{"title":"Unit Transformation Graphs: Modeling Students’ Mathematics in Meeting the Cognitive Demands of Fractions Multiplication Tasks","authors":"A. Norton, C. Ulrich, Sarah Kerrigan","doi":"10.5951/jresematheduc-2021-0031","DOIUrl":"https://doi.org/10.5951/jresematheduc-2021-0031","url":null,"abstract":"This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in fraction multiplication settings. UTGs account for the constraint of working memory in sequencing mental actions to solve mathematical tasks. They also explain the power of units coordinating structures in offloading demands on working memory. At the end of the article, we consider some of the research implications for these findings—specifically, ways that UTGs can lend explanatory and illustrative power to analyses of students’ mathematics.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42951657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Janet D. K. Walkoe, Caroline (Caro) Williams-Pierce, Virginia J. Flood, M. Walton
{"title":"Toward Professional Development for Multimodal Teacher Noticing","authors":"Janet D. K. Walkoe, Caroline (Caro) Williams-Pierce, Virginia J. Flood, M. Walton","doi":"10.5951/jresematheduc-2020-0326","DOIUrl":"https://doi.org/10.5951/jresematheduc-2020-0326","url":null,"abstract":"Considerable research has been conducted on the critical role of gesture and action in children’s mathematical thinking. However, teacher professional development (PD) has not tended to include specific supports for attending to nonverbal student thinking. In this Brief Report, we argue for including supports for multimodal teacher noticing in teacher PD. We illustrate how a targeted intervention can relatively quickly support teachers in learning to notice multimodal student thinking and demonstrate how shifting teachers’ attention to gesture can enrich how they interpret the details of students’ thinking.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44380998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Oyemolade Osibodu, Sung-Kook Byun, Victoria Hand, Carlos A. LópezLeiva
{"title":"A Participatory Turn in Mathematics Education Research: Possibilities and Tensions","authors":"Oyemolade Osibodu, Sung-Kook Byun, Victoria Hand, Carlos A. LópezLeiva","doi":"10.5951/jresematheduc-2021-0147","DOIUrl":"https://doi.org/10.5951/jresematheduc-2021-0147","url":null,"abstract":"Mathematics education researchers concerned with justice and rehumanizing mathematics education are increasingly calling for research that takes seriously the values, commitments, and voices of the communities for which the research is most consequential. Exclusion of or superficial engagement with these perspectives and experiences in research and design processes have perpetuated deficit perspectives of minoritized communities, rendering them simply the object of reform efforts. Consequently, this Research Commentary conceptualizes a participatory turn in mathematics education research, offering a set of commitments that guide and examine the possibilities and tensions of such a turn.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46840546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rarely Discussed and Often Ignored: Classroom Factors Affecting Black Students’ Experiences in Developmental Mathematics","authors":"Maxine T. Roberts, Daniel J. Almeida","doi":"10.5951/jresematheduc-2020-0257","DOIUrl":"https://doi.org/10.5951/jresematheduc-2020-0257","url":null,"abstract":"We present findings from a study about obstacles that Black students who succeeded in developmental mathematics in community college reported having endured in those mathematics classrooms. To understand the types of obstacles that can arise for students in these classrooms, we analyze data using two frameworks: mathematics identity and dimensions of mathematics classrooms. Study participants faced obstacles in three categories: (a) impressions of faculty’s instructional practices for problem solving; (b) negative race-related perceptions they believed classmates had about them; and (c) perceptions about instructors’ expectations. These findings contribute to literature on Black students’ progress in mathematics by identifying obstacles experienced by students who achieve in these courses and can also inform professional development learning for mathematics faculty.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":"1 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42563954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Local Instruction Theory for Emergent Graphical Shape Thinking: A Middle School Case Study","authors":"Teo Paoletti, Allison L. Gantt, Julien Corven","doi":"10.5951/jresematheduc-2021-0066","DOIUrl":"https://doi.org/10.5951/jresematheduc-2021-0066","url":null,"abstract":"Emergent graphical shape thinking (EGST) involves interpreting or constructing a graph as dynamically generated, which is useful across science, technology, engineering, and mathematics fields. Although evidence suggests that students as young as middle school can engage in EGST with support, other research indicates most college students and U.S. teachers do not spontaneously engage in such reasoning when potentially productive. We describe a local instruction theory (LIT) to support middle school students developing EGST as part of their graphing meanings. We then present a case study to show how two students engaged with a task sequence designed with the LIT in mind to develop meanings for EGST. This article illustrates general principles researchers and educators could use to promote students’ graphing meanings.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48951246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Chazan, P. Herbst, Sandra Crespo, Percival G. Matthews, Erin K. Lichtenstein
