ethanporcaro/eric-fulltext-meta huggingface dataset:
Identifying Similar Polygons: Comparing Prospective Teachers&apos; Routines with a Mathematician&apos;s
Author: Wang, Sasha
Date: 2015-11-00
Type: Reports - Research
Subjects: Preservice Teachers,Mathematics Teachers,Professional Personnel,Mathematics Instruction,Geometric Concepts,Visual Perception,Discussion (Teaching Technique),Mathematical Logic,Preservice Teacher Education,College Faculty

This paper reports two prospective teachers' and a mathematician's ways of identifying similar triangles and hexagons through the analysis of routines, a characteristic of geometric discourse. The findings show that visual recognition was a common approach for the mathematician as well as the two prospective teachers. However, when asked for justification, their routines of identifying similar polygons diverged. The paper also discusses the implication of classroom discourse practices to enhance prospective teachers' communication and reasoning skills while learning geometric concepts such as similarity. [For the complete proceedings, see ED583989.]
The Narrative Structure of Mathematics Lectures
Author: Weinberg, Aaron
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Lecture Method,College Mathematics,Teaching Methods,Mathematical Concepts,Algebra,Graphs

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the structure of lectures. In this paper, we apply ideas from narrative analysis to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture as consisting of collections of narratives, to identify connections between the narratives, and to use the narrative structure to identify key features of the lecture. By looking at repetitions of the mathematical concepts across the narratives, graph theory tools provide a means of examining the structure of the lecture. The analysis highlights the demands that students may face to understand the connections between the various mathematical ideas that the instructor introduces. [For the complete proceedings, see ED583989.]
Exploring Roles of Cognitive Studies in Equity: A Case for Knowledge in Pieces
Author: Adiredja, Aditya P.
Date: 2015-11-00
Type: Reports - Research
Subjects: College Mathematics,Epistemology,Power Structure,Mexican Americans,Hispanic American Students,Undergraduate Students,Case Studies,Interviews

Underrepresentation of people of color in mathematics at the postsecondary level warrants more focus on equity issues. The prevalence of cognitive studies at the undergraduate level is met with the call for critical analysis about the kinds of knowledge that get privileged in mathematics education. Connecting to the Funds of Knowledge work, this paper discusses the utility of diSessa's Knowledge in Pieces cognitive framework to uncover productive informal knowledge in learning formal mathematics. Seeing the valorization of knowledge as related to issues of power, a case of a Chicana student's productive sense making about the formal definition of a limit illustrates the way diSessa's framework can help challenge what counts as productive mathematical knowledge and reasoning. [For the complete proceedings, see ED583989.]
Toward a Framework for Attending to Reflexivity in the Context of Conducting Teaching Experiments
Author: Tallman, Michael A.
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Researchers,Models,Mathematical Logic,Reflection,Learning Theories,Research Methodology,Data Analysis,Mathematical Concepts,Interaction

In this paper, we present an analytical framework for attending to reflexivity in the context of conducting teaching experiments and rationalize its components by appealing to the constructivist foundations on which the methodology is based. To illustrate the importance and utility of this framework, we discuss our analysis of recent mathematics education literature that has employed the teaching experiment methodology. In so doing, we reveal the extent to which researchers' presentations of their models of students' mathematical thinking and learning reflect these researchers' attention to reflexivity. We conclude by reflecting on the implications of researchers attending to reflexivity in the context of conducting teaching experiments. [For the complete proceedings, see ED583989.]
The Development of Informal Inferential Reasoning via Resampling: Eliciting Bootstrapping Methods
Author: McLean, Jeffrey A.
Date: 2015-11-00
Type: Reports - Research
Subjects: College Mathematics,College Students,Statistics,Statistical Inference,Manipulative Materials,Simulation,Educational Technology,Technology Uses in Education,Mathematical Logic,Sampling,Qualitative Research,Case Studies

This study focuses on the development of four tertiary introductory statistics students' informal inferential reasoning while engaging in data driven repeated sampling and resampling activities. Through the use of hands-on manipulatives and simulations with technology, the participants constructed empirical sampling distributions in order to investigate the inferences that can be drawn from the data. Students' developing reasoning of sampling and informal inference is reported as they move from repeated sampling methods to resampling methods, along with their reasoning of bootstrapping methods and how this reasoning was applied to make informal inferential claims. [For the complete proceedings, see ED583989.]
Reframing Urban Mathematics Education: The Spatial Politics of Opportunity
Author: Bullock, Erika C.
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Urban Schools,Mathematics Education,Equal Education,Geographic Location,Educational Policy,Urban Education,Geography,Educational Methods,Relevance (Education),Social Influences,Environmental Influences

