Pub Date : 2022-12-23DOI: 10.52214/jmetc.v13i2.9385
Alden Ducharme, C. Smith, Barbara King
Learning to facilitate whole-class mathematical discussions is a complex task. Teachers must become adept at using discourse moves to elicit and extend student thinking and move discussions towards a mathematical point. Practice-based mathematics methods courses give pre-service teachers opportunities to rehearse these moves in a controlled setting. Providing opportunities for practice, often called rehearsals or approximations of practice, have been shown to be effective at developing pre-service teachers' abilities to use discourse moves, but we still do not have a clear understanding of the types of discourse moves pre-service teachers use during discussions or how these moves change over the course of a discussion. In this article, we analyze. whole-class discussions facilitated by pre-service teachers to determine the types of discourse moves used as the discussion progresses. Based on this data and relevant literature, we propose a framework for the structure of whole-class mathematical discussions.
{"title":"Pre-Service Teachers' Discourse Moves During Whole Class Mathematical Discussions: An Analysis and Proposed Framework","authors":"Alden Ducharme, C. Smith, Barbara King","doi":"10.52214/jmetc.v13i2.9385","DOIUrl":"https://doi.org/10.52214/jmetc.v13i2.9385","url":null,"abstract":"Learning to facilitate whole-class mathematical discussions is a complex task. Teachers must become adept at using discourse moves to elicit and extend student thinking and move discussions towards a mathematical point. Practice-based mathematics methods courses give pre-service teachers opportunities to rehearse these moves in a controlled setting. Providing opportunities for practice, often called rehearsals or approximations of practice, have been shown to be effective at developing pre-service teachers' abilities to use discourse moves, but we still do not have a clear understanding of the types of discourse moves pre-service teachers use during discussions or how these moves change over the course of a discussion. In this article, we analyze. whole-class discussions facilitated by pre-service teachers to determine the types of discourse moves used as the discussion progresses. Based on this data and relevant literature, we propose a framework for the structure of whole-class mathematical discussions.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41326063","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 : 2022-12-23DOI: 10.52214/jmetc.v13i2.10059
K. Duggan
Improving Discourse in Mathematics Education
改进数学教育中的话语
{"title":"Empathy in the Math Classroom","authors":"K. Duggan","doi":"10.52214/jmetc.v13i2.10059","DOIUrl":"https://doi.org/10.52214/jmetc.v13i2.10059","url":null,"abstract":"Improving Discourse in Mathematics Education","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44397858","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 : 2022-12-23DOI: 10.52214/jmetc.v13i2.9009
Christos Markopoulos, Patrick Bruck, Koralia Petta
This paper examines Grade 6 students’ thinking about geometrical solids and their properties in the context of a computer-based task. The main focus is to explore how students interact with a number of tasks based on the dynamic transformation of computer-based representations of 3D solids in a geometry classroom with the aid of a Dynamic Geometric Environment. The analysis of two teaching experiments suggests that the dynamic transformations of geometrical solids encourage the students to investigate relationships between the solids and their properties and their 2D representations. Through the tasks, students realize the existence of non-trivial conventions in 2D representations and become aware that angles and edge dimensions may be distorted. The study provides insight into student learning around geometric solids and their properties, and consequently an opportunity to enhance the teaching of 3D geometry.
