ethanporcaro/eric-fulltext-meta huggingface dataset:
Connecting Teaching and Learning in Curriculum Adaptations
Author: Choppin, Jeffrey
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Middle School Teachers,Knowledge Base for Teaching,Teaching Methods,Learning Strategies,Cognitive Processes,Student Centered Learning,Mathematics Instruction,Secondary School Mathematics,Discussion (Teaching Technique),Interviews,Video Technology,Curriculum Development,Mathematics Curriculum

This study of six teachers focuses on the ways they organized the classroom discourse, attended to student thinking, and adapted complex tasks from a Standard-based middle school curriculum. The study explores Cohen's (2011) premise that the knowledge teachers develop is related to their attentiveness to student teaching. This study explores the relationship between the extent to which teachers were successfully able to elicit and organize instruction around student strategies and their ability to productively adapt tasks in terms of being responsive and maintaining cognitive demand. The results show that teachers with the most student-centered discourse practices were also able to provide the most detailed justifications for task adaptations and to productively adapt tasks from the Connected Mathematics Program (CMP) curriculum. [For the complete proceedings, see ED584443.]
Visually Grouping Operands: Perceptual Factors Influence Arithmetic Performance
Author: Jiang, Matthew J.
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Equations (Mathematics),Problem Solving,Mathematical Concepts,Undergraduate Students,Symbols (Mathematics),Arithmetic,Group Activities,Error Patterns

Perceptual characteristics of mathematical equations may influence solvers' problem solving. For example, in a study of equations involving addition and multiplication, Landy and Goldstone (2010) showed that participants tended to perform narrowly spaced operations first, suggesting that spacing affects how symbols are grouped for problem solving. Building on this past work, we examined whether perceptual factors affect participants' interpretations of the minus sign. In an experiment with undergraduates, we manipulated the spacing of the operands and the position of the minus sign relative to its neighboring operands. Both the operands' spacing and the position of the minus sign affected performance. These results hold implications for the processing of symbolic representations and for mathematics education. [For the complete proceedings, see ED584443.]
Correspondence and Covariation: Quantities Changing Together
Author: Ellis, Amy B.
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Concepts,Cognitive Processes,Mathematical Logic,Comprehension,Algebra,Middle School Students,Grade 8,Educational Technology,Technology Uses in Education

Exponential functions are important topic in school algebra and in higher mathematics, but research on students' thinking suggests that understanding exponential growth remains an instructional challenge. This paper reports the results of a small-scale teaching experiment with students who explored exponential functions in the context of two continuously covarying quantities, height and time. We present two major conceptual paths that occurred in the development of an understanding of exponential growth, the covariation view and the correspondence view, and discuss the influence of each perspective on the growth of students' understanding. [For the complete proceedings, see ED584443.]
Incidents of Intrusion: Disruptions of Mathematics Teaching and Learning by the Traditional Western Worldview
Author: Russell, Gale L.
Date: 2013-11-00
Type: Reports - Research
Subjects: Mathematics Instruction,Teaching Methods,World Views,Student Attitudes,Mathematics Achievement,Western Civilization,Indigenous Knowledge,Learning Processes,Teacher Attitudes,Elementary School Teachers,Elementary School Students,Rural Schools,Canada Natives,Foreign Countries,American Indians,American Indian Students,Observation,Surveys,Audio Equipment

This paper reports on a theme, the intrusion of the Traditional Western worldview, emerging from an ongoing study of the impact of teachers' engagement in the Transreform approach to the teaching and learning of mathematics on students' affective and cognitive responses to and achievement in mathematics. Newly theorized (Russell &amp; Chernoff, 2011, 2012), the Transreform approach occurs when the teaching and learning of mathematics is grounded within an Indigenous worldview. This paper identifies and analyzes incidents captured within the study's data that demonstrate ways in which the Traditional Western worldview can intrude on an Indigenous worldview and upon the teaching and learning of mathematics. [The authors of this paper acknowledge partial funding of this research by the Dr. Stirling McDowell Foundation for Research Into Teaching. For the complete proceedings, see ED584443.]
Gesture as a Window to Justification and Proof
Author: Boncoddo, Rebecca
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Nonverbal Communication,Undergraduate Students,Mathematical Logic,Problem Solving,Validity,Learning Theories,Coding

