首页 > 最新文献

Mathematics Education Research Journal最新文献

英文 中文
Teacher–child interactions during shared book reading in the domain of early mathematics 早期数学领域师幼共同阅读图书时的互动
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-09-05 DOI: 10.1007/s13394-024-00503-2
Emke Op ‘t Eynde, Mayra Lara Mascareño, Fien Depaepe, Lieven Verschaffel, Joke Torbeyns

This study examined the teacher–child interactions during shared book reading (SBR) in the domain of early mathematics. We investigated preschool teachers’ and children’s talk in terms of (1) communicative acts, mathematical focus, and level of abstraction (literal versus inferential), (2) the sequential relation between teacher’s talk and children’s mathematical inferential talk, and (3) the contribution of the type of picture book (mathematical versus non-mathematical) and teachers’ pedagogical content knowledge (MPCK) to the amount of mathematical inferential talk and the strength of the sequential relation. Twelve preschool teachers read one mathematical and one non-mathematical picture book to their preschoolers, resulting in 24 reading sessions. All 24 sessions were video-recorded, transcribed, and coded. Our analyses revealed that teachers’ mathematical talk was dominated by initiations, follow-ups and comments, and children’s mathematical talk by responses and comments. About 30% of teachers’ mathematical initiations and children’s mathematical responses were inferential; approximately 25% of children’s mathematical comments were inferential. Next, we observed a strong sequential relation between teachers’ mathematical inferential prompts and children’s mathematical inferential responses. Finally, the type of picture book, but not preschool teachers’ MPCK, contributed to the SBR interaction: preschool teachers formulated more inferential elaborative follow-ups when reading a mathematical compared to a non-mathematical picture book, and the sequential relation between teacher’s mathematical inferential prompts and children’s mathematical inferential responses was stronger for mathematical picture books.

本研究探讨了早期数学领域中教师与儿童在共享图书阅读(SBR)过程中的互动。我们从以下几个方面对学前教师和儿童的谈话进行了研究:(1)交流行为、数学重点和抽象程度(字面与推理);(2)教师谈话和儿童数学推理谈话之间的顺序关系;(3)图画书类型(数学与非数学)和教师的教学内容知识(MPCK)对数学推理谈话的数量和顺序关系强度的影响。12 位学前教师为学前儿童阅读了一本数学绘本和一本非数学绘本,共进行了 24 次阅读。我们对所有 24 个阅读过程进行了录像、转录和编码。我们的分析表明,教师的数学对话主要以发起、跟进和评论为主,而儿童的数学对话则以回应和评论为主。在教师的数学启发和儿童的数学回应中,约有 30% 是推论性的;在儿童的数学评论中,约有 25% 是推论性的。其次,我们观察到教师的数学推理提示和儿童的数学推理回答之间有很强的顺序关系。最后,图画书的类型(而非学前教师的多语种能力)对 SBR 的交互作用起了作用:与非数学图画书相比,学前教师在阅读数学图画书时提出了更多的推论性详细追问,而且数学图画书中教师的数学推论性提示与儿童的数学推论性回答之间的顺序关系更强。
{"title":"Teacher–child interactions during shared book reading in the domain of early mathematics","authors":"Emke Op ‘t Eynde, Mayra Lara Mascareño, Fien Depaepe, Lieven Verschaffel, Joke Torbeyns","doi":"10.1007/s13394-024-00503-2","DOIUrl":"https://doi.org/10.1007/s13394-024-00503-2","url":null,"abstract":"<p>This study examined the teacher–child interactions during shared book reading (SBR) in the domain of early mathematics. We investigated preschool teachers’ and children’s talk in terms of (1) communicative acts, mathematical focus, and level of abstraction (literal versus inferential), (2) the sequential relation between teacher’s talk and children’s mathematical inferential talk, and (3) the contribution of the type of picture book (mathematical versus non-mathematical) and teachers’ pedagogical content knowledge (MPCK) to the amount of mathematical inferential talk and the strength of the sequential relation. Twelve preschool teachers read one mathematical and one non-mathematical picture book to their preschoolers, resulting in 24 reading sessions. All 24 sessions were video-recorded, transcribed, and coded. Our analyses revealed that teachers’ mathematical talk was dominated by initiations, follow-ups and comments, and children’s mathematical talk by responses and comments. About 30% of teachers’ mathematical initiations and children’s mathematical responses were inferential; approximately 25% of children’s mathematical comments were inferential. Next, we observed a strong sequential relation between teachers’ mathematical inferential prompts and children’s mathematical inferential responses. Finally, the type of picture book, but not preschool teachers’ MPCK, contributed to the SBR interaction: preschool teachers formulated more inferential elaborative follow-ups when reading a mathematical compared to a non-mathematical picture book, and the sequential relation between teacher’s mathematical inferential prompts and children’s mathematical inferential responses was stronger for mathematical picture books.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219542","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}
引用次数: 0
Defining and measuring quality in students’ mathematical writing: a systematic literature review 定义和衡量学生数学写作的质量:系统文献综述
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-08-28 DOI: 10.1007/s13394-024-00501-4
Anna Teledahl, Cecilia Kilhamn, Linda Marie Ahl, Ola Helenius