{"title":"Research Commentaries: Engaging in Stewardship of Our Field","authors":"D. Chazan, P. Herbst, Sandra Crespo, Percival G. Matthews, Erin K. Lichtenstein","doi":"10.5951/jresematheduc-2023-0014","DOIUrl":"https://doi.org/10.5951/jresematheduc-2023-0014","url":null,"abstract":"In this editorial, we suggest that writing and reviewing Research Commentaries for the Journal for Research in Mathematics Education (JRME) are avenues through which all researchers on mathematics education can serve as stewards of our field.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47560944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computer-Supported Assessment of Geometric Exploration Using Variation Theory","authors":"Yael Luz, Michal Yerushalmy","doi":"10.5951/jresematheduc-2020-0260","DOIUrl":"https://doi.org/10.5951/jresematheduc-2020-0260","url":null,"abstract":"We report on an innovative design of algorithmic analysis that supports automatic online assessment of students’ exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic activity format for if–then propositions and implemented the activity on a platform that collects and analyzes students’ work. Finally, we searched for ways to use variation theory to analyze ninth-grade students’ recorded work. We scored and classified data and found correlation between patterns in exploration stages and the conjectures students generated. We demonstrate how automatic identification of mistakes in the early stages is later reflected in the quality of conjectures.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44706369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Investigating Problem Solving on Calculator Items in a Large-Scale Digitally Based Assessment: A Data Mining Approach","authors":"Yang Jiang, Gabrielle A. Cayton-Hodges","doi":"10.5951/jresematheduc-2020-0290","DOIUrl":"https://doi.org/10.5951/jresematheduc-2020-0290","url":null,"abstract":"This exploratory study investigated the behaviors and content of onscreen calculator usage by a nationally representative sample of eighth-grade students who responded to items from the 2017 National Assessment of Educational Progress mathematics assessment. Meaningful features were generated from the process data to infer whether students spontaneously used calculators for mathematical problem solving, how frequently and when they used them, and the nature of the operations performed on calculators. Sequential pattern mining was applied on sequences of calculator keystrokes to obtain patterns of operations that were representative of students’ problem-solving strategies or processes. Results indicated that higher scoring students not only were more likely to use calculators, but also used them in a more goal-driven manner than lower scoring students.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43035504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"What Can the Realization Tree Assessment Tool Reveal About Explorative Classroom Discussions?","authors":"Merav Weingarden, Einat Heyd-Metzuyanim","doi":"10.5951/jresematheduc-2020-0084","DOIUrl":"https://doi.org/10.5951/jresematheduc-2020-0084","url":null,"abstract":"One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion, depicting the realizations of the mathematical object manifested during the discussion and the narratives that articulate the links between these realizations. We applied the tool to 34 classroom discussions about a growing-pattern algebraic task and, through cluster analysis, found three types of whole-class discussion. Associations with classroom-level variables (track, but not grade level or teacher seniority) were also found. Implications with respect to applications and usefulness of the tool are discussed.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48973427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"In Memoriam Jeremy Kilpatrick: An Editor’s Editor","authors":"P. Herbst","doi":"10.5951/jresematheduc-2022-0190","DOIUrl":"https://doi.org/10.5951/jresematheduc-2022-0190","url":null,"abstract":"My academic family lost our patriarch, Jeremy Kilpatrick, on September 17, 2022. As I write this in October, reflecting on his legacy to our field feels timely. After a brief biographical sketch, I explore how Jeremy's influence, particularly in his role as Editor in Chief of JRME, shaped our fieldand my own work as editor.","PeriodicalId":48084,"journal":{"name":"Journal for Research in Mathematics Education","volume":" ","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47175195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}