The role of the body, particularly gesture, in supporting mathematical reasoning is an emerging area of research in mathematics education. In the present study, we examine undergraduate students providing a justification for a task about a system of alternating gears, which involves concepts of number relating to even/odd patterns. Some participants were directed to perform gestures relevant to alternation and parity before attempting their justification, while others were not. Although these directed actions did not seem to influence the gestures participants used to solve the problem, we found an important relationship between gesture and mathematical reasoning. In particular, certain types of gestures during problem solving were associated with valid justifications. This research provides insight into the link between action and mathematical reasoning, and has implications for supporting students' proof activities. [For the complete proceedings, see ED584443.]
The Effects of Diagrams and Questioning-While-Reading on Learning from a Statistics Lesson
Author: Clinton, Virginia
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Teaching Methods,Probability,Undergraduate Students,Visual Aids,Questioning Techniques,Pretests Posttests,Randomized Controlled Trials,Comparative Analysis,Problem Solving,Scores,Hypothesis Testing,Statistical Analysis

This study examined the effectiveness of two methods of increasing student learning from posterior probability lessons: diagrams and questioning while reading. Undergraduate students (N = 245) read a lesson in one of three diagram conditions and one of three questioning-while-reading conditions (embedded questions, elaboration interrogations, and control in which they read twice). Diagrams helped students in the control group accurately solve posterior probability problems on the posttest, but only if the information presented in the diagram was also presented in the text. Contrary to expectation, students in the control condition accurately solved more posterior probability problems on the posttest than did students in the questioning conditions. Poor answer quality for the embedded questions and elaborative interrogations is a possible explanation for the unexpected results. [For the complete proceedings, see ED584443.]
Collaborative Design Work of Teacher Educators: A Case from Statistics
Author: Lee, Hollylynne S.
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Statistics,Teacher Educators,Graduate Study,Thinking Skills,Mathematical Concepts,Instructional Design,Teacher Collaboration,Faculty Development,Pedagogical Content Knowledge,Knowledge Base for Teaching,Preservice Teachers,Teacher Education Programs,Teacher Attitudes,Student Attitudes,Probability

Our study, situated within graduate-level courses for teachers focused on statistics, illustrates work across institutions for making sense of teachers' statistical thinking. Using a common assessment instrument, we identify and discuss four items that indicate strong statistical thinking and two that highlight concepts with which teachers struggle. We discuss potential course elements that may be contributing to areas of success. Implications for collaborative course (re)design and shared assessment items are discussed. [For the complete proceedings, see ED584443.]
Strategically Chosen Examples Leading to Proof Insight: A Case Study of A Mathematician&apos;s Proving Process
Author: Lockwood, Elise
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Validity,Mathematical Logic,Mathematics,Case Studies,College Faculty,Mathematics Education,Interviews

Examples play a critical role in the exploration and proving of conjectures. Although proof has been studied extensively, the precise ways in which examples might facilitate successful proofs are not well documented or understood. Working within a larger set of studies that argue for the value of examples in proof-related activity, in this paper we present a case study of one mathematician's work on a conjecture in which his strategic, intentional use of examples led to a proof of that conjecture. By examining his work in detail, we highlight specific mechanisms by which the mathematician's examples led to successful proof production. These mechanisms shed light on precise ways in which examples can directly lead to proof and inform our understanding of the conceptual landscape of the interplay between examples and proof. [For the complete proceedings, see ED584443.]
SLOPE: A Network of Connected Components
Author: Nagle, Courtney R.
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Mathematics Curriculum,Mathematical Concepts,Secondary School Mathematics,High School Students,Middle School Students,Mathematics Instruction,Algebra,Calculus

In this study, we build on previous work on conceptualizations of slope to suggest a framework of slope across the landscape of the mathematics curriculum. Data from multiple studies on students', teachers', and college instructors' conceptualizations of slope are revisited in light of theory on procedural versus conceptual understanding and visual versus analytic interpretations of slope. This synthesis leads to a description of five key slope components. A detailed description of each component is provided and implications for future research are discussed. [For the complete proceedings, see ED584443.]
Middle Grades Teachers&apos; Enactment of Knowledge of Sampling
Author: Cross, Dionne I.
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Middle School Teachers,Statistics,Pedagogical Content Knowledge,Video Technology,Qualitative Research,Mathematics Instruction,Teaching Methods,Classroom Communication,Sampling,Middle School Students,Task Analysis

In this study, we examined the ways in which teachers' statistical knowledge is enacted during instructional practice. Using classroom video recordings from three middle-grades' teachers, we qualitatively analyzed the conversations around a task designed to develop students' knowledge of statistical sampling. Our analyses showed how teachers' selection and use of contexts during instruction impacted students' opportunities for statistical reasoning. Our research extends other literature that has begun to identify the statistical knowledge needed for teaching. [For the complete proceedings, see ED584443.]
Linear Algebra in New Environments (LINE)
Author: Cooley, Laurel
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Algebra,Mathematics Instruction,Learning Theories,Communities of Practice,Learning Modules,College Faculty,College Students,Student Attitudes,Validity,Mathematical Logic,Group Discussion

