Pub Date : 2020-12-09DOI: 10.1080/10986065.2020.1855376
Jeffrey Choppin, Amy Roth Mcduffie, C. Drake, Jon D. Davis
ABSTRACT We studied how the distal policy mechanisms of curricular aims and objectives articulated in official curriculum documents influenced classroom instruction, and the factors that were associated with the enactment of those curricular aims and objectives. The study was set in the U.S. context, where there is an ambitious effort to transform curriculum and instruction via the Common Core State Standards for Mathematics (CCSSM). The CCSSM represented the curricular aims and objectives in most of the U.S. at the time of the study. We analyzed enactments of this official curriculum in terms of the rigor of mathematical activity in 47 middle school mathematics lessons from multiple state and curriculum contexts. The enactment of the CCSSM was not uniform across contexts, and the lack of uniformity was associated in part with the type of instructional materials used by teachers. The use of instructional materials classified as delivery mechanism was associated with activity we characterized as routine procedural rigor. In lessons involving instructional materials classified as thinking device, we found greater variation and more occurrences of non-routine forms of rigor. These differences between types of instructional materials occurred despite the finding that teachers across the sample held similar views of the CCSSM. We conclude that the teachers responded more to features in the instructional materials than to the curriculum aims and objectives articulated in the CCSSM while planning and enacting lessons, which has implications for policy makers who aim to influence instruction through national standards and for school districts as they select materials.
{"title":"The role of instructional materials in the relationship between the official curriculum and the enacted curriculum","authors":"Jeffrey Choppin, Amy Roth Mcduffie, C. Drake, Jon D. Davis","doi":"10.1080/10986065.2020.1855376","DOIUrl":"https://doi.org/10.1080/10986065.2020.1855376","url":null,"abstract":"ABSTRACT We studied how the distal policy mechanisms of curricular aims and objectives articulated in official curriculum documents influenced classroom instruction, and the factors that were associated with the enactment of those curricular aims and objectives. The study was set in the U.S. context, where there is an ambitious effort to transform curriculum and instruction via the Common Core State Standards for Mathematics (CCSSM). The CCSSM represented the curricular aims and objectives in most of the U.S. at the time of the study. We analyzed enactments of this official curriculum in terms of the rigor of mathematical activity in 47 middle school mathematics lessons from multiple state and curriculum contexts. The enactment of the CCSSM was not uniform across contexts, and the lack of uniformity was associated in part with the type of instructional materials used by teachers. The use of instructional materials classified as delivery mechanism was associated with activity we characterized as routine procedural rigor. In lessons involving instructional materials classified as thinking device, we found greater variation and more occurrences of non-routine forms of rigor. These differences between types of instructional materials occurred despite the finding that teachers across the sample held similar views of the CCSSM. We conclude that the teachers responded more to features in the instructional materials than to the curriculum aims and objectives articulated in the CCSSM while planning and enacting lessons, which has implications for policy makers who aim to influence instruction through national standards and for school districts as they select materials.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"123 - 148"},"PeriodicalIF":1.6,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1855376","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43507841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT Previous studies have found that block play results in better spatial ability which may lead to greater mathematical skills. The current study examined a specific type of block play, structured block play in which a copy of a block configuration is constructed. Structured block play is a difficult cognitive task that requires an understanding of spatial relations, hand-eye coordination, and spatial working memory among others. This preliminary study was designed to determine whether training using structured block play would lead to improvements in skills linked to mathematical thinking. Two groups of children participated in the study. One group played a competitive structured block building game once a week for 8 weeks. A control group was also tested. All participants completed a kindergarten readiness assessment before and after the 8-week period. Children in the block play group showed significant improvements in the computation module of the assessment, showing improvements in the makes a set of objects smaller or larger skills. No such effect was observed for the control group. The results presented demonstrate that young children can, with assistance, engage in structured block play and that they have cognitive benefits from such block building activities.
