ethanporcaro/eric-fulltext-meta huggingface dataset:
Imprecision in Classroom Mathematics Discourse
Author: Leatham, Keith R.
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Classroom Communication,Classroom Techniques,Mathematics Instruction,Discourse Communities,Ambiguity (Semantics),Language Usage,Teaching Models,Instructional Effectiveness,Educational Practices,Educational Strategies

We theorize about ambiguity in mathematical communication and define a certain subset of ambiguous language usage as imprecise. For us, imprecision in classroom mathematics discourse hinders in-the-moment communication because the instance of imprecision is likely to create inconsistent interpretations of the same statement among individuals. We argue for the importance of attending to such imprecision as a critical aspect of attending to precision. We illustrate various types of imprecision that occur in mathematics classrooms and the ramifications of not addressing this imprecision. Based on our conceptualization of these types and ramifications, we discuss implications for research on classroom mathematics discourse. [For the complete proceedings, see ED583608.]
Transcending Traditional/Reform Dichotomies in Mathematics Education
Author: Metz, Martina
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Educational Change,Teaching Methods,Mastery Learning,Learning Theories,Learning Motivation,Achievement Gains,Guidelines,Pedagogical Content Knowledge,Elementary School Teachers

Here, we report on the development of a theoretical framework for mathematics teaching that looks aside from common traditional/reform dichotomies. Attention is focused on managing the amount of new information students must attend to, while structuring that information in a manner that allows discernment of key features and continuous extension of meaning. Drawing on and combining ideas based on mastery learning and on the variation theory of learning, we propose an alternative where fluency and emergent knowing are inseparable and mutually reinforcing, and motivation is based on success and the challenge of pressing the boundaries of knowing. Gains in student achievement associated with this framework have been significantly faster than national norms. [For the complete proceedings, see ED583608.]
Designing a Stage-Sensitive Written Assessment of Elementary Students&apos; Scheme for Multiplicative Reasoning
Author: Hodkowski, Nicola M.
Date: 2016-11-00
Type: Reports - Descriptive
Subjects: Elementary School Students,Mathematics Instruction,Multiplication,Thinking Skills,Inferences,Student Evaluation,Evaluation Methods,Number Concepts,Interviews,Cues,Item Analysis

In this paper we examine the application of Tzur's (2007) fine-grained assessment to the design of an assessment measure of a particular multiplicative scheme so that non-interview, good enough data can be obtained (on a large scale) to infer into elementary students' reasoning. We outline three design principles that surfaced through our recent effort to devise a sequence of items to assess at which stage--participatory or anticipatory--a child might have constructed the multiplicative double counting (mDC) scheme (Tzur et al., 2013). These principles include the nature and sequencing of prompts, number choice, and authenticity of responses. [For the complete proceedings, see ED583608.]
Dual Analyses Examining Proving Process: Grounded Theory and Knowledge Analysis
Author: Adiredja, Aditya P.
Date: 2016-11-00
Type: Reports - Research
Subjects: Grounded Theory,Undergraduate Students,Novices,Expertise,Knowledge Level,Mathematics Skills,Qualitative Research,Mathematics Education,Majors (Students),Interviews,Student Attitudes,Problem Solving,Mathematical Logic

This report presents dual analyses of an undergraduate student, Cassie, whose work provides nice contrasts between Grounded Theory (GT) analysis and Knowledge Analysis (KA). The analyses highlight particular methodological differences, such as grain size of findings, positioning of novices and more general implications about expert-novice studies. The combination of the two methods results in a more complete and nuanced description of Cassie as a prover, while mediating many of the methodological concerns from the individual analysis. [For the complete proceedings, see ED583608.]
Greater Number of Larger Pieces: A Strategy to Promote Prospective Teachers&apos; Fraction Number Sense Development
Author: Olanoff, Dana
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Fractions,Mathematical Concepts,Concept Formation,Numbers,Knowledge Base for Teaching,Problem Solving,Teaching Methods,Comparative Analysis,Mathematics Instruction

Prospective teachers (PTs) need opportunities to develop fraction number sense, yet little research has explicated how this development occurs. Our research team collaboratively designed a task targeted at helping PTs develop fraction number sense through an exploration of fraction comparison strategies. This paper focuses on developing one particular strategy, which we call Greater Number of Larger Pieces (GLP). We argue that understanding this strategy has the potential to support PTs' number sense, particularly in regards to the measure interpretation of fractions. Analysis of data from two iterations of this task (implemented by five mathematics teacher educators at five US institutions with 124 PTs) showed an improvement in the task's ability to naturally elicit the GLP strategy from PTs. We share our task, results from each iteration, and discuss modifications that we believe led to increased usage of the GLP strategy. [For the complete proceedings, see ED583608.]
Conceptualizing the Teaching Practice of Building on Student Mathematical Thinking
Author: Van Zoest, Laura R.
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Teaching Methods,Mathematics Instruction,Thinking Skills,Instructional Effectiveness,Educational Principles,Classroom Communication,Faculty Development,Preservice Teacher Education