Mathematical communication, encompassing writing in, about, and for mathematics, is a critical competency. Defining excellent mathematical writing standards, however, remains challenging. To address this, we conducted a systematic review of 48 scholarly works on quality in mathematical writing. Our findings reveal mathematical writing for different purposes under scrutiny, including general mathematical writing, proof writing, reflective writing, expository writing, and descriptive writing during problem solving. To assess quality, researchers explore a variety of facets, such as syntax and semantics. Progression pathways vary, with both quantitative and qualitative evaluations—analysing text structure, writing style, and the use of different semiotic elements. It seems that in mathematics education, a consensus on quality measurement remains elusive. Proof writing is a notable exception. Among reviewed articles examining proof writing, a common set of standards emerges and provides valuable guidance. We propose that mathematical writing, perhaps especially in the context of reporting solutions in problem solving, can draw from proof writing standards. ‘Good’ mathematical writing would then require students to focus on (1) defining assumptions and assigning variables; (2) producing a coherent narrative, including relevant calculations (semantic issues); (3) using correct language, representations, and mathematical symbols (syntax issues); and (4) attending to what is appropriate in the context.

数学交流,包括数学写作、关于数学的写作和为数学而写作,是一项重要的能力。然而,定义优秀的数学写作标准仍然具有挑战性。为此,我们对 48 篇有关数学写作质量的学术著作进行了系统回顾。我们的研究结果表明,不同目的的数学写作都受到了严格的审查,包括一般数学写作、证明写作、反思写作、说明性写作和问题解决过程中的描述性写作。为了评估写作质量,研究人员探讨了语法和语义等多个方面。进阶途径各不相同,既有定量评价,也有定性评价--分析文本结构、写作风格和不同符号元素的使用。在数学教育中,似乎仍未就质量衡量达成共识。证明写作是一个明显的例外。在审查证明写作的文章中,出现了一套共同的标准,并提供了有价值的指导。我们建议,数学写作,尤其是在报告问题解决过程中的解决方案时,可以借鉴证明写作的标准。好的 "数学写作将要求学生专注于:(1)定义假设和分配变量;(2)进行连贯的叙述,包括相关的计算(语义问题);(3)使用正确的语言、表述和数学符号(语法问题);以及(4)关注语境中的适当内容。
{"title":"Defining and measuring quality in students’ mathematical writing: a systematic literature review","authors":"Anna Teledahl, Cecilia Kilhamn, Linda Marie Ahl, Ola Helenius","doi":"10.1007/s13394-024-00501-4","DOIUrl":"https://doi.org/10.1007/s13394-024-00501-4","url":null,"abstract":"<p>Mathematical communication, encompassing writing in, about, and for mathematics, is a critical competency. Defining excellent mathematical writing standards, however, remains challenging. To address this, we conducted a systematic review of 48 scholarly works on quality in mathematical writing. Our findings reveal mathematical writing for different purposes under scrutiny, including general mathematical writing, proof writing, reflective writing, expository writing, and descriptive writing during problem solving. To assess quality, researchers explore a variety of facets, such as syntax and semantics. Progression pathways vary, with both quantitative and qualitative evaluations—analysing text structure, writing style, and the use of different semiotic elements. It seems that in mathematics education, a consensus on quality measurement remains elusive. Proof writing is a notable exception. Among reviewed articles examining proof writing, a common set of standards emerges and provides valuable guidance. We propose that mathematical writing, perhaps especially in the context of reporting solutions in problem solving, can draw from proof writing standards. ‘Good’ mathematical writing would then require students to focus on (1) defining assumptions and assigning variables; (2) producing a coherent narrative, including relevant calculations (semantic issues); (3) using correct language, representations, and mathematical symbols (syntax issues); and (4) attending to what is appropriate in the context.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227369","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}
引用次数: 0
Pre-service mathematics teachers’ personal meanings proclaiming about the characteristics of realistic mathematics problems 职前数学教师对现实数学问题特征的个人意义宣示
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-08-22 DOI: 10.1007/s13394-024-00497-x
Serife Sevinc