{"title":"Spatial training using game play in preschoolers improves computational skills","authors":"Sharlene D. Newman, Erin Loughery, Ambur Ecklund, Marriah Smothers, Jefney Ongeri","doi":"10.1080/10986065.2021.1969866","DOIUrl":"https://doi.org/10.1080/10986065.2021.1969866","url":null,"abstract":"ABSTRACT Previous studies have found that block play results in better spatial ability which may lead to greater mathematical skills. The current study examined a specific type of block play, structured block play in which a copy of a block configuration is constructed. Structured block play is a difficult cognitive task that requires an understanding of spatial relations, hand-eye coordination, and spatial working memory among others. This preliminary study was designed to determine whether training using structured block play would lead to improvements in skills linked to mathematical thinking. Two groups of children participated in the study. One group played a competitive structured block building game once a week for 8 weeks. A control group was also tested. All participants completed a kindergarten readiness assessment before and after the 8-week period. Children in the block play group showed significant improvements in the computation module of the assessment, showing improvements in the makes a set of objects smaller or larger skills. No such effect was observed for the control group. The results presented demonstrate that young children can, with assistance, engage in structured block play and that they have cognitive benefits from such block building activities.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"252 - 258"},"PeriodicalIF":1.6,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49324120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-14DOI: 10.1080/10986065.2020.1843231
D. Clements, Holland W. Banse, J. Sarama, C. Tatsuoka, Candace Joswick, A. Hudyma, Douglas W. Van Dine, K. Tatsuoka
ABSTRACT Researchers often develop instruments using correctness scores (and a variety of theories and techniques, such as Item Response Theory) for validation and scoring. Less frequently, observations of children’s strategies are incorporated into the design, development, and application of assessments. We conducted individual interviews of 833 prekindergartens to Grade 3 children using 70 length measurement assessment items, recording both correctness and strategy use. We performed qualitative analyses of children’s strategies to validate or refine our hypotheses of how items align with strategies, and the concepts and procedures underlying them. We then used these analyses to refine: (a) our definitions of those strategies, concepts, and procedures; (b) the items in the assessment instrument; and (c) the alignment of both. The results will form the foundation of a Computer-Adaptive Test for length measurement, which we intend to validate in future research.
{"title":"Young children’s actions on length measurement tasks: strategies and cognitive attributes","authors":"D. Clements, Holland W. Banse, J. Sarama, C. Tatsuoka, Candace Joswick, A. Hudyma, Douglas W. Van Dine, K. Tatsuoka","doi":"10.1080/10986065.2020.1843231","DOIUrl":"https://doi.org/10.1080/10986065.2020.1843231","url":null,"abstract":"ABSTRACT Researchers often develop instruments using correctness scores (and a variety of theories and techniques, such as Item Response Theory) for validation and scoring. Less frequently, observations of children’s strategies are incorporated into the design, development, and application of assessments. We conducted individual interviews of 833 prekindergartens to Grade 3 children using 70 length measurement assessment items, recording both correctness and strategy use. We performed qualitative analyses of children’s strategies to validate or refine our hypotheses of how items align with strategies, and the concepts and procedures underlying them. We then used these analyses to refine: (a) our definitions of those strategies, concepts, and procedures; (b) the items in the assessment instrument; and (c) the alignment of both. The results will form the foundation of a Computer-Adaptive Test for length measurement, which we intend to validate in future research.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"181 - 202"},"PeriodicalIF":1.6,"publicationDate":"2020-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1843231","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42854569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-11DOI: 10.1080/10986065.2020.1842968
S. Hopkins, J. Russo, R. Siegler
ABSTRACT There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition problems using a min-counting strategy and were accurate using it. We investigated if these children were adaptive when it came to using retrieval for simple addition and if they were disadvantaged when it came to demonstrating mental computational flexibility with multi-digit addition. We found accurate-min-counters represented over 30% of participants. These children were often incorrect when they were required to use retrieval for simple addition and were less flexible than most peers with mental computation strategies. The findings indicate that educators should be concerned about the prevalence of accurate-min-counting and call into question the widely held view that it is mostly children with a mathematics learning disability (or persistent low achievement) who display the protracted use of counting-based strategies for simple addition. Further research is needed to investigate if, and how, current teaching approaches are encouraging children to rely on counting beyond a time when it is advantageous to do so.