Although equity-oriented discourse is working to move the mathematics education community from achievement-gap rhetoric toward a focus on opportunity gaps, it does not currently recognize the role of space and the politics of space in creating and maintaining opportunity gaps as it relates to mathematics education in urban settings. The purpose of this paper is to engage the task of reconceptualizing urban mathematics education by proposing a framework for scholarship, policy, and practice. The authors engage scholarship in mathematics education, urban education, critical geography, and urban sociology to substantiate a socio-spatial framework for urban mathematics education, which features a visual schematic that locates mathematics teaching and learning--vis-à-vis a mathematics-instructional triad--within a system of socio-spatial considerations relevant to U.S. urban contexts. [For the complete proceedings, see ED583989.]
A Framework for Analyzing Informal Inferential Reasoning Tasks in Middle School Textbooks
Author: Huey, Maryann E.
Date: 2015-11-00
Type: Reports - Research
Subjects: Secondary School Mathematics,Middle Schools,Middle School Students,Mathematics Education,Textbooks,Inferences,Logical Thinking,Data Analysis,Statistics,Mathematics Skills,Problem Solving,Textbook Content,Content Analysis,Grade 7,Common Core State Standards,Alignment (Education)

Building upon the work of Zieffler, Garfield, DelMas and Reading (2008) and others, we developed a framework for assessing informal inferential tasks in middle school mathematics textbooks. The framework both embodies the key recommendations for developing informal inferential reasoning and captures common trimming attributes, which lower the cognitive demand and opportunities to learn. Researchers believe that introducing inferential reasoning informally will assist students later in developing argumentation structures necessary for understanding formal methods (Wild &amp; Pfannkuch, 1999). Inferential reasoning has long been a key learning goal of statistics education and provides access to viewing knowledge of core statistical concepts and reasoning about data distributions. Tools are needed to assess the fidelity of tasks in alignment with both national and research-based recommendations. [For the complete proceedings, see ED583989.]
The Discourse of Attending to Precision in Secondary Classrooms
Author: Engledowl, Christopher
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Teaching Methods,Secondary School Mathematics,Coding,Discussion (Teaching Technique),Metacognition,High School Students,Accuracy,Problem Solving,Mathematical Logic,Rural Schools,Video Technology,Audio Equipment,Observation,Validity

Attending to precision (ATP) is essential in mathematics. This study examined ATP instances through the lens of univocal (functioning to convey information) and dialogic (functioning to generate new meaning) discourse. Analysis of data from five secondary mathematics classrooms focused on whole-class instances of ATP with coding based on the univocal or dialogic nature of the discourse. Although instances were predominantly univocal, there was variation in whether the teacher's or student's idea was being transmitted. We share examples of the rare dialogic instances where the co-construction of meaning through discourse involved ATP in qualitatively different ways than the univocal instances. [This study was supported by the University of Missouri Research Council and the University of Missouri System Research Board. For the complete proceedings, see ED583989.]
The Relationship between Mathematics Identity and Personality Attributes with Students&apos; Career Goals
Author: Cribbs, Jennifer
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Calculus,Student Surveys,College Students,Student Attitudes,College Mathematics,Occupational Aspiration,Career Choice,Mathematics,STEM Education,Identification (Psychology),Personality Traits,Persistence,Correlation,Regression (Statistics),Gender Differences,Self Concept

In this study, we surveyed 570 Calculus I and Calculus II students at two large public universities in the Northeastern region of the United States. We explored the relationship between these students' career goals in mathematics and other STEM fields, with their mathematics identity and self-identified personality attributes. Our findings suggest that mathematics identity can be used as a way of explaining persistence in mathematics and other STEM fields. We also found certain personality attributes to be correlated with persistence in these fields and these personality attributes varied based on gender. We conclude with a detailed analysis of our findings and some implications. [For the complete proceedings, see ED583989.]
Maintaining Conventions and Constraining Abstraction
Author: Moore, Kevin C.
Date: 2015-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Traditionalism,Student Experience,Educational Opportunities,Mathematical Concepts,Mathematics Activities,Abstract Reasoning,Conventional Instruction,Constructivism (Learning),Illustrations,Educational Practices,Instructional Innovation

Conventions play an important communicative role in mathematics. Likely due to the complex relationship between conventions and school mathematics, few education researchers have questioned or investigated the consequences of instruction and curricula that primarily, if not unquestionably, maintain conventions. Drawing on Piagetian notions of abstraction and our work with students and teachers, we argue that students' repeated experiences with instruction and curricula that maintain conventions likely constrain students' learning opportunities. We hypothesize that by 'breaking' conventions, educators could better support students in differentiating those aspects of their activity essential to a concept from those that are unessential. We characterize student work on two tasks to illustrate potential relationships between the nature of students' abstractions and what we perceive to be conventions. [For the complete proceedings, see ED583989.]
Mathematics, Language, and Degrees of Certainty: Bilingual Students&apos; Mathematical Communication and Probability
Author: Culligan, Karla
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Vocabulary,Bilingual Students,Interpersonal Communication,Probability,French,Immersion Programs,Language Usage,Discourse Analysis,Correlation,Multilingualism,Longitudinal Studies,Grade 3,Elementary School Students,Interviews,Audio Equipment,Video Technology,Foreign Countries

