Pub Date : 2019-12-14DOI: 10.7916/JMETC.V10I2.4193
M. George, Yevgeniy Milman
Low passing rates in developmental mathematics have been a serious concern for community colleges for many years. A course in Quantitative Literacy (QL) offers non-STEM students an alternative option to introductory algebra as a path to a degree. This paper describes the implementation and evolution of QL at the Borough of Manhattan Community College. Students enrolled in the 17 sections of QL were compared to a matched sample of students from Elementary Algebra. The students enrolled in QL in the Spring of 2013 were 175% more likely to have passed a credit-bearing mathematics course one year later, indicating that QL represents a valuable alternative for non-STEM college students placed into algebra level remediation. Further, the implementation and preliminary results of a corequisite course combining QL with college level Quantitative Reasoning (QR) are presented.
{"title":"Quantitative Literacy: Alternative Pathway for College Developmental Mathematics Students.","authors":"M. George, Yevgeniy Milman","doi":"10.7916/JMETC.V10I2.4193","DOIUrl":"https://doi.org/10.7916/JMETC.V10I2.4193","url":null,"abstract":"Low passing rates in developmental mathematics have been a serious concern for community colleges for many years. A course in Quantitative Literacy (QL) offers non-STEM students an alternative option to introductory algebra as a path to a degree. This paper describes the implementation and evolution of QL at the Borough of Manhattan Community College. Students enrolled in the 17 sections of QL were compared to a matched sample of students from Elementary Algebra. The students enrolled in QL in the Spring of 2013 were 175% more likely to have passed a credit-bearing mathematics course one year later, indicating that QL represents a valuable alternative for non-STEM college students placed into algebra level remediation. Further, the implementation and preliminary results of a corequisite course combining QL with college level Quantitative Reasoning (QR) are presented.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"29-35"},"PeriodicalIF":0.0,"publicationDate":"2019-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42239492","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 : 2019-12-14DOI: 10.7916/JMETC.V10I2.4192
Robert E. Reys, Barbara J. Reys, Jeffrey C. Shih
Doctoral programs in mathematics education were established more than a century ago in the United States. From 2010-2014 over 120 different institutions graduated at least one doctorate in mathematics education. There has been limited research reported on the nature of doctoral programs in mathematics education and/or their doctoral graduates. This paper provides a synthesis of research findings related to doctoral preparation in mathematics education that is accompanied by a reflection on the findings and suggestions for future research. The intent of our paper is to provide a rallying call for more widespread and coordinated research on doctoral programs in mathematics education in order to strengthen the quality of doctoral preparation for the next generation of mathematics educators.
{"title":"Doctoral Preparation in Mathematics Education: Time for Research and a Widespread Professional Conversation","authors":"Robert E. Reys, Barbara J. Reys, Jeffrey C. Shih","doi":"10.7916/JMETC.V10I2.4192","DOIUrl":"https://doi.org/10.7916/JMETC.V10I2.4192","url":null,"abstract":"Doctoral programs in mathematics education were established more than a century ago in the United States. From 2010-2014 over 120 different institutions graduated at least one doctorate in mathematics education. There has been limited research reported on the nature of doctoral programs in mathematics education and/or their doctoral graduates. This paper provides a synthesis of research findings related to doctoral preparation in mathematics education that is accompanied by a reflection on the findings and suggestions for future research. The intent of our paper is to provide a rallying call for more widespread and coordinated research on doctoral programs in mathematics education in order to strengthen the quality of doctoral preparation for the next generation of mathematics educators.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"21-27"},"PeriodicalIF":0.0,"publicationDate":"2019-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46587986","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 : 2019-12-14DOI: 10.7916/JMETC.V10I2.4190
Steve Deihl, Mara P. Markinson
High school students often ask questions about the nature of infinity. When contemplating what the “largest number” is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or “set theory,” are generally unknown to high school students. The authors propose a method for introducing basic ideas in set theory to high school trigonometry students by connecting prior knowledge of the tangent function and the unit circle to Georg Cantor’s ideas about infinity. By doing so, high school teachers have an opportunity to inspire their students with rich mathematics.
