数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-49
Leslie Dietiker, Rashmi Singh, Meghan Riling, Hector I. Nieves
{"title":"What makes a mathematics lesson interesting to students?","authors":"Leslie Dietiker, Rashmi Singh, Meghan Riling, Hector I. Nieves","doi":"10.51272/PMENA.42.2020-49","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-49","url":null,"abstract":"How can we design mathematical lessons that spark student interest? To answer this, we analyzed teacher-designed and enacted lessons that students described as interesting for how the content unfolded. When compared to those the same students describe as uninteresting, multiple distinguishing characteristics are evident, such as the presence of misdirection, mathematical questions that remain unanswered for extended time, and a greater number of questions that are unanswered at each point of the lesson. Low-interest lessons did not contain many special narrative features and mostly had questions that were answered immediately. Our findings offer guidance for the design of lessons that can shift student mathematical dispositions.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72381122","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/pmena.42.2020-178
María José Aviña González, Angelina Alvarado Monroy
{"title":"Report of a classroom experience for the development of distribution models / Experiencia en el aula para el desarrollo de modelos para el reparto","authors":"María José Aviña González, Angelina Alvarado Monroy","doi":"10.51272/pmena.42.2020-178","DOIUrl":"https://doi.org/10.51272/pmena.42.2020-178","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"43 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72412513","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-192
Irma E. Stevens
{"title":"“Solving versus relating”: Pre-service teachers’ conflicting images of formulas and dynamic contexts","authors":"Irma E. Stevens","doi":"10.51272/PMENA.42.2020-192","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-192","url":null,"abstract":"Researchers have identified both the affordances of engaging students in symbolization activities and students’ difficulties in meaningfully representing contexts through algebraic expressions/formulas. In a semester-long teaching experiment, two pre-service teachers demonstrated their conflicting meanings for formulas with their images of a context when engaging in a task about a dynamic geometric object. The two students could construct both normative formulas by reasoning with a context and descriptions of covariational relationships between quantities within the context, but both still struggled to relate their formulas and quantitative relationships to one another. This result highlights the importance of attending to what students’ formulas mean to them, which for the students in this study, could be either a way of “solving” or “relating” quantities.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84376149","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-116
Brendan T Dames, Corey Webel
{"title":"Evolution of elementary math leaders’ collaborative plans for school-level change","authors":"Brendan T Dames, Corey Webel","doi":"10.51272/PMENA.42.2020-116","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-116","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"73 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81927740","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-193
Omar Arenas Bonifacio, E. Sánchez
{"title":"First fundamental theorem of calculus: How do engineering students interpret and apply it? / Primer teorema fundamental del cálculo: ¿cómo lo interpretan y aplican estudiantes de ingeniería?","authors":"Omar Arenas Bonifacio, E. Sánchez","doi":"10.51272/PMENA.42.2020-193","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-193","url":null,"abstract":"The first fundamental theorem of calculus relates differential and integral calculus, one of its important aspects according to Bressoud (2011) is that it shows the existence of two ways of calculating an integral: with the limit of a Riemann sum and by an antiderivative. Larsen, Marrongelle, Bressoud and Graham (2017) indicate that calculus is a barrier to the academic progress of many students and that there is a need for research that seeks to develop proposals for instruction to improve the understanding of its concepts. Therefore, with the idea of carrying out this type of research in the future, the present study seeks to identify the common interpretation of the first theorem of calculus and whether it is useful in solving contextual problems. Answering these questions will provide some elements to develop a proposal for instruction. This study involved 18 students between the ages of 18 and 21 from engineering careers at a university located in Mexico City, who had completed a calculus course. The instrument was a set of three problems, in two, we propose contextual situations that can be solved by applying the first fundamental theorem of the calculus or by performing integration and derivation operations (one situation is about the ratio of change of the volume of water contained in a tank, with respect to time, where water falls to a variable ratio; the other is about the ratio of change of the volume of water contained in a cylindrical tank with respect to the height of water). In the last problem, the same type of situation is posed in abstract form: If F(x) = f t dt ! ! , obtain F′(x), justify your answer.","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":"79679262","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-93
Lili Zhou, S. Richardson
{"title":"A narrative inquiry of GEMS women’s experience with STEM","authors":"Lili Zhou, S. Richardson","doi":"10.51272/PMENA.42.2020-93","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-93","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84665418","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-187
A. Mirin
{"title":"Function identity and the fundamental theorem of calculus","authors":"A. Mirin","doi":"10.51272/PMENA.42.2020-187","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-187","url":null,"abstract":"By analyzing the responses of 100 introductory calculus students to two questions, this study addresses how students understand the fundamental theorem of calculus as it relates to function identity. One question involves students’ understandings of the fundamental theorem of calculus, and the other involves their concept definitions of function sameness. This analysis aims to better understand students’ concept images of function sameness, both in the context of the fundamental theorem of calculus and in general.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85296026","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-396
Carolyn Mitten
{"title":"FALA framework: A learning progression for novice teachers’ use of formative assessment","authors":"Carolyn Mitten","doi":"10.51272/PMENA.42.2020-396","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-396","url":null,"abstract":"Formative assessment has been identified as one way that teachers can gather critical information about a student’s level of understanding in order to make informed instructional adaptations that meet the needs of all students (NCTM, 2000; Shepard et al., 2005). Over several decades, research has shown the potential of formative assessment to effectively improve student achievement (Black & Wiliam, 1998; Kingston & Nash, 2011). Despite its potential, issues in preparing teachers to implement formative assessment practices has kept its potential from being realized (Schoenfeld, 2015) and many teachers have limited understanding of its use (Shepard et al., 2005). In order to better understand how to prepare teachers to use formative assessment, a trajectory describing how teachers develop formative assessment knowledge and practice is needed. The Formative Assessment Levels of Appropriation (FALA) framework evolved from a larger qualitative research study on the evolution of formative assessment knowledge and practice of novice teachers from teacher preparation through their third year of teaching. Grounded in activity theory, the FALA framework describes the levels of appropriation (Grossman et al., 1998) for the five aspects of formative assessment defined by Black & Wiliam (2009). Table 1 provides an example of the framework for one aspect of formative assessment—clarifying intentions and criteria for success.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85359494","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-373
Michael S. Meagher, Jennifer N. Lovett, Allison W. McCulloch
{"title":"Middle school students’ development of an understanding of the concept of function","authors":"Michael S. Meagher, Jennifer N. Lovett, Allison W. McCulloch","doi":"10.51272/PMENA.42.2020-373","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-373","url":null,"abstract":"Middle school students (n=144) worked with an applet specially designed to introduce the concept of function without using algebraic representations. The purpose of the study was to examine whether the applet would help students to understand function as a relationship between a set of inputs and a set of outputs and to begin to develop a definition of function based on that relationship. Results indicate that, by focusing on consistency of the outputs the students, at a rate of approximately 80%, are able to distinguish functions from non-functions. Also, students showed some promise in recognising constant functions as functions, a known area of common misconceptions.","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":"81687800","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}
数学教学通讯Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-292
Joe Champion, Angela R. Crawford, Michele B. Carney
{"title":"Articulating effective middle grades instructional practices in a teacher-researcher alliance","authors":"Joe Champion, Angela R. Crawford, Michele B. Carney","doi":"10.51272/PMENA.42.2020-292","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-292","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84054992","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}