An important aspect of effective teaching is taking advantage of in-the-moment expressions of student thinking that, by becoming the object of class discussion, can help students better understand important mathematical ideas. We call these high-potential instances of student thinking MOSTs and the productive use of them building. The purpose of this paper is to conceptualize the teaching practice of building on MOSTs as a first step toward developing a common language for and an understanding of productive use of high-potential instances of student thinking. We situate this work in the existing literature, introduce core principles that underlie our conception of building, and present a prototype of the teaching practice of building on MOSTs that includes four sub-practices. We conclude by discussing the need for future research and our research agenda for studying the building prototype. [For the complete proceedings, see ED583608.]
Pre-Service and First-Year Teachers&apos; Views on the Influence of Mathematics Methods Textbooks
Author: Brass, Amber
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Methods Courses,Preservice Teachers,Preservice Teacher Education,Beginning Teachers,Mathematics Education,Textbook Content,Textbook Evaluation,Teaching Experience,Teaching Methods,Student Teacher Attitudes,Teacher Attitudes,Semi Structured Interviews,Grounded Theory

We investigated how pre-service and first-year teachers engaged with the pedagogy textbooks from their mathematics methods courses. Sixteen participants--seven pre-service teachers and nine first-year teachers--were interviewed about their interactions with mathematics methods texts and their perceptions about the texts. This paper focuses on participants' views regarding the messages sent by their mathematics methods textbooks about how to teach. Findings describe the tensions that exist between pedagogy textbooks and participants' experiences in the classroom. Implications for teacher educators are also discussed. [For the complete proceedings, see ED583608.]
From Speaking to Writing: The Role of the Reversal Poetic Structure in Problem-Solving
Author: Staats, Susan
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Teaching Methods,Algebra,Problem Solving,Poetry,Discourse Analysis,Role,Sentence Structure,Verbal Communication,Thinking Skills,Speech Communication,Classroom Communication,Undergraduate Students,Video Technology,Interpersonal Communication

Speakers in conversation typically repeat and modify earlier comments. In mathematics conversations, these repetitions, or poetic structures, can facilitate the collaborative discovery of mathematical relationships. A close analysis of 90 turns of an algebraic problem-solving conversation reveals eight types of poetic structures. This report summarizes the general results of the analysis and highlights the role of a particular type of poetic structure, the reversal. In a reversal poetic structure, two elements switch places syntactically, for example, subject and predicate or adjective and noun switch roles. Students working with no teacher intervention used the reversal poetic structure as they rearranged variables and coefficients in their verbal method, and as they transitioned from a spoken method to written mathematical notation. This analysis highlights the ways in which speaking supports mathematical thinking. [For the complete proceedings, see ED583608.]
Not All Questions Are Alike: Creating a Categorization for Student Questions in Mathematics Lessons
Author: Kemmerle, Melissa
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Questioning Techniques,Classification,Secondary School Mathematics,Secondary School Students,Student Developed Materials,Item Analysis,Classroom Communication,Semi Structured Interviews,Teacher Attitudes,Student Surveys,Transcripts (Written Records),Discourse Modes

Students ask a variety of questions during mathematics lessons. Some questions focus on procedures or formal notation, while others focus on ideas, connections, or representations. Student questions are important as they provide vastly different learning opportunities for students. In order to support teachers as they help students learn to ask productive questions in mathematics lessons, we need to first understand the types of questions students ask. This paper describes the process of creating a categorization for student questions in middle and high school mathematics classrooms. [For the complete proceedings, see ED583608.]
Teachers&apos; Instructional Practices within a Connected Classroom Technology Environment to Support Representational Fluency
Author: Gunpinar, Yasemin
Date: 2016-11-00
Type: Reports - Research
Subjects: Mathematics Instruction,Mathematics Achievement,Scores,Pretests Posttests,Algebra,Achievement Gains,Video Technology,Instructional Effectiveness,Teaching Methods,Problem Solving,Educational Technology,Handheld Devices,Technology Uses in Education,Mathematical Concepts,Concept Formation,Observation

