Pub Date : 2022-10-27DOI: 10.1080/19477503.2022.2139091
Sara Donaldson, Karen S. Karp
ABSTRACT As instructional leaders who work closely with teachers within and across schools, elementary mathematics specialists (EMS) are positioned well to promote cohesive implementation of impactful pedagogy throughout school districts. However, EMS’s work can be impeded if they do not have structured opportunities to collectively grapple with the nuances of terminology included in teaching and learning initiatives in terms of expectations for what practices look like within classrooms. Using narrative data collected from EMS team discussions about the meaning of student engagement in mathematics classrooms, we share a five-phase framework for using a collective doubting process to promote professional learning through the development of shared understanding of common language. By positioning moments of doubt as opportunities for collaborative learning, this framework serves as a flexible structure to guide the development of knowledge-in-practice from the identification of a practice-centered inquiry goal to cohesive understanding and systemic transformation.
{"title":"Developing Cohesion through Collective Doubting: Framing Practice-Based Professional Learning for Mathematics Coaches","authors":"Sara Donaldson, Karen S. Karp","doi":"10.1080/19477503.2022.2139091","DOIUrl":"https://doi.org/10.1080/19477503.2022.2139091","url":null,"abstract":"ABSTRACT As instructional leaders who work closely with teachers within and across schools, elementary mathematics specialists (EMS) are positioned well to promote cohesive implementation of impactful pedagogy throughout school districts. However, EMS’s work can be impeded if they do not have structured opportunities to collectively grapple with the nuances of terminology included in teaching and learning initiatives in terms of expectations for what practices look like within classrooms. Using narrative data collected from EMS team discussions about the meaning of student engagement in mathematics classrooms, we share a five-phase framework for using a collective doubting process to promote professional learning through the development of shared understanding of common language. By positioning moments of doubt as opportunities for collaborative learning, this framework serves as a flexible structure to guide the development of knowledge-in-practice from the identification of a practice-centered inquiry goal to cohesive understanding and systemic transformation.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"15 1","pages":"118 - 134"},"PeriodicalIF":0.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47174723","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 : 2022-10-27DOI: 10.1080/19477503.2022.2139094
Lynsey Gibbons, Ada Okun
ABSTRACT Mathematics specialists tasked with the responsibility of supporting teacher learning face both the opportunity and the challenge of transforming the organization of the school workplace to support educators’ collective, ongoing learning, which is not the norm in most school settings. In this study, we examine a coaching routine called Teacher Time Out (TTO), which was organically developed by a school-based mathematics coach and the teachers with whom she worked. Through the routine, coaches and teachers work through complex, in-the-moment pedagogical decision making while collectively facilitating mathematics discussions among students. The routine thus opens opportunities for educators to learn about ambitious teaching alongside their colleagues. We report findings from an analysis of 360 TTOs that occurred over three years of one coach’s work supporting a school-wide, multi-year instructional reform effort in mathematics teaching and learning. We found that the coaching routine fostered teachers’ collective inquiry into practice, as they engaged with the unpredictability of teaching during real-time instruction with students. We discuss the potential of this routine to support coaching as a lever for organizational reform, reshaping mathematics teaching across many classrooms.
{"title":"Examining a Coaching Routine to Support Teacher Learning","authors":"Lynsey Gibbons, Ada Okun","doi":"10.1080/19477503.2022.2139094","DOIUrl":"https://doi.org/10.1080/19477503.2022.2139094","url":null,"abstract":"ABSTRACT Mathematics specialists tasked with the responsibility of supporting teacher learning face both the opportunity and the challenge of transforming the organization of the school workplace to support educators’ collective, ongoing learning, which is not the norm in most school settings. In this study, we examine a coaching routine called Teacher Time Out (TTO), which was organically developed by a school-based mathematics coach and the teachers with whom she worked. Through the routine, coaches and teachers work through complex, in-the-moment pedagogical decision making while collectively facilitating mathematics discussions among students. The routine thus opens opportunities for educators to learn about ambitious teaching alongside their colleagues. We report findings from an analysis of 360 TTOs that occurred over three years of one coach’s work supporting a school-wide, multi-year instructional reform effort in mathematics teaching and learning. We found that the coaching routine fostered teachers’ collective inquiry into practice, as they engaged with the unpredictability of teaching during real-time instruction with students. We discuss the potential of this routine to support coaching as a lever for organizational reform, reshaping mathematics teaching across many classrooms.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"15 1","pages":"11 - 28"},"PeriodicalIF":0.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47222512","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 : 2022-10-27DOI: 10.1080/19477503.2022.2139096
Susan Swars Auslander, Carla L. Tanguay, Kayla D. Myers, Gary E. Bingham, Sterline Caldwell, Michael Vo
ABSTRACT This 5-year mathematics professional development project involves 27 elementary teachers prepared and supported as Elementary Mathematics Specialists (EMSs) in high-need, urban schools. The EMSs are a distinctive population as informal teacher leaders, with a primary responsibility of teaching students. Described here are data collected at the end of Year 1 via a survey of coaching practices, a teacher leader record, and individual and focus group interviews. The findings illuminate the variety of ways they were serving as a more knowledgeable other and practicing agency in this teacher leadership. They were agentic in their teacher leader efforts by navigating constraints through: focusing on incremental changes; developing collegial, trusting relationships with peers; and leaning into the network of teacher support in the project. The findings also provide insights into how their primary and concurrent role as teacher of students provided credibility and understanding with fellow teachers, contributing to affordances in their informal teacher leader capacity.
