Jennifer M. Zosh, Brenna Hassinger-Das, Tamara Spiewak Toub, K. Hirsh-Pasek, R. Golinkoff
International rankings show children in the United States perform well below average in mathematics. There are also large mathematics achievement gaps between children of lower- and higher-socioeconomic status. As today’s teachers face these challenges, they are also faced with the pressures of sweeping educational reforms that arrived with the adoption of No Child Left Behind and continue into the Common Core State Standards era. These strict standards and the implications of low-performance can easily push teachers and parents towards the belief that direct instruction is the only way to help children learn effectively. In this article, we review evidence from the literature about playful learning as an alternative and powerful pedagogical approach. We apply the principles of playful learning to specific state standards for mathematics and illustrate promising ways to improve mathematics learning in the classroom.
{"title":"Playing with Mathematics: How Play Supports Learning and the Common Core State Standards","authors":"Jennifer M. Zosh, Brenna Hassinger-Das, Tamara Spiewak Toub, K. Hirsh-Pasek, R. Golinkoff","doi":"10.7916/JMETC.V7I1.787","DOIUrl":"https://doi.org/10.7916/JMETC.V7I1.787","url":null,"abstract":"International rankings show children in the United States perform well below average in mathematics. There are also large mathematics achievement gaps between children of lower- and higher-socioeconomic status. As today’s teachers face these challenges, they are also faced with the pressures of sweeping educational reforms that arrived with the adoption of No Child Left Behind and continue into the Common Core State Standards era. These strict standards and the implications of low-performance can easily push teachers and parents towards the belief that direct instruction is the only way to help children learn effectively. In this article, we review evidence from the literature about playful learning as an alternative and powerful pedagogical approach. We apply the principles of playful learning to specific state standards for mathematics and illustrate promising ways to improve mathematics learning in the classroom.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"7 1","pages":"45-49"},"PeriodicalIF":0.0,"publicationDate":"2016-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368753","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}
This paper analyzes how a teacher of mathematics used problem posing in the assessment of the cognitive development of 26 students at the grade-four level. The students, ages 8 to 10 years, were from a rural elementary school in western Jamaica. Using a picture as a prompt, students were asked to generate three arithmetic problems and to offer their solution to one of these problems. The teacher used both formative and summative assessments to evaluate students’ levels of cognition in mathematics. Formative assessment revealed that some students’ mathematical ability were higher than their reading ability. Summative assessment showed that more advanced students generated more complex questions. The teacher was able to use the information gathered from the problem posing activity to create better lesson plans for the class.
{"title":"Assessment of a Problem Posing Task in a Jamaican Grade Four Mathematics Classroom","authors":"Kayan Lloyd Munroe","doi":"10.7916/JMETC.V7I1.788","DOIUrl":"https://doi.org/10.7916/JMETC.V7I1.788","url":null,"abstract":"This paper analyzes how a teacher of mathematics used problem posing in the assessment of the cognitive development of 26 students at the grade-four level. The students, ages 8 to 10 years, were from a rural elementary school in western Jamaica. Using a picture as a prompt, students were asked to generate three arithmetic problems and to offer their solution to one of these problems. The teacher used both formative and summative assessments to evaluate students’ levels of cognition in mathematics. Formative assessment revealed that some students’ mathematical ability were higher than their reading ability. Summative assessment showed that more advanced students generated more complex questions. The teacher was able to use the information gathered from the problem posing activity to create better lesson plans for the class.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"7 1","pages":"51-58"},"PeriodicalIF":0.0,"publicationDate":"2016-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368760","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}
Teaching for social justice is a critical pedagogy used to empower students to be social agents in the world they live. This critical pedagogy has extended to mathematics education. Over the last decade, mathematics education researchers have conceptualized what it means to teach mathematics for social justice, but little is known about preservice teachers’ perspectives on this topic. The purpose of this study was to examine elementary preservice teachers’ conceptions of teaching mathematics for social justice at the beginning and end of a mathematics methods course. Preservice elementary teachers (n = 230) enrolled in mathematics methods coursework at three universities across the United States described what it meant to teach mathematics for social justice in response to an open-ended question on the Mathematics Experiences and Conceptions Surveys.
