Pub Date : 2021-05-25DOI: 10.1515/9783110661941-019
Sabine Stephany
Tasks presenting mathematical information as text, known as word problems, are one of the key components in the teaching of mathematics in primary school. Still, they are also one of the most difficult ones. Studies have revealed that word problems are solved up to 30% less successfully than tasks in numerical notation (Duarte et al., 2011). This discrepancy indicates that besides mathematical competence aspects of language play a significant role in the processing of word problems as well (Duarte et al., 2011; Gürsoy, 2016; Heinze et al., 2011; Prediger et al., 2015; Verschaffel et al., 2000). In order to solve a word problem, students not only need to perform the necessary mathematical operations, they also need to understand the text of the task. There are two intertwining factors central to understanding the text of a word problem: the task text itself and the problem solver’s individual reading competence. Both can cause difficulties. In recent years, increasing attention has been paid to the task text and its linguistic characteristics that are considered to challenge the processing of the task, such as academic language (Abedi & Lord, 2001; Gürsoy, 2016; Haag et al., 2015; Martinello, 2008; Prediger et al., 2015). However, there have only been a few studies that focus on reading skills as a factor in explaining students’ difficulties in dealing with word problems. Since reading and understanding the text of a task are fundamental for solving word problems, it can be assumed that, in addition to the linguistic characteristics of the task text itself, reading competence also has an important influence on the solution process. Hence, the present study examines the impact of reader characteristics on the handling of word problems in primary school and explores aspects of reading competence that may be relevant for their solution. Putting mathematical content and processes aside, word problems are primarily texts that have to be read and understood. In addition to the mathematical perspective on solving word problems (Section 2), the reading process is therefore examined from a cognitive-psychological perspective to transfer relevant conclusions to mathematics (Section 3). This may lead to important conclusions on ways of promoting
以文本形式呈现数学信息的任务，即文字问题，是小学数学教学的重要组成部分之一。尽管如此，它们也是最难的一个。研究表明，文字问题的解决成功率比数字符号任务低30% (Duarte et al.， 2011)。这种差异表明，除了数学能力之外，语言的各个方面也在文字问题的处理中发挥着重要作用(Duarte et al.， 2011;Gursoy, 2016;Heinze et al.， 2011;Prediger et al.， 2015;Verschaffel et al.， 2000)。为了解决一个单词问题，学生不仅需要进行必要的数学运算，他们还需要理解任务的文本。有两个相互交织的因素是理解应用题文本的核心:任务文本本身和问题解决者的个人阅读能力。两者都会造成困难。近年来，人们越来越关注任务文本及其语言特征，这些特征被认为对任务的处理构成挑战，如学术语言(Abedi & Lord, 2001;Gursoy, 2016;Haag et al.， 2015;Martinello, 2008;Prediger et al.， 2015)。然而，只有少数研究将阅读技能作为解释学生在处理单词问题时遇到困难的一个因素。由于阅读和理解任务文本是解决单词问题的基础，因此可以认为，除了任务文本本身的语言特征外，阅读能力对解决过程也有重要影响。因此，本研究考察了读者特征对小学生处理文字问题的影响，并探讨了与解决这些问题有关的阅读能力方面。把数学内容和过程放在一边，单词问题主要是需要阅读和理解的文本。因此，除了从数学的角度解决单词问题(第2节)外，还从认知心理学的角度考察了阅读过程，以将相关结论转移到数学(第3节)。这可能会导致关于促进方式的重要结论
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Pub Date : 2021-05-25DOI: 10.1515/9783110661941-002
Juliane Hartmann, Annemarie Fritz
When children are about 18 months old their speech output rapidly increases. It’s like an explosion where about 10 new words are learned every day. It seems as if children suddenly understand how they can use language to interact with their surroundings. At 21 months of age the 100-word milestone in productive vocabularies is reached (Pine, 2005). Words are still mostly content words, used to refer to concrete objects and to describe the relationship between objects with expressions such as “car there,” “mommy’s mug,” or “doggy sleep” being common. Around their second birthday they start to use words to describe the relationship of singular and plural. After being able to say and point out “car there” and doing so for all the cars seen at that moment, all of the sudden they say “car there, many car,” pointing out all the cars observed (Barner et al., 2007). With the usage of natural quantifiers infants engage verbally with the world of numerical relationships. Soon after this development, children are able to describe objects as being “two.” What seems like simply naming a group of things needs in fact the development of deep lexical concepts, which rely, on the one hand, on innate structures, and which, on the other hand, is learned from conversational interactions (Carey, 2009). Being able to name the number of things seen in their surroundings means that infants refer to lexical concepts which are concrete and abstract at the same time. The twoness of something is concrete because of being unique and distinct from being “three” or “one”; on the other hand, it is abstract because it names and highlights just one feature of the objects seen. At the same time the word “two” has a whole bundle of different significations. We are, for example, referring to two cars meaning the magnitude, to the second car meaning the numerical order, and to two gallons of water describing a continuous substance. So, while “two” always has the same numerical value, it differs in shape, color, form, and size (Wiese, 2007). To integrate all these and even more information into one lexical concept requires about six years to develop as we will elaborate in the chapter.
