Pub Date : 2021-05-25DOI: 10.1515/9783110661941-015
R. Moura, V. G. Haase, J. B. Lopes-Silva, L. T. Batista, Fernanda Rocha de Freitas, J. Bahnmueller, K. Moeller
Literacy and numeracy are culturally acquired abilities that are well established as crucial for educational and vocational prospects (Parsons & Bynner, 1997; Ritchie & Bates, 2013; Romano et al., 2010). When investigating these abilities in children, researchers from educational and cognitive sciences often focus on the writing and reading of either words or numbers. Accordingly, these usually represent two independent lines of research. Nevertheless, in recent years there is increasing research interest into relevant commonalities between learning to read and write words as well as numbers (e.g., Lopes-Silva et al., 2016). It has been argued that efficient processing of words and numbers requires a partially overlapping cognitive architecture including basic perceptual abilities, attention, working memory (WM), verbal, visuo-spatial and visuo-constructional processing as well as graphomotor sequencing, among others (e.g., Collins & Laski, 2019; Geary, 2005). Over the last decades, researchers have mostly been focusing on either phonological processing as a cognitive precursor of reading and writing words (Castles & Coltheart, 2004) or on numerical magnitude understanding as the most important precursor of number processing (Siegler & Braithwaite, 2017). In this chapter, we aim at bringing together both lines of research by discussing the role of phonological and magnitude processing for the understanding of words and numbers, as well as interactions between these processes in more detail. In particular, we will address aspects of the structure and the acquisition of symbolic (both verbal and Arabic) codes in young children. Moreover, we will discuss similarities and specificities of both codes and how they acquire semantic meaning in early stages of human development. Furthermore, we will elaborate on the comorbidity between math and reading difficulties in light of the interaction between the development of symbolic codes for words and numbers. Finally, we will integrate these lines of argument
{"title":"Reading and writing words and numbers: Similarities, differences, and implications","authors":"R. Moura, V. G. Haase, J. B. Lopes-Silva, L. T. Batista, Fernanda Rocha de Freitas, J. Bahnmueller, K. Moeller","doi":"10.1515/9783110661941-015","DOIUrl":"https://doi.org/10.1515/9783110661941-015","url":null,"abstract":"Literacy and numeracy are culturally acquired abilities that are well established as crucial for educational and vocational prospects (Parsons & Bynner, 1997; Ritchie & Bates, 2013; Romano et al., 2010). When investigating these abilities in children, researchers from educational and cognitive sciences often focus on the writing and reading of either words or numbers. Accordingly, these usually represent two independent lines of research. Nevertheless, in recent years there is increasing research interest into relevant commonalities between learning to read and write words as well as numbers (e.g., Lopes-Silva et al., 2016). It has been argued that efficient processing of words and numbers requires a partially overlapping cognitive architecture including basic perceptual abilities, attention, working memory (WM), verbal, visuo-spatial and visuo-constructional processing as well as graphomotor sequencing, among others (e.g., Collins & Laski, 2019; Geary, 2005). Over the last decades, researchers have mostly been focusing on either phonological processing as a cognitive precursor of reading and writing words (Castles & Coltheart, 2004) or on numerical magnitude understanding as the most important precursor of number processing (Siegler & Braithwaite, 2017). In this chapter, we aim at bringing together both lines of research by discussing the role of phonological and magnitude processing for the understanding of words and numbers, as well as interactions between these processes in more detail. In particular, we will address aspects of the structure and the acquisition of symbolic (both verbal and Arabic) codes in young children. Moreover, we will discuss similarities and specificities of both codes and how they acquire semantic meaning in early stages of human development. Furthermore, we will elaborate on the comorbidity between math and reading difficulties in light of the interaction between the development of symbolic codes for words and numbers. Finally, we will integrate these lines of argument","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131815028","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 : 2021-05-25DOI: 10.1515/9783110661941-004
A. Dowker
International comparisons such as those carried out by TIMSS and PISA (e.g., Mullis et al., 2016a, b; OECD, 2016) tend to show considerably better arithmetical performance by children in some countries than in others. The position of countries can vary over time, but one consistent finding is that children from countries in the Far East, such as Japan, Korea, Singapore, and China, tend to perform better in arithmetic than do children in most parts of Europe and America. Stevenson et al. (1993) looked at performance in different subjects. They found that Japanese and Korean children outperformed American children to a greater extent in mathematics than in reading. This may be in part because of specific difficulties with regard to reading that are posed by East Asian writing systems; but it is also likely that the results reflect a special focus on mathematics in East Asian countries.
