do not occur automatically, and the neglect of their development leads to students’ insufficient adoption of substitution. The submitted contribution presents a new way of teaching substitution, the stages of which support the gradual development of the necessary competences of students, so that substitution becomes part of their computing apparatus. The effectiveness of the mentioned method of teaching substitution was also verified experimentally. By conducting a pedagogical experiment, it was confirmed that the application of the substitution teaching method developed by us led to more frequent use of substitution by students from the experimental group (47 students) compared to students from the control group (82 students) who learned substitution in the usual way. It emerged from the interview with experimental group students that they considered the proposed method suitable and that it encouraged them to learn substitution in depth.
{"title":"Developing the concept of task substitution and transformation by defining own equivalences","authors":"Anna Tirpáková, Dalibor Gonda, Adriana Wiegerová, Hana Navrátilová","doi":"10.1007/s10649-023-10264-7","DOIUrl":"https://doi.org/10.1007/s10649-023-10264-7","url":null,"abstract":"Abstract The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to the results of several researches, these changes do not occur automatically, and the neglect of their development leads to students’ insufficient adoption of substitution. The submitted contribution presents a new way of teaching substitution, the stages of which support the gradual development of the necessary competences of students, so that substitution becomes part of their computing apparatus. The effectiveness of the mentioned method of teaching substitution was also verified experimentally. By conducting a pedagogical experiment, it was confirmed that the application of the substitution teaching method developed by us led to more frequent use of substitution by students from the experimental group (47 students) compared to students from the control group (82 students) who learned substitution in the usual way. It emerged from the interview with experimental group students that they considered the proposed method suitable and that it encouraged them to learn substitution in depth.","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136313812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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