Pub Date : 2020-08-13DOI: 10.1080/19477503.2020.1804273
G. Matney, Alyssa Lustgarten, T. Nicholson
ABSTRACT In this study, we share our broad and deep search for what is known from blind-peer-reviewed research publications about the efficacy of the instructional practice of Number Talks. We describe our process for literature review and the subsequent analysis that revealed a shallow depth of articles for which one can discern the factors of quality of Number Talks, as an instructional practice, taking place in K-12 classrooms. Further analysis revealed a new construct for researchers to consider which we call a Black Hole of research on instructional practice. We explain the meaning of a Black Hole using Number Talks as a case example of the phenomenon, which occurs at the intersection of research and practice. Implications for the future of research and teaching practice are discussed. Many areas of possible research are illuminated.
{"title":"Black Holes of Research on Instructional Practice: The Case of Number Talks","authors":"G. Matney, Alyssa Lustgarten, T. Nicholson","doi":"10.1080/19477503.2020.1804273","DOIUrl":"https://doi.org/10.1080/19477503.2020.1804273","url":null,"abstract":"ABSTRACT In this study, we share our broad and deep search for what is known from blind-peer-reviewed research publications about the efficacy of the instructional practice of Number Talks. We describe our process for literature review and the subsequent analysis that revealed a shallow depth of articles for which one can discern the factors of quality of Number Talks, as an instructional practice, taking place in K-12 classrooms. Further analysis revealed a new construct for researchers to consider which we call a Black Hole of research on instructional practice. We explain the meaning of a Black Hole using Number Talks as a case example of the phenomenon, which occurs at the intersection of research and practice. Implications for the future of research and teaching practice are discussed. Many areas of possible research are illuminated.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"246 - 260"},"PeriodicalIF":0.0,"publicationDate":"2020-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2020.1804273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42929910","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 : 2020-06-07DOI: 10.1080/19477503.2020.1772035
R. Brown, Martha L. Epstein, C. Orrill
Teacher knowledge, especially of proportional reasoning, is important, particularly in middle school grades in the United States. In this instrumental case study, one teacher’s understanding of con...
{"title":"When Constant in a Proportional Relationship Isn’t Constant—A Sign of Not-So-Shared Understandings","authors":"R. Brown, Martha L. Epstein, C. Orrill","doi":"10.1080/19477503.2020.1772035","DOIUrl":"https://doi.org/10.1080/19477503.2020.1772035","url":null,"abstract":"Teacher knowledge, especially of proportional reasoning, is important, particularly in middle school grades in the United States. In this instrumental case study, one teacher’s understanding of con...","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2020.1772035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47175227","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 : 2020-04-02DOI: 10.1080/19477503.2019.1670891
Stefanie D. Livers, Jeremy Zelkowski, Kristin E. Harbour, Sara C. McDaniel, J. Gleason
ABSTRACT Teacher self-efficacy and teaching practices are both related to effective teaching and learning of mathematics. Given the theoretical and empirical basis for the importance of teacher self-efficacy, we hypothesized that teacher reported self-efficacy would be positively related to teacher self-reported effective teaching practices. This study examined the self-reported construct data across in-service educator grade level (i.e., elementary and secondary) and educator position (i.e., general education or special education) to determine the associations of constructs and the potential for differences between groups. Correlations between self-efficacy and teacher practices in-service teachers were analyzed using Kendall’s Tau. A Kruskal-Wallis one-way analysis of variance was used to analyze the three participant groups (general education: elementary, general education: secondary, and special education) for the teacher self-efficacy and self-reported teaching practices constructs. Similarities and differences among the relationships between educator grade level, educator position, self-efficacy, and teaching practices are discussed. In addition, implications for future research and professional development with educators are outlined.