While all mathematics is mediated by language, the role of language is especially complex in bi- and multilingual mathematics classrooms, and more so in bilingual education programs in which the explicit goals of both language and mathematics learning intersect. We explore bilingual French immersion students' linguistic and mathematical repertoires as they work through a series of probability problems. Focusing on the collaborative dialogue that occurred between students and researchers, our discourse analysis was informed by sociocultural theory and systemic functional linguistics. Findings indicate that students' linguistic and mathematical repertoires are intertwined, and that collaboration can offer opportunities for supporting bilingual learners' language and mathematics development. We conclude with implications and challenges for bilingual mathematics education. [For the complete proceedings, see ED583989.]
Bilinguals&apos; Non-Linguistic Communication: Gestures and Touchscreen Dragging in Calculus
Author: Ng, Oi-Lam
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Bilingual Students,Nonverbal Communication,Mathematics Instruction,Mathematical Logic,High School Students,Secondary School Mathematics,Calculus,Language Usage,Educational Technology,Technology Uses in Education,Cooperative Learning,Interpersonal Communication,Foreign Countries,Handheld Devices,Telecommunications,Grade 12

This paper discusses the importance of considering bilingual learners' non-linguistic forms of communication for understanding their mathematical thinking. In particular, I provide an analysis of communication involving a pair of high school calculus bilingual learners, who interacted with a touchscreen-based DGE (dynamic geometry environment). The paper focuses on the word-use, gestures, and touchscreen dragging actions in student-pair communication. Findings suggest that the students relied on gestures and dragging as multimodal features of the mathematical discourse to communicate dynamic aspects of calculus. This paper raises questions about new forms of communication mobilized in dynamic, touchscreen environments, particularly for bilingual learners. [For the complete proceedings, see ED583989.]
A Mixed Methods Study of Elementary Teachers&apos; Experiences with and Perspectives on the CCSS-Mathematics
Author: Swars, Susan Lee
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Mixed Methods Research,Elementary School Teachers,Mathematics Instruction,Common Core State Standards,Urban Schools,Questionnaires,Teacher Surveys,Interviews,Familiarity,Teacher Competencies,Teacher Attitudes,Pedagogical Content Knowledge,Alignment (Education),Readiness,English Language Learners,Professional Development Schools,Comparative Analysis

This mixed methods study explored elementary teachers' (n = 73) experiences with and perspectives on the newly implemented CCSS-Mathematics at a high-needs, urban Professional Development School in a state where roll-out of the standards has been fraught with opposition. Analysis of the survey, questionnaire, and interview data reveals the findings cluster around: familiarity with and preparation to use the standards; implementation of the standards, including incorporation and teacher change; and tensions associated with enactment of the standards. Notably, the teachers believed in the merit of the standards but were constrained by their inadequate content knowledge, limited aligned curricular resources, lack of student readiness, and a perceived mismatch with ELLs. The results illuminate the professional needs of teachers during this critical time of transition and also add to the scant research in this area. [For the complete proceedings, see ED583989.]
Attributes of Student Mathematical Thinking That Is Worth Building on in Whole-Class Discussion
Author: Van Zoest, Laura R.
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Mathematics Instruction,Classroom Communication,Thinking Skills,Accuracy,Prior Learning,Mathematics Skills,Comprehension,Cognitive Processes,Secondary School Mathematics,Secondary School Students

This study investigated the attributes of 297 instances of student mathematical thinking during whole-class interactions that were identified as having the potential to foster learners' understanding of important mathematical ideas (MOSTs). Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in-the-moment, the accuracy of the thinking, and the type of the thinking (e.g., sense making). Findings both illuminate the complexity of identifying student thinking worth building on during whole-class discussion and provide insight into important attributes of MOSTs that teachers can use to better recognize them. For example, 96% of MOSTs were of three types, making these three particularly salient types of student mathematical thinking for teachers to develop skills in recognizing. [For the complete proceedings, see ED583989.]
Developing a Framework for Assessing the Impact of Whiteness in Mathematics Education
Author: Battey, Dan
Date: 2015-11-00
Type: Reports - Research
Subjects: Mathematics Education,Racial Bias,Whites,Ideology,Equal Education,Learning Theories,Racial Discrimination