{"title":"Elementary Mathematics Specialists as Emergent Informal Teacher Leaders in Urban Schools: Engagement and Navigations","authors":"Susan Swars Auslander, Carla L. Tanguay, Kayla D. Myers, Gary E. Bingham, Sterline Caldwell, Michael Vo","doi":"10.1080/19477503.2022.2139096","DOIUrl":"https://doi.org/10.1080/19477503.2022.2139096","url":null,"abstract":"ABSTRACT This 5-year mathematics professional development project involves 27 elementary teachers prepared and supported as Elementary Mathematics Specialists (EMSs) in high-need, urban schools. The EMSs are a distinctive population as informal teacher leaders, with a primary responsibility of teaching students. Described here are data collected at the end of Year 1 via a survey of coaching practices, a teacher leader record, and individual and focus group interviews. The findings illuminate the variety of ways they were serving as a more knowledgeable other and practicing agency in this teacher leadership. They were agentic in their teacher leader efforts by navigating constraints through: focusing on incremental changes; developing collegial, trusting relationships with peers; and leaning into the network of teacher support in the project. The findings also provide insights into how their primary and concurrent role as teacher of students provided credibility and understanding with fellow teachers, contributing to affordances in their informal teacher leader capacity.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"15 1","pages":"50 - 66"},"PeriodicalIF":0.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49252334","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 : 2022-10-02DOI: 10.1080/19477503.2022.2139090
Angela R. Crawford
ABSTRACT Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this teaching experiment was to explore a diverse learner’s understandings about equipartitioning and relational reasoning. Across eleven 45-min individualized sessions, the equipartitioning learning trajectory (EPLT) served as the framework for investigating the student’s thinking and learning. Findings illustrate how a student’s actual trajectory can be focused on developing a many-to-one meaning for fractions and relational reasoning, rather than strictly adhering to the sequence of proficiencies hypothesized by the EPLT. Further, the student’s engagement with cognitive elements which characterize mental activity reveals ways instruction might be tailored to support a student’s relational reasoning. Implications include a more nuanced perspective on individual learning of equipartitioning and important considerations for educators who support relational reasoning in diverse learners.
{"title":"Exploring a Diverse Learner’s Equipartitioning Learning Trajectory","authors":"Angela R. Crawford","doi":"10.1080/19477503.2022.2139090","DOIUrl":"https://doi.org/10.1080/19477503.2022.2139090","url":null,"abstract":"ABSTRACT Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this teaching experiment was to explore a diverse learner’s understandings about equipartitioning and relational reasoning. Across eleven 45-min individualized sessions, the equipartitioning learning trajectory (EPLT) served as the framework for investigating the student’s thinking and learning. Findings illustrate how a student’s actual trajectory can be focused on developing a many-to-one meaning for fractions and relational reasoning, rather than strictly adhering to the sequence of proficiencies hypothesized by the EPLT. Further, the student’s engagement with cognitive elements which characterize mental activity reveals ways instruction might be tailored to support a student’s relational reasoning. Implications include a more nuanced perspective on individual learning of equipartitioning and important considerations for educators who support relational reasoning in diverse learners.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"14 1","pages":"288 - 304"},"PeriodicalIF":0.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45402460","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 : 2022-10-02DOI: 10.1080/19477503.2022.2139092
Siddhi Desai, Farshid Safi, Sarah B. Bush, Trena Wilkerson, Janet B. Andreasen, D. Orey
ABSTRACT This article presents a synthesis of existing literature on ethnomodeling and the ways in which it extends mathematical modeling research in mathematics teacher education. We also call on the field to consider ways to connect and value culture and content in teaching mathematics. There have been increasing calls for integration of a culturally responsive mathematics curriculum. Additionally, mathematics teacher educators and researchers have also emphasized the critical role of deep and meaningful mathematical content within curricular efforts that focus on culture and student identity. In this paper, we present how ethnomodeling connects to and extends current literature to apply mathematical modeling to shift toward culturally relevant and sustaining teaching practices while maintaining a focus on deep and meaningful mathematical content. We start by describing the various existing calls, present a synthesis of the literature supporting the components of ethnomodeling, and conclude by proposing a new call to action for the field to deepen existing efforts and plan for actionable steps for using an ethnomodeling approach to impact teacher education programs.