{"title":"An Examination of the Relationships of Mathematics Self-Efficacy and Teaching Practices among Elementary, Secondary, and Special Education Educators","authors":"Stefanie D. Livers, Jeremy Zelkowski, Kristin E. Harbour, Sara C. McDaniel, J. Gleason","doi":"10.1080/19477503.2019.1670891","DOIUrl":"https://doi.org/10.1080/19477503.2019.1670891","url":null,"abstract":"ABSTRACT Teacher self-efficacy and teaching practices are both related to effective teaching and learning of mathematics. Given the theoretical and empirical basis for the importance of teacher self-efficacy, we hypothesized that teacher reported self-efficacy would be positively related to teacher self-reported effective teaching practices. This study examined the self-reported construct data across in-service educator grade level (i.e., elementary and secondary) and educator position (i.e., general education or special education) to determine the associations of constructs and the potential for differences between groups. Correlations between self-efficacy and teacher practices in-service teachers were analyzed using Kendall’s Tau. A Kruskal-Wallis one-way analysis of variance was used to analyze the three participant groups (general education: elementary, general education: secondary, and special education) for the teacher self-efficacy and self-reported teaching practices constructs. Similarities and differences among the relationships between educator grade level, educator position, self-efficacy, and teaching practices are discussed. In addition, implications for future research and professional development with educators are outlined.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"109 - 96"},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2019.1670891","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43102576","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 : 2020-04-02DOI: 10.1080/19477503.2019.1681834
J. Thomas, David M. Dueber, Molly H. Fisher, C. Jong, E. Schack
ABSTRACT Teacher noticing and the related construct of professional noticing of children's mathematical thinking have proven to be fertile ground for education researchers. Professional noticing is a framework for a teaching practice consisting of three component parts: attending, interpreting, and deciding. The current study investigates the conceptions and enactment of professional noticing of 24 elementary and middle grades teachers participating in professional learning programs that incorporated professional noticing. These teachers demonstrated a wide range of interpretations of professional noticing which varied in consistency with respect to the literature in this area. This diversity of conceptions is seen as a consequence of teachers having different definitions and scopes of application for professional noticing. This study adds to current discussions about the meaning and role of professional noticing by considering the perspective of practitioners, a group whose input is often secondary to education researchers but whose conceptions and enactment of such noticing is critical for student success.
{"title":"Professional Noticing into Practice: An Examination of Inservice Teachers’ Conceptions and Enactment","authors":"J. Thomas, David M. Dueber, Molly H. Fisher, C. Jong, E. Schack","doi":"10.1080/19477503.2019.1681834","DOIUrl":"https://doi.org/10.1080/19477503.2019.1681834","url":null,"abstract":"ABSTRACT Teacher noticing and the related construct of professional noticing of children's mathematical thinking have proven to be fertile ground for education researchers. Professional noticing is a framework for a teaching practice consisting of three component parts: attending, interpreting, and deciding. The current study investigates the conceptions and enactment of professional noticing of 24 elementary and middle grades teachers participating in professional learning programs that incorporated professional noticing. These teachers demonstrated a wide range of interpretations of professional noticing which varied in consistency with respect to the literature in this area. This diversity of conceptions is seen as a consequence of teachers having different definitions and scopes of application for professional noticing. This study adds to current discussions about the meaning and role of professional noticing by considering the perspective of practitioners, a group whose input is often secondary to education researchers but whose conceptions and enactment of such noticing is critical for student success.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"110 - 123"},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2019.1681834","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46242694","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 : 2020-04-02DOI: 10.1080/19477503.2019.1630546
K. Raymond, S. Reeder
ABSTRACT Teachers’ perceptions of written curriculum influence the way in which they use the curriculum. As multiple states begin to implement state specific standards, understanding the perceptions teachers may have of these standards is critical. This study used quantitative and qualitative methods to investigate the perceptions teachers had of one state’s new standards a year after implementation. Data was themed and coded for factors that influenced teachers’ perceptions, reported changes in teachers’ practices, and perceived strengths and weaknesses of the state standards. Professional development emerged as a key factor that influenced teachers’ perceptions of the state standards. Lack of resources, uncertainty regard depth of knowledge required by the standards, a quick implementation process, and lack of alignment of standardized test emerged as weaknesses across all teachers. However, the perceived strength differed; teachers who had experienced professional development focused on the standards were more likely to view the included processes standards as strengths, and reported greater change in their focus on these process standards. While the findings show that ongoing professional development is needed, they also point to the influence of even minimal professional development and the need for systematic support for teachers as new standards are implemented.