{"title":"Language and mathematics: How children learn arithmetic through specifying their lexical concepts of natural numbers","authors":"Juliane Hartmann, Annemarie Fritz","doi":"10.1515/9783110661941-002","DOIUrl":"https://doi.org/10.1515/9783110661941-002","url":null,"abstract":"When children are about 18 months old their speech output rapidly increases. It’s like an explosion where about 10 new words are learned every day. It seems as if children suddenly understand how they can use language to interact with their surroundings. At 21 months of age the 100-word milestone in productive vocabularies is reached (Pine, 2005). Words are still mostly content words, used to refer to concrete objects and to describe the relationship between objects with expressions such as “car there,” “mommy’s mug,” or “doggy sleep” being common. Around their second birthday they start to use words to describe the relationship of singular and plural. After being able to say and point out “car there” and doing so for all the cars seen at that moment, all of the sudden they say “car there, many car,” pointing out all the cars observed (Barner et al., 2007). With the usage of natural quantifiers infants engage verbally with the world of numerical relationships. Soon after this development, children are able to describe objects as being “two.” What seems like simply naming a group of things needs in fact the development of deep lexical concepts, which rely, on the one hand, on innate structures, and which, on the other hand, is learned from conversational interactions (Carey, 2009). Being able to name the number of things seen in their surroundings means that infants refer to lexical concepts which are concrete and abstract at the same time. The twoness of something is concrete because of being unique and distinct from being “three” or “one”; on the other hand, it is abstract because it names and highlights just one feature of the objects seen. At the same time the word “two” has a whole bundle of different significations. We are, for example, referring to two cars meaning the magnitude, to the second car meaning the numerical order, and to two gallons of water describing a continuous substance. So, while “two” always has the same numerical value, it differs in shape, color, form, and size (Wiese, 2007). To integrate all these and even more information into one lexical concept requires about six years to develop as we will elaborate in the chapter.","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"60 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":"131408427","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: 10.1515/9783110661941-005
Susanne Prediger, Á. Uribe
Many language policy documents worldwide have called for treating students’ multiple languages as resources in subject matter classrooms (Beacco et al., 2015). Many qualitative observation studies (Adler, 2001; Barwell et al., 2016; Planas, 2018) and some quantitative intervention studies in mathematics education (Schüler-Meyer et al., 2019) have also shown that teaching approaches that activate students’ multilingual resources can be beneficial. However, most of these studies refer to classrooms with shared bilingualism, which means teachers and students share at least two languages. In contrast, Meyer et al. (2016) describe European schools as superdiverse language contexts in which more than five non-shared languages can be present in a classroom with only the language of instruction being shared. This is exemplified in the German-language context: In German schools, 30% of all students are multilingual, with most of them being secondto fourth-generation children of immigrant families. Typical classes in urban areas have five to seven languages, with only German being shared by all students and English learned as a foreign language. Teachers might speak one immigrant language, but not all. Usually, using home languages is allowed in small group work, but not encouraged and built upon. The prevalence of non-shared multilingualism raises the question of how teaching approaches for activating multilingual resources can be transferred from classrooms with shared bilingualism to superdiverse classrooms with nonshared multilingualism. In this paper, we argue that this transfer is possible when the focus is not only on the communicative role of multiple languages (i.e., so that students can
