Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-132
Jose Saul Barbosa, C. Duffer
When studying mathematics education and student success, most research tends to study the inclassroom teaching aspect. Another important aspect of mathematics education occurs outside the traditional classroom with tutors. While it has been shown that tutoring leads to student success (Xu, Hartman, Uribe, & Mencke, 2001), research has not necessarily focused on what tutoring is or what makes it effective. In recent years, efforts have been made to expand research in this field. Two major themes are the study of the types of knowledge necessary for effective tutoring and the interplay between these domains of knowledge to better understand the tutoring process.
{"title":"A study on the relationship between tutor’s content knowledge and their tutoring decisions","authors":"Jose Saul Barbosa, C. Duffer","doi":"10.51272/PMENA.42.2020-132","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-132","url":null,"abstract":"When studying mathematics education and student success, most research tends to study the inclassroom teaching aspect. Another important aspect of mathematics education occurs outside the traditional classroom with tutors. While it has been shown that tutoring leads to student success (Xu, Hartman, Uribe, & Mencke, 2001), research has not necessarily focused on what tutoring is or what makes it effective. In recent years, efforts have been made to expand research in this field. Two major themes are the study of the types of knowledge necessary for effective tutoring and the interplay between these domains of knowledge to better understand the tutoring process.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85609054","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.42.2020-86
Paula Patricia Guerra Lombardi, Raisa Lopez, Elisa Pereyra
{"title":"Mathematics problems and real world connections: How political is too political?","authors":"Paula Patricia Guerra Lombardi, Raisa Lopez, Elisa Pereyra","doi":"10.51272/PMENA.42.2020-86","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-86","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81534316","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.42.2020-236
Ian Whitacre, K. Findley, Ş. Atabaş
Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers’ (PSTs) knowledge of fractions and has given little attention to the productive resources that PSTs bring to teacher education. We surveyed 26 PSTs using a set of 9 fraction-comparison tasks. We report the frequency of complete strategyarguments and the perspectives (ways of reasoning) used for each item. We further examine incomplete strategy-arguments, noting substantial evidence for productive seeds of reasoning. Using data from interviews with 10 of these PSTs, we identify evidence suggesting these seeds are, in fact, productive in that they provide foundations for further development. We argue that this type of research is needed in order to further mathematics teacher education.
{"title":"Productive seeds in preservice teachers’ reasoning about fraction comparisons","authors":"Ian Whitacre, K. Findley, Ş. Atabaş","doi":"10.51272/PMENA.42.2020-236","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-236","url":null,"abstract":"Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers’ (PSTs) knowledge of fractions and has given little attention to the productive resources that PSTs bring to teacher education. We surveyed 26 PSTs using a set of 9 fraction-comparison tasks. We report the frequency of complete strategyarguments and the perspectives (ways of reasoning) used for each item. We further examine incomplete strategy-arguments, noting substantial evidence for productive seeds of reasoning. Using data from interviews with 10 of these PSTs, we identify evidence suggesting these seeds are, in fact, productive in that they provide foundations for further development. We argue that this type of research is needed in order to further mathematics teacher education.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90686503","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.42.2020-85
Sean P. Freeland
{"title":"Blackness and whiteness in Appalachian mathematics classrooms","authors":"Sean P. Freeland","doi":"10.51272/PMENA.42.2020-85","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-85","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90719254","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。
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Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-322
Carola Manolino
{"title":"The semiosphere: A lens to look at lesson study practices in their cultural context","authors":"Carola Manolino","doi":"10.51272/PMENA.42.2020-322","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-322","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91020119","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.42.2020-103
José Luis Soto Munguía, Manuel Alfredo Urrea Bernal, César Fabián Romero Félix
{"title":"Difficulties to justify geometric propositions when solving loci problems with GeoGebra / Dificultades para justificar proposiciones geométricas al resolver problemas de lugares geométricos con GeoGebra","authors":"José Luis Soto Munguía, Manuel Alfredo Urrea Bernal, César Fabián Romero Félix","doi":"10.51272/pmena.42.2020-103","DOIUrl":"https://doi.org/10.51272/pmena.42.2020-103","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81983437","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.42.2020-330
Meghan Shaughnessy, Nicole Garcia, Jillian Peterson, Kristen D’Anna Pynes
This study is an effort to address the challenge of supporting the enhancement of teaching practice. Our model situates professional development (PD) in mathematics instruction occurring in a summer program for fifth grade students. This PD model has two parts. First, participants engage in “legitimate peripheral participation” (Lave & Wenger, 1991) in teaching in this fifth grade classroom through structured conversations about the lesson plans, close observation of teaching, and analysis of student tasks. Second, participants engage in focused learning on leading mathematics discussions through simulations and rehearsals. Two groups of teachers participated, one onsite with a facilitator, and the second at a remote site with an in-person facilitator who delivered the leading mathematics discussion professional development. We study the impact of our PD model. Specifically, we ask: Does teachers’ participation impact their own teaching practice, and if so, in what ways? Twenty-one teachers participated across the two groups. We collected and analyzed a set of preand post-videos of classroom discussions. Participants were asked to record three mathematics discussions two months before the PD occurred and three such lessons two months after participation. A tool that captured techniques named in our decomposition of discussion (Selling et al., 2015), including advanced techniques utilized by experienced teachers, was applied to all videos by two research team members. Prior to the intervention, the means of technique usage of the remote participants were higher than those of the onsite group on almost every dimension (p < .05). Thus, we share the findings for the two groups separately. The onsite group (lower pre-intervention mean) did not appear to be leading discussions before the intervention. They showed slight increases in both orienting students to the thinking of others and concluding discussions. Since the intervention was focused on orienting students, likely an unfamiliar area of work, we hypothesize that this was the focus of their practice post-intervention. Conversely, the remote group (higher pre-intervention mean), who appeared to be leading discussions before the intervention, decreased on several categories and showed near significant growth on connecting and extending student thinking. One possible explanation for these decreases is the timing of the post-data collection at the beginning of the year when they may have been explicitly teaching their students how to engage in discussion, leading to fewer instances of particular discussion-leading moves. The increase in connecting and extending may have been due to readiness to take on this difficult work.