{"title":"Failure to Launch: Oklahoma’s Academic Standards in Mathematics","authors":"K. Raymond, S. Reeder","doi":"10.1080/19477503.2019.1630546","DOIUrl":"https://doi.org/10.1080/19477503.2019.1630546","url":null,"abstract":"ABSTRACT Teachers’ perceptions of written curriculum influence the way in which they use the curriculum. As multiple states begin to implement state specific standards, understanding the perceptions teachers may have of these standards is critical. This study used quantitative and qualitative methods to investigate the perceptions teachers had of one state’s new standards a year after implementation. Data was themed and coded for factors that influenced teachers’ perceptions, reported changes in teachers’ practices, and perceived strengths and weaknesses of the state standards. Professional development emerged as a key factor that influenced teachers’ perceptions of the state standards. Lack of resources, uncertainty regard depth of knowledge required by the standards, a quick implementation process, and lack of alignment of standardized test emerged as weaknesses across all teachers. However, the perceived strength differed; teachers who had experienced professional development focused on the standards were more likely to view the included processes standards as strengths, and reported greater change in their focus on these process standards. While the findings show that ongoing professional development is needed, they also point to the influence of even minimal professional development and the need for systematic support for teachers as new standards are implemented.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"82 - 95"},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2019.1630546","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46815322","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 : 2020-04-02DOI: 10.1080/19477503.2020.1740383
Jessica F. Shumway, Kaitlin Bundock, Jessica King, Monika Burnside, H. Gardner, Felicia Messervy
ABSTRACT Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual understanding of numbers while learning to operate with abstract symbols. In this mixed-methods study, we examined the variations and shifts in second-grade students’ NSK outcomes after participating in an instructional treatment focused on building their NSK through visual representations. After receiving professional development in the instructional treatment, five classroom teachers implemented a systematically planned series of 27 visual number activities across 9 weeks. Analysis using a general linear model indicates that, based on 75 students’ pretest and posttest achievement data, students made significant improvements in NSK that are most likely attributable to the instructional treatment. Additional analyses indicate that students with the lowest pretest scores made the greatest gains and the most substantial shifts in their thinking following the instructional treatment.
{"title":"Visualizing Number: Instruction for Number System Knowledge in Second-Grade Classrooms","authors":"Jessica F. Shumway, Kaitlin Bundock, Jessica King, Monika Burnside, H. Gardner, Felicia Messervy","doi":"10.1080/19477503.2020.1740383","DOIUrl":"https://doi.org/10.1080/19477503.2020.1740383","url":null,"abstract":"ABSTRACT Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual understanding of numbers while learning to operate with abstract symbols. In this mixed-methods study, we examined the variations and shifts in second-grade students’ NSK outcomes after participating in an instructional treatment focused on building their NSK through visual representations. After receiving professional development in the instructional treatment, five classroom teachers implemented a systematically planned series of 27 visual number activities across 9 weeks. Analysis using a general linear model indicates that, based on 75 students’ pretest and posttest achievement data, students made significant improvements in NSK that are most likely attributable to the instructional treatment. Additional analyses indicate that students with the lowest pretest scores made the greatest gains and the most substantial shifts in their thinking following the instructional treatment.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"142 - 161"},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2020.1740383","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46330436","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 : 2020-03-18DOI: 10.1080/19477503.2020.1740382
Tye G. Campbell, Shande King
ABSTRACT This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students’ abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal criteria for proof and subsequently worked in small groups to collaboratively construct arguments which attempted to meet the communally-negotiated criteria. The findings revealed there was no significant correlation between the number of times a group appealed to communal criteria and the quality of their argument. However, the qualitative analysis revealed groups who created valid arguments utilized communal criteria in productive ways, while groups who created invalid arguments superficially engaged with communal criteria or exhibited fundamental misunderstandings of some criteria. These findings imply developing and utilizing communal criteria is a promising support for improving school-aged students’ proving capacities, but further theoretical and empirical research is needed to determine how to develop communal criteria in ways that all students within a classroom community can meaningfully utilize the criteria to mediate their abilities to create arguments.