{"title":"Is counting hindering learning? An investigation into children’s proficiency with simple addition and their flexibility with mental computation strategies","authors":"S. Hopkins, J. Russo, R. Siegler","doi":"10.1080/10986065.2020.1842968","DOIUrl":"https://doi.org/10.1080/10986065.2020.1842968","url":null,"abstract":"ABSTRACT There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition problems using a min-counting strategy and were accurate using it. We investigated if these children were adaptive when it came to using retrieval for simple addition and if they were disadvantaged when it came to demonstrating mental computational flexibility with multi-digit addition. We found accurate-min-counters represented over 30% of participants. These children were often incorrect when they were required to use retrieval for simple addition and were less flexible than most peers with mental computation strategies. The findings indicate that educators should be concerned about the prevalence of accurate-min-counting and call into question the widely held view that it is mostly children with a mathematics learning disability (or persistent low achievement) who display the protracted use of counting-based strategies for simple addition. Further research is needed to investigate if, and how, current teaching approaches are encouraging children to rely on counting beyond a time when it is advantageous to do so.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"52 - 69"},"PeriodicalIF":1.6,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1842968","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41415582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1080/10986065.2020.1848273
Sanne Rathé, Joke Torbeyns, B. Smedt, L. Verschaffel
ABSTRACT Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievement. Participants were 159 kindergartners (4-5-year-olds) who completed measures of SFONS, SFON, numerical abilities, mathematics achievement, spatial ability, and language ability. Confirmatory factor analysis revealed that a two-factor model representing a separate SFONS and SFON factor best fitted the data, indicating that SFONS is separate from SFON. Correlation and regression analyses showed that SFONS was associated with numerical abilities and mathematics achievement. These associations – except for verbal counting – remained after controlling for age, parental education, spatial ability, language ability, and SFON. These findings suggest that SFONS is a unique component of early mathematical development that deserves attention in early mathematics education.
{"title":"Spontaneous focusing on Arabic number symbols: A unique component of children’s early mathematical development?","authors":"Sanne Rathé, Joke Torbeyns, B. Smedt, L. Verschaffel","doi":"10.1080/10986065.2020.1848273","DOIUrl":"https://doi.org/10.1080/10986065.2020.1848273","url":null,"abstract":"ABSTRACT Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievement. Participants were 159 kindergartners (4-5-year-olds) who completed measures of SFONS, SFON, numerical abilities, mathematics achievement, spatial ability, and language ability. Confirmatory factor analysis revealed that a two-factor model representing a separate SFONS and SFON factor best fitted the data, indicating that SFONS is separate from SFON. Correlation and regression analyses showed that SFONS was associated with numerical abilities and mathematics achievement. These associations – except for verbal counting – remained after controlling for age, parental education, spatial ability, language ability, and SFON. These findings suggest that SFONS is a unique component of early mathematical development that deserves attention in early mathematics education.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"22 1","pages":"281 - 295"},"PeriodicalIF":1.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1848273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48483021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-29DOI: 10.1080/10986065.2020.1824056
H. Johnson
ABSTRACT It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton’s Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the same type of graph to represent a relationship between variables in a situation. With this approach, designers, teachers, and researchers can engineer opportunities for students to discern, or separate, features of representation systems, such as the Cartesian coordinate system, and in turn, promote students’ mathematical reasoning.
{"title":"Task design for graphs: rethink multiple representations with variation theory","authors":"H. Johnson","doi":"10.1080/10986065.2020.1824056","DOIUrl":"https://doi.org/10.1080/10986065.2020.1824056","url":null,"abstract":"ABSTRACT It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton’s Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the same type of graph to represent a relationship between variables in a situation. With this approach, designers, teachers, and researchers can engineer opportunities for students to discern, or separate, features of representation systems, such as the Cartesian coordinate system, and in turn, promote students’ mathematical reasoning.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"91 - 98"},"PeriodicalIF":1.6,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1824056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47114855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-27DOI: 10.1080/10986065.2020.1818470
M. Hannula-Sormunen, C. Nanu, Katri Luomaniemi, M. Heinonen, Anne Sorariutta, I. Södervik, Aino Mattinen
ABSTRACT In this study we investigated the effects of two naturalistic 2- to 4-year-old children’s intervention programs aimed at promoting children’s Spontaneous Focusing On Numerosity (SFON) and early numerical skills. The study consisted of a quasi-experimental, pretest-posttest design with a delayed posttest and an active control group participating in the Let’s Read and Talk program. All conditions had 6 weeks of intensive training followed by a 4-month rehearsal phase, when intervention activities were integrated into normal day care. The results of both numerical interventions in the whole group level show positive, small- to medium-sized long-term effects on cardinality-related skills from pretest to delayed posttest. The SFON tendency increased more from pretest to posttest in both studies but the group differences vanished in the delayed posttest. The children in the Count, how many programs developed more in SFON tendency from pretest to posttest, while the better development of SFON from pretest to posttest was significant only for the low group in the One, two, how many programs. There were no group differences in vocabulary or story comprehension skills. Educational implications suggest that combining SFON and cardinality-related skill training at day care results in developmentally effective activities for early educators and children.