{"title":"Culture and language: How do these influence arithmetic?","authors":"A. Dowker","doi":"10.1515/9783110661941-004","DOIUrl":"https://doi.org/10.1515/9783110661941-004","url":null,"abstract":"International comparisons such as those carried out by TIMSS and PISA (e.g., Mullis et al., 2016a, b; OECD, 2016) tend to show considerably better arithmetical performance by children in some countries than in others. The position of countries can vary over time, but one consistent finding is that children from countries in the Far East, such as Japan, Korea, Singapore, and China, tend to perform better in arithmetic than do children in most parts of Europe and America. Stevenson et al. (1993) looked at performance in different subjects. They found that Japanese and Korean children outperformed American children to a greater extent in mathematics than in reading. This may be in part because of specific difficulties with regard to reading that are posed by East Asian writing systems; but it is also likely that the results reflect a special focus on mathematics in East Asian countries.","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114858863","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 : 2021-05-25DOI: 10.1515/9783110661941-010
Helga Klein
One of the major questions in the field of cognitive psychology is the extent to which our thought is dependent on, or formed by, the language we speak. In the mid-1900s, proponents of the linguistic relativity principle claimed that different languages with distinct grammatical properties and lexicons would have a major impact on the way the native speakers of that language perceived reality. This idea was based on the work of the anthropologists Sapir (1949), and Whorf (1956), and named the “Sapir-Whorf-Hypothesis” by Hoijer (1971). The opposite view is expressed by the theory of cultural universality (Au, 1983), meaning that basic concepts innate to human beings can be found in every culture irrespective of linguistic differences. The concept of number seems to be a good example for a theory of cultural universality at first sight, as all known cultures have developed at least some number words, and even pre-verbal infants and animals are able to single out the larger of two sets based on the respective number of items. The term “numerosity” was used by Dehaene (1997) for the awareness of quantity. Yet, it is still not clear whether nature has provided us with the concept of exact number or if this is a cultural acquirement based on the acquisition of verbal counting procedures. This chapter will review evidence supporting the language relativity hypothesis for the instance of exact number representations in a small number range (up to 10); other chapters in this book focus on the linguistic specificities of multi-digit number word systems and other aspects of mathematics Bahnmüller, this volume; Dowker, this volume). Presenting studies from different fields, this chapter will propose that the concept of exact numerosity is based on natural language, and furthermore that linguistic specificities even put constraints on the form of exact numerosity representations. The first focus is on the finding that grammatical properties shape the development of the concepts for one versus two, three, and more. Second, studies that describe a representational change in adults who learn a new number word system (including symbols for numerosities higher than four or five) will be presented. Third, differences in arithmetic fact retrieval in both first and second language will be reviewed. These findings will be discussed in the light of the “access-deficit-hypothesis” regarding developmental dyscalculia, suggesting that children with mathematical difficulties may have a problem in accessing number magnitude from symbols (e.g., presenting with longer response times
{"title":"Exact number representations in first and second language","authors":"Helga Klein","doi":"10.1515/9783110661941-010","DOIUrl":"https://doi.org/10.1515/9783110661941-010","url":null,"abstract":"One of the major questions in the field of cognitive psychology is the extent to which our thought is dependent on, or formed by, the language we speak. In the mid-1900s, proponents of the linguistic relativity principle claimed that different languages with distinct grammatical properties and lexicons would have a major impact on the way the native speakers of that language perceived reality. This idea was based on the work of the anthropologists Sapir (1949), and Whorf (1956), and named the “Sapir-Whorf-Hypothesis” by Hoijer (1971). The opposite view is expressed by the theory of cultural universality (Au, 1983), meaning that basic concepts innate to human beings can be found in every culture irrespective of linguistic differences. The concept of number seems to be a good example for a theory of cultural universality at first sight, as all known cultures have developed at least some number words, and even pre-verbal infants and animals are able to single out the larger of two sets based on the respective number of items. The term “numerosity” was used by Dehaene (1997) for the awareness of quantity. Yet, it is still not clear whether nature has provided us with the concept of exact number or if this is a cultural acquirement based on the acquisition of verbal counting procedures. This chapter will review evidence supporting the language relativity hypothesis for the instance of exact number representations in a small number range (up to 10); other chapters in this book focus on the linguistic specificities of multi-digit number word systems and other aspects of mathematics Bahnmüller, this