{"title":"Exploring Students’ Geometrical Thinking Through Dynamic Transformations Using 3D Computer-Based Representations","authors":"Christos Markopoulos, Patrick Bruck, Koralia Petta","doi":"10.52214/jmetc.v13i2.9009","DOIUrl":"https://doi.org/10.52214/jmetc.v13i2.9009","url":null,"abstract":"This paper examines Grade 6 students’ thinking about geometrical solids and their properties in the context of a computer-based task. The main focus is to explore how students interact with a number of tasks based on the dynamic transformation of computer-based representations of 3D solids in a geometry classroom with the aid of a Dynamic Geometric Environment. The analysis of two teaching experiments suggests that the dynamic transformations of geometrical solids encourage the students to investigate relationships between the solids and their properties and their 2D representations. Through the tasks, students realize the existence of non-trivial conventions in 2D representations and become aware that angles and edge dimensions may be distorted. The study provides insight into student learning around geometric solids and their properties, and consequently an opportunity to enhance the teaching of 3D geometry.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45695713","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 South African Language in Education Policy (LiEP) advocates using African languages in the Foundation Phase (FP) which is the first phase of formal schooling in South Africa. This paper seeks to identify the challenges in implementing the language provisions prescribed in the LiEP in South Africa and within the region. Using the challenge-based learning (CBL) approach, this paper provides a glimpse into the challenges that 50 FP teachers based in six rural schools in South Africa face when using African languages as LoLT when teaching mathematics. Data collected through questionnaires, focus-group interviews, and observations in mathematics classrooms were used to illuminate these challenges. The results indicate that teachers experienced three main challenges: multilingual learners and learners who were taught in English in pre-school, English scripted lesson plans, and teacher training that was only provided in English. Importantly this paper identified a language disjuncture between policy and practice where the policy requires teachers to teach in African languages while the teaching material is written in English.
{"title":"Challenges in Using African Languages as the Language of Learning and Teaching (LoLT) for Mathematics in Rural Schools: Foundation Phase Teachers’ Perspectives","authors":"Ramashego Shila Mphahlele, Mmapeu Margret Manyaka, Patricia Ouma Nomsa Moshaba","doi":"10.52214/jmetc.v13i2.9451","DOIUrl":"https://doi.org/10.52214/jmetc.v13i2.9451","url":null,"abstract":"The South African Language in Education Policy (LiEP) advocates using African languages in the Foundation Phase (FP) which is the first phase of formal schooling in South Africa. This paper seeks to identify the challenges in implementing the language provisions prescribed in the LiEP in South Africa and within the region. Using the challenge-based learning (CBL) approach, this paper provides a glimpse into the challenges that 50 FP teachers based in six rural schools in South Africa face when using African languages as LoLT when teaching mathematics. Data collected through questionnaires, focus-group interviews, and observations in mathematics classrooms were used to illuminate these challenges. The results indicate that teachers experienced three main challenges: multilingual learners and learners who were taught in English in pre-school, English scripted lesson plans, and teacher training that was only provided in English. Importantly this paper identified a language disjuncture between policy and practice where the policy requires teachers to teach in African languages while the teaching material is written in English.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46705552","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 : 2022-05-25DOI: 10.52214/jmetc.v13i1.9722
Alyssa MacMahon, D. Barr
Notes from the Field Introduction
现场介绍笔记
{"title":"Reflections on the Algebra I Classroom Introduction","authors":"Alyssa MacMahon, D. Barr","doi":"10.52214/jmetc.v13i1.9722","DOIUrl":"https://doi.org/10.52214/jmetc.v13i1.9722","url":null,"abstract":"Notes from the Field Introduction","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41502797","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 : 2022-05-25DOI: 10.52214/jmetc.v13i1.9726
Journal Editor
{"title":"Inside Cover Spring 2022","authors":"Journal Editor","doi":"10.52214/jmetc.v13i1.9726","DOIUrl":"https://doi.org/10.52214/jmetc.v13i1.9726","url":null,"abstract":"","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41655142","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 : 2022-05-25DOI: 10.52214/jmetc.v13i1.9188
Michelle Longhitano
Reflections on the Algebra I Classroom
关于代数I课堂的思考
{"title":"Evaluating the SSATSEL Algebra I Lab Model: Objectives and Challenges","authors":"Michelle Longhitano","doi":"10.52214/jmetc.v13i1.9188","DOIUrl":"https://doi.org/10.52214/jmetc.v13i1.9188","url":null,"abstract":"Reflections on the Algebra I Classroom","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47878665","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 : 2022-05-25DOI: 10.52214/jmetc.v13i1.9727
Journal Editor
{"title":"About the Authors and Reviewer Acknowledgement Spring 2022","authors":"Journal Editor","doi":"10.52214/jmetc.v13i1.9727","DOIUrl":"https://doi.org/10.52214/jmetc.v13i1.9727","url":null,"abstract":"","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45122430","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 : 2022-05-25DOI: 10.52214/jmetc.v13i1.9017
Lioubov Pogorelova
Though the curriculum reform movement that began in 1989 has had a significant impact on calculus pedagogy and content (Windham, 2008), the question remains to what extent reform-based calculus textbooks reflect these reforms. This paper explores this question by analyzing the mathematical content and pedagogical approach of the chapter on functions in Hughes-Hallett et al.’s (2018) reform-based college textbook Calculus: Single and Multivariable (CS&M). To conduct this analysis, the paper first synthesizes Hwang et al.’s (2021) framework for analyzing mathematics textbooks along with Sood and Jitendra’s (2007) framework for comparing traditional and reform-based mathematics textbooks. The paper then applies the synthesized frameworks to identify elements of reform from the big ideas, contextual features, mediated scaffolding, problem solving activities, and STEM integration found in the CS&M chapter. The results suggest that, although the chapter integrates many reform-based principles, there may be scope for further integration. Such efforts, however, may be constrained by influential stakeholders.