摘要在本研究中，我们调查了两个2至4岁儿童自然干预计划的效果，旨在促进儿童自发关注数字（SFON）和早期数字技能。这项研究包括一个准实验性的前测后测设计，其中包括一个延迟后测和一个参与Let's Read and Talk计划的主动对照组。所有条件都有6周的强化训练，然后是4个月的排练阶段，干预活动被纳入正常的日托。从前测到延迟后测，两种数值干预在整个组水平上的结果都显示出对基数相关技能的积极、中小型长期影响。在两项研究中，从前测到后测，SFON倾向增加得更多，但在延迟后测中，组间差异消失了。计数中的儿童，从前测到后测，有多少个项目的SFON倾向发展得更多，而从前测再到后测的SFON发展得更好，仅对一、二、多少个项目中的低组显著。在词汇或故事理解能力方面没有群体差异。教育意义表明，将SFON和日托中心的基数相关技能培训相结合，可以为早期教育工作者和儿童带来有效的发展活动。
{"title":"Promoting spontaneous focusing on numerosity and cardinality-related skills at day care with one, two, how many and count, how many programs","authors":"M. Hannula-Sormunen, C. Nanu, Katri Luomaniemi, M. Heinonen, Anne Sorariutta, I. Södervik, Aino Mattinen","doi":"10.1080/10986065.2020.1818470","DOIUrl":"https://doi.org/10.1080/10986065.2020.1818470","url":null,"abstract":"ABSTRACT In this study we investigated the effects of two naturalistic 2- to 4-year-old children’s intervention programs aimed at promoting children’s Spontaneous Focusing On Numerosity (SFON) and early numerical skills. The study consisted of a quasi-experimental, pretest-posttest design with a delayed posttest and an active control group participating in the Let’s Read and Talk program. All conditions had 6 weeks of intensive training followed by a 4-month rehearsal phase, when intervention activities were integrated into normal day care. The results of both numerical interventions in the whole group level show positive, small- to medium-sized long-term effects on cardinality-related skills from pretest to delayed posttest. The SFON tendency increased more from pretest to posttest in both studies but the group differences vanished in the delayed posttest. The children in the Count, how many programs developed more in SFON tendency from pretest to posttest, while the better development of SFON from pretest to posttest was significant only for the low group in the One, two, how many programs. There were no group differences in vocabulary or story comprehension skills. Educational implications suggest that combining SFON and cardinality-related skill training at day care results in developmentally effective activities for early educators and children.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"22 1","pages":"312 - 331"},"PeriodicalIF":1.6,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1818470","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46842226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-18DOI: 10.1080/10986065.2020.1818467
M. Mazzocco, Jenny Yun Chen Chan, Jeffrey K. Bye, Emily R Padrutt, Taylor L. Praus-Singh, Sarah L. Lukowski, Ethan C. Brown, Rachel E Olson
ABSTRACT Children’s spontaneous focus on numerosity (SFON) is described as an unprompted tendency that is stable across contexts. The attention to number task (AtN), an experimental forced-choice picture-matching task designed to evaluate select aspects of children’s focus on numerosity, may reveal whether task materials can implicitly prompt children to focus on numerosity. In two studies, we replicate earlier findings showing an effect of task context on children’s performance on the AtN: When asked to identify one or more matches to a target picture from an array of four options, the frequency with which preschoolers and adults identify a numerosity-based match varies as a function of the features on which the remaining match options are based. We addressed a limitation of the original AtN study by including novel combinations of features as additional trials, with which we continued to demonstrate contextual effects. We also showed that adults seemed more susceptible than children to be primed to attend to numerosity on subsequent trials. Children’s focus on numerosity under these experimental conditions was remarkably low. We discuss the implications of these findings for better understanding the SFON construct.