volume; Dowker, this volume). Presenting studies from different fields, this chapter will propose that the concept of exact numerosity is based on natural language, and furthermore that linguistic specificities even put constraints on the form of exact numerosity representations. The first focus is on the finding that grammatical properties shape the development of the concepts for one versus two, three, and more. Second, studies that describe a representational change in adults who learn a new number word system (including symbols for numerosities higher than four or five) will be presented. Third, differences in arithmetic fact retrieval in both first and second language will be reviewed. These findings will be discussed in the light of the “access-deficit-hypothesis” regarding developmental dyscalculia, suggesting that children with mathematical difficulties may have a problem in accessing number magnitude from symbols (e.g., presenting with longer response times","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125306419","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 : 2021-05-25DOI: 10.1515/9783110661941-012
K. Schuchardt, C. Mähler
School children with specific language disorders (SLI) often experience massive learning difficulties that concern not only literacy but also numeracy. Since preschool basic numerical precursor competencies have a great influence on the later development of arithmetic at school, this chapter is interested in potential early difficulties in counting skills, numerical knowledge, understanding of quantities, and early arithmetic skills. Given the close link between learning difficulties and working memory, a second question is whether these potential early difficulties can be associated with functional problems of working memory. One of early childhood’s central developmental tasks lies in the development of language. Yet, not every child achieves the milestones of language development smoothly. Specific language disorders rank among the most frequently occurring developmental dysfunctions during childhood and adolescence, with a total incidence between 5% and 8%. Boys are affected three times as often as girls (Tomblin et al., 1997). The relevant individuals typically display anomalies in language acquisition which do not result from cognitive deficits, physical illness, impaired hearing, or lack of stimuli due to unfavorable or stressful surroundings. SLI is defined by a considerable deviation from normal speech and language development, both in quantity and in quality. Language production as well as language comprehension may be affected (World Health Organization, 2011). The most severe effects manifest themselves in the acquisition of grammatical structures, but also pragmatic competence may be affected (Leonard, 2014). Frequently, articulatory deficits can be detected; however, an isolated functional impairment of articulation does not justify the diagnosis of SLI (Leonard, 2014). Speech anomalies resulting from certain illnesses (i.e., autism) will be excluded from this consideration. These cases are rather referred to as unspecific or secondary language development impairments. Because of their speech difficulties, children suffering from SLI stand out at an early age. Language delay is a typical sign, along with a relatively small vocabulary and a late usage of phrases of two or more words (Desmarais et al., 2008). This initial deficit in language acquisition will further increase over the developmental course. While affected children show progress in language acquisition to some extent and are capable of understanding and producing simple sentences over the course of their development, they are never going to reach the level of individuals unaffected by SLI. Oftentimes, a number of accompanying
患有特殊语言障碍(SLI)的学龄儿童经常经历巨大的学习困难，不仅涉及识字，还涉及计算。由于学前基本的数字能力对以后在学校的算术发展有很大的影响，本章对计数技能、数字知识、数量理解和早期算术技能的潜在早期困难感兴趣。鉴于学习困难和工作记忆之间的密切联系，第二个问题是这些潜在的早期困难是否与工作记忆的功能问题有关。儿童早期发展的主要任务之一是语言的发展。然而，并不是每个孩子都能顺利地达到语言发展的里程碑。特殊语言障碍是儿童和青少年时期最常见的发育障碍之一，总发病率在5%至8%之间。男孩受影响的频率是女孩的三倍(Tomblin et al.， 1997)。相关个体典型地表现出语言习得的异常，这些异常不是由于认知缺陷、身体疾病、听力受损或由于不利或紧张的环境而缺乏刺激造成的。特殊语言障碍的定义是在数量和质量上与正常的言语和语言发展有相当大的偏差。语言产生和语言理解可能受到影响(世界卫生组织，2011年)。最严重的影响表现在语法结构的习得上，但也可能影响语用能力(Leonard, 2014)。通常，可以检测到发音缺陷;然而，孤立的发音功能障碍并不能作为特殊语言障碍的诊断依据(Leonard, 2014)。由某些疾病(如自闭症)导致的语言异常将被排除在这一考虑之外。这些病例被称为非特异性或继发性语言发育障碍。由于语言障碍，患有特殊语言障碍的儿童在很小的时候就很突出。语言延迟是一个典型的标志，同时词汇量相对较少，两个或两个以上单词的短语使用较晚(Desmarais et al.， 2008)。这种最初的语言习得缺陷将在发展过程中进一步增加。虽然受影响的儿童在语言习得方面取得了一定程度的进步，并且在他们的发展过程中能够理解和产生简单的句子，但他们永远不会达到未受特殊语言障碍影响的个体的水平。常常结伴而行
{"title":"Numerical competencies in preschoolers with language difficulties","authors":"K. Schuchardt, C. Mähler","doi":"10.1515/9783110661941-012","DOIUrl":"https://doi.org/10.1515/9783110661941-012","url":null,"abstract":"School children with specific language disorders (SLI) often experience massive learning difficulties that concern not only literacy but also numeracy. Since preschool basic numerical precursor competencies have a great influence on the later development of arithmetic at school, this chapter is interested in potential early difficulties in counting skills, numerical knowledge, understanding of quantities, and early arithmetic skills. Given the close link between learning difficulties and working memory, a second question is whether these potential early difficulties can be associated with functional problems of working memory. One of early childhood’s central developmental tasks lies in the development of language. Yet, not every child achieves the milestones of language development smoothly. Specific language disorders rank among the most frequently occurring developmental dysfunctions during childhood