Pub Date : 2020-07-15DOI: 10.7916/JMETC.V11I1.6704
J. Thomas, Taylor Marzilli, Brittney Sawyer, C. Jong, E. Schack, Molly H. Fisher
This study examines potential bias with respect to perceived gender and ethnicity in preservice teachers’ professional noticing of children’s mathematical thinking. The goal of the study was to explore how, and to what extent bias emerges within pre-service teachers’ professional noticing of children of differing perceived races and genders. Our findings suggest that bias tends to emerge in the interpreting phase of professional noticing; however, such emergence did not appear to vary in conjunction with the perceived ethnicity and gender of the student. Further, our findings suggest that the inclusion of visual imagery (i.e. photos) influence the manifestation of bias among preservice teachers to some degree when professionally noticing in the context of a written case.
{"title":"Investigating the Manifestations of Bias in Professional Noticing of Mathematical Thinking among Preservice Teachers.","authors":"J. Thomas, Taylor Marzilli, Brittney Sawyer, C. Jong, E. Schack, Molly H. Fisher","doi":"10.7916/JMETC.V11I1.6704","DOIUrl":"https://doi.org/10.7916/JMETC.V11I1.6704","url":null,"abstract":"This study examines potential bias with respect to perceived gender and ethnicity in preservice teachers’ professional noticing of children’s mathematical thinking. The goal of the study was to explore how, and to what extent bias emerges within pre-service teachers’ professional noticing of children of differing perceived races and genders. Our findings suggest that bias tends to emerge in the interpreting phase of professional noticing; however, such emergence did not appear to vary in conjunction with the perceived ethnicity and gender of the student. Further, our findings suggest that the inclusion of visual imagery (i.e. photos) influence the manifestation of bias among preservice teachers to some degree when professionally noticing in the context of a written case.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48270409","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 : 2020-07-15DOI: 10.7916/JMETC.V11I1.6706
Michael C. Osborne, Xin Ma
Using the nationally representative sample from the United States in the 2012 Programme for International Student Assessment (N = 7,429 students from 240 schools), the present study examined the effects of student help-seeking behaviors on eight measures of student mathematics achievement. To account for the multilevel structure of the data with students nested within schools (i.e., students attending different schools), a two-level hierarchical linear model was used in the data analysis. Student help-seeking behaviors showed statistically significant positive effects on all eight measures of mathematics achievement, even after controlling for student characteristics and school characteristics. Furthermore, for all eight measures of mathematics achievement, the positive effects of student help-seeking behaviors on student mathematics achievement are independent of which schools students attend.
{"title":"Effects of Student Help-Seeking Behaviors on Student Mathematics Achievement.","authors":"Michael C. Osborne, Xin Ma","doi":"10.7916/JMETC.V11I1.6706","DOIUrl":"https://doi.org/10.7916/JMETC.V11I1.6706","url":null,"abstract":"Using the nationally representative sample from the United States in the 2012 Programme for International Student Assessment (N = 7,429 students from 240 schools), the present study examined the effects of student help-seeking behaviors on eight measures of student mathematics achievement. To account for the multilevel structure of the data with students nested within schools (i.e., students attending different schools), a two-level hierarchical linear model was used in the data analysis. Student help-seeking behaviors showed statistically significant positive effects on all eight measures of mathematics achievement, even after controlling for student characteristics and school characteristics. Furthermore, for all eight measures of mathematics achievement, the positive effects of student help-seeking behaviors on student mathematics achievement are independent of which schools students attend.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"21-31"},"PeriodicalIF":0.0,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47257114","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 : 2020-07-15DOI: 10.7916/JMETC.V11I1.6708
M. A. Solé
Developmental mathematics, which is designed to prepare students for college-level mathematics courses, can be a barrier to students’ success. In the United States, the majority of students placed into developmental mathematics courses fail to complete the developmental sequence. Alternative mathematics pathways offer some benefits when integrated with “just-in- time support” or expedited instruction on specific prerequisite concepts needed solely for the current lesson. This study compares two statistics courses taught at a public community college: a complete course taught in one semester and a two-semester version with just-in-time develop- mental content integrated into the course. The study found that students placed into the one- semester statistics course accumulated significantly more credits after one and two years of college. These students also completed an associate’s degree within two years at a significantly higher rate than students placed into the two-semester statistics course. The study also found students deemed non-proficient by the college’s placement exam, who also had a strong high school average were significantly more likely to earn a grade of A- or higher or a grade of B- or higher compared to students originally deemed proficient.
