ethanporcaro/eric-fulltext-meta huggingface dataset:
Directing Focus and Enabling Inquiry with Representations of Practice: Written Cases, Storyboards, and Teacher Education
Author: Herbst, Patricio
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Inquiry,Educational Practices,Race,Educational Opportunities,Teaching Experience,Sense of Community,Teacher Educators,Preservice Teacher Education,Case Method (Teaching Technique),Mathematics Teachers,Mathematics Instruction,Teaching Methods

We discuss affordances and liabilities of using a storyboard to depict a written case of a teacher's dilemma that involves race, opportunity to learn, and student community. We rely on reflections by the teacher educator who authored the written case and later depicted it as a storyboard to use it with his preservice teachers (PSTs). The analysis involved, first, organizing the signifiers in each of the two representations of practice into what we call concentric spheres of stratification, and secondly, contrasting the various meanings attributed to signifiers by both the author and his PSTs. We suggest that the resources of storyboard allow for more inquiry and alternative narratives than is available from the single modality of text in the written case. [For complete proceedings, see ED581294.]
Extending Appropriateness: Further Exploration of Teachers&apos; Knowledge Resources for Proportional Reasoning
Author: Orrill, Chandra Hawley
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Knowledge Level,Mathematical Logic,Mathematical Concepts,Middle School Teachers,Knowledge Base for Teaching,Numbers,Grade 4,Grade 5,Grade 6,Grade 7,Grade 8,Interviews,Video Technology,Qualitative Research,Coding

In this study we extend our prior exploration focused on the extent to which middle school teachers appropriately identified proportional situations and whether there were relationships between attributes of the teachers and their ability to identify proportional situations. For this study, we analyzed both a larger dataset (n = 32) and two dynamic scenarios in which participants were asked to consider aspects of the relationship shown in the diagrams. We found teachers who were correctly able to discern that a situation was not proportional were more likely to use important knowledge resources to evaluate the tasks. [For complete proceedings, see ED581294.]
Mathematical Making in Teacher Preparation: What Knowledge Is Brought to Bear?
Author: Greenstein, Steven
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Teachers,Preservice Teachers,Preservice Teacher Education,Design,Hypothesis Testing,Knowledge Level,Prior Learning,Teacher Role,Elementary School Teachers,Student Projects,Coding,Constructivism (Learning),Manipulative Materials,Problem Solving,Academic Standards

In this paper, we describe an experience within mathematics teacher preparation that engages preservice teachers (PSTs) in Making and design practices that we hypothesized would inform their conceptual and pedagogical thinking. With a focus on the design of new tools to support mathematics teaching and learning, this Learning by Design experience has PSTs exploring at the crossroads of content, pedagogy, and Making. We report our findings of the variety of forms of knowledge that PSTs brought to bear on their design work. As the engagement and advancement of these forms of knowledge is essential to effective mathematics teaching, these findings suggest the promise of a making-oriented experience within mathematics teacher preparation coursework. [For complete proceedings, see ED581294.]
Role of Representation in Prospective Teachers&apos; Fractions Schemes
Author: Boyce, Steven
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Elementary School Teachers,Preservice Teachers,Mathematical Concepts,Concept Formation,Fractions,Student Evaluation,Elementary School Mathematics,Methods Courses,Statistical Analysis

This research report explores relationships between fractions' task representations (discrete, rectangular, or circular) and elementary prospective teachers' (PTs) fractions conceptions. Studies show PTs' conceptions of fractions are centered on a part-whole understanding, which may be problematic when teaching children about improper fractions. We studied PTs' conceptions of fractions using a task-based written assessment. The assessment also included PTs' rankings of task difficulty. We found that PTs' responses involving circles representations aligned best with the empirical trajectory of children's developing understandings of fractions. We discuss implications for supporting PTs in conceptualizing fractions as measures. [For complete proceedings, see ED581294.]
Supporting Learning to Teach in Early Field Experiences: The UTE Model
Author: Bieda, Kristen N.
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teacher Education,Experiential Learning,Secondary School Teachers,Secondary School Mathematics,Mathematics Teachers,Mentors,Teacher Educators,Observation,Transformative Learning,Methods Courses,Semi Structured Interviews,Team Teaching,Video Technology,Lesson Plans,Student Attitudes,Program Effectiveness