{"title":"Teaching Mathematics for Social Justice: Examining Preservice Teachers' Conceptions.","authors":"C. Jong, Christa Jackson","doi":"10.7916/JMETC.V7I1.785","DOIUrl":"https://doi.org/10.7916/JMETC.V7I1.785","url":null,"abstract":"Teaching for social justice is a critical pedagogy used to empower students to be social agents in the world they live. This critical pedagogy has extended to mathematics education. Over the last decade, mathematics education researchers have conceptualized what it means to teach mathematics for social justice, but little is known about preservice teachers’ perspectives on this topic. The purpose of this study was to examine elementary preservice teachers’ conceptions of teaching mathematics for social justice at the beginning and end of a mathematics methods course. Preservice elementary teachers (n = 230) enrolled in mathematics methods coursework at three universities across the United States described what it meant to teach mathematics for social justice in response to an open-ended question on the Mathematics Experiences and Conceptions Surveys.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"7 1","pages":"27-34"},"PeriodicalIF":0.0,"publicationDate":"2016-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368747","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}
This meta-ethnography explores qualitative studies around the Cognitively Guided Instruction (CGI) framework of mathematics and illustrates how CGI epitomizes differentiation. The meta-ethnographic process is used to synthesize CGI as differentiation, specifically within the elementary mathematics classroom. Thomas P. Carpenter is credited as one of the foundational researchers of this instructional model, along with his team of Fennema, Franke, Levi, and Empson. Six qualitative pieces from this author group are synthesized to create a reciprocal translation, described by Noblit and Hare (1988) as a generation of a metaphor across similar studies. In this case, the pieces work together to form a metaphor of differentiation across the themes of student centered pacing, alternative forms of assessment and teacher scaffolding.
{"title":"A Living Metaphor of Differentiation: A Meta-Ethnography of Cognitively Guided Instruction in the Elementary Classroom","authors":"Katherine Baker, M. Harter","doi":"10.7916/JMETC.V6I2.616","DOIUrl":"https://doi.org/10.7916/JMETC.V6I2.616","url":null,"abstract":"This meta-ethnography explores qualitative studies around the Cognitively Guided Instruction (CGI) framework of mathematics and illustrates how CGI epitomizes differentiation. The meta-ethnographic process is used to synthesize CGI as differentiation, specifically within the elementary mathematics classroom. Thomas P. Carpenter is credited as one of the foundational researchers of this instructional model, along with his team of Fennema, Franke, Levi, and Empson. Six qualitative pieces from this author group are synthesized to create a reciprocal translation, described by Noblit and Hare (1988) as a generation of a metaphor across similar studies. In this case, the pieces work together to form a metaphor of differentiation across the themes of student centered pacing, alternative forms of assessment and teacher scaffolding.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"6 1","pages":"27-35"},"PeriodicalIF":0.0,"publicationDate":"2015-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368720","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}
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a three-semester project to help secondary mathe matics teacher candidates inform their teaching using abstract algebra.
{"title":"Abstract Algebra to Secondary School Algebra: Building Bridges.","authors":"D. Christy, Rebecca Sparks","doi":"10.7916/JMETC.V6I2.617","DOIUrl":"https://doi.org/10.7916/JMETC.V6I2.617","url":null,"abstract":"The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a three-semester project to help secondary mathe matics teacher candidates inform their teaching using abstract algebra.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"6 1","pages":"37-42"},"PeriodicalIF":0.0,"publicationDate":"2015-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368728","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}
Mathematics anxiety is recognized as a significant performance impediment that affects students across multiple ethnic and economic backgrounds. However, research has yet to fully examine the possible differential effect of mathematics anxiety on underrepresented K-12 students. Specifically, given the long-standing achievement gap between African American and White students it is imperative that the possible differential effect of mathematics anxiety on African American students be addressed. The purpose of this study was to utilize the techniques of meta-analysis to summarize the effects of anxiety on mathematics achievement in K-12 African American student populations. The results suggest that anxiety has a statistically significant effect on the mathematics achievement of representative samples of African American students. Furthermore, this effect is mediated by student grade level. More representative research is needed to better ascertain the factors that promote and sustain mathematics anxiety in African American student populations. In particular, studies that disaggregate results based on student race are necessary for more robust estimates of this phenomenon.
{"title":"Anxious for Answers: A Meta-Analysis of the E!ects of Anxiety on African American K-12 Students’ Mathematics Achievement","authors":"J. Young, Jemimah L. Young","doi":"10.7916/JMETC.V6I2.611","DOIUrl":"https://doi.org/10.7916/JMETC.V6I2.611","url":null,"abstract":"Mathematics anxiety is recognized as a significant performance impediment that affects students across multiple ethnic and economic backgrounds. However, research has yet to fully examine the possible differential effect of mathematics anxiety on underrepresented K-12 students. Specifically, given the long-standing achievement gap between African American and White students it is imperative that the possible differential effect of mathematics anxiety on African American students be addressed. The purpose of this study was to utilize the techniques of meta-analysis to summarize the effects of anxiety on mathematics achievement in K-12 African American student populations. The results suggest that anxiety has a statistically significant effect on the mathematics achievement of representative samples of African American students. Furthermore, this effect is mediated by student grade level. More representative research is needed to better ascertain the factors that promote and sustain mathematics anxiety in African American student populations. In particular, studies that disaggregate results based on student race are necessary for more robust estimates of this phenomenon.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"6 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2015-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369169","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}
This paper provides empirical findings from a study that examined how three grade 7-12 flipped mathematics educators utilized class time when implementing a flipped learning model. Additionally, the researchers investigated the educators' purposes for various in-class tasks as well as their general use of class time. The data revealed flipped mathematics educators engaged students in multiple mathematical activities throughout each class period so as to provide the opportunity for students to develop their (1) introductory content knowledge and procedural fluency, (2) conceptual understanding of mathematical topics, and (3) mathematical problem-solving abilities. Implications from this study contribute to the literature on secondary mathematics classroom teachers’ purposes and provide insights into the classroom practices of flipped mathematics educators.