This study aimed to elicit middle school pre-service mathematics teachers’ personal meanings of realistic mathematics problems. The study presents a portion of a larger design-based study involving teacher training sessions encompassing small-group discussions, writing realistic mathematics problems, and whole-group discussions. The audio records of the pre-service teachers’ discussions and their written artifacts were analyzed in three coding cycles. The findings indicated that the pre-service teachers’ personal meanings of realistic mathematics problems comprised both in-school situations that students themselves could experience and real-life situations that mostly required occupational decisions such as optimization in engineering. Besides, pre-service teachers considered that realistic situations often involve multiple information and could be solved by multiple solution methods that might lead to multiple acceptable answers. This study highlighted the informative role of articulating pre-service mathematics teachers’ personal meanings of realistic mathematics problems in designing teacher education courses and further discussed such implications for mathematics teacher education.

本研究旨在了解初中职前数学教师对现实数学问题的个人理解。本研究是一项大型设计型研究的一部分,涉及教师培训课程,包括小组讨论、撰写现实数学问题和全组讨论。通过三个编码周期,对职前教师讨论的音频记录及其书面材料进行了分析。研究结果表明,职前教师对现实数学问题的个人理解既包括学生自己能体验到的校内情境,也包括现实生活中大多需要职业决策的情境,如工程中的优化。此外,职前教师认为现实情境往往涉及多种信息,可以用多种解题方法来解决,从而得出多种可接受的答案。本研究强调了在教师教育课程设计中阐明职前数学教师对现实数学问题的个人意义的信息作用,并进一步讨论了这些问题对数学教师教育的影响。
{"title":"Pre-service mathematics teachers’ personal meanings proclaiming about the characteristics of realistic mathematics problems","authors":"Serife Sevinc","doi":"10.1007/s13394-024-00497-x","DOIUrl":"https://doi.org/10.1007/s13394-024-00497-x","url":null,"abstract":"<p>This study aimed to elicit middle school pre-service mathematics teachers’ personal meanings of realistic mathematics problems. The study presents a portion of a larger design-based study involving teacher training sessions encompassing small-group discussions, writing realistic mathematics problems, and whole-group discussions. The audio records of the pre-service teachers’ discussions and their written artifacts were analyzed in three coding cycles. The findings indicated that the pre-service teachers’ personal meanings of realistic mathematics problems comprised both in-school situations that students themselves could experience and real-life situations that mostly required occupational decisions such as optimization in engineering. Besides, pre-service teachers considered that realistic situations often involve multiple information and could be solved by multiple solution methods that might lead to multiple acceptable answers. This study highlighted the informative role of articulating pre-service mathematics teachers’ personal meanings of realistic mathematics problems in designing teacher education courses and further discussed such implications for mathematics teacher education.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219543","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}
引用次数: 0
Teachers’ goal communication in Nordic mathematics classrooms 北欧数学课堂中的教师目标交流
IF 1.4 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-08-10 DOI: 10.1007/s13394-024-00498-w
Alexander J. V. Selling, Kirsti Klette, Guri A. Nortvedt
{"title":"Teachers’ goal communication in Nordic mathematics classrooms","authors":"Alexander J. V. Selling, Kirsti Klette, Guri A. Nortvedt","doi":"10.1007/s13394-024-00498-w","DOIUrl":"https://doi.org/10.1007/s13394-024-00498-w","url":null,"abstract":"","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141919973","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}
引用次数: 0
Errors and misconceptions of secondary school students in absolute values: a systematic literature review 中学生在绝对值方面的错误和误解:系统文献综述
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-08-05 DOI: 10.1007/s13394-024-00499-9
John P. Papadouris, Vassilis Komis, Konstantinos Lavidas