Most teacher preparation programs require prospective teachers (PTs) to engage in early field experiences (EFEs) prior to completing required coursework. These EFEs, however, may lack meaningful connections to course content and provide limited opportunities to experience the demands of classroom teaching. In this paper, we share evidence from the implementation of a novel kind of EFE, the &quot;University Teaching Experience&quot; (UTE) model, where secondary mathematics PTs receive mentoring from teacher educators (TEs) as they teach in a undergraduate mathematics course Findings reveal the importance of both guidance from TEs and observations of peer teaching for PTs learning in EFEs. [For complete proceedings, see ED581294.]
An Exploration of How Aspects of a Noticing Intervention Supported Prospective Mathematics Teacher Noticing
Author: Stockero, Shari L.
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Teachers,Preservice Teachers,Attention,Intervention,Teaching Skills,Mathematical Logic,Thinking Skills,Program Effectiveness,Preservice Teacher Education,Video Technology,Observation,Elementary Secondary Education,Coding,Group Discussion

Numerous studies, including our own, have documented that teacher noticing interventions can be effective in developing teachers' abilities to notice salient aspects of the mathematics classroom. In this study, we explore how specific aspects of one such intervention may have supported three prospective teachers in learning to notice high-potential instances of student mathematical thinking. The findings provide evidence that it was not one particular aspect of the intervention that was effective in supporting their noticing, but a combination of factors that include the use of a noticing framework, interactions with their peers and a facilitator, and targeted learning-to-notice activities. [For complete proceedings, see ED581294.]
Teachers&apos; Quantitative Understanding of Algebraic Symbols: Associated Conceptual Challenges and Possible Resolutions
Author: Hawthorne, Casey
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Algebra,Secondary School Teachers,Symbols (Mathematics),Generalization,Concept Formation,Grade 8,Semi Structured Interviews,Mathematical Formulas

While the mathematics education community encourages teachers to support students in developing a more meaningful contextual understanding of algebraic symbols, very little is known about teachers' quantitative understandings of algebraic symbols themselves. The goal of this study was to fill this gap and examine secondary teachers' ability to contextualize algebraic symbols, in particular notation that results from algebraic generalization. The results led to the identification of various conceptual hurdles that teachers encountered as they endeavored to articulate the underlying quantities as well as various conceptualizations they invoked, both productive and unproductive, in their attempt to overcome these challenges. [For complete proceedings, see ED581294.]
An Analysis of Students&apos; Mistakes on Routine Slope Tasks
Author: Cho, Peter
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Task Analysis,College Students,Error Correction,Error Patterns,Statistical Analysis,Qualitative Research,Concept Teaching,Mathematical Concepts,Algebra,Difficulty Level,Performance Based Assessment,Problem Solving,Mathematical Aptitude

This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct quantitative and qualitative analysis of students' mistakes to extract information regarding slope conceptualizations described in prior research. Results delineate procedural proficiencies and conceptual underpinnings related to various slope conceptualizations that can help both teachers and researchers pinpoint students' understanding and make appropriate instructional decisions to help students advance their understanding. [For complete proceedings, see ED581294.]
Manufacturing Licorice: Modeling with Data in Third Grade
Author: English, Lyn D.
Date: 2017-10-00
Type: Reports - Research
Subjects: Grade 3,Elementary School Students,Data Analysis,Models,STEM Education,Inferences,Mathematics Instruction,Statistics,Elementary School Mathematics,Experiential Learning,Longitudinal Studies

This paper reports on a study of 3rd-grade students' modeling with data, which involves comprehensive investigations that draw upon STEM-based concepts, contexts, and questions, and generate products supported by evidence and open to informal inferential thinking. Within a real-world STEM-based context of licorice manufacturing, students experienced the &quot;creation of variation&quot; as they compared and represented the masses of &quot;licorice sticks&quot; they made by hand (using Play-Doh) and those using a Play-Doh extruder. By generating their own statistical measures, students could observe the features of data distributions including center, range, typical, and middle, at a much younger age than usual. They could draw inferences from the models they created, with awareness of how variation limits the certainty with which predictions can be made. The study supports a potential route for advancing early statistical learning. [For complete proceedings, see ED581294.]
Towards a Hypothetical Learning Trajectory for Questioning
Author: Conner, Kimberly
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Questioning Techniques,Preservice Teacher Education,Preservice Teachers,Educational Practices,Educational Strategies,Thinking Skills,Teaching Skills,Classification,Evaluation Criteria,Learning Processes,Elementary School Curriculum,Beliefs,Values