{"title":"Ethnomodeling: Extending Mathematical Modeling Research in Teacher Education","authors":"Siddhi Desai, Farshid Safi, Sarah B. Bush, Trena Wilkerson, Janet B. Andreasen, D. Orey","doi":"10.1080/19477503.2022.2139092","DOIUrl":"https://doi.org/10.1080/19477503.2022.2139092","url":null,"abstract":"ABSTRACT This article presents a synthesis of existing literature on ethnomodeling and the ways in which it extends mathematical modeling research in mathematics teacher education. We also call on the field to consider ways to connect and value culture and content in teaching mathematics. There have been increasing calls for integration of a culturally responsive mathematics curriculum. Additionally, mathematics teacher educators and researchers have also emphasized the critical role of deep and meaningful mathematical content within curricular efforts that focus on culture and student identity. In this paper, we present how ethnomodeling connects to and extends current literature to apply mathematical modeling to shift toward culturally relevant and sustaining teaching practices while maintaining a focus on deep and meaningful mathematical content. We start by describing the various existing calls, present a synthesis of the literature supporting the components of ethnomodeling, and conclude by proposing a new call to action for the field to deepen existing efforts and plan for actionable steps for using an ethnomodeling approach to impact teacher education programs.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"14 1","pages":"305 - 319"},"PeriodicalIF":0.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46636057","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 : 2022-10-02DOI: 10.1080/19477503.2022.2145100
Ceylan Şen, Gürsel Güler
ABSTRACT This study was conducted to examine the effectiveness of proof tasks in the transition from conjecture to proof in Euclidean geometry on freshmen’s proof schemes. In line with this aim, the proof schemes of the freshmen who performed conjecture-proof and theorem-proof tasks were compared. The freshmen were composed of 109 pre-service middle school mathematics teachers who are enrolled in their first year of undergraduate education. The study was modeled as a multiple-case study. Fifty-three freshmen performed conjecture-proof tasks in Case-1, and fifty-six freshmen performed theorem-proof tasks in Case-2. The video recordings, including the written proof reports, reflection papers, and proof explanations of the freshmen, were used as data collection tools in the tasks. The proof schemes were used as construct maps to evaluate the proofs of freshmen and analyzed using Winsteps Rasch software. The proof schemes in freshmen’s proof tasks were evaluated by the Wright Map and supported with direct quotations from the proofs. In the study, it was observed that the proof schemes of freshmen who made proofs based on their own conjectures were mostly empirical and analytical proof schemes, while the proof schemes of freshmen who made proof of the presented theorem were generally external and empirical proof schemes.