{"title":"Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students.","authors":"Steve Deihl, Mara P. Markinson","doi":"10.7916/JMETC.V10I2.4190","DOIUrl":"https://doi.org/10.7916/JMETC.V10I2.4190","url":null,"abstract":"High school students often ask questions about the nature of infinity. When contemplating what the “largest number” is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or “set theory,” are generally unknown to high school students. The authors propose a method for introducing basic ideas in set theory to high school trigonometry students by connecting prior knowledge of the tangent function and the unit circle to Georg Cantor’s ideas about infinity. By doing so, high school teachers have an opportunity to inspire their students with rich mathematics.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2019-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46869604","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 : 2019-12-14DOI: 10.7916/JMETC.V10I2.4191
Indira Gil, Laura Zamudio-Orozco, Barbara King
When teaching through problem solving, effective mathematics teachers need to lead discussions that assist students in making connections between different solution strategies. However, while teaching a methods course for preservice teachers (PSTs), we noticed that after solving a problem and presenting various solution strategies, many PSTs seemed lost on how to proceed with the mathematics lesson. To address this issue, we designed an action research study where we implemented Smith and Stein’s (2011) five practices for orchestrating productive classroom discussions, and focused our attention on the fifth practice, making connections. Specifically, we designed an instructional intervention to examine the type of connections made by PSTs and how these connections changed as the course progressed to aid PSTs’ connection making skills. We identified three types of connections made by PSTs: superficial knowledge connections, procedural knowledge connections, and conceptual knowledge connections. Additionally, we observed a decrease in the amount of superficial knowledge connections and an increase in the amounts of procedural knowledge connections and conceptual knowledge connections made by PSTs throughout the course.
{"title":"After Presenting Multiple Solution Strategies, What’s Next? Examining the Mathematical Connections Made by Preservice Teachers","authors":"Indira Gil, Laura Zamudio-Orozco, Barbara King","doi":"10.7916/JMETC.V10I2.4191","DOIUrl":"https://doi.org/10.7916/JMETC.V10I2.4191","url":null,"abstract":"When teaching through problem solving, effective mathematics teachers need to lead discussions that assist students in making connections between different solution strategies. However, while teaching a methods course for preservice teachers (PSTs), we noticed that after solving a problem and presenting various solution strategies, many PSTs seemed lost on how to proceed with the mathematics lesson. To address this issue, we designed an action research study where we implemented Smith and Stein’s (2011) five practices for orchestrating productive classroom discussions, and focused our attention on the fifth practice, making connections. Specifically, we designed an instructional intervention to examine the type of connections made by PSTs and how these connections changed as the course progressed to aid PSTs’ connection making skills. We identified three types of connections made by PSTs: superficial knowledge connections, procedural knowledge connections, and conceptual knowledge connections. Additionally, we observed a decrease in the amount of superficial knowledge connections and an increase in the amounts of procedural knowledge connections and conceptual knowledge connections made by PSTs throughout the course.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"9-20"},"PeriodicalIF":0.0,"publicationDate":"2019-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45897498","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 : 2019-06-01DOI: 10.7916/JMETC.V10I1.1668
C. Thomas, R. Berry
This article uses Culturally Relevant Pedagogy (CRP) and Culturally Responsive Teaching (CRT) as the theoretical frameworks and qualitative metasynthesis as the methodological framework to synthesize qualitative research published between 1994 and February of 2016. Initial searches produced 1,224 articles, but through a process of appraisals, 12 articles were synthesized to understand how researchers interpret mathematics teaching practices that support CRP and CRT in pre-kindergarten through 12th grade. There were five findings focused on teacher practices, classroom interactions, and student experiences with CRP and CRT within mathematics education, including: caring, context, cultural competency, high expectations, and mathematics instruction.
{"title":"A Qualitative Metasynthesis of Culturally Relevant Pedagogy & Culturally Responsive Teaching: Unpacking Mathematics Teaching Practices","authors":"C. Thomas, R. Berry","doi":"10.7916/JMETC.V10I1.1668","DOIUrl":"https://doi.org/10.7916/JMETC.V10I1.1668","url":null,"abstract":"This article uses Culturally Relevant Pedagogy (CRP) and Culturally Responsive Teaching (CRT) as the theoretical frameworks and qualitative metasynthesis as the methodological framework to synthesize qualitative research published between 1994 and February of 2016. Initial searches produced 1,224 articles, but through a process of appraisals, 12 articles were synthesized to understand how researchers interpret mathematics teaching practices that support CRP and CRT in pre-kindergarten through 12th grade. There were five findings focused on teacher practices, classroom interactions, and student experiences with CRP and CRT within mathematics education, including: caring, context, cultural competency, high expectations, and mathematics instruction.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"21-30"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41831115","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 : 2019-06-01DOI: 10.7916/JMETC.V10I1.1665
Joan Gujarati
This article examines how the Child Mathematics Inquiry Portfolio (CMIP), a semester-long field experience project attached to an elementary mathematics methods course, can impact preservice teachers’ understanding about teaching and learning mathematics and set them on more positive mathematics teaching journeys as they prepare to enter the field. This action research study, grounded in reflective practice, was contextualized in undergraduate and graduate elementary mathematics methods courses with 92 participants over two academic years. Data came from preservice teachers’ written reflections on the child mathematics inquiry process. Findings reveal that the CMIP impacted the preservice teachers’ mathematics teaching and learning in four major areas: bridge between mathematics methods course, textbook, and actual classroom experience; mathematical confidence; greater understanding of how teachers shape students’ mathematics dispositions; and personal. Implications for mathematics teacher education are discussed.