We report on efforts to better understand the questioning practices used by preservice elementary teachers (PSTs), including the range of preferred question types and the values they invoke when evaluating their questions. We sought to determine whether teachers exhibited consistent patterns in selecting questions with certain features, such as funneling students to a particular strategy or eliciting student thinking, across different instructional situations. We found that such patterns did exist; in this paper we use the patterns to propose a trajectory for developing the skill of asking questions that elicit and build on student thinking. The trajectory describes the beliefs, values, and questioning practices associated with PSTs at each stage. [For complete proceedings, see ED581294.]
Exploring High School Students Beginning Reasoning about Significance Tests with Technology
Author: García, Víctor N.
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: High School Students,Logical Thinking,Hypothesis Testing,Computer Simulation,Sampling,Statistical Inference,Statistical Significance,Computer Uses in Education,Secondary School Mathematics,Grade 11,Grounded Theory,Questionnaires,Mathematics Instruction

In the present study we analyze how students reason about or make inferences given a particular hypothesis testing problem (without having studied formal methods of statistical inference) when using Fathom. They use Fathom to create an empirical sampling distribution through computer simulation. It is found that most student´s reasoning rely on data and assimilate natural sampling variation, which are two fundamental ideas of inference. This result represents a significant change in their natural reasoning. An important misconception is believed Fathom simulates samples of the real population instead of a hypothetical one. [For complete proceedings, see ED581294.]
Contextualized Mathematics Problems and Transfer of Knowledge: Establishing Problem Spaces and Boundaries
Author: McGraw, Rebecca
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Secondary School Teachers,Mathematics Teachers,Teacher Collaboration,Problem Solving,Group Discussion,Faculty Development,Video Technology,Audio Equipment,Teacher Role,Group Dynamics,Interaction

In this study, we examine how inservice secondary mathematics teachers working together on a contextualized problem negotiate issues arising from the ill-structured nature of the problem such as what assumptions one may make, what real-world considerations should be taken into account, and what constitutes a satisfactory solution. We conceptualize the process of negotiating these questions as the construction of a &quot;problem space,&quot; characterized by the boundary between considerations deemed relevant or essential to the problem and ones thought to be beyond the scope of the problem. We use data from group discussions of the problem to consider ways in which problem spaces are co-constructed by learners, instructors, and problem authors and how these problem spaces evolve over time. We conclude by discussing implications of these findings for the design and implementation of contextualized mathematics problems. [For complete proceedings, see ED581294.]
Explicating the Concept of Contrapositive Equivalence
Author: Dawkins, Paul Christian
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Concepts,Case Studies,Mathematics Instruction,Mathematical Logic,Validity,College Students,College Mathematics,Learning Processes

This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and negation, representing these sets by closed regions in space, and linking conditional truth to a subset relation between these regions in space. Our case study serves to portray that students must construct all of these elements to achieve a sense of necessity in the equivalence. This study thus contributes a set of learning goals for any introductory logic instruction using Euler (or Venn) diagrams, which has been little studied in the mathematics education literature. [For complete proceedings, see ED581294.]
Generalization across Domains: The Relating-Forming-Extending Generalization Framework
Author: Ellis, Amy
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Generalization,Abstract Reasoning,Semi Structured Interviews,Middle School Students,High School Students,Undergraduate Students,Algebra,Mathematics,Grounded Theory,Mathematics Education

Generalization is a critical aspect of doing mathematics, with policy makers recommending that it be a central component of mathematics instruction at all levels. This recommendation poses serious challenges, however, given researchers consistently identifying students' difficulties in creating and expressing normative mathematical generalizations. We address these challenges by introducing a comprehensive framework characterizing students' generalizing, the Relating-Forming-Extending framework. Based on individual interviews with 90 students, we identify three major forms of generalizing and address relationships between forms of abstraction and forms of generalization. This paper presents the generalization framework and discusses the ways in which different forms of generalizing can play out in activity. [For complete proceedings, see ED581294.]
Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics
Author: Wickstrom, Megan H.
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Models,Elementary School Mathematics,Elementary School Teachers,Teacher Attitudes,Teaching Methods,Relevance (Education),Student Empowerment,Observation,Interviews,Discourse Analysis,Worksheets,Student Journals,Group Activities,Teacher Role,Student Role,Qualitative Research

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and identity. I then highlight, through four themes, how mathematical modeling challenged the ways in which both the teachers and students understood what it means to know and do mathematics. Findings suggest that the practice of mathematical modeling allowed for access, empowerment, and real world connections that were typically not present in classroom instruction. In addition, it challenged student positioning in the classroom in terms of who was framed as capable of doing mathematics. [For complete proceedings, see ED581294.]
Toward Multimodal Poetic Analysis: A Case of Property Noticing
Author: Staats, Susan
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Discourse Analysis,Mathematics Instruction,Algebra,Mathematics Activities,Cooperative Learning,Discourse Modes,Word Problems (Mathematics),Problem Solving,Cognitive Processes,Mathematical Logic,Undergraduate Students,Case Studies