Although absolute value is of interest to mathematics teaching researchers, since many students face problems with it, there does not seem to be an integrated record of students’ errors. The present study attempts to conduct a systematic review to identify and categorize errors and misconceptions of secondary school students aged 12–18 concerning the concept of absolute value. Following the PRISMA method, empirical studies published in English later since 1990 studying the errors and misconceptions of secondary school students with absolute value were looked up through the databases Scopus and Web of Sciences as well as through the Google Scholar search engine. From the 11 empirical studies that were eventually found, a categorization of misconceptions and corresponding errors arose. The first main category concerns the transition from the arithmetic to the algebraic domain while the second main category concerns the definition of absolute value in the form of a piecewise function. It is noteworthy that these two categories sometimes interact and are linked. Based on these findings, practical implications are discussed that strengthen the understanding of mathematical literacy.

虽然绝对值是数学教学研究人员关注的问题,因为许多学生都面临着绝对值的问题,但似乎并没有关于学生错误的综合记录。本研究试图对 12-18 岁中学生关于绝对值概念的错误和误解进行系统回顾和分类。按照 PRISMA 方法,我们通过 Scopus 和 Web of Sciences 数据库以及 Google Scholar 搜索引擎,查找了 1990 年以后发表的、研究中学生在绝对值方面的错误和误解的英文实证研究。从最终找到的 11 项实证研究中,我们对误解和相应的错误进行了分类。第一大类涉及从算术领域到代数领域的过渡,第二大类涉及以片断函数形式定义绝对值。值得注意的是,这两类错误有时是相互影响和联系的。基于这些发现,讨论了加强对数学素养理解的实际意义。
{"title":"Errors and misconceptions of secondary school students in absolute values: a systematic literature review","authors":"John P. Papadouris, Vassilis Komis, Konstantinos Lavidas","doi":"10.1007/s13394-024-00499-9","DOIUrl":"https://doi.org/10.1007/s13394-024-00499-9","url":null,"abstract":"<p>Although absolute value is of interest to mathematics teaching researchers, since many students face problems with it, there does not seem to be an integrated record of students’ errors. The present study attempts to conduct a systematic review to identify and categorize errors and misconceptions of secondary school students aged 12–18 concerning the concept of absolute value. Following the PRISMA method, empirical studies published in English later since 1990 studying the errors and misconceptions of secondary school students with absolute value were looked up through the databases Scopus and Web of Sciences as well as through the Google Scholar search engine. From the 11 empirical studies that were eventually found, a categorization of misconceptions and corresponding errors arose. The first main category concerns the transition from the arithmetic to the algebraic domain while the second main category concerns the definition of absolute value in the form of a piecewise function. It is noteworthy that these two categories sometimes interact and are linked. Based on these findings, practical implications are discussed that strengthen the understanding of mathematical literacy.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969460","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}
引用次数: 0
A proposal for the study of mathematics teachers’ beliefs through the analysis of their practices 通过分析数学教师的实践来研究其信念的建议
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-07-02 DOI: 10.1007/s13394-024-00496-y
Graciela Acevedo, Luis Roberto Pino-Fan