and adolescence, with a total incidence between 5% and 8%. Boys are affected three times as often as girls (Tomblin et al., 1997). The relevant individuals typically display anomalies in language acquisition which do not result from cognitive deficits, physical illness, impaired hearing, or lack of stimuli due to unfavorable or stressful surroundings. SLI is defined by a considerable deviation from normal speech and language development, both in quantity and in quality. Language production as well as language comprehension may be affected (World Health Organization, 2011). The most severe effects manifest themselves in the acquisition of grammatical structures, but also pragmatic competence may be affected (Leonard, 2014). Frequently, articulatory deficits can be detected; however, an isolated functional impairment of articulation does not justify the diagnosis of SLI (Leonard, 2014). Speech anomalies resulting from certain illnesses (i.e., autism) will be excluded from this consideration. These cases are rather referred to as unspecific or secondary language development impairments. Because of their speech difficulties, children suffering from SLI stand out at an early age. Language delay is a typical sign, along with a relatively small vocabulary and a late usage of phrases of two or more words (Desmarais et al., 2008). This initial deficit in language acquisition will further increase over the developmental course. While affected children show progress in language acquisition to some extent and are capable of understanding and producing simple sentences over the course of their development, they are never going to reach the level of individuals unaffected by SLI. Oftentimes, a number of accompanying","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125876405","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 : 2021-05-25DOI: 10.1515/9783110661941-017
Judit Moschkovich, Judith A. Scott
This paper describes language issues in mathematics word problems for English language learners (ELLs). We first summarize research relevant to the linguistic complexity of mathematics word problems from studies in mathematics education, reading comprehension, and vocabulary. Based on that research, we make recommendations for addressing language complexity and vocabulary in designing word problems for instruction, curriculum, or assessment. We then use examples of word problems to illustrate how to apply those recommendations to designing or revising word problems and creating supports for students to work with word problems.
{"title":"Language issues in mathematics word problems for English learners","authors":"Judit Moschkovich, Judith A. Scott","doi":"10.1515/9783110661941-017","DOIUrl":"https://doi.org/10.1515/9783110661941-017","url":null,"abstract":"This paper describes language issues in mathematics word problems for English language learners (ELLs). We first summarize research relevant to the linguistic complexity of mathematics word problems from studies in mathematics education, reading comprehension, and vocabulary. Based on that research, we make recommendations for addressing language complexity and vocabulary in designing word problems for instruction, curriculum, or assessment. We then use examples of word problems to illustrate how to apply those recommendations to designing or revising word problems and creating supports for students to work with word problems.","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114967779","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 : 2021-05-25DOI: 10.1515/9783110661941-009
Sarit Ashkenazi, Nitza Mark-Zigdon
the experiment performed analysis of
实验进行了分析
{"title":"Directionality of number space associations in Hebrew-speaking children: Evidence from number line estimation","authors":"Sarit Ashkenazi, Nitza Mark-Zigdon","doi":"10.1515/9783110661941-009","DOIUrl":"https://doi.org/10.1515/9783110661941-009","url":null,"abstract":"the experiment performed analysis of","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130344886","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 : 2021-05-25DOI: 10.1515/9783110661941-016
S. R. Powell, S. Bos, Xin Lin
Students use academic language, which involves vocabulary, grammatical structures, and linguistic functions, to learn knowledge and perform tasks in a specific discipline (e.g., mathematics; Cummins, 2000). Understanding these disciplinespecific ways of using language requires deep knowledge of discipline-specific content and a keen understanding connecting academic language to learning (Fang, 2012). Therefore, not surprisingly, academic language has been shown to be closely related to academic performance (Kleemans et al., 2018) and a significant predictor of academic achievement (Townsend et al., 2012). Mathematics, a challenging discipline for many students (Berch & Mazzocco, 2007), also develops academic language specific to the discipline, which is often referred to as mathematics language. Mathematics language is used to express mathematical ideas and to define mathematical concepts, and it can facilitate connections among different representations of mathematical ideas (Bruner, 1966). In this Introduction, we provide a definition of mathematics vocabulary and discuss the importance of understanding mathematics vocabulary. Then, we review why and how students experience difficulty with mathematics vocabulary. In the rest of the chapter, we describe the development and testing of several measures of mathematics vocabulary. These measures could be used by educators to understand which mathematics vocabulary cause difficulty for students and could be a focus of mathematics instruction.
