Diversity Dimensions in Mathematics and Language Learning最新文献

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}