The purpose of this study was to examine the ways that teachers use Connected Classroom Technology (CCT) to potentially support achievement on translation problems that require moving between algebraic representations. Four mathematics classrooms were chosen based on their gain scores on pre- and post-test Algebraic translation problems. Two classrooms with the highest and the lowest gain scores were chosen among the classrooms with pre-test scores that were below 50%. This study used video-recorded observational data and found that teachers in effective classrooms created environments wherein students used multiple representations simultaneously and translated between representations through discussion. In contrast, teachers in less effective classrooms fostered environments wherein students used representations independently and missed opportunities to translate representations through discussion. [For the complete proceedings, see ED583608.]
Critical Mathematics Education: Extending the Borders of Mathematics Teacher Education
Author: Goodson-Espy, Tracy
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Mathematics Teachers,Critical Theory,Preservice Teachers,Social Justice,Educational Opportunities,Cultural Pluralism,Cultural Differences,Likert Scales,Qualitative Research,Statistical Analysis,Integrated Curriculum,Controversial Issues (Course Content),Teaching Methods,Pretests Posttests

This study describes efforts at two institutions to integrate critical pedagogy within the context of two mathematics content and pedagogy courses for K-8 pre-service teachers (PSTs). The purpose of the curriculum within these courses was to focus PSTs' attention on how issues pertaining to social justice may be taught within mathematics contexts. The desired goals were for PSTs to: 1) come to appreciate individuals within their own communities as valid practitioners of mathematics; and 2) come to understand the responsibility that they, their school districts, curriculum developers, and others bear to ensure that all students have equitable opportunities to learn mathematics. [For the complete proceedings, see ED583608.]
What Knowledge and Skill Do Mathematics Teacher Educators Need and (How) Can We Support Its Development?
Author: Shaughnessy, Meghan
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Educational Needs,Teaching Skills,Teacher Educators,Methods Courses,Teacher Competencies,Pedagogical Content Knowledge,Skill Analysis,Mathematics Teachers,Educational Practices,Teacher Educator Education

Refocusing teacher preparation on the practice of teaching calls for new and different knowledge and skill. We describe the types of knowledge and skill that teacher educators need in order to teach a practice-focused mathematics methods course and report on one program's exploration of possible supports to develop this knowledge in teacher educators. [For the complete proceedings, see ED583608.]
Praxes Proxies: Revisiting Educational Manipulatives from an Ecological Dynamics Perspective
Author: Abrahamson, Dor
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Educational Technology,Technology Uses in Education,Mathematics Instruction,Constructivism (Learning),Phenomenology,Mathematics Skills,Manipulative Materials,Athletics,Teaching Methods,Training,Praxis,Perceptual Motor Learning

The recent proliferation of technological devices with natural user interfaces (e.g., touchscreen tablets) is regenerating scholarship on the role of sensorimotor interaction in conceptual learning. Some researchers of mathematical education have adopted views from constructivism, phenomenology, enactivism, and ecological dynamics to interpret implicit sensorimotor schemes as both forming and manifesting disciplinary competence. Drawing on these views, this theoretical paper returns to the enduring question of what it means to develop a new skill by way of task-oriented interaction with objects. Beginning with sports then moving to mathematics, we focus on a subcategory of pedagogical artifacts that serve students only during training activities yet constitute proxies for developing target schemes toward normative application. We argue for the contribution of these views to conceptualizing the design of effective mathematics instruction. [For the complete proceedings, see ED583608.]
Perspectives on Teaching Mathematics and Science in Historical and Cultural Contexts
Author: Pourdavood, Ronald G.
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Science Instruction,Cultural Context,Historical Interpretation,Qualitative Research,Student Teacher Attitudes,Preservice Teachers,Transcripts (Written Records),Reading Assignments,Classroom Communication,Class Activities,Teaching Methods,Science Education History,Observation

This qualitative and descriptive study examines the evolution of secondary preservice teachers' views on teaching and learning mathematics and science in historical and cultural contexts. Data were collected throughout participants' enrollment in a semester-long course entitled, Perspectives on Science and Mathematics, which is taken in conjunction with student teaching. Data sources included university classroom observations and field notes as well as preservice teachers' verbal and written responses to class discussions, reading assignments, and course activities. Common themes and categories of response were derived from the triangulation of data to include prospective teachers' critical reflections on teaching and learning. The paper ends with a discussion of findings and concluding remarks. [For the complete proceedings, see ED583608.]
Improving Pre-Service Teachers&apos; Noticing While Learning to Launch
Author: Wieman, Rob
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Preservice Teacher Education,Secondary School Teachers,Mathematics Instruction,Mathematics Teachers,Mathematical Concepts,Misconceptions,Mathematical Logic,Attention,Cognitive Processes,Word Problems (Mathematics),Problem Solving