{"title":"The assessment of mathematics vocabulary in the elementary and middle school grades","authors":"S. R. Powell, S. Bos, Xin Lin","doi":"10.1515/9783110661941-016","DOIUrl":"https://doi.org/10.1515/9783110661941-016","url":null,"abstract":"Students use academic language, which involves vocabulary, grammatical structures, and linguistic functions, to learn knowledge and perform tasks in a specific discipline (e.g., mathematics; Cummins, 2000). Understanding these disciplinespecific ways of using language requires deep knowledge of discipline-specific content and a keen understanding connecting academic language to learning (Fang, 2012). Therefore, not surprisingly, academic language has been shown to be closely related to academic performance (Kleemans et al., 2018) and a significant predictor of academic achievement (Townsend et al., 2012). Mathematics, a challenging discipline for many students (Berch & Mazzocco, 2007), also develops academic language specific to the discipline, which is often referred to as mathematics language. Mathematics language is used to express mathematical ideas and to define mathematical concepts, and it can facilitate connections among different representations of mathematical ideas (Bruner, 1966). In this Introduction, we provide a definition of mathematics vocabulary and discuss the importance of understanding mathematics vocabulary. Then, we review why and how students experience difficulty with mathematics vocabulary. In the rest of the chapter, we describe the development and testing of several measures of mathematics vocabulary. These measures could be used by educators to understand which mathematics vocabulary cause difficulty for students and could be a focus of mathematics instruction.","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128751026","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 : 2021-05-25DOI: 10.1515/9783110661941-013
Elisabeth Moser Opitz, V. Schindler
Several studies have established that the mathematical achievement of language minority students (students whose first language differs from the language of instruction) is poorer than that of native speakers (students whose first language is the academic language of the instruction; Haag et al., 2015; Paetsch & Felbrich, 2016; Vukovic & Lesaux, 2013; Warren & Miller, 2015). However, despite the expanding literature on the mathematical learning of language minority students and of native speakers, very little is known about the relationship between mathematical learning disabilities and second-language acquisition. More detailed research on this topic is important for several reasons: Gonzáles and Artiles (2015) report that Latina/o students in the United States who perform below expectations in literacy tests are often diagnosed as having learning difficulties, which, in turn, often leads to their exclusion from mainstream education. Further, language minority students with low mathematical achievement in Switzerland – and probably also in other countries – often receive special second-language support, but they do not receive support for mathematics because it is assumed that their mathematical problems are caused by their language background. Therefore, it is important to investigate the extent to which the problems of language students with mathematical learning disabilities may be caused by math-related, as opposed to language-related, factors. This study investigates whether the relationship between selected language variables and mathematical achievement gains is similar for native speakers with mathematical learning disabilities and language minority students with mathematical learning disabilities. The research was conducted by evaluating grade 3 students (students who are in the third year of school after attending kindergarten) over the course of a school year.