{"title":"Reflecting on Action: Implications from the Child Mathematics Inquiry Portfolio","authors":"Joan Gujarati","doi":"10.7916/JMETC.V10I1.1665","DOIUrl":"https://doi.org/10.7916/JMETC.V10I1.1665","url":null,"abstract":"This article examines how the Child Mathematics Inquiry Portfolio (CMIP), a semester-long field experience project attached to an elementary mathematics methods course, can impact preservice teachers’ understanding about teaching and learning mathematics and set them on more positive mathematics teaching journeys as they prepare to enter the field. This action research study, grounded in reflective practice, was contextualized in undergraduate and graduate elementary mathematics methods courses with 92 participants over two academic years. Data came from preservice teachers’ written reflections on the child mathematics inquiry process. Findings reveal that the CMIP impacted the preservice teachers’ mathematics teaching and learning in four major areas: bridge between mathematics methods course, textbook, and actual classroom experience; mathematical confidence; greater understanding of how teachers shape students’ mathematics dispositions; and personal. Implications for mathematics teacher education are discussed.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44041475","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 : 2019-06-01DOI: 10.7916/JMETC.V10I1.1667
K. Johnson, Amy L. Nebesniak, Theodore J. Rupnow
Curriculum change is inevitable in schooling. For content areas such as mathematics that are already under the national spotlight, transitioning to new curriculum materials while concurrently enacting instructional reform creates both a challenge and an opportunity. This paper discusses how partnerships between two state universities and respective neighboring school districts resulted in the creation and implementation of graduate courses for teachers targeted at curricular and instructional reform specific to each district. Common course components between both university-district partnerships were identified in the areas of mathematics research, practice, and leadership advocacy and found to be instrumental in supporting instructional reform and fostering sustained development. Implications for collaborative partnerships, curriculum implementation and research are discussed.
{"title":"District-University Collaborations to Support Reform-Based Mathematics Curriculum Implementation.","authors":"K. Johnson, Amy L. Nebesniak, Theodore J. Rupnow","doi":"10.7916/JMETC.V10I1.1667","DOIUrl":"https://doi.org/10.7916/JMETC.V10I1.1667","url":null,"abstract":"Curriculum change is inevitable in schooling. For content areas such as mathematics that are already under the national spotlight, transitioning to new curriculum materials while concurrently enacting instructional reform creates both a challenge and an opportunity. This paper discusses how partnerships between two state universities and respective neighboring school districts resulted in the creation and implementation of graduate courses for teachers targeted at curricular and instructional reform specific to each district. Common course components between both university-district partnerships were identified in the areas of mathematics research, practice, and leadership advocacy and found to be instrumental in supporting instructional reform and fostering sustained development. Implications for collaborative partnerships, curriculum implementation and research are discussed.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"17-20"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45014892","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 : 2019-06-01DOI: 10.7916/JMETC.V10I1.1666
A. Gibbons
Maryam Mirzakhani is the first and the only female winner of the Fields Medal since its establishment in 1936. She is arguably one of the greatest mathematicians of our generation. This biographical paper outlines her life and work. Her mathematical theorems and noteworthy accomplishments are just as impressive as her determination, imagination, and optimistic outlook on life. Mirzakhani’s success came from her passion, creativity, and playful approach to mathematics. She felt the most rewarding part of mathematics was the enjoyment of understanding or discovering something. Mirzakhani’s work was visual and focused on patterns and ideas rather than on numbers and algorithms. She constructed mathematics in an artistic way, and her goal was to always find truth and beauty in the world. Mirzakhani will forever be an inspiration to anyone who has studied her work and read her story.