We report on some results from a multiyear development of new techniques and materials for teaching linear algebra. Our goals were to (a) to create a professional learning community across STEM disciplines, (b) to combine expertise in content and pedagogy in designing effective instructional practice, and (c) to use learning theories to support the conceptual alignment of content and pedagogical goals. In particular, our approach combines the use of domain-specific problems, APOS learning theory, and the development of the professional learning community. This set of practices was developed and deployed across four diverse institutions, in diverse linear algebra courses, and was effective across this diversity. We discuss the development of teaching materials, and present reflections from students and faculty which were shared during and after these &quot;modules&quot; were used in classes. [For the complete proceedings, see ED584443.]
A Characterization of Teachers&apos; Implementations of a Mathematical Decision-Making Curriculum
Author: Holstein, Krista
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Curriculum,Mathematics Instruction,Teacher Surveys,Teacher Attitudes,Teaching Methods,Correlation,Mixed Methods Research,Pedagogical Content Knowledge,Program Implementation,Decision Making,Instructional Effectiveness,Teachers,Observation,Educational Practices,Alignment (Education),Expectation,Elementary Secondary Education

The purpose of this study was to examine teachers' implementation of a specific mathematics curriculum and how their conceptions influenced this implementation. An innovative, powerful tool, known as &quot;teacher logs,&quot; was used to examine teachers' implementations of the curriculum; a survey was used to study teachers' conceptions related to their implementations. Results suggest that teachers tend to implement the materials closely to the written text, but there was variety shown both within and among teachers. A relationship was shown between teachers' implementation levels and their beliefs about mathematics and their beliefs about students. The results of this study reveal that teachers may or may not stray from the authors' intended curriculum, and whether or not they stray often relates to their conceptions. [For the complete proceedings, see ED584443. For a related dissertation, see ED550966.]
The Limit Notation as a Mediator of Mathematical Discourse
Author: Güçler, Beste
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Logic,Thinking Skills,Symbols (Mathematics),Case Studies,Undergraduate Students,College Mathematics,Calculus,Mathematics Teachers

Symbols play important roles in higher-level mathematical thinking by providing flexibility and reducing cognitive load. However, they often have a dual nature since they can signify both processes and products of mathematics. The limit notation is considered to be a visual and symbolic mediator that reflects such duality, which presents challenges for students. This study focuses on one instructor's utilization of the limit notation and examines how it mediates his discourse on limits. The findings indicate that the process and product aspects of limit were both present in the instructor's use of the limit notation. Although he differentiated between these two aspects depending on the mathematical context, the distinction remained implicit for the students in the classroom. The study concludes that it is important for teachers to unpack the meanings inherent in symbols in the classroom to enhance mathematical communication. [For the complete proceedings, see ED584443.]
Teachers&apos; Decisions on Task Enactment and Opportunities for Students to Learn
Author: Kim, Ok-Kyeong
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Elementary School Mathematics,Decision Making,Academic Achievement,Fidelity,Instructional Materials,Instructional Design,Elementary School Teachers,Mathematics Teachers,Observation,Interviews

Drawing on data from teachers using various elementary mathematics curriculum programs, this study highlights prevalent decisions teachers make to enact the task from the written curriculum and the potential of such decisions for student learning. In doing so, we examine teachers' instructional design decisions, especially those that teachers make when they face things that are not specified in the curriculum and when they see the need to fill in a gap in the teacher's guide in order to enact the task in their classrooms. We also examine whether such decisions can actually create opportunities for students to learn. [For the complete proceedings, see ED584443.]
Evaluating the Impact of Computer-Based and Traditional Learning Environments on Students&apos; Knowledge of Algebra
Author: Krupa, Erin
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Algebra,Mathematics Instruction,Quasiexperimental Design,Comparative Analysis,Multiple Choice Tests,Problem Solving,Computer Assisted Testing,Lecture Method,Mathematics Tests,Mathematics Achievement,College Students,Teaching Methods,Thinking Skills,Statistical Analysis,Scores,Predictor Variables,College Entrance Examinations

We share results from a quasi-experimental study in which we compared achievement between traditional lecture-based and computer-based sections of college algebra on a common multiple choice exam as well as performance on problem solving items. Students in the computer-based group performed better on the final exam and were also more likely to complete the problem solving tasks correctly than students in the traditional courses. However, the computer-based group showed limited ability to interpret an equation and relate it to a contextual situation. [For the complete proceedings, see ED584443.]
Characterizing Pivotal Teaching Moments in Experienced Mathematics Teachers&apos; Practice
Author: Sun, Li
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Teachers,Mathematics Instruction,Video Technology,Teacher Education,Algebra,Mathematical Logic,Knowledge Base for Teaching,Educational Opportunities,Secondary School Teachers,Decision Making,Teaching Methods