{"title":"Emerging Proof Productions of Freshmen in Euclidean Geometry Proof Tasks between Conjecturing and Proving","authors":"Ceylan Şen, Gürsel Güler","doi":"10.1080/19477503.2022.2145100","DOIUrl":"https://doi.org/10.1080/19477503.2022.2145100","url":null,"abstract":"ABSTRACT This study was conducted to examine the effectiveness of proof tasks in the transition from conjecture to proof in Euclidean geometry on freshmen’s proof schemes. In line with this aim, the proof schemes of the freshmen who performed conjecture-proof and theorem-proof tasks were compared. The freshmen were composed of 109 pre-service middle school mathematics teachers who are enrolled in their first year of undergraduate education. The study was modeled as a multiple-case study. Fifty-three freshmen performed conjecture-proof tasks in Case-1, and fifty-six freshmen performed theorem-proof tasks in Case-2. The video recordings, including the written proof reports, reflection papers, and proof explanations of the freshmen, were used as data collection tools in the tasks. The proof schemes were used as construct maps to evaluate the proofs of freshmen and analyzed using Winsteps Rasch software. The proof schemes in freshmen’s proof tasks were evaluated by the Wright Map and supported with direct quotations from the proofs. In the study, it was observed that the proof schemes of freshmen who made proofs based on their own conjectures were mostly empirical and analytical proof schemes, while the proof schemes of freshmen who made proof of the presented theorem were generally external and empirical proof schemes.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"14 1","pages":"320 - 342"},"PeriodicalIF":0.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41723859","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 : 2022-10-02DOI: 10.1080/19477503.2022.2145079
T. Wilkerson
ABSTRACT Mathematics teaching and learning are critical aspects of education that impact our world. There are implications for the mathematics education research community that should push us to have critical conversations about our research and how it informs mathematics education. I present a brief overview of research in mathematics education through the lens of Investigations in Mathematics Learning, the official journal of the Research Council on Mathematics Learning, using issues from 2017-2021. Included are findings from qualitative analyses and ideas calling on the mathematics education community to consider that provide a positioning for mathematics education researchers (MERs). I challenge us to consider multiple questions with regard to our research: What does it add to the field of mathematics education? How does it contribute to broadening and deepening our understandings? How does it inform practice to further effective equitable teaching and learning of mathematics? Are we being inclusive? Are we a leading voice in mathematics education research and are we being effective curators and stewards of this work? As MERs, as a field, as professional organizations, what could and should we do? We have a unique opportunity at this juncture to work together to inform and impact mathematics learning in profound ways.
{"title":"2022 Founder’s Lecture: Current Research Trends in Mathematics Learning that Guide Us for the Future","authors":"T. Wilkerson","doi":"10.1080/19477503.2022.2145079","DOIUrl":"https://doi.org/10.1080/19477503.2022.2145079","url":null,"abstract":"ABSTRACT Mathematics teaching and learning are critical aspects of education that impact our world. There are implications for the mathematics education research community that should push us to have critical conversations about our research and how it informs mathematics education. I present a brief overview of research in mathematics education through the lens of Investigations in Mathematics Learning, the official journal of the Research Council on Mathematics Learning, using issues from 2017-2021. Included are findings from qualitative analyses and ideas calling on the mathematics education community to consider that provide a positioning for mathematics education researchers (MERs). I challenge us to consider multiple questions with regard to our research: What does it add to the field of mathematics education? How does it contribute to broadening and deepening our understandings? How does it inform practice to further effective equitable teaching and learning of mathematics? Are we being inclusive? Are we a leading voice in mathematics education research and are we being effective curators and stewards of this work? As MERs, as a field, as professional organizations, what could and should we do? We have a unique opportunity at this juncture to work together to inform and impact mathematics learning in profound ways.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"14 1","pages":"251 - 264"},"PeriodicalIF":0.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47886762","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 : 2022-07-31DOI: 10.1080/19477503.2022.2105104
Min Wang, Candace A. Walkington, A. Rouse
ABSTRACT The purpose of this meta-analysis is to examine the effect of problem-posing on students’ mathematical academic outcomes, including problem-solving skills, problem-posing skills, mathematical dispositions, and mathematics achievement. Twenty-one studies that were published between 1990 and 2019 with problem-posing as the intervention were included in the meta-analysis. A random-effects model was employed with robust variance estimation (RVE) to correct for the intercorrelation between effect sizes when necessary. The estimated average standardized mean difference effect size of problem-posing interventions (g = 0.64) demonstrated that problem-posing had a positive impact on students’ academic outcomes. Specifically, across the interventions, students’ problem-solving skills and mathematical achievement improved by engaging in problem-posing activities. The moderator analyses revealed that problem-posing interventions were more effective when structured, semi-structured, and free problem-posing tasks were all implemented, and longer-duration intervention was associated with larger improvement in students’ mathematical dispositions.
