Pub Date : 2020-12-23DOI: 10.51272/pmena.42.2020-102
Luz Graciela Orozco Vaca
{"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}
Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-262
Susie Morrissey, Ozgul Kartal, G. Popović
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.
{"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}
Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-316
Alexis Spina, Meghan Macias, Paul N. Reimer
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.
{"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}
Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-369
Z. Pearson, A. Manouchehri
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?
{"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}
Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-107
K. Francis, S. Rothschuh, Brent D. Davis
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.
理论视角。我们认为，编程机器人移动可以导致数学理解的增长，并有助于发展空间推理。我们借鉴Pirie和Kieren (PK)(1994)的数学理解增长模型，该模型将参与数学概念的模式描述为七个不同的抽象层次。我们怀疑空间推理对所有模式都是必不可少的，但它与前三个要素(原始认知、图像生成和图像拥有)尤其相关。“推理……是指识别和(在心理上)操纵物体的空间属性以及物体之间的空间关系的能力”(Bruce et al.， 2017, p. 147)。Davis等人(2015年，第141页)试图将与空间推理相关的许多能力和习惯收集到一个模型中，该模型代表了空间推理技能的新兴复杂性，即精神和身体行为的共同进化和互补性质。研究的问题。我们质疑编程机器人如何为儿童提供获得数学理解和发展空间推理的机会。数据收集技术和分析。与Knoblauch et al.(2013)的解释性视频分析概念一致，我们根据9个月来收集的32名四年级学生在2个教室的每周视频中可观察到的空间参与实例，审查并选择了一个视频。在这个视频中，一对学生正试图编程EV3乐高头脑风暴机器人跟踪五边形的第三个顶点，在前两个直转段之后取得成功。根据Davis et al.(2015)的框架，我们确定了两名学生互动中的空间元素，而他们正在决定如何引导他们的机器人绕108顶点行进。然后，我们根据PK模型分析了数学理解水平。调查结果摘要。在这个视频中，我们可以观察到孩子们在空间推理和数学理解的许多方面的工作。根据Davis et al.(2015)的空间推理要素，学生们同时进行解释、构建、移动、定位、改变和感觉。在视频中，我们观察到这两个人在机器人转动的距离与轮子转动的次数之间的关系。数学概念包括加法思维、角度、形状属性、测量(距离、机器人转弯)、乘法思维(车轮旋转次数)、模式识别和正比例。学生的理解成长在原始认识、意象形成、意象拥有之间动态发展。我们的研究结果强调了编程机器人如何支持PK在数学理解方面的成长的内部模式，并有助于发展空间能力。
{"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}
Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-181
Rachel Lambert, E. Harriss
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.
{"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}
Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-349
Verónica Hoyos, E. Navarro, Victor J. Raggi
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.
{"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}
Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-283
M. Lloyd
{"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}
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