{"title":"How Much Reform?","authors":"Lioubov Pogorelova","doi":"10.52214/jmetc.v13i1.9017","DOIUrl":"https://doi.org/10.52214/jmetc.v13i1.9017","url":null,"abstract":"Though the curriculum reform movement that began in 1989 has had a significant impact on calculus pedagogy and content (Windham, 2008), the question remains to what extent reform-based calculus textbooks reflect these reforms. This paper explores this question by analyzing the mathematical content and pedagogical approach of the chapter on functions in Hughes-Hallett et al.’s (2018) reform-based college textbook Calculus: Single and Multivariable (CS&M). To conduct this analysis, the paper first synthesizes Hwang et al.’s (2021) framework for analyzing mathematics textbooks along with Sood and Jitendra’s (2007) framework for comparing traditional and reform-based mathematics textbooks. The paper then applies the synthesized frameworks to identify elements of reform from the big ideas, contextual features, mediated scaffolding, problem solving activities, and STEM integration found in the CS&M chapter. The results suggest that, although the chapter integrates many reform-based principles, there may be scope for further integration. Such efforts, however, may be constrained by influential stakeholders.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48716537","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 : 2022-05-25DOI: 10.52214/jmetc.v13i1.8984
Marc Husband, Parinaz Nikfarjam
This study explores peer feedback in a combined fifth and sixth-grade classroom.Drawing on Hattie and Timperley’s (2007) model for feedback, we analyzed 334 peer feedback comments gathered during six mathematics lessons. Our analysis revealed evidence of peer feedback being beneficial to the students who provide it as well as those who receive it. Specifically, we share examples of how peer feedback can support opportunities for providers of feedback to 1) self-regulate by choosing mathematics strategies, 2) make connections between their own mathematical ideas and those of their peers, and 3) engage in ongoing back-and-forth conversations. Findings from our study point to recommendations for teachers to be more purposeful in their prompts to students about the types of feedback they might provide one another.
{"title":"Peer Feedback in the Mathematics Classroom","authors":"Marc Husband, Parinaz Nikfarjam","doi":"10.52214/jmetc.v13i1.8984","DOIUrl":"https://doi.org/10.52214/jmetc.v13i1.8984","url":null,"abstract":"This study explores peer feedback in a combined fifth and sixth-grade classroom.Drawing on Hattie and Timperley’s (2007) model for feedback, we analyzed 334 peer feedback comments gathered during six mathematics lessons. Our analysis revealed evidence of peer feedback being beneficial to the students who provide it as well as those who receive it. Specifically, we share examples of how peer feedback can support opportunities for providers of feedback to 1) self-regulate by choosing mathematics strategies, 2) make connections between their own mathematical ideas and those of their peers, and 3) engage in ongoing back-and-forth conversations. Findings from our study point to recommendations for teachers to be more purposeful in their prompts to students about the types of feedback they might provide one another.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43734197","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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