In recent years, research on mathematics teachers’ beliefs has increasingly shifted its focus toward understanding their connection with instructional practices. This article introduces a model designed to explore mathematics teachers’ beliefs through a comprehensive analysis of their practices. The contributions of models that study the relationship between beliefs and practices of teachers, such as those from Schoenfeld (Journal of Mathematical Behavior, 18(3), 243–261, 2000) and Cobb and Yackel (Educational Psychologist, 31(3), 175–190, 1996), were reviewed and considered. Additionally, it includes methodological considerations from Leatham and Speer for studying beliefs. These approaches are integrated by utilizing the notions of practice, types of didactic-mathematical practices and norms, derived from the onto-semiotic approach, as the central organizing axis. Furthermore, we demonstrate the application of these stages of analysis for exploring teachers’ beliefs by analyzing the beliefs of a prospective mathematics teacher. The findings enable us to identify the beliefs held by this prospective teacher regarding the use of introductory activities characterized by a high motivational level but a low mathematical level. Additionally, these results provide insights into potential avenues for developing training programs aimed at instigating a shift in these beliefs, thereby fostering an enhancement in teaching practices. These outcomes show the feasibility of the analytical model proposed in this article.

近年来,有关数学教师信念的研究越来越多地将重点转向了解数学教师信念与教学实践的联系。本文介绍了一种旨在通过全面分析数学教师的教学实践来探究其教学信念的模式。文章回顾并考虑了 Schoenfeld(《数学行为杂志》,18(3),243-261,2000 年)和 Cobb 和 Yackel(《教育心理学家》,31(3),175-190,1996 年)等研究教师信念与教学实践之间关系的模式的贡献。此外,它还包括 Leatham 和 Speer 在研究信念方面的方法考虑。这些方法通过利用实践、教学-数学实践类型和规范等概念进行整合,这些概念源于to-semiotic 方法,并以此为中心组织轴。此外,我们还通过分析一位未来数学教师的信念,展示了这些分析阶段在探索教师信念方面的应用。研究结果使我们能够确定这位准教师在使用动机水平高而数学水平低的导入活动时所持有的信念。此外,这些结果还为制定培训计划提供了潜在的途径,旨在促使这些信念发生转变,从而促进教学实践的改进。这些结果表明,本文提出的分析模型是可行的。
{"title":"A proposal for the study of mathematics teachers’ beliefs through the analysis of their practices","authors":"Graciela Acevedo, Luis Roberto Pino-Fan","doi":"10.1007/s13394-024-00496-y","DOIUrl":"https://doi.org/10.1007/s13394-024-00496-y","url":null,"abstract":"<p>In recent years, research on mathematics teachers’ beliefs has increasingly shifted its focus toward understanding their connection with instructional practices. This article introduces a model designed to explore mathematics teachers’ beliefs through a comprehensive analysis of their practices. The contributions of models that study the relationship between beliefs and practices of teachers, such as those from Schoenfeld (Journal of Mathematical Behavior, 18(3), 243–261, 2000) and Cobb and Yackel (Educational Psychologist, 31(3), 175–190, 1996), were reviewed and considered. Additionally, it includes methodological considerations from Leatham and Speer for studying beliefs. These approaches are integrated by utilizing the notions of practice, types of didactic-mathematical practices and norms, derived from the onto-semiotic approach, as the central organizing axis. Furthermore, we demonstrate the application of these stages of analysis for exploring teachers’ beliefs by analyzing the beliefs of a prospective mathematics teacher. The findings enable us to identify the beliefs held by this prospective teacher regarding the use of introductory activities characterized by a high motivational level but a low mathematical level. Additionally, these results provide insights into potential avenues for developing training programs aimed at instigating a shift in these beliefs, thereby fostering an enhancement in teaching practices. These outcomes show the feasibility of the analytical model proposed in this article.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141524759","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}
引用次数: 0
First- and second-grade prospective teachers reconstructing definitions of polygon diagonals 一、二年级准教师重构多边形对角线的定义
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-07-01 DOI: 10.1007/s13394-024-00495-z
Huda Shayeb, Juhaina Awawdeh Shahbari, Aehsan Haj-Yahya

The current study examined how prospective first- and second-grade mathematics teachers define the polygon diagonals concept, how they reconstruct their definition during and following an intervention, and how their concept images develop over time. Twenty-three prospective teachers participated in the study, during which they were asked to analyze mathematical events involving a conflict that could be resolved using a precise mathematical definition of a polygon diagonal. Data were collected from prequestionnaires, postquestionnaires, and observations of class discussions. The study findings indicate that before the intervention, all participants provided incorrect definitions and struggled to identify nonprototypical examples of polygon diagonals in the prequestionnaire. However, the process of analyzing mathematical events helped the participants reconstruct their definitions of polygon diagonals and identify the critical attributes of this concept, which improved their ability to extend the concept’s image to include nonprototypical examples. The participants’ improved understanding was evident in the significant improvements in the postquestionnaire.

