数学教学通讯最新文献

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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":"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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":"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":null,"pages":null},"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":"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}