{"title":"Streamlining Time Spent in Alternative Developmental Mathematics Pathways: Increasing Access to College-Level Mathematics Courses by Altering Placement Procedures","authors":"M. A. Solé","doi":"10.7916/JMETC.V11I1.6708","DOIUrl":"https://doi.org/10.7916/JMETC.V11I1.6708","url":null,"abstract":"Developmental mathematics, which is designed to prepare students for college-level mathematics courses, can be a barrier to students’ success. In the United States, the majority of students placed into developmental mathematics courses fail to complete the developmental sequence. Alternative mathematics pathways offer some benefits when integrated with “just-in- time support” or expedited instruction on specific prerequisite concepts needed solely for the current lesson. This study compares two statistics courses taught at a public community college: a complete course taught in one semester and a two-semester version with just-in-time develop- mental content integrated into the course. The study found that students placed into the one- semester statistics course accumulated significantly more credits after one and two years of college. These students also completed an associate’s degree within two years at a significantly higher rate than students placed into the two-semester statistics course. The study also found students deemed non-proficient by the college’s placement exam, who also had a strong high school average were significantly more likely to earn a grade of A- or higher or a grade of B- or higher compared to students originally deemed proficient.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"43-54"},"PeriodicalIF":0.0,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44238776","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 : 2020-07-15DOI: 10.7916/JMETC.V11I1.6705
Michael S. Meagher, S. A. Özgün-Koca, M. Edwards
Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also reflect, throughout the task, on how they might nurture the generation and exploration of mathematical conjectures with their own students.
{"title":"Nurturing the Generation and Exploration of Mathematical Conjectures with Preservice Teachers: An Example with a Perimeters Task.","authors":"Michael S. Meagher, S. A. Özgün-Koca, M. Edwards","doi":"10.7916/JMETC.V11I1.6705","DOIUrl":"https://doi.org/10.7916/JMETC.V11I1.6705","url":null,"abstract":"Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also reflect, throughout the task, on how they might nurture the generation and exploration of mathematical conjectures with their own students.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"13-20"},"PeriodicalIF":0.0,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46963934","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 : 2020-01-01DOI: 10.7916/JMETC.V11I2.7833
K. Barba
Mathematics problems are shared rapidly across all social media platforms, and the relative anonymity granted to users can lead to unfiltered discourse. This study examined 1,046 comments from a mathematics problem posted twice to YouTube in February 2016 to determine the underlying narratives that indicate the commenters’ mathematical mindsets and their mathematical identities. These two factors contribute to mathematics success in general. Qualitative themes emerged regarding attributions, motivational goals, response to failure, defensive processing, normative comparisons, and positional acts. A fixed mathematical mindset was the dominant mindset and corresponded to positional acts of superiority, inferiority, or authority. This finding suggests that intellectual capacity or ranking was a core component of the mathematical identities for these users. The growth mathematical mindset was linked to spectator and instructor or solidarity positions, suggesting that these users had more robust mathematical identities that were unthreatened by performance indicators. Further examination of social media discourse andits relation to mathematical mindsets and mathematical identities can lead to a better understanding of the interactions outside the classroom that either encourage or inhibit mathematics success.