本研究考察了未来的一年级和二年级数学教师如何定义多边形对角线的概念,他们在干预过程中和干预后如何重建自己的定义,以及他们的概念图像如何随着时间的推移而发展。23 名准教师参与了这项研究,在研究过程中,他们被要求分析涉及冲突的数学事件,这些冲突可以用多边形对角线的精确数学定义来解决。数据收集来自课前问卷、课后问卷以及对课堂讨论的观察。研究结果表明,在干预前,所有参与者都提供了不正确的定义,并且在前置问卷中很难找出多边形对角线的非典型例子。然而,分析数学事件的过程帮助学员重新构建了多边形对角线的定义,并确定了这一概念的关键属性,从而提高了他们扩展概念形象的能力,使其包括非原型的例子。学员们对多边形对角线的理解能力的提高在课后问卷中得到了明显的体现。
{"title":"First- and second-grade prospective teachers reconstructing definitions of polygon diagonals","authors":"Huda Shayeb, Juhaina Awawdeh Shahbari, Aehsan Haj-Yahya","doi":"10.1007/s13394-024-00495-z","DOIUrl":"https://doi.org/10.1007/s13394-024-00495-z","url":null,"abstract":"<p>The current study examined how prospective first- and second-grade mathematics teachers define the polygon diagonals concept, how they reconstruct their definition during and following an intervention, and how their concept images develop over time. Twenty-three prospective teachers participated in the study, during which they were asked to analyze mathematical events involving a conflict that could be resolved using a precise mathematical definition of a polygon diagonal. Data were collected from prequestionnaires, postquestionnaires, and observations of class discussions. The study findings indicate that before the intervention, all participants provided incorrect definitions and struggled to identify nonprototypical examples of polygon diagonals in the prequestionnaire. However, the process of analyzing mathematical events helped the participants reconstruct their definitions of polygon diagonals and identify the critical attributes of this concept, which improved their ability to extend the concept’s image to include nonprototypical examples. The participants’ improved understanding was evident in the significant improvements in the postquestionnaire.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141524752","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}
引用次数: 0
The development of elementary teachers’ personal meanings of problem-solving through engaging in open-ended tasks 通过参与开放式任务发展小学教师解决问题的个人意义
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-07-01 DOI: 10.1007/s13394-024-00493-1
Serife Sevinc, Dionne Cross Francis, Rick Hudson, Jinqing Liu

In this study, we explored elementary school teachers’ experiences working on open-ended mathematics tasks during a 10-day professional development (PD) workshop. Teachers engaged with the tasks daily in a session call Morning Math (MM). Thirty-two elementary teachers from three school districts in the USA participated in a 2-year professional development (PD) program. Analysis of videos of teacher engagement in the tasks and interviews shows that the use of open-ended mathematics tasks embedded within problem-solving focused PD could shape elementary school teachers’ personal meanings about learning mathematics through problem-solving. The findings indicate that the teachers’ take-aways from the PD were not limited to the mathematical content of the MM problems (i.e., mathematical residue), instead teachers’ experiences with open-ended mathematics tasks engendered personal meanings reflecting pedagogical residue with cognitive, affective, and social components. This result shows the crucial role of PD in shaping teachers’ mathematics-related personal meanings which research suggests that it will subsequently influence their beliefs and instruction.