This report presents the findings of a study that was designed to characterize the pivotal teaching moments (PTMs), as defined by Stockero &amp; Van Zoest, (2012), faced by experienced mathematics teachers. To better understand how experienced mathematics teachers identify the PTMs and appropriately respond to them, the mathematics teaching videos from Annenberg Learner's multimedia resources were analyzed. Implications for teacher education are discussed. [For the complete proceedings, see ED584443.]
How Are Geometric Proof Problems Presented? Conceptualizing and Measuring Teachers&apos; Recognition of the Diagrammatic Register
Author: Herbst, Patricio
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Geometry,Mathematics Instruction,Teaching Methods,High School Students,Mathematical Logic,Visual Aids,Vignettes,Spatial Ability,Thinking Skills,Mathematics Teachers,Reliability,Statistical Analysis,Correlation,Recognition (Psychology),Teacher Surveys,Teacher Attitudes

We describe the development of measures of teachers' recognition of an instructional norm--that proof problems in high school geometry are presented in a diagrammatic register. A first instrument required participants to openly respond to depictions of classroom scenarios in which the norm was breached. A second instrument was a survey that required participants to rate the extent to which they agreed with various explicit statements about instruction. A third instrument capitalized on pros of the other two. We demonstrate how this instrument development process improved our conceptualization of the components included in the diagrammatic register norm. [For the complete proceedings, see ED584443.]
Individual Adherence to Inquiry-Oriented Norms of Defining in Advanced Mathematics
Author: Dawkins, Paul Christian
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Undergraduate Students,Advanced Courses,Mathematics Instruction,College Faculty,Teacher Attitudes,Mathematics Teachers,Values,Definitions,Student Attitudes,Expectation,Abstract Reasoning,Mathematical Logic,Observation,Interviews,Personal Autonomy,Inquiry

This study investigates students' individual patterns of adherence to a norm for creating and assessing definitions in an undergraduate real analysis classroom. Our findings indicate that, though all students understood the expectation to define, students differed in their individual adherence to the norm depending upon their perception of the nature of the defining activity and their associated role in the classroom. While some students primarily attributed the expectation to define to the teacher (taken-as-expected), others understood the expectation as truly shared as a means toward classroom learning (taken-as-beneficial). A third group of students internalized the expectation as a means of their membership in the mathematical community (taken-as-meaningful) and were therein willing to challenge the professor's defining choices in light of their values for mathematical defining. [For the complete proceedings, see ED584443.]
Understanding Prospective Teachers&apos; Levels of Geometric Thoughts: Insights from a Discursive Analysis
Author: Wang, Sasha
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Geometric Concepts,Discourse Analysis,Interviews,Pretests Posttests,Preservice Teachers,Preservice Teacher Education,Student Teacher Attitudes,Mathematics Tests,Achievement Rating,Knowledge Level,Mathematical Logic

The study investigates the characteristics of prospective teachers' geometric discourses at the van Hiele model of thinking (1959/1985), using Sfard's (2008) discursive framework. In this report, I align two prospective teachers' pre- and post-van Hiele geometry test (Usiskin, 1982) results with the analyses of their geometric discourses from clinical interviews, to illustrate changes in geometric discourse when a student's test results showed no change in van Hiele levels, and changes in geometric discourse when a student developed her thinking to the next van Hiele level. Revisiting the van Hiele model of thinking, complemented with a discursive lens, helped to understand learning as change in discourses, as prospective teacher develop thinking toward a higher van Hiele level. [For the complete proceedings, see ED584443.]
Supporting Teachers&apos; and Students&apos; Knowledge of Geometric Similarity
Author: Seago, Nanette
Date: 2013-11-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Geometry,Faculty Development,Knowledge Base for Teaching,Teacher Participation,Video Technology,Teaching Methods,Mathematical Logic,Thinking Skills,Comparative Analysis,Pretests Posttests,Mathematics Teachers,Common Core State Standards,Transformations (Mathematics),Geometric Concepts,Inservice Teacher Education,Experimental Groups,Control Groups

The main goal of the Learning and Teaching Geometry (LTG) project is to build professional development (PD) materials that provide opportunities for teachers to engage in learning about geometric similarity through the use of video cases, in which specific and increasingly complex mathematical ideas are presented within the dynamics of classroom practice. The central component of the LTG materials is the Foundation Module, which includes 30 hours of PD and is intended to provide teachers with a thorough grounding in key mathematical and pedagogical issues related to similarity. Field test data indicate that the Foundation Module supports gains in both teachers' and students' knowledge of similarity. [For the complete proceedings, see ED584443.]