{"title":"Eighth-grade Students’ Use of Communal Criteria for Collaborative Proving","authors":"Tye G. Campbell, Shande King","doi":"10.1080/19477503.2020.1740382","DOIUrl":"https://doi.org/10.1080/19477503.2020.1740382","url":null,"abstract":"ABSTRACT This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students’ abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal criteria for proof and subsequently worked in small groups to collaboratively construct arguments which attempted to meet the communally-negotiated criteria. The findings revealed there was no significant correlation between the number of times a group appealed to communal criteria and the quality of their argument. However, the qualitative analysis revealed groups who created valid arguments utilized communal criteria in productive ways, while groups who created invalid arguments superficially engaged with communal criteria or exhibited fundamental misunderstandings of some criteria. These findings imply developing and utilizing communal criteria is a promising support for improving school-aged students’ proving capacities, but further theoretical and empirical research is needed to determine how to develop communal criteria in ways that all students within a classroom community can meaningfully utilize the criteria to mediate their abilities to create arguments.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"124 - 141"},"PeriodicalIF":0.0,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2020.1740382","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48074876","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 : 2020-01-02DOI: 10.1080/19477503.2019.1595360
Aline Abassian, Farshid Safi, Sarah B. Bush, J. Bostic
ABSTRACT This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications discussed in this article include realistic modeling, educational modeling, models and modeling perspective, socio-critical modeling, and epistemological modeling. For each perspective, we present (a) the goals of mathematical modeling, (b) the definition of a mathematical model, (c) the mathematical modeling cycle, (d) the design of the modeling task, and (e) key researchers and research foci. In this article, we aim to present the different perspectives of mathematical modeling in an organized way so as to (1) demonstrate the rich and diverse background of mathematical modeling and (2) clarify theoretical foundations of seminal works in mathematical modeling.
{"title":"Five different perspectives on mathematical modeling in mathematics education","authors":"Aline Abassian, Farshid Safi, Sarah B. Bush, J. Bostic","doi":"10.1080/19477503.2019.1595360","DOIUrl":"https://doi.org/10.1080/19477503.2019.1595360","url":null,"abstract":"ABSTRACT This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications discussed in this article include realistic modeling, educational modeling, models and modeling perspective, socio-critical modeling, and epistemological modeling. For each perspective, we present (a) the goals of mathematical modeling, (b) the definition of a mathematical model, (c) the mathematical modeling cycle, (d) the design of the modeling task, and (e) key researchers and research foci. In this article, we aim to present the different perspectives of mathematical modeling in an organized way so as to (1) demonstrate the rich and diverse background of mathematical modeling and (2) clarify theoretical foundations of seminal works in mathematical modeling.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"53 - 65"},"PeriodicalIF":0.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2019.1595360","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44500957","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 : 2020-01-02DOI: 10.1080/19477503.2019.1614386
Linda C. H. Venenciano, Seanyelle L. Yagi, Fay K. Zenigami, Barbara J. Dougherty
ABSTRACT First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations from the Common Core State Standards for Mathematics (CCSSI, 2010) against a learning progression which we proposed as one that develops early algebraic thinking. We described lesson clusters and shared evidence of student thinking to illustrate our learning progression. Findings from this work have implications for what has been considered the start of the learning progression for mathematics.
{"title":"Supporting the Development of Early Algebraic Thinking, an Alternative Approach to Number","authors":"Linda C. H. Venenciano, Seanyelle L. Yagi, Fay K. Zenigami, Barbara J. Dougherty","doi":"10.1080/19477503.2019.1614386","DOIUrl":"https://doi.org/10.1080/19477503.2019.1614386","url":null,"abstract":"ABSTRACT First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations from the Common Core State Standards for Mathematics (CCSSI, 2010) against a learning progression which we proposed as one that develops early algebraic thinking. We described lesson clusters and shared evidence of student thinking to illustrate our learning progression. Findings from this work have implications for what has been considered the start of the learning progression for mathematics.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"38 - 52"},"PeriodicalIF":0.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2019.1614386","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47315363","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 : 2020-01-02DOI: 10.1080/19477503.2019.1619148
Blake E. Peterson, Keith R. Leatham, Lindsay M. Merrill, Laura R. Van Zoest, Shari L. Stockero
ABSTRACT Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking. We illustrate clarifiable ambiguity that occurs in mathematics classrooms and consider ramifications of not addressing it. We conclude the paper with a discussion about addressing clarifiable ambiguity through seeking focused clarification.
{"title":"Clarifiable Ambiguity in Classroom Mathematics Discourse","authors":"Blake E. Peterson, Keith R. Leatham, Lindsay M. Merrill, Laura R. Van Zoest, Shari L. Stockero","doi":"10.1080/19477503.2019.1619148","DOIUrl":"https://doi.org/10.1080/19477503.2019.1619148","url":null,"abstract":"ABSTRACT Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking. We illustrate clarifiable ambiguity that occurs in mathematics classrooms and consider ramifications of not addressing it. We conclude the paper with a discussion about addressing clarifiable ambiguity through seeking focused clarification.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"12 1","pages":"28 - 37"},"PeriodicalIF":0.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/19477503.2019.1619148","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49298007","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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