{"title":"The Life of Maryam Mirzakhani.","authors":"A. Gibbons","doi":"10.7916/JMETC.V10I1.1666","DOIUrl":"https://doi.org/10.7916/JMETC.V10I1.1666","url":null,"abstract":"Maryam Mirzakhani is the first and the only female winner of the Fields Medal since its establishment in 1936. She is arguably one of the greatest mathematicians of our generation. This biographical paper outlines her life and work. Her mathematical theorems and noteworthy accomplishments are just as impressive as her determination, imagination, and optimistic outlook on life. Mirzakhani’s success came from her passion, creativity, and playful approach to mathematics. She felt the most rewarding part of mathematics was the enjoyment of understanding or discovering something. Mirzakhani’s work was visual and focused on patterns and ideas rather than on numbers and algorithms. She constructed mathematics in an artistic way, and her goal was to always find truth and beauty in the world. Mirzakhani will forever be an inspiration to anyone who has studied her work and read her story.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"11-16"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46242537","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 : 2019-06-01DOI: 10.7916/JMETC.V10I1.1669
R. Ahuja
This paper describes the theory of professional competence in teaching of mathematics developed through a cross-cultural examination of teaching practices of mathematics teachers recommended as competent by their principals in two selected high-achieving high schools of India and the United States. A detailed study of teacher cases from both of the research settings yielded a rich conceptualization of the relationship between teachers’ professional knowledge base and professional competence in the teaching of mathematics. The substantive theory explains the processes of both the development and the display of professional competence and enables predictions of the ways teachers would most likely utilize to meet the performance expectations of their work environments. The study makes a unique contribution to the field of teacher education and views professional competence as a dynamic interplay of various components of teachers’ professional knowledge base activated in actual teaching situations in the context of the classroom, school, and wider social culture.
{"title":"Theory of Professional Competence in Teaching of Mathematics: Development and Explication through Cross-cultural Examination of Teaching Practices in India and the United States","authors":"R. Ahuja","doi":"10.7916/JMETC.V10I1.1669","DOIUrl":"https://doi.org/10.7916/JMETC.V10I1.1669","url":null,"abstract":"This paper describes the theory of professional competence in teaching of mathematics developed through a cross-cultural examination of teaching practices of mathematics teachers recommended as competent by their principals in two selected high-achieving high schools of India and the United States. A detailed study of teacher cases from both of the research settings yielded a rich conceptualization of the relationship between teachers’ professional knowledge base and professional competence in the teaching of mathematics. The substantive theory explains the processes of both the development and the display of professional competence and enables predictions of the ways teachers would most likely utilize to meet the performance expectations of their work environments. The study makes a unique contribution to the field of teacher education and views professional competence as a dynamic interplay of various components of teachers’ professional knowledge base activated in actual teaching situations in the context of the classroom, school, and wider social culture.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"31-48"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44745685","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}
Growth mindset is an important belief for students to be successful in mathematics and in their current and future lives. Solving open-ended problems also has many positive benefits for students. Little research has been conducted though on growth mindset and mathematics at the middle school level and particularly growth mindset with open-ended problems. This study explored middle school students’ mindsets before and after a four-week Saturday program that incorporated open-ended problems. We also looked at the quality of solutions developed by the students. It was found that the students generally had growth mindsets with some fixed ideas at the beginning of the study that improved to strong growth mindsets at the conclusion of the four weeks. The students also improved on their quality of solutions from the first to the last open- ended activity. Implications for the implementation and research of open-ended problems are discussed.
{"title":"Middle School Students’ Mindsets Before and After Open-Ended Problems","authors":"Micah S. Stohlmann, Xing Huang, Lina Devaul","doi":"10.7916/JMETC.V9I2.587","DOIUrl":"https://doi.org/10.7916/JMETC.V9I2.587","url":null,"abstract":"Growth mindset is an important belief for students to be successful in mathematics and in their current and future lives. Solving open-ended problems also has many positive benefits for students. Little research has been conducted though on growth mindset and mathematics at the middle school level and particularly growth mindset with open-ended problems. This study explored middle school students’ mindsets before and after a four-week Saturday program that incorporated open-ended problems. We also looked at the quality of solutions developed by the students. It was found that the students generally had growth mindsets with some fixed ideas at the beginning of the study that improved to strong growth mindsets at the conclusion of the four weeks. The students also improved on their quality of solutions from the first to the last open- ended activity. Implications for the implementation and research of open-ended problems are discussed.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"9 1","pages":"27-36"},"PeriodicalIF":0.0,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42051732","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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