{"title":"Disentangling the relationship between mathematical learning disability and second-language acquisition","authors":"Elisabeth Moser Opitz, V. Schindler","doi":"10.1515/9783110661941-013","DOIUrl":"https://doi.org/10.1515/9783110661941-013","url":null,"abstract":"Several studies have established that the mathematical achievement of language minority students (students whose first language differs from the language of instruction) is poorer than that of native speakers (students whose first language is the academic language of the instruction; Haag et al., 2015; Paetsch & Felbrich, 2016; Vukovic & Lesaux, 2013; Warren & Miller, 2015). However, despite the expanding literature on the mathematical learning of language minority students and of native speakers, very little is known about the relationship between mathematical learning disabilities and second-language acquisition. More detailed research on this topic is important for several reasons: Gonzáles and Artiles (2015) report that Latina/o students in the United States who perform below expectations in literacy tests are often diagnosed as having learning difficulties, which, in turn, often leads to their exclusion from mainstream education. Further, language minority students with low mathematical achievement in Switzerland – and probably also in other countries – often receive special second-language support, but they do not receive support for mathematics because it is assumed that their mathematical problems are caused by their language background. Therefore, it is important to investigate the extent to which the problems of language students with mathematical learning disabilities may be caused by math-related, as opposed to language-related, factors. This study investigates whether the relationship between selected language variables and mathematical achievement gains is similar for native speakers with mathematical learning disabilities and language minority students with mathematical learning disabilities. The research was conducted by evaluating grade 3 students (students who are in the third year of school after attending kindergarten) over the course of a school year.","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114851060","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 : 2021-05-25DOI: 10.1515/9783110661941-014
M. Buyle, C. Marlair, Virginie Crollen
When children acquire numerical skills, they have to learn a variety of specific numerical tools. The most obvious are the numerical codes such as number words (one, two, three, etc.) or Arabic numerals (1, 2, 3, etc.). Other skills will be relatively more abstract: arithmetical facts (i.e., 4 × 2 = 8), arithmetical procedures (i.e., borrowing), or arithmetical laws (i.e., a + b = b + a). The acquisition of these numerical tools is complex and probably not facilitated by the fact that a numerical expression does not have a single meaning. Indeed, numbers can be used as a kind of label or proper name (i.e., Bus 51). They can also be part of a familiar fixed sequence (i.e., 51 comes immediately after 50 and before 52). They can be used to refer to continuous analogue quantities (i.e., 51,2 grams) (Butterworth, 2005; Fuson, 1988) and, most importantly, they can be used to denote the number of things in a set – the cardinality of the set. Children are able to understand the special meaning of cardinality because they possess a specific and innate capacity for dealing with quantities (Feigenson et al., 2004). Supporting the innate nature of the “number sense,” it has been found, for instance, that fetuses in the last trimester are already able to discriminate auditory numerical quantities (Schleger et al., 2014). A large set of behavioral studies using the classic method of habituation has also revealed sensitivity to small numerosities (e.g., Starkey & Cooper, 1980) in young children. In the study of Starkey and Cooper (1980), for example, slides with a fixed number of 2 dots were repeatedly presented to 4to 6-month-old infants until their looking time decreased, indicating habituation. At that point, a slide with a deviant number of 3 dots was presented and yielded significantly longer looking times, indicating dishabituation and therefore discrimination between the numerosities 2 and 3. This effect was replicated with newborns (Antell & Keating, 1983) and with various stimuli such as sets of realistic objects (Strauss & Curtis, 1981), targets in motion (Van Loosbroek & Smitsman, 1990; Wynn et al., 2002), twoand threesyllable words (Bijeljac-Babic et al., 1991), or puppet making two or three sequential jumps (Wood & Spelke, 2005; Wynn, 1996). However, it was not observed