The ideology of whiteness has received little attention in mathematics education. In this paper, we develop a framework for documenting how whiteness shapes mathematics education as a racialized space. Drawing on the sociological concept of &quot;white institutional space&quot; (Feagin, Vera, &amp; Imani, 1996; Moore, 2008), the framework examines mathematics education across institutional, interpersonal, and individual levels of analysis. The authors argue that this framework captures how ideological discourses of whiteness and colorblindness (Lewis, 2004) and racialized hierarchies of mathematics ability (Martin, 2009) are perpetuated through institutional structures and interpersonal relations in mathematics education. [For the complete proceedings, see ED583989.]
Mathematical and Financial Literacy with Families
Author: Baron, Lorraine M.
Date: 2015-11-00
Type: Reports - Research
Subjects: Money Management,Social Justice,Family Characteristics,Numeracy,Mathematics Skills,Family Programs,Community Programs,Program Effectiveness,Self Esteem,Skill Development,Literacy Education,At Risk Persons,Pretests Posttests,Semi Structured Interviews,Knowledge Level

There is a strong link between citizens' quantitative literacy abilities and their financial prosperity. This study applied a social justice perspective to describe families' personal flourishing within the context of numerical, mathematical, and financial literacy (NMFL) education. Four families participated in a weekly community program with mathematical and financial literacy goals. The data showed that participants gained confidence and skills and felt empowered to teach/transfer that knowledge to their children. The author proposes a conceptual framework linking personal flourishing with NMFLs, and suggests the framework be used to investigate and describe quantitative and financial literacy in future empowering pedagogies research. [For the complete proceedings, see ED583989.]
The Influence of a Graduate Course on Teachers&apos; Self-Efficacy to Teach Statistics
Author: Thrasher, Emily
Date: 2015-11-00
Type: Reports - Research
Subjects: Mathematics Instruction,Self Efficacy,Graduate Students,Statistical Inference,Data Analysis,Educational Technology,Technology Uses in Education,Pretests Posttests,Program Effectiveness,Teacher Competencies,Knowledge Level,Surveys,Likert Scales,Scores,Faculty Development

This paper explores the impact on teachers' self-efficacy to teach statistics from a graduate course aimed to develop teachers' knowledge of inferential statistics through engaging in data analysis using technology. This study uses qualitative and quantitative data from the Self-Efficacy to Teach Statistics Survey (Harrell-Williams et al., 2013) to provide data about teachers' confidence to teach statistical topics. The survey was given to 27 participants from two different institutions before and after the graduate course. We found that participants' self-efficacy to teach statistics increased after participation in the graduate course and references to specific course activities will be identified. [For the complete proceedings, see ED583989.]
Novice Elementary Teachers&apos; Instructional Practices: Opportunities for Problem-Solving and Discourse
Author: Lee, Carrie W.
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Beginning Teachers,Elementary School Teachers,Educational Practices,Problem Solving,Classroom Communication,Mathematics Teachers,Mathematics Instruction,Recordkeeping,Likert Scales,Data Collection

The purpose of this study was to examine the mathematics instructional practices of 75 second-year elementary teachers (K-5) in terms of the learning opportunities provided to their students. On average, each teacher completed instructional logs for 43 days across the school year. Select items were analyzed in order to better understand the elementary students' opportunities to engage in problem solving and discourse. Results indicated frequent opportunities for discussion but limited opportunities for engagement with more open-ended tasks and explanation. Implications for future research and mathematics teacher education are discussed. [For the complete proceedings, see ED583989.]
Pawnshops to Teach Percent and Percent to Teach Pawnshops
Author: Rubel, Laurie H.
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: High School Students,Learning Modules,Mathematics Instruction,Mathematics Achievement,Student Improvement,Teaching Methods,Mathematical Concepts,Concept Teaching,Critical Thinking,Student Projects,Observation

This paper focuses on student learning in the context of a curricular module on pawnshops piloted with 15 students in an urban high school. The paper describes pedagogical frameworks guiding the development of the module and summarizes key features of its curriculum. Analysis focuses on student growth with respect to mathematical understanding of percent and opinions about pawnshops. Findings include student adoption of ratio strategies indicative of conceptual understanding of percent, and development of critical opinions about pawnshops as a lending system. [For the complete proceedings, see ED583989.]
What Is Equity? Ways of Seeing
Author: Jackson, Christa
Date: 2015-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Cultural Influences,Preservice Teacher Education,African American Students,Males,Behavior Problems,Student Behavior,Classroom Techniques,Educational Strategies,Equal Education,Elementary School Mathematics,Methods Courses,Vignettes,Class Activities,Teaching Methods

Prospective teachers must be prepared for their role in providing equitable access for learning high quality mathematics. Therefore, it is imperative that mathematics teacher educators provide opportunities to develop an equity-centered orientation in teacher preparation courses. In this study, we begin to address this issue by identifying what prospective teachers attend to in a classroom vignette of an African American male student who is above grade level in mathematics and exhibits disruptive behavior during instruction. The results of the study indicate that while participants are beginning to attend to cultural influences, most responses are focused on classroom management strategies. [For the complete proceedings, see ED583989.]