本研究旨在解决如何支持教学实践的挑战。我们的模型将专业发展(PD)置于五年级学生暑期课程的数学教学中。该PD模型分为两部分。首先，参与者通过结构化的课程计划对话、密切观察教学和分析学生任务，参与五年级课堂教学中的“合法外围参与”(Lave & Wenger, 1991)。其次，参与者通过模拟和排练，集中学习领先的数学讨论。两组教师参加，一组在现场有一名辅导员，另一组在远程现场有一名辅导员，由他亲自主持数学专业发展讨论。我们研究PD模型的影响。具体来说，我们的问题是:教师的参与是否会影响他们自己的教学实践，如果会，影响的是什么?两组共有21名教师参与。我们收集并分析了一组课堂讨论前后的视频。参与者被要求在PD发生前两个月记录三次数学讨论，并在参与后两个月记录三次这样的课程。一个工具捕获了我们分解讨论中提到的技术(Selling et al.， 2015)，包括经验丰富的教师使用的先进技术，由两名研究团队成员应用于所有视频。干预前，远程被试在几乎所有维度上的技术使用手段均高于现场被试(p < 0.05)。因此，我们分别分享了两组的研究结果。现场组(干预前均值较低)在干预前似乎没有主导讨论。他们在引导学生思考他人的想法和总结讨论方面都略有提高。由于干预的重点是引导学生，可能是一个不熟悉的工作领域，我们假设这是干预后他们练习的重点。相反，在干预前似乎主导讨论的远程组(干预前平均水平较高)在几个类别上有所下降，在连接和扩展学生思维方面表现出接近显著的增长。对这些下降的一个可能的解释是，数据收集的时间是在年初，当时他们可能已经明确地教学生如何参与讨论，导致较少的特定讨论引导动作的实例。连接和扩展的增加可能是由于准备好承担这项困难的工作。
{"title":"Challenges in improving and measuring mathematics discussion leading practice","authors":"Meghan Shaughnessy, Nicole Garcia, Jillian Peterson, Kristen D’Anna Pynes","doi":"10.51272/PMENA.42.2020-330","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-330","url":null,"abstract":"This study is an effort to address the challenge of supporting the enhancement of teaching practice. Our model situates professional development (PD) in mathematics instruction occurring in a summer program for fifth grade students. This PD model has two parts. First, participants engage in “legitimate peripheral participation” (Lave & Wenger, 1991) in teaching in this fifth grade classroom through structured conversations about the lesson plans, close observation of teaching, and analysis of student tasks. Second, participants engage in focused learning on leading mathematics discussions through simulations and rehearsals. Two groups of teachers participated, one onsite with a facilitator, and the second at a remote site with an in-person facilitator who delivered the leading mathematics discussion professional development. We study the impact of our PD model. Specifically, we ask: Does teachers’ participation impact their own teaching practice, and if so, in what ways? Twenty-one teachers participated across the two groups. We collected and analyzed a set of preand post-videos of classroom discussions. Participants were asked to record three mathematics discussions two months before the PD occurred and three such lessons two months after participation. A tool that captured techniques named in our decomposition of discussion (Selling et al., 2015), including advanced techniques utilized by experienced teachers, was applied to all videos by two research team members. Prior to the intervention, the means of technique usage of the remote participants were higher than those of the onsite group on almost every dimension (p < .05). Thus, we share the findings for the two groups separately. The onsite group (lower pre-intervention mean) did not appear to be leading discussions before the intervention. They showed slight increases in both orienting students to the thinking of others and concluding discussions. Since the intervention was focused on orienting students, likely an unfamiliar area of work, we hypothesize that this was the focus of their practice post-intervention. Conversely, the remote group (higher pre-intervention mean), who appeared to be leading discussions before the intervention, decreased on several categories and showed near significant growth on connecting and extending student thinking. One possible explanation for these decreases is the timing of the post-data collection at the beginning of the year when they may have been explicitly teaching their students how to engage in discussion, leading to fewer instances of particular discussion-leading moves. The increase in connecting and extending may have been due to readiness to take on this difficult work.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80369237","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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