当孩子们获得数字技能时，他们必须学习各种具体的数字工具。最明显的是数字编码，如数字单词(1、2、3等)或阿拉伯数字(1、2、3等)。其他技能将相对更加抽象:算术事实(即4 × 2 = 8)，算术过程(即借用)或算术定律(即a + b = b + a)。这些数值工具的获得是复杂的，并且可能不会因为数值表达式没有单一含义而变得容易。事实上，数字可以用作一种标签或专有名称(例如，总线51)。它们也可以是一个熟悉的固定序列的一部分(例如，51紧接在50之后，52之前)。它们可以用来指连续的模拟量(即51.2克)(Butterworth, 2005;Fuson, 1988)，最重要的是，它们可以用来表示集合中事物的数量——集合的基数。儿童能够理解基数的特殊含义，因为他们拥有处理数量的特定和天生的能力(Feigenson et al.， 2004)。例如，研究发现，在最后三个月的胎儿已经能够区分听觉数字数量，这支持了“数字感”的先天本质(Schleger et al.， 2014)。大量使用经典习惯化方法的行为研究也揭示了幼儿对小数字的敏感性(例如，Starkey & Cooper, 1980)。例如，在Starkey和Cooper(1980)的研究中，他们反复向4 - 6个月大的婴儿展示固定数量的2个点的幻灯片，直到他们看的时间减少，这表明他们已经习惯了。在这一点上，出现了一个带有3个偏差点的幻灯片，并且产生了明显更长的观看时间，这表明不习惯，因此区分了数字2和3。这种效应在新生儿(Antell & Keating, 1983)和各种刺激(如一系列现实物体(Strauss & Curtis, 1981)、运动中的目标(Van Loosbroek & Smitsman, 1990;Wynn et al.， 2002)，二音节和三音节的单词(bijeljack - babic et al.， 1991)，或者木偶连续跳两到三次(Wood & Spelke, 2005;永利,1996)。然而，它没有被观察到
{"title":"Blindness and deafness: A window to study the visual and verbal basis of the number sense","authors":"M. Buyle, C. Marlair, Virginie Crollen","doi":"10.1515/9783110661941-014","DOIUrl":"https://doi.org/10.1515/9783110661941-014","url":null,"abstract":"When children acquire numerical skills, they have to learn a variety of specific numerical tools. The most obvious are the numerical codes such as number words (one, two, three, etc.) or Arabic numerals (1, 2, 3, etc.). Other skills will be relatively more abstract: arithmetical facts (i.e., 4 × 2 = 8), arithmetical procedures (i.e., borrowing), or arithmetical laws (i.e., a + b = b + a). The acquisition of these numerical tools is complex and probably not facilitated by the fact that a numerical expression does not have a single meaning. Indeed, numbers can be used as a kind of label or proper name (i.e., Bus 51). They can also be part of a familiar fixed sequence (i.e., 51 comes immediately after 50 and before 52). They can be used to refer to continuous analogue quantities (i.e., 51,2 grams) (Butterworth, 2005; Fuson, 1988) and, most importantly, they can be used to denote the number of things in a set – the cardinality of the set. Children are able to understand the special meaning of cardinality because they possess a specific and innate capacity for dealing with quantities (Feigenson et al., 2004). Supporting the innate nature of the “number sense,” it has been found, for instance, that fetuses in the last trimester are already able to discriminate auditory numerical quantities (Schleger et al., 2014). A large set of behavioral studies using the classic method of habituation has also revealed sensitivity to small numerosities (e.g., Starkey & Cooper, 1980) in young children. In the study of Starkey and Cooper (1980), for example, slides with a fixed number of 2 dots were repeatedly presented to 4to 6-month-old infants until their looking time decreased, indicating habituation. At that point, a slide with a deviant number of 3 dots was presented and yielded significantly longer looking times, indicating dishabituation and therefore discrimination between the numerosities 2 and 3. This effect was replicated with newborns (Antell & Keating, 1983) and with various stimuli such as sets of realistic objects (Strauss & Curtis, 1981), targets in motion (Van Loosbroek & Smitsman, 1990; Wynn et al., 2002), twoand threesyllable words (Bijeljac-Babic et al., 1991), or puppet making two or three sequential jumps (Wood & Spelke, 2005; Wynn, 1996). However, it was not observed","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117311353","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 : 2021-05-25DOI: 10.1515/9783110661941-018
Moritz Herzog, Erkan Gürsoy, Caroline C. Long, Annemarie Fritz
Mathematical word problems challenge students significantly, as empirical studies have shown (e.g., Bush & Karp, 2013; Lewis & Mayer, 1987). Difficulties mostly arise from two aspects, mathematical characteristics, and linguistic structure. Mathematical characteristics of the word problem, such as number size, number and complexity of required operations, and applicable strategies, increase problem difficulties. While on the linguistic side, semantic as well as syntactical characteristics of word problems add to the difficulty (for an overview, see Daroczy et al., 2015). Besides these factors, it is building a mathematical model based on a situation described in a text that is a main difficulty to identify in empirical research (Jupri & Drijvers, 2016; Leiss et al., 2010; Maaß, 2010). We use the term “situation” to refer to a context, which serves the purpose of exemplifying a concept or set of related concepts. As a situation is related to a specific mathematical conceptual field, it formulates a mathematical problem that requires a predictive response. Thus, situations go beyond stimuli, which cause a specific behavior, but are rather typical settings in which mathematical