Effectively launching a task involves surfacing and addressing misconceptions so that students can make progress on the task. Launching a task is supported by teachers' noticing (interpreting and responding to students' thinking). We investigated the degree to which an intervention supported improvements in pre-service secondary teachers' (PSTs') abilities to notice when launching a rich proportional reasoning task. Through the use of representations of practice and an intervention consisting of opportunities to make sense of and discuss multiple choice options for interpreting and responding to students' thinking, we analyzed whether PSTs improved their abilities to notice. After the intervention, PSTs improved in responding to a student's misconception when PSTs concurrently exhibited expertise with interpreting students' thinking. [For the complete proceedings, see ED583608.]
&quot;You Can&apos;t Go on the Other Side of the Fence&quot;: Preservice Teachers and Real-World Problems
Author: Simic-Muller, Ksenija
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Problem Based Learning,Beliefs,Student Teacher Attitudes,Social Influences,Political Influences,Interviews,Problem Solving,Student Surveys,Learning Experience,Questioning Techniques,Case Studies

Our study investigates preservice teachers' perceptions of real-world problems; their beliefs about teaching real-world contexts, especially ones sociopolitical in nature; and their ability to pose meaningful real-world problems. In this paper we present cases of three preservice teachers who participated in interviews that probed their thinking about real-world problems, and asked them to create problems they would consider using in their future classrooms. We use the three cases to propose a potential trajectory for preservice teachers from ambivalence to certainty about teaching mathematics through real-world and controversial contexts. [For the complete proceedings, see ED583608.]
Preservice Teachers&apos; Conception of Effective Problem-Solving Instruction and Their Problem Solving
Author: Son, Ji-Won
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Problem Solving,Preservice Teachers,Instructional Effectiveness,Student Teacher Attitudes,Student Surveys,Beliefs,Mathematics Activities,Teacher Competencies,Teaching Skills,Best Practices,Statistical Analysis

Despite the importance of teachers' conception of effective problem-solving instruction, limited attention is given to this area in the current literature. In this study we examined 96 preservice teachers' (PSTs) views on effective problem-solving instruction and how their conceptions are related and reflected in their views on problem solving and problem solving performance. Analyses of survey responses revealed that our PSTs seem to develop narrow views on effective problem-solving instruction. In addition, we found a positive association between PSTs' conceptions of effective problem-solving instruction and problem solving. However, no such connection exists between PSTs' views problem-solving instruction and their performance. [For the complete proceedings, see ED583608.]
Pre-Service Secondary Mathematics Teachers&apos; Perceptions of Ability, Engagement, and Motivation during Field Experiences
Author: Frank, Toya Jones
Date: 2016-11-00
Type: Speeches/Meeting Papers
Subjects: Secondary School Mathematics,Preservice Teachers,Preservice Teacher Education,Field Experience Programs,Student Teacher Attitudes,Methods Courses,Secondary School Students,Learner Engagement,Student Interests,Beliefs,Student Diversity,Focus Groups,Autobiographies,Cognitive Ability,Mathematical Aptitude,Accountability,Cooperating Teachers,Teacher Role,Student Motivation,Qualitative Research

We conducted a self-study to learn more about how to support the first author's pre-service teachers (PSTs) during their field experiences in an introductory secondary mathematics methods course. The findings highlight how the PSTs' perceptions of the secondary students' mathematics ability was closely related to how they viewed the students' levels of engagement and interest. The data also indicated that PSTs often diminished the role that the cooperating teachers played in co-constructing student ability, motivation and engagement, particularly in situations where the students displayed unfavorable behaviors. The findings inform curricular development for methods courses and field experiences, both for the authors and for the mathematics educators who support PSTs in diverse school settings. [For the complete proceedings, see ED583608.]
Issues in Evaluating Special Education Teachers: Challenges and Current Perspectives
Author: Johnson, Evelyn S.
Date: 2016-00-00
Type: Reports - Evaluative
Subjects: Special Education Teachers,Teacher Evaluation,Observation,Evidence Based Practice,Disabilities,Professional Recognition,Educational Practices,Individualized Instruction,Scoring Rubrics,Teacher Improvement,Interrater Reliability,Outcomes of Education

Observation systems can provide teachers with information about how to improve their instructional practice and can lead to improved student outcomes. However, most observation systems have not been designed to address issues specific to special education. An effective special education teacher evaluation system must measure and provide targeted, corrective feedback on instructional practice, rely on the use of raters and observers with content specific expertise and be correlated with individualized student growth measures. In this article, we explore the question of whether objective measures of special education teaching can be created and implemented in a valid and fair way that yields useful and reliable results, and examine issues related to the content of the observation, requirements for raters, and the type of feedback that will be required to support instructional change in the context of a recently funded research project, Recognizing Effective Special Education Teachers (RESET). [This article was published in &quot;Texas Education Review&quot; v4 n1 p71-83 2016.]