在这项研究中,我们探讨了小学教师在为期 10 天的专业发展(PD)工作坊中完成开放式数学任务的经验。教师们在名为 "晨间数学"(MM)的课程中每天都要完成这些任务。来自美国三个学区的 32 名小学教师参加了为期两年的专业发展(PD)项目。对教师参与任务的视频和访谈分析表明,在以问题解决为重点的专业发展项目中使用开放式数学任务,可以塑造小学教师通过问题解决学习数学的个人意义。研究结果表明,教师从教学实践活动中获得的收获并不局限于数学问题的数学内容(即数学残余),相反,教师对开放式数学任务的体验产生了个人意义,反映了教学残余的认知、情感和社会成分。这一结果表明,教学设计在塑造教师与数学相关的个人意义方面起着至关重要的作用。
{"title":"The development of elementary teachers’ personal meanings of problem-solving through engaging in open-ended tasks","authors":"Serife Sevinc, Dionne Cross Francis, Rick Hudson, Jinqing Liu","doi":"10.1007/s13394-024-00493-1","DOIUrl":"https://doi.org/10.1007/s13394-024-00493-1","url":null,"abstract":"<p>In this study, we explored elementary school teachers’ experiences working on open-ended mathematics tasks during a 10-day professional development (PD) workshop. Teachers engaged with the tasks daily in a session call Morning Math (MM). Thirty-two elementary teachers from three school districts in the USA participated in a 2-year professional development (PD) program. Analysis of videos of teacher engagement in the tasks and interviews shows that the use of open-ended mathematics tasks embedded within problem-solving focused PD could shape elementary school teachers’ personal meanings about learning mathematics through problem-solving. The findings indicate that the teachers’ take-aways from the PD were not limited to the mathematical content of the MM problems (i.e., mathematical residue), instead teachers’ experiences with open-ended mathematics tasks engendered personal meanings reflecting pedagogical residue with cognitive, affective, and social components. This result shows the crucial role of PD in shaping teachers’ mathematics-related personal meanings which research suggests that it will subsequently influence their beliefs and instruction.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503897","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}
引用次数: 0
The confluence of attitudes towards mathematics and pedagogical practice: evaluating the use of mathematical manipulatives 数学态度与教学实践的结合:评估数学操作材料的使用情况
IF 1.8 Q3 EDUCATION, SCIENTIFIC DISCIPLINES Pub Date : 2024-06-20 DOI: 10.1007/s13394-024-00494-0
Kate Quane

The use of manipulatives to develop conceptual understanding is a prevalent practice in many mathematical learning experiences, particularly in the early years of schooling. From primary student perspectives, our understanding of the impact of manipulatives in mathematics education on students’ attitudes is limited. This study evaluates the impact of mathematical manipulatives on Young Children’s Attitudes Towards Mathematics (YCATM) by examining children’s drawings, as well as their written and verbal descriptions of their drawings from 106 year 2 and year 3 students. Classroom observations were conducted to investigate how attitudes towards mathematics are enacted during mathematical learning experiences. The modified three-dimensional model of attitude (MTMA) and Bruner’s experiential stages were used to investigate how manipulatives influence YCATM. Data analyses used systematic, numerical coding, and thematic and comparative approaches, employing inductive, deductive, and anticipatory coding for data from both lesson and non-lesson contexts. The findings suggest that young children enjoyed using manipulatives, contributing to their vision of mathematics and perceived competence. However, the transition between enactive, iconic, and symbolic experiences can contribute to the formation of negative attitudes. The present study also emphasizes the importance of context, content, and familiarity with the use of manipulatives.