{"title":"The Mathematical Mindsets and Mathematical Identities Revealed in Social Media Discourse","authors":"K. Barba","doi":"10.7916/JMETC.V11I2.7833","DOIUrl":"https://doi.org/10.7916/JMETC.V11I2.7833","url":null,"abstract":"Mathematics problems are shared rapidly across all social media platforms, and the relative anonymity granted to users can lead to unfiltered discourse. This study examined 1,046 comments from a mathematics problem posted twice to YouTube in February 2016 to determine the underlying narratives that indicate the commenters’ mathematical mindsets and their mathematical identities. These two factors contribute to mathematics success in general. Qualitative themes emerged regarding attributions, motivational goals, response to failure, defensive processing, normative comparisons, and positional acts. A fixed mathematical mindset was the dominant mindset and corresponded to positional acts of superiority, inferiority, or authority. This finding suggests that intellectual capacity or ranking was a core component of the mathematical identities for these users. The growth mathematical mindset was linked to spectator and instructor or solidarity positions, suggesting that these users had more robust mathematical identities that were unthreatened by performance indicators. Further examination of social media discourse andits relation to mathematical mindsets and mathematical identities can lead to a better understanding of the interactions outside the classroom that either encourage or inhibit mathematics success.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"23-34"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368948","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 : 2020-01-01DOI: 10.7916/JMETC.V11I2.7835
Leah M. Simon
This classroom study immersed high school geometry students in the creative and intellectually challenging design task of developing unique logos using mathematics and technology. The students applied and deepened their knowledge of transformations while using dynamic geometry software. One of the main aims of the task was to elevate student creativity andautonomy within the mathematics classroom while they engaged in mathematical design thinking to create their logos. The discussion provides insight into considering student work from a design perspective, which can offer students new ways to engage with mathematical concepts and make their thinking more explicit
{"title":"Mathematical Design Thinking in the Classroom through Graphic Art","authors":"Leah M. Simon","doi":"10.7916/JMETC.V11I2.7835","DOIUrl":"https://doi.org/10.7916/JMETC.V11I2.7835","url":null,"abstract":"This classroom study immersed high school geometry students in the creative and intellectually challenging design task of developing unique logos using mathematics and technology. The students applied and deepened their knowledge of transformations while using dynamic geometry software. One of the main aims of the task was to elevate student creativity andautonomy within the mathematics classroom while they engaged in mathematical design thinking to create their logos. The discussion provides insight into considering student work from a design perspective, which can offer students new ways to engage with mathematical concepts and make their thinking more explicit","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"47-54"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368958","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 : 2020-01-01DOI: 10.7916/JMETC.V11I2.7836
Ann Wheeler, S. Smith, David Gardner
In this paper, we discuss the utilization of an innovative learning tool, the Sphero BOLT robot, in a 10-day algebra-based mathematics education course for graduate students. Students created routes for their BOLTs to travel and determined ways to measure the distance, rate, and time of their robots’ movements. The student prompt, sample student work, class time considerations, and sample student-written reflections about the activity are detailed, in addition to implications and suggestions for teacher educators
{"title":"Using the Sphero BOLT to Engage Students Mathematically","authors":"Ann Wheeler, S. Smith, David Gardner","doi":"10.7916/JMETC.V11I2.7836","DOIUrl":"https://doi.org/10.7916/JMETC.V11I2.7836","url":null,"abstract":"In this paper, we discuss the utilization of an innovative learning tool, the Sphero BOLT robot, in a 10-day algebra-based mathematics education course for graduate students. Students created routes for their BOLTs to travel and determined ways to measure the distance, rate, and time of their robots’ movements. The student prompt, sample student work, class time considerations, and sample student-written reflections about the activity are detailed, in addition to implications and suggestions for teacher educators","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"55-60"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368965","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 : 2020-01-01DOI: 10.7916/JMETC.V11I2.7832
Tye G. Campbell, Sheunghyun Yeo
While a growing body of research examines teachers’ facilitation of discourse-rich classrooms, surprisingly little research is devoted to learners’ responsibilities in such classrooms. In this paper, we share a theoretical model for explaining students’ responsibilities in yielding mathematical learning in discourse-rich classrooms. These responsibilities consist of the following: (1) determined listening and striving to understand others’ contributions; (2) proactive contribution; (3) maintaining equal positioning; (4) willingness to resolve incommensurability; and (5) on-task talk. Each of the responsibilities is interdependent, suggesting that failure to meet one responsibility decreases the likelihood that another responsibility will be met. The model suggests important implications for supporting learners in discourse-rich classrooms.