世界各地的许多语言政策文件都呼吁在主题课堂上将学生的多种语言视为资源(Beacco et al.， 2015)。许多定性观察研究(Adler, 2001;Barwell et al.， 2016;Planas, 2018)和一些数学教育定量干预研究(sch勒-迈耶等人，2019)也表明，激活学生多语言资源的教学方法可能是有益的。然而，这些研究大多涉及共享双语的课堂，这意味着教师和学生共享至少两种语言。相比之下，Meyer等人(2016)将欧洲学校描述为超多样化的语言环境，在这种环境中，教室中可以存在五种以上的非共享语言，而只有教学语言是共享的。这一点在德语环境中得到了体现:在德国学校，30%的学生掌握多种语言，其中大多数是移民家庭的第二代至第四代子女。城市地区的典型班级有五到七种语言，只有德语是所有学生共用的，英语是作为外语学习的。教师可能会说一种移民语言，但不是所有的。通常，在小组工作中使用母语是允许的，但不鼓励使用。非共享多语的盛行提出了一个问题，即如何将激活多语资源的教学方法从共享双语的课堂转移到非共享多语的超多样化课堂。在本文中，我们认为，这种转移是可能的，当关注不仅仅是多语言的交际作用(即，使学生能够
{"title":"Exploiting the epistemic role of multilingual resources in superdiverse mathematics classrooms: Design principles and insights into students’ learning processes","authors":"Susanne Prediger, Á. Uribe","doi":"10.1515/9783110661941-005","DOIUrl":"https://doi.org/10.1515/9783110661941-005","url":null,"abstract":"Many language policy documents worldwide have called for treating students’ multiple languages as resources in subject matter classrooms (Beacco et al., 2015). Many qualitative observation studies (Adler, 2001; Barwell et al., 2016; Planas, 2018) and some quantitative intervention studies in mathematics education (Schüler-Meyer et al., 2019) have also shown that teaching approaches that activate students’ multilingual resources can be beneficial. However, most of these studies refer to classrooms with shared bilingualism, which means teachers and students share at least two languages. In contrast, Meyer et al. (2016) describe European schools as superdiverse language contexts in which more than five non-shared languages can be present in a classroom with only the language of instruction being shared. This is exemplified in the German-language context: In German schools, 30% of all students are multilingual, with most of them being secondto fourth-generation children of immigrant families. Typical classes in urban areas have five to seven languages, with only German being shared by all students and English learned as a foreign language. Teachers might speak one immigrant language, but not all. Usually, using home languages is allowed in small group work, but not encouraged and built upon. The prevalence of non-shared multilingualism raises the question of how teaching approaches for activating multilingual resources can be transferred from classrooms with shared bilingualism to superdiverse classrooms with nonshared multilingualism. In this paper, we argue that this transfer is possible when the focus is not only on the communicative role of multiple languages (i.e., so that students can","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"39 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":"131853098","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: 10.1515/9783110661941-007
D. Annemie, Ceulemans Annelies, S. Rousseau, M. Roelants
: This study explored the importance of the amount of “ parental talk ” fo-cusing on numerical cues as “ opportunity factor ” in the prediction of diversity in mathematics learning. Thirty-one children were followed up from toddlerhood (24 months of age) till kindergarten (48 months of age). Mathematics learning was tested with a number discrimination task at 24 months. At 48 months children ’ s mathematics learning was examined with a procedural and conceptual counting task and a calculation task. The amount of parental talk was operationalized via a questionnaire and via a structured play Duplo or Lego building session. The study confirmed a substantial amount of diversity in the frequency of parental talk with the results of the questionnaire and the observation positively related to each other. A positive concurrent association was found between the amount of observed parental talk and children ’ s calculation skills in kindergarten. Parental talk with toddlers was also positively predicting children ’ s mathematics learning in kindergarten. There was a trend of positive association between the amount of parental talk with toddlers and children ’ s conceptual counting abilities in kindergarten. There was a positive quadratic predictive contribution of parental talk in toddlers for “ calculation ” in kindergarten. These results confirmed that mathematics learning might not be unitary even in young children and that parental talk should be considered as one of the opportunity factors to explain some of the diversities in mathematics learning.