{"title":"In-Class Purposes of Flipped Mathematics Educators","authors":"L. A. Eisenhut, C. Taylor","doi":"10.7916/JMETC.V6I2.615","DOIUrl":"https://doi.org/10.7916/JMETC.V6I2.615","url":null,"abstract":"This paper provides empirical findings from a study that examined how three grade 7-12 flipped mathematics educators utilized class time when implementing a flipped learning model. Additionally, the researchers investigated the educators' purposes for various in-class tasks as well as their general use of class time. The data revealed flipped mathematics educators engaged students in multiple mathematical activities throughout each class period so as to provide the opportunity for students to develop their (1) introductory content knowledge and procedural fluency, (2) conceptual understanding of mathematical topics, and (3) mathematical problem-solving abilities. Implications from this study contribute to the literature on secondary mathematics classroom teachers’ purposes and provide insights into the classroom practices of flipped mathematics educators.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"6 1","pages":"17-25"},"PeriodicalIF":0.0,"publicationDate":"2015-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369175","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}
This article presents several of the challenges facing postsecondary mathematics education and describes how the undergraduate Learning Assistant (LA) program has been used as a catalyst to engage faculty and students in redesigning opportunities to learn mathematics. Characteristics of the LA program that have been used to transform introductory undergraduate science courses are discussed. We then describe how the LA program was implemented in a mathematics department vis-a-vis the specific contextual features of a mathematics department at the University of Colorado Boulder.
{"title":"Rousing Students’ Minds in Postsecondary Mathematics: The Undergraduate Learning Assistant Model","authors":"David C. Webb, E. Stade, R. Grover","doi":"10.7916/JMETC.V5I2.653","DOIUrl":"https://doi.org/10.7916/JMETC.V5I2.653","url":null,"abstract":"This article presents several of the challenges facing postsecondary mathematics education and describes how the undergraduate Learning Assistant (LA) program has been used as a catalyst to engage faculty and students in redesigning opportunities to learn mathematics. Characteristics of the LA program that have been used to transform introductory undergraduate science courses are discussed. We then describe how the LA program was implemented in a mathematics department vis-a-vis the specific contextual features of a mathematics department at the University of Colorado Boulder.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"5 1","pages":"39-47"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369151","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}
Traditionally, teacher education programs have placed little emphasis on preparing mathematics teachers to work with students who struggle in mathematics. Therefore, it is crucial that mathematics teacher educators explicitly prepare prospective teachers to instruct students who struggle with mathematics by providing strategies and practices that specifically address their needs. In this study, we describe the principles of Universal Design for Learning and Response to Intervention. More specifically, we discuss how one Mathematics Teacher Educator uses these frame works in her mathematics methods course to help prospective teachers become cognizant of early interventions and effective strategies that can be implemented to provide all students with the greatest opportunity to learn.
{"title":"Integrating Universal Design and Response to Intervention in Methods Courses for General Education Mathematics Teachers","authors":"Kelley E Buchheister, Christa Jackson, C. Taylor","doi":"10.7916/JMETC.V5I2.656","DOIUrl":"https://doi.org/10.7916/JMETC.V5I2.656","url":null,"abstract":"Traditionally, teacher education programs have placed little emphasis on preparing mathematics teachers to work with students who struggle in mathematics. Therefore, it is crucial that mathematics teacher educators explicitly prepare prospective teachers to instruct students who struggle with mathematics by providing strategies and practices that specifically address their needs. In this study, we describe the principles of Universal Design for Learning and Response to Intervention. More specifically, we discuss how one Mathematics Teacher Educator uses these frame works in her mathematics methods course to help prospective teachers become cognizant of early interventions and effective strategies that can be implemented to provide all students with the greatest opportunity to learn.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"5 1","pages":"63-71"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369164","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}
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator’s use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that prospective teachers expressed either benefiting or not benefitting from the literature circle practice in this mathematics class. Finally, conclusions and recommendations for future work are shared.
{"title":"Using Mathematics Literature with Prospective Secondary Mathematics Teachers.","authors":"C. Jett","doi":"10.7916/JMETC.V5I2.654","DOIUrl":"https://doi.org/10.7916/JMETC.V5I2.654","url":null,"abstract":"Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator’s use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that prospective teachers expressed either benefiting or not benefitting from the literature circle practice in this mathematics class. Finally, conclusions and recommendations for future work are shared.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"5 1","pages":"49-53"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369157","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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