This paper uses multimodal discourse analysis to show that discursive form, in addition to words, gestures and sound dimensions of speech, is an important linguistic resource for expressing mathematical meaning. During a collaborative task, a student spoke an insight about an algebraic property five times over a few minutes, in slightly different ways. He consistently used repetition of grammar and words, a speech form known as poetic structure. These poetic structures were marked elaborately through discursive modes such as pause, intonation and gestures, suggesting that they form a meaning-making mode that is real to the speaker. [For complete proceedings, see ED581294.]
Investigating the Relational Nature of Feedback Practice
Author: Kastberg, Signe E.
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematics Teachers,Teacher Educators,Feedback (Response),Preservice Teacher Education,Teaching Methods,Knowledge Base for Teaching,Personal Narratives,Preservice Teachers,Dialogs (Language),Discussion (Teaching Technique),Written Language,Teaching Skills,Elementary Secondary Education

At the crossroads of our prior research on prospective teachers' feedback to mathematics-learners and our mathematics teacher educator feedback practices, we study written feedback as part of relational practice. Using self-study methodology and an analysis of our narratives and conversations about written feedback, we identified factors that frame and motivate our written feedback. We argue that, assuming the central goal of teacher education is the development of relational practice, written feedback should support prospective mathematics teachers' skills and knowledge relevant to tasks involved in teaching mathematics and extend prospective teachers' views of mathematics teaching and learning by drawing on their experiences, insecurities, problems, and views of mathematics teaching and learning. [For complete proceedings, see ED581294.]
Collaborative Gestures When Proving Geometric Conjectures
Author: Walkington, Candace
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Nonverbal Communication,Teaching Methods,Geometry,Geometric Concepts,Cognitive Processes,Imitation,Concept Formation,Undergraduate Students,Preservice Teachers,Elementary School Mathematics,Video Games,Educational Technology,Technology Uses in Education,Educational Games,Mathematical Logic,Validity,Spatial Ability

Research in mathematics education has established that gestures--spontaneous movements of the hand that accompany speech--are important for learning. In the present study, we examine how students use gestures to communicate with each other while proving geometric conjectures, arguing that this communication represents an example of extended cognition. We identify three kinds of &quot;collaborative gestures&quot;--gestures that are physically distributed over multiple learners. Learners make echoing gestures by copying another learner's hand gestures, mirroring gestures by gesturing identically and simultaneously with another learner, and joint gestures where multiple learners collectively make a single gesture of a mathematical object using more than one set of hands. The identification and description of these kinds of collaborative gestures offers insight into how learners build distributed mathematical understanding. [For complete proceedings, see ED581294.]
Teachers&apos; Responses to a Common Set of High Potential Instances of Student Mathematical Thinking
Author: Stockero, Shari L.
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Logic,Mathematics Instruction,Thinking Skills,Discussion (Teaching Technique),Responses,Classroom Communication,Interviews,Algebra,Geometry,Vignettes,Video Technology,Secondary School Teachers,Coding,Teaching Methods

This study investigates teacher responses to a common set of high potential instances of student mathematical thinking to better understand the role of the teacher in shaping meaningful mathematical discourse in their classrooms. Teacher responses were coded using a scheme that disentangles the teacher move from other aspects of the teacher response, including who the response is directed to and the degree to which the student thinking is honored. Teachers tended to direct their response to the student who had shared their thinking and to explicitly incorporate ideas core to the student thinking in their response. We consider the nature of these responses in relation to principles of productive use of student mathematical thinking. [For complete proceedings, see ED581294.]
Teachers&apos; Interpretations of Student Statements about Slope
Author: Nagle, Courtney
Date: 2017-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematics Teachers,Mathematical Concepts,Concept Formation,Knowledge Level,Algebra,Mathematical Logic,Mathematics Skills,Knowledge Base for Teaching,Faculty Development,Coding,Secondary School Teachers,Secondary School Mathematics,Pedagogical Content Knowledge

This paper describes seven in-service teachers' interpretations of student statements about slope. The teachers interpreted sample student work, conjectured about student contributions, assessed the students' understanding, and positioned the students' statements in the mathematics curriculum. The teachers' responses provide insight into their Knowledge of Content and Students (KCS) and Knowledge of Content and Curriculum (KCC). Results suggest these teachers value academic terminology related to slope, have limited perspectives on slope in real world contexts, and struggle to describe the extension of slope to precalculus. [For complete proceedings, see ED581294.]