{"title":"The relative importance of “parental talk” as a predictor of the diversity in mathematics learning in young children","authors":"D. Annemie, Ceulemans Annelies, S. Rousseau, M. Roelants","doi":"10.1515/9783110661941-007","DOIUrl":"https://doi.org/10.1515/9783110661941-007","url":null,"abstract":": This study explored the importance of the amount of “ parental talk ” fo-cusing on numerical cues as “ opportunity factor ” in the prediction of diversity in mathematics learning. Thirty-one children were followed up from toddlerhood (24 months of age) till kindergarten (48 months of age). Mathematics learning was tested with a number discrimination task at 24 months. At 48 months children ’ s mathematics learning was examined with a procedural and conceptual counting task and a calculation task. The amount of parental talk was operationalized via a questionnaire and via a structured play Duplo or Lego building session. The study confirmed a substantial amount of diversity in the frequency of parental talk with the results of the questionnaire and the observation positively related to each other. A positive concurrent association was found between the amount of observed parental talk and children ’ s calculation skills in kindergarten. Parental talk with toddlers was also positively predicting children ’ s mathematics learning in kindergarten. There was a trend of positive association between the amount of parental talk with toddlers and children ’ s conceptual counting abilities in kindergarten. There was a positive quadratic predictive contribution of parental talk in toddlers for “ calculation ” in kindergarten. These results confirmed that mathematics learning might not be unitary even in young children and that parental talk should be considered as one of the opportunity factors to explain some of the diversities in mathematics learning.","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"26 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":"127862645","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 : 1900-01-01DOI: 10.1515/9783110661941-fm
{"title":"Frontmatter","authors":"","doi":"10.1515/9783110661941-fm","DOIUrl":"https://doi.org/10.1515/9783110661941-fm","url":null,"abstract":"","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"234 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133987761","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 : 1900-01-01DOI: 10.1515/9783110661941-020
F. Mackay, J. Smit, A. Bakker, R. Keijzer
Teachers often are unaware of language issues and avoid linguistic challenges in their classrooms to focus on mathematics (e.g., Van Eerde et al., 2008). Specifically, teachers typically do not attend to the language students need for mathematical learning, and rarely know how to support the development of subject-specific language required for mathematical learning (e.g., Hajer & Norén, 2017). Yet students, especially those with low language proficiency, require support from teachers within this subject because shortcomings in subject-specific language can impede their development of mathematical understanding (Moschkovich, 2010). Despite the importance of improving language-responsive teaching, there is a profound lack of opportunity for teachers to develop the required teaching practices, especially in mathematics (Essien et al., 2016). The required teaching practices integrate language learning and mathematics in a domain-specific way (Van Eerde & Hajer, 2009). Although there are some insights into the professional development of secondary school teachers (e.g., Prediger, 2019), relatively little is known about how to support primary school teachers in realizing languageresponsive teaching. This chapter provides insights into how teachers can be supported within a professional development program (PDP), focusing on genre awareness and scaffolding students’ language for mathematical learning.
{"title":"Supporting teachers to scaffold students’ language for mathematical learning","authors":"F. Mackay, J. Smit, A. Bakker, R. Keijzer","doi":"10.1515/9783110661941-020","DOIUrl":"https://doi.org/10.1515/9783110661941-020","url":null,"abstract":"Teachers often are unaware of language issues and avoid linguistic challenges in their classrooms to focus on mathematics (e.g., Van Eerde et al., 2008). Specifically, teachers typically do not attend to the language students need for mathematical learning, and rarely know how to support the development of subject-specific language required for mathematical learning (e.g., Hajer & Norén, 2017). Yet students, especially those with low language proficiency, require support from teachers within this subject because shortcomings in subject-specific language can impede their development of mathematical understanding (Moschkovich, 2010). Despite the importance of improving language-responsive teaching, there is a profound lack of opportunity for teachers to develop the required teaching practices, especially in mathematics (Essien et al., 2016). The required teaching practices integrate language learning and mathematics in a domain-specific way (Van Eerde & Hajer, 2009). Although there are some insights into the professional development of secondary school teachers (e.g., Prediger, 2019), relatively little is known about how to support primary school teachers in realizing languageresponsive teaching. This chapter provides insights into how teachers can be supported within a professional development program (PDP), focusing on genre awareness and scaffolding students’ language for mathematical learning.","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131123025","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 : 1900-01-01DOI: 10.1515/9783110661941-204
{"title":"Acknowledgments","authors":"","doi":"10.1515/9783110661941-204","DOIUrl":"https://doi.org/10.1515/9783110661941-204","url":null,"abstract":"","PeriodicalId":345296,"journal":{"name":"Diversity Dimensions in Mathematics and Language Learning","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115721373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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