在许多数学学习经验中,特别是在学前教育阶段,使用操作材料来发展概念理解是一种普遍的做法。从小学生的角度来看,我们对数学教育中的操作材料对学生态度的影响了解有限。本研究通过观察 106 名二、三年级学生的儿童绘画作品,以及他们对绘画作品的书面和口头描述,评估数学操作材料对幼儿数学态度(YCATM)的影响。我们还对课堂进行了观察,以调查在数学学习经历中如何体现对数学的态度。修改后的态度三维模型(MTMA)和布鲁纳的经验阶段被用来研究操作材料如何影响 YCATM。数据分析采用了系统、数字编码、主题和比较方法,对课程和非课程情境中的数据进行了归纳、演绎和预期编码。研究结果表明,幼儿喜欢使用操作材料,这有助于提高他们对数学的认识和能力。然而,在活动经验、图标经验和符号经验之间的过渡可能会导致消极态度的形成。本研究还强调了使用操作材料的情境、内容和熟悉程度的重要性。
{"title":"The confluence of attitudes towards mathematics and pedagogical practice: evaluating the use of mathematical manipulatives","authors":"Kate Quane","doi":"10.1007/s13394-024-00494-0","DOIUrl":"https://doi.org/10.1007/s13394-024-00494-0","url":null,"abstract":"<p>The use of manipulatives to develop conceptual understanding is a prevalent practice in many mathematical learning experiences, particularly in the early years of schooling. From <i>primary student perspectives</i>, our understanding of the impact of manipulatives in mathematics education on students’ <i>attitudes</i> is limited. This study evaluates the impact of mathematical manipulatives on Young Children’s Attitudes Towards Mathematics (YCATM) by examining children’s drawings, as well as their written and verbal descriptions of their drawings from 106 year 2 and year 3 students. Classroom observations were conducted to investigate how attitudes towards mathematics are enacted during mathematical learning experiences. The modified three-dimensional model of attitude (MTMA) and Bruner’s experiential stages were used to investigate how manipulatives influence YCATM. Data analyses used systematic, numerical coding, and thematic and comparative approaches, employing inductive, deductive, and anticipatory coding for data from both lesson and non-lesson contexts. The findings suggest that young children enjoyed using manipulatives, contributing to their vision of mathematics and perceived competence. However, the transition between enactive, iconic, and symbolic experiences can contribute to the formation of negative attitudes. The present study also emphasizes the importance of context, content, and familiarity with the use of manipulatives.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503898","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}
引用次数: 0
Designing specific tools to enhance the numeracy of adults with intellectual disabilities 设计特定工具,提高智障成人的计算能力
IF 1.8 Q1 Mathematics Pub Date : 2024-05-06 DOI: 10.1007/s13394-024-00492-2
Lorraine Vera Gaunt

Numeracy is important for everyday life. Being numerate has a positive impact on the quality of life of individuals, with positive economic, health, and social outcomes. Despite this, little is known about the role of numeracy in the lives of adults with intellectual disability (ID). Design research has been used to develop ways to support mathematical learning for typically developing students. This study investigates the use of design research to develop context-specific, physical tools to support adults with intellectual disability to improve their numeracy capabilities and engagement in daily tasks. Using observation and interview data, findings demonstrate increased engagement and participation in the numeracy demands of these tasks. Participants reported positive perceptions of improved competence and independence. This study demonstrates the application of design research to the field of numeracy for adults with intellectual disability, and the usefulness of designing context-specific tools to support their numeracy development and independence.

计算能力对日常生活非常重要。精通算术对个人的生活质量有着积极的影响,对经济、健康和社会都有积极的作用。尽管如此,人们对计算能力在智障成人(ID)生活中的作用却知之甚少。设计研究已被用于开发支持典型发育学生数学学习的方法。本研究调查了如何利用设计研究来开发针对具体情况的物理工具,以支持智障成人提高计算能力和参与日常工作。通过观察和访谈数据,研究结果表明,这些任务对计算能力的要求提高了参与度。参与者对能力和独立性的提高有积极的看法。这项研究展示了设计研究在智障成人算术领域的应用,以及设计针对具体情况的工具来支持他们的算术发展和独立性的实用性。
{"title":"Designing specific tools to enhance the numeracy of adults with intellectual disabilities","authors":"Lorraine Vera Gaunt","doi":"10.1007/s13394-024-00492-2","DOIUrl":"https://doi.org/10.1007/s13394-024-00492-2","url":null,"abstract":"<p>Numeracy is important for everyday life. Being numerate has a positive impact on the quality of life of individuals, with positive economic, health, and social outcomes. Despite this, little is known about the role of numeracy in the lives of adults with intellectual disability (ID). Design research has been used to develop ways to support mathematical learning for typically developing students. This study investigates the use of design research to develop context-specific, physical tools to support adults with intellectual disability to improve their numeracy capabilities and engagement in daily tasks. Using observation and interview data, findings demonstrate increased engagement and participation in the numeracy demands of these tasks. Participants reported positive perceptions of improved competence and independence. This study demonstrates the application of design research to the field of numeracy for adults with intellectual disability, and the usefulness of designing context-specific tools to support their numeracy development and independence.</p>","PeriodicalId":46887,"journal":{"name":"Mathematics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930496","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}
引用次数: 0
期刊
Mathematics Education Research Journal
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1