{"title":"Attention to numerosity varies across individuals and task contexts","authors":"M. Mazzocco, Jenny Yun Chen Chan, Jeffrey K. Bye, Emily R Padrutt, Taylor L. Praus-Singh, Sarah L. Lukowski, Ethan C. Brown, Rachel E Olson","doi":"10.1080/10986065.2020.1818467","DOIUrl":"https://doi.org/10.1080/10986065.2020.1818467","url":null,"abstract":"ABSTRACT Children’s spontaneous focus on numerosity (SFON) is described as an unprompted tendency that is stable across contexts. The attention to number task (AtN), an experimental forced-choice picture-matching task designed to evaluate select aspects of children’s focus on numerosity, may reveal whether task materials can implicitly prompt children to focus on numerosity. In two studies, we replicate earlier findings showing an effect of task context on children’s performance on the AtN: When asked to identify one or more matches to a target picture from an array of four options, the frequency with which preschoolers and adults identify a numerosity-based match varies as a function of the features on which the remaining match options are based. We addressed a limitation of the original AtN study by including novel combinations of features as additional trials, with which we continued to demonstrate contextual effects. We also showed that adults seemed more susceptible than children to be primed to attend to numerosity on subsequent trials. Children’s focus on numerosity under these experimental conditions was remarkably low. We discuss the implications of these findings for better understanding the SFON construct.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"22 1","pages":"258 - 280"},"PeriodicalIF":1.6,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1818467","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43765402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-18DOI: 10.1080/10986065.2020.1818468
Sanne Rathé, Joke Torbeyns, B. Smedt, L. Verschaffel
ABSTRACT Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievement. Participants were 159 kindergartners (4-5-year-olds) who completed measures of SFONS, SFON, numerical abilities, mathematics achievement, spatial ability, and language ability. Confirmatory factor analysis revealed that a two-factor model representing a separate SFONS and SFON factor best fitted the data, indicating that SFONS is separate from SFON. Correlation and regression analyses showed that SFONS was associated with numerical abilities and mathematics achievement. These associations – except for verbal counting – remained after controlling for age, parental education, spatial ability, language ability, and SFON. These findings suggest that SFONS is a unique component of early mathematical development that deserves attention in early mathematics education.
{"title":"Spontaneous focusing on Arabic number symbols: A unique component of children’s early mathematical development?","authors":"Sanne Rathé, Joke Torbeyns, B. Smedt, L. Verschaffel","doi":"10.1080/10986065.2020.1818468","DOIUrl":"https://doi.org/10.1080/10986065.2020.1818468","url":null,"abstract":"ABSTRACT Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievement. Participants were 159 kindergartners (4-5-year-olds) who completed measures of SFONS, SFON, numerical abilities, mathematics achievement, spatial ability, and language ability. Confirmatory factor analysis revealed that a two-factor model representing a separate SFONS and SFON factor best fitted the data, indicating that SFONS is separate from SFON. Correlation and regression analyses showed that SFONS was associated with numerical abilities and mathematics achievement. These associations – except for verbal counting – remained after controlling for age, parental education, spatial ability, language ability, and SFON. These findings suggest that SFONS is a unique component of early mathematical development that deserves attention in early mathematics education.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"24 1","pages":"38 - 51"},"PeriodicalIF":1.6,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2020.1818468","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48204809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-18DOI: 10.1080/10986065.2020.1814977
N. Panorkou, Erell Germia
ABSTRACT Integrating mathematics content into science usually plays a supporting role, where students use their existing mathematical knowledge for solving science tasks without exhibiting any new mathematical meanings during the process. To help students explore the reciprocal relationship between math and science, we designed an instructional module that prompted them to reason covariationally about the quantities involved in the phenomenon of the gravitational force. The results of a whole-class design experiment with sixth-grade students showed that covariational reasoning supported students’ understanding of the phenomenon of gravity. Also, the examination of the phenomenon of gravity provided a constructive space for students to construct meanings about co-varying quantities. Specifically, students reasoned about the change in the magnitudes and values of mass, distance, and gravity as those changed simultaneously as well as the multiplicative change of these quantities as they changed in relation to each other. They also reasoned multivariationally illustrating that they coordinated mass and distance working together to define the gravitational force. Their interactions with the design, which included the tool, tasks, representations, and questioning, showed to be a structuring factor in the formation and reorganization of meanings that students exhibited. Thus, this study illustrates the type of design activity that provided a constructive space for students’ forms of covariational reasoning in the context of gravity. This design can be used to develop other STEM modules that integrate scientific phenomena with covariational reasoning through technology.
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