concepts become visible. Situations can be given by illustrations and also by contextual descriptions with mathematics concepts embedded. While research on word problems has focused on contextual descriptions of situations, this chapter aims at investigating how children produce word problems from engaging with illustrated situations. Children encounter word problems that contextualize a more, or less, complex mathematical task in a real-world situation in different ways (Verschaffel et al., 2000). A typical, simple word problem is: “Alex has 3 packages of chocolate. In every package there are 5 pieces. How many pieces of chocolate does Alex have in total?” In this example, the encoded arithmetic task (3*5 = ?) is rather transparent in the word problem, as all numbers are given and the multiplicative structure is highlighted by cue words or phrases (here: “in every”) (LeBlanc & Weber-Russell, 1996). Jupri and Drijvers (2016) report that finding all these cue words and phrases is a main obstacle for students while mathematizing a situation. In such tasks, the real-world context often appears to be designed for the task, thereby casting the word problem’s authenticity into doubt
正如实证研究所表明的那样，数学应用题对学生的挑战很大(例如，Bush & Karp, 2013;Lewis & Mayer, 1987)。困难主要来自数学特性和语言结构两个方面。单词问题的数学特征，如数字大小，所需操作的数量和复杂性，以及适用的策略，增加了问题的难度。而在语言方面，单词问题的语义和句法特征增加了难度(概述，参见Daroczy et al.， 2015)。除了这些因素之外，它正在根据文本中描述的情况建立一个数学模型，这是实证研究中难以识别的主要困难(Jupri & drivers, 2016;Leiss et al.， 2010;Maaß,2010)。我们使用术语“情境”来指代上下文，它用于举例说明一个概念或一组相关概念。当一种情况与一个特定的数学概念领域相关时，它就形成了一个需要预测性响应的数学问题。因此，情境超越了导致特定行为的刺激，而是数学概念变得可见的典型设置。情境可以通过插图来给出，也可以通过嵌入数学概念的上下文描述来给出。虽然对单词问题的研究主要集中在情境的语境描述上，但本章的目的是研究儿童如何通过参与图示情境来产生单词问题。儿童遇到的单词问题以不同的方式将现实世界中或多或少复杂的数学任务语境化(Verschaffel et al.， 2000)。一个典型的、简单的文字问题是:“Alex有3包巧克力。每包有5件。亚历克斯总共有多少块巧克力?”在这个例子中，编码的算术任务(3*5 = ?)在单词问题中是相当透明的，因为所有的数字都是给定的，乘法结构通过提示词或短语(这里:“In every”)突出显示(LeBlanc & Weber-Russell, 1996)。Jupri和drivers(2016)报告说，找到所有这些提示词和短语是学生在数学化情境时的主要障碍。在这样的任务中，现实世界的上下文通常是为任务设计的，从而使单词问题的真实性受到怀疑
{"title":"Fifth-grade students’ production of mathematical word problems","authors":"Moritz Herzog, Erkan Gürsoy, Caroline C. Long, Annemarie Fritz","doi":"10.1515/9783110661941-018","DOIUrl":"https://doi.org/10.1515/9783110661941-018","url":null,"abstract":"Mathematical word problems challenge students significantly, as empirical studies have shown (e.g., Bush & Karp, 2013; Lewis & Mayer, 1987). Difficulties mostly arise from two aspects, mathematical characteristics, and linguistic structure. Mathematical characteristics of the word problem, such as number size, number and complexity of required operations, and applicable strategies, increase problem difficulties. While on the linguistic side, semantic as well as syntactical characteristics of word problems add to the difficulty (for an overview, see Daroczy et al., 2015). Besides these factors, it is building a mathematical model based on a situation described in a text that is a main difficulty to identify in empirical research (Jupri & Drijvers, 2016; Leiss et al., 2010; Maaß, 2010). We use the term “situation” to refer to a context, which serves the purpose of exemplifying a concept or set of related concepts. As a situation is related to a specific mathematical conceptual field, it formulates a mathematical problem that requires a predictive response. Thus, situations go beyond stimuli, which cause a specific behavior, but are rather typical settings in which mathematical concepts become visible. Situations can be given by illustrations and also by contextual descriptions with mathematics concepts embedded. While research on word problems has focused on contextual descriptions of situations, this chapter aims at investigating how children produce word problems from engaging with illustrated situations. Children encounter word problems that contextualize a more, or less, complex mathematical task in a real-world situation in different ways (Verschaffel et al., 2000). A typical, simple word problem is: “Alex has 3 packages of chocolate. In every package there are 5 pieces. How many pieces of chocolate does Alex have in total?” In this example, the encoded arithmetic task (3*5 = ?) is rather transparent in the word problem, as all numbers are given and the multiplicative structure is highlighted by cue words or phrases (here: “in every”) (LeBlanc & Weber-Russell, 1996). Jupri and Drijvers (2016) report that finding all these cue words and phrases is a main obstacle for students while mathematizing a situation. In such tasks, the real-world context often appears to be designed for the task, thereby casting the word problem’s authenticity into doubt","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130910354","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：