{"title":"A Meta-Analysis on the Effects of Problem-Posing in Mathematics Education on Performance and Dispositions","authors":"Min Wang, Candace A. Walkington, A. Rouse","doi":"10.1080/19477503.2022.2105104","DOIUrl":"https://doi.org/10.1080/19477503.2022.2105104","url":null,"abstract":"ABSTRACT The purpose of this meta-analysis is to examine the effect of problem-posing on students’ mathematical academic outcomes, including problem-solving skills, problem-posing skills, mathematical dispositions, and mathematics achievement. Twenty-one studies that were published between 1990 and 2019 with problem-posing as the intervention were included in the meta-analysis. A random-effects model was employed with robust variance estimation (RVE) to correct for the intercorrelation between effect sizes when necessary. The estimated average standardized mean difference effect size of problem-posing interventions (g = 0.64) demonstrated that problem-posing had a positive impact on students’ academic outcomes. Specifically, across the interventions, students’ problem-solving skills and mathematical achievement improved by engaging in problem-posing activities. The moderator analyses revealed that problem-posing interventions were more effective when structured, semi-structured, and free problem-posing tasks were all implemented, and longer-duration intervention was associated with larger improvement in students’ mathematical dispositions.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"14 1","pages":"265 - 287"},"PeriodicalIF":0.0,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48684833","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 : 2022-07-03DOI: 10.1080/19477503.2022.2105028
Kristi Martin, J. Hunt
ABSTRACT One challenge facing the fields of mathematics education and special education is how to design instruction on fraction concepts that can meet the needs of diverse learners. An innovation that shows promise is to base instructional design upon well-established trajectories of students’ fraction learning. However, little research has been done to establish the effectiveness of this approach. We report the results of the second of two small studies of an intervention developed using a validated trajectory of students’ fraction concepts. Mixed methods analyses were conducted on students’ problem-solving actions across instructional sessions as well as their performance on a standards-aligned measure of fractional knowledge before and after instruction. Results suggest increases in both conceptual understanding and performance for nine students. We discuss the findings in relation to practice from the fields of mathematics education and special education and point to areas for future research.
{"title":"Learning Trajectory Based Fraction Intervention: Building A Mathematics Education Evidence Base","authors":"Kristi Martin, J. Hunt","doi":"10.1080/19477503.2022.2105028","DOIUrl":"https://doi.org/10.1080/19477503.2022.2105028","url":null,"abstract":"ABSTRACT One challenge facing the fields of mathematics education and special education is how to design instruction on fraction concepts that can meet the needs of diverse learners. An innovation that shows promise is to base instructional design upon well-established trajectories of students’ fraction learning. However, little research has been done to establish the effectiveness of this approach. We report the results of the second of two small studies of an intervention developed using a validated trajectory of students’ fraction concepts. Mixed methods analyses were conducted on students’ problem-solving actions across instructional sessions as well as their performance on a standards-aligned measure of fractional knowledge before and after instruction. Results suggest increases in both conceptual understanding and performance for nine students. We discuss the findings in relation to practice from the fields of mathematics education and special education and point to areas for future research.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"14 1","pages":"235 - 249"},"PeriodicalIF":0.0,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46905430","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 : 2022-07-03DOI: 10.1080/19477503.2022.2095781
C. Brady, Rita Borromeo Ferri, R. Lesh
ABSTRACT Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their explicit models are accessible – those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its impacts on mathematical modeling remain largely inaccessible to such approaches. To understand when and how tacit knowledge can emerge onto the explicit plane as insight during modeling, we present an exploratory and instrumental single-case study. We analyze the embodied interactions of a pair of ninth grade (age 14–15) students as they collaboratively solved a modeling problem. We introduce the phenomenon of embodied insight as a pattern of interaction, in which tacit knowledge becomes explicit and shapes modeling work, and we analyze three such episodes from this pair’s modeling. This work contributes to the field by illustrating the potential in studying embodied social discourse in collaboration to reveal the operation of tacit knowledge in mathematical modeling and its expression on the explicit plane.
{"title":"Tacit Knowledge and Embodied Insight in Mathematical Modeling","authors":"C. Brady, Rita Borromeo Ferri, R. Lesh","doi":"10.1080/19477503.2022.2095781","DOIUrl":"https://doi.org/10.1080/19477503.2022.2095781","url":null,"abstract":"ABSTRACT Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their explicit models are accessible – those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its impacts on mathematical modeling remain largely inaccessible to such approaches. To understand when and how tacit knowledge can emerge onto the explicit plane as insight during modeling, we present an exploratory and instrumental single-case study. We analyze the embodied interactions of a pair of ninth grade (age 14–15) students as they collaboratively solved a modeling problem. We introduce the phenomenon of embodied insight as a pattern of interaction, in which tacit knowledge becomes explicit and shapes modeling work, and we analyze three such episodes from this pair’s modeling. This work contributes to the field by illustrating the potential in studying embodied social discourse in collaboration to reveal the operation of tacit knowledge in mathematical modeling and its expression on the explicit plane.","PeriodicalId":36817,"journal":{"name":"Investigations in Mathematics Learning","volume":"14 1","pages":"215 - 234"},"PeriodicalIF":0.0,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44149222","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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