{"title":"Conceptualizing Student Responsibilities in Discourse-Rich Classrooms","authors":"Tye G. Campbell, Sheunghyun Yeo","doi":"10.7916/JMETC.V11I2.7832","DOIUrl":"https://doi.org/10.7916/JMETC.V11I2.7832","url":null,"abstract":"While a growing body of research examines teachers’ facilitation of discourse-rich classrooms, surprisingly little research is devoted to learners’ responsibilities in such classrooms. In this paper, we share a theoretical model for explaining students’ responsibilities in yielding mathematical learning in discourse-rich classrooms. These responsibilities consist of the following: (1) determined listening and striving to understand others’ contributions; (2) proactive contribution; (3) maintaining equal positioning; (4) willingness to resolve incommensurability; and (5) on-task talk. Each of the responsibilities is interdependent, suggesting that failure to meet one responsibility decreases the likelihood that another responsibility will be met. The model suggests important implications for supporting learners in discourse-rich classrooms.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"13-21"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368941","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 : 2020-01-01DOI: 10.7916/JMETC.V11I2.7831
Hung-hsi Wu
The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics—to be called TSM—that is predominant in almost all the school textbooks. By analyzing how the long division algorithm is taught and why it becomes so mystifying to school students, we explore how to provide themissing reasoning that makes sense of the algorithm. The article also suggests some concrete steps we can take to eradicate TSM.
{"title":"Misconceptions About the Long Division Algorithm in School Mathematics","authors":"Hung-hsi Wu","doi":"10.7916/JMETC.V11I2.7831","DOIUrl":"https://doi.org/10.7916/JMETC.V11I2.7831","url":null,"abstract":"The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics—to be called TSM—that is predominant in almost all the school textbooks. By analyzing how the long division algorithm is taught and why it becomes so mystifying to school students, we explore how to provide themissing reasoning that makes sense of the algorithm. The article also suggests some concrete steps we can take to eradicate TSM.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"11 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368935","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.V10I2.4194
Angela M. Hodge, Janice F. Rech, Michael Matthews, K. Johnson, Paula M. Jakopovic
Mentoring is an important aspect of mathematics teacher education, and in particular, pre-service teacher education. Faculty at a large Midwestern university developed and refined a mentoring program designed to help pre-service secondary mathematics teachers, called Scholars, become future leaders in mathematics education. This paper describes how faculty mentors leveraged challenges in the mentoring program’s early stages based on their reflections and initial mentee outcomes to create a more effective mentoring program. Recommendations based on research and practice are provided for other university programs interested in mentoring future mathematics teachers.
{"title":"Mentoring Future Mathematics Teachers: Lessons Learned from Four Mentoring Partnerships.","authors":"Angela M. Hodge, Janice F. Rech, Michael Matthews, K. Johnson, Paula M. Jakopovic","doi":"10.7916/JMETC.V10I2.4194","DOIUrl":"https://doi.org/10.7916/JMETC.V10I2.4194","url":null,"abstract":"Mentoring is an important aspect of mathematics teacher education, and in particular, pre-service teacher education. Faculty at a large Midwestern university developed and refined a mentoring program designed to help pre-service secondary mathematics teachers, called Scholars, become future leaders in mathematics education. This paper describes how faculty mentors leveraged challenges in the mentoring program’s early stages based on their reflections and initial mentee outcomes to create a more effective mentoring program. Recommendations based on research and practice are provided for other university programs interested in mentoring future mathematics teachers.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"10 1","pages":"37-43"},"PeriodicalIF":0.0,"publicationDate":"2019-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48170625","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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