数学教学通讯最新文献

{"title":"Self-instructions for applying writing in geometry problem resolution / Autoinstrucciones para aplicar la escritura en la resolución de problemas de geometría","authors":"Luz Graciela Orozco Vaca","doi":"10.51272/pmena.42.2020-102","DOIUrl":"https://doi.org/10.51272/pmena.42.2020-102","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83103644","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}

{"title":"Explicit teaching of questioning in math methods course: Preservice teachers’ attempts to ask probing questions","authors":"Susie Morrissey, Ozgul Kartal, G. Popović","doi":"10.51272/PMENA.42.2020-262","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-262","url":null,"abstract":"After an explicit unit of core activities on questioning, preservice teachers (PTs) completed an assignment to select a problem-solving task, anticipate student solutions, and plan probing questions. After analyzing PTs’ work, we discovered that, although most PTs planned probing questions, many also planned questions focused on information or procedures. Next steps include exposing PTs to probing questions focused on meanings, context, or representations.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89041909","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}

{"title":"How facilitators define, design, and implement effective early childhood mathematics professional development","authors":"Alexis Spina, Meghan Macias, Paul N. Reimer","doi":"10.51272/PMENA.42.2020-316","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-316","url":null,"abstract":"The call to improve mathematics outcomes for children ages zero to eight requires the development of effective professional development approaches for early childhood mathematics educators. In this study, we looked at how six facilitators created workshops on spatial reasoning, mathematical play, number sense, and theories of learning for early childhood educators. Drawing on Desimone’s components of effective professional development, we interviewed these facilitators to understand how they defined a successful professional development and how these definitions aligned with the workshops they created. Interviews showed that all the facilitators in this study designed their workshops to be engaging and interactive for their participants while drawing on the components of coherence, collective participation, and duration.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88930320","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}

{"title":"The interplay between a visual task and elementary students’ mathematical discourse","authors":"Z. Pearson, A. Manouchehri","doi":"10.51272/PMENA.42.2020-369","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-369","url":null,"abstract":"This research was conducted by a fourth-grade teacher and doctoral student in mathematics education in conjunction with their advisor, a professor of mathematics education. A growing body of research in mathematics education has highlighted the importance of recognizing mathematics learning as a socially mediated activity. Indeed, mathematics education researchers have increasingly focused on how classroom dialogue can facilitate students’ creation of shared understandings. Aligned with this theoretical heritage, we recognize that human life and learning are inherently social and rooted in communication. We also recognize that student discourse is connected to student cognition and thus learning. Accordingly, this study relied on socio-cultural discourse analysis (Hennesy, et al., 2016, Mercer, 2010) both as a theoretical and a methodological tool to examine the nature of dialogue in one classroom in the context of students’ collaborative work on one visual task. We ask, given the centrality of task selection to fostering discourse, how the use of a visual task, as an instructional tool, might affect students’ peer-to-peer discourse practices?","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85079966","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}

{"title":"Growth in mathematical understanding and spatial reasoning with programming robots","authors":"K. Francis, S. Rothschuh, Brent D. Davis","doi":"10.51272/PMENA.42.2020-107","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-107","url":null,"abstract":"Theoretical Perspective. We argue that programming robots to move could lead to growth in mathematical understanding and contribute to developing spatial reasoning. We draw on Pirie and Kieren’s (PK) (1994) model of growth in mathematical understanding which describes modes of engagement with mathematical concepts as seven distinct levels with increasing abstraction. We suspect that spatial reasoning is essential to all modes, but that it is especially relevant to the first three elements (primitive knowing, image making, and image having). “[S]patial reasoning ... refers to the ability to recognize and (mentally) manipulate the spatial properties of objects and the spatial relations among objects” (Bruce et al., 2017, p. 147). Davis et al. (2015, p. 141) attempted to collect the many competencies and habits associated with spatial reasoning into a model that represents the emergent complexity of spatial reasoning skills as coevolved and complementary nature of the mental and physical actions. Research Question. We questioned how programming robots might provide children with opportunities to gain mathematical understanding and develop spatial reasoning. Data Collection Techniques and Analyses. Consistent with Knoblauch et al.’s (2013) notions of interpretive video analysis, we reviewed and selected one video based on instances of observable spatial engagement from 9 months of weekly videos collected of 32 Grade 4 students in 2 classrooms. In this video, a pair of students is attempting to program an EV3 LEGO Mindstorm robot to trace the third vertex of a pentagon having previous success following the first two straight-turn segments. We identified spatial elements in the two students’ interactions according to Davis et al.’s (2015) framework while they engaged in determining how to steer their robot to travel around the 108 vertex. We then analysed levels of mathematical understanding according to the PK model. Summary of Findings. In this video one can observe the children working with many aspects of spatial reasoning and mathematical understanding. Drawing upon Davis et al.’s (2015) elements of spatial reasoning, the students were simultaneously INTERPRETING, [DE]CONSTRUCTING, MOVING, SITUATING, ALTERING and SENSATING. In the video, we observed the pair engage in how the distance the robot turns relates to the number of wheel rotations. The mathematical concepts included additive thinking, angles, properties of shape, measurement (distances, robot turns), multiplicative thinking (number of wheel rotations), pattern recognition, and direct proportion. Students’ growth in understanding dynamically progressed between primitive knowing, image making, and image having. Our findings highlight how programming robots could support both the inner modes of PK’s growth in mathematical understanding and contribute to developing spatial ability.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85154165","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}

{"title":"“Dyslexia is naturally commutative”: Insider accounts of dyslexia from research mathematicians","authors":"Rachel Lambert, E. Harriss","doi":"10.51272/PMENA.42.2020-181","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-181","url":null,"abstract":"Using neurodiversity as our theoretical framework, rather than a deficit or medical model, we analyze the narratives of five dyslexic research mathematicians to find common strengths and challenges for dyslexic thinkers at the highest level of mathematics. We report on 3 themes: 1) highly visual and intuitive ways of mathematical thinking, 2) pronounced issues with memorization of mathematical facts and procedures, and 3) resilience as a strength of dyslexia that matters in mathematics. We introduce the idea of Neurodiversity for Mathematics, a research agenda to better understand the strengths (as well as challenges) of neurodiverse individuals and to use that knowledge to design better mathematical learning experiences for all.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84661138","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}

{"title":"A mathematics teacher’s curricular decisions","authors":"Elizabeth Suazo‐Flores","doi":"10.51272/PMENA.42.2020-331","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-331","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86889652","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}

{"title":"Hybrid environments of learning: Potential for student collaboration and distributed knowledge","authors":"Verónica Hoyos, E. Navarro, Victor J. Raggi","doi":"10.51272/PMENA.42.2020-349","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-349","url":null,"abstract":"An exploratory study of the impact on transforming mathematics teaching and learning practices into the classroom is presented by means of introducing a hybrid learning environment, in this case, designed to address the topic of functions in the first year of finance at college. This topic is normally covered in two weeks in the classroom. In this exploration, the students worked independently on the topic using materials or resources available in a digital teaching platform throughout the first week. In addition, the topic was addressed in the classroom under the teacher's guidance during the second week. The results show collaboration between students to refine or validate their conceptions, which also could support connectivist hypothesis of distributed knowledge.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81574515","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}

{"title":"Educational neuroscience: past, present and future prospects","authors":"S. R. Campbell","doi":"10.51272/PMENA.42.2020-4","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-4","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90941883","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}

{"title":"Mathematics is everywhere: intersection of PST perceptions and non-mathematics-education faculty perceptions and observable actions","authors":"M. Lloyd","doi":"10.51272/PMENA.42.2020-283","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-283","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90603914","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}