ethanporcaro/eric-fulltext-meta huggingface dataset:
The Development of the Visual Perception of the Cartesian Coordinate System: An Eye Tracking Study
Author: Chumachemko, Dmitry
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Eye Movements,Visual Perception,Mathematics Education,Geometry,Expertise,Novices,College Freshmen,High School Students

The aim of the research is to investigate the transformation of the perception process through mathematics education, by an example of scanning the Cartesian coordinate system in order to locate a target point. We compared participants with different competence in mathematics. Historically, motion along axes appeared as a specific &quot;theoretical&quot; action that constituted the Cartesian coordinate system. We detected this specificity as a dominance of vertical and horizontal saccades of eye movements in perception processes of all groups of participants. Experts-novices differences dealt with an ability of experts to use additional essential information and to discard unnecessary data. Furthermore, a lot of evidences of shortening of the perception actions from novices to experts are presented. [For the complete proceedings, see ED597799.]
Using Thematic Analysis to Study Curriculum Enactments
Author: Choppin, Jeffrey
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Curriculum,Curriculum Development,Instructional Materials,Mathematical Concepts,Mathematics Instruction,Discourse Analysis,Language Usage,Semantics,Concept Mapping,Concept Formation

We use thematic analysis to explore how mathematical concepts are developed in four enactments of the same task. Thematic analysis emerges from Systemic Functional Linguistics and provides a means to explore the development of mathematical ideas in the classroom discourse. Thematic analysis was used to explore how themes related to the comparison of like quantities were developed in a task designed to introduce different types of comparisons and different ways to represent comparisons. The thematic analysis showed similarities across the four teachers' enactments, suggesting an influence from the design of the task. There were also differences that pointed to teachers' different emphasis and their own understanding of the thematic pattern. [For the complete proceedings, see ED597799.]
&quot;That Sounds Greek to Me!&quot; Primary Children&apos;s Additive and Proportional Responses to Unreadable Word Problems
Author: Degrande, Tine
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Word Problems (Mathematics),Logical Thinking,Mathematical Logic,Elementary School Students,Grade 3,Grade 4,Grade 5,Grade 6,Mathematical Concepts,Greek,Age Differences,Foreign Countries,Addition

Both additive and proportional reasoning are types of quantitative analogical (QA) reasoning. We investigated the development and nature of primary school children's QA reasoning by offering two missing-value word problems to 3rd to 6th graders. In one problem, ratios between given numbers were integer, in the other ratios were non-integer. These word problems were written in the Greek alphabet, and thus totally incomprehensible to the children. QA answers considerably increased with age. Younger children more frequently chose additive relations, whereas older children chose more proportional relations. The nature of the ratios between the given numbers also affected the answers, particularly in 5th grade. [For the complete proceedings, see ED597799.]
Teachers&apos; Beliefs about Students&apos; Generalization of Learning
Author: Diamond, Jaime Marie
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Teacher Attitudes,Transfer of Training,Beliefs,Urban Schools,Mathematics Teachers,Mathematical Concepts,Student Attitudes,Problem Solving,Novelty (Stimulus Dimension),Self Concept,Learning

Researchers in psychology and mathematics education have been conducting systematic investigations of students' generalization (or transfer) of learning since the beginning of the 20th century. However, we do not know how teachers, the people typically associated with student learning, think about this phenomenon. This study, thus, identified teachers' beliefs about students' generalization of learning. Five categories of teacher beliefs were identified, highlighting the importance of bringing teachers into the ongoing transfer conversation as the categories identified both extend current conceptualizations of transfer into the domain of mathematics education and identify new beliefs regarding students' transfer of learning. [For the complete proceedings, see ED597799.]
Shaping Mathematics Classroom Discourse: Relating Professional Development and Classroom Practice
Author: Cavanna, Jillian M.
Date: 2014-00-00
Type: Reports - Research
Subjects: Discourse Analysis,Classroom Communication,Mathematics Instruction,Faculty Development,Teacher Attitudes,Teaching Methods,Middle School Teachers,Mathematics Teachers

Professional development that furthers teachers' understanding of mathematics classroom discourse offers possibilities to improve students' learning of mathematics. It is not clear, however, how teachers relate such professional development experiences to their own classroom practice. In this paper, I discuss the features of mathematics classroom discourse that were most salient for teachers in relation to their classroom practice as they engaged in professional development focused on secondary mathematics classroom discourse. [For the complete proceedings, see ED597799.]
Teachers&apos; Productive Mathematical Noticing during Lesson Preparation
Author: Choy, Ban Heng
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Teachers,Observation,Lesson Plans,Fractions,Student Evaluation,Mathematics Instruction,Elementary School Teachers,Foreign Countries,Teaching Methods,Elementary School Mathematics,Vignettes,Mathematical Concepts

This study uses lesson study to investigate what mathematics teachers notice about students' mathematical reasoning during the planning of a lesson on fractions. Most research examines teaching noticing during or after a lesson, and focuses on the specificity of what teachers notice as a characteristic of noticing expertise. In this paper I propose a new notion of productive noticing, and apply it to analyse two vignettes of teachers' mathematical noticing during lesson preparation. Findings suggest that teachers' noticing is most productive when it goes beyond the specificity of what teachers notice to include justification based on what they have noticed about students' thinking. The study also demonstrates the usefulness of this construct in analysing what mathematics teachers notice when planning lessons. [For the complete proceedings, see ED597799.]
Cognition in the Workplace: Analyses of Heuristics in Action
Author: Chahine, Iman C.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Vendors,Employees,Bus Transportation,Mathematics Activities,Heuristics,Problem Solving

Studies on cognition have capitalized on the role of contexts and experience in shaping our cognitive competence. In the past few decades, the mathematical education research field has begun to pay increased attention to the mathematics practices of both adults and children that take place in non-academic settings. As a result, theoretical fields such as ethnomathematics, situated cognition, and workplace mathematics have gained prominence. In this paper, we use Vergnaud's theory of conceptual fields to highlight the workplace mathematical activities of two groups of practitioners-Street vendors in Lebanon, and Bus conductors in India. [For the complete proceedings, see ED597799.]
How Students Come to Understand the Domain and Range for the Graphs of Functions
Author: Cho, Peter
Date: 2014-00-00
Type: Reports - Research
Subjects: Community Colleges,Two Year College Students,College Mathematics,Mathematical Concepts,Graphs,Learning Strategies,Knowledge Level,Misconceptions,Comprehension,Difficulty Level

To understand the mathematical concept of function, students must understand certain subconcepts, such as domain and range. Many researchers have studied students' understanding of functions, but no study has focused on how students come to understand the domain and range for the graphs of functions. In this study, we identified four common strategies, two transitional conceptions, and two representational challenges evidenced by students. In general, determining the range was more difficult than determining the domain for the students. [For the complete proceedings, see ED597799.]
Is a Mathematics Teacher&apos;s Efficacy Influential to Their Students&apos; Mathematics Self-Efficacy and Mathematical Achievement?
Author: Chang, Yu-Liang
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Grade 5,Elementary School Teachers,Teacher Effectiveness,Self Efficacy,Elementary School Students,Mathematics Instruction,Mathematics Achievement,Foreign Countries,Teacher Influence,Correlation,Predictor Variables

The main purpose of this study was to examine the effects of fifth-grade mathematics teachers' efficacy (MTE) on their students' mathematics self-efficacy (SMSE) and mathematical achievement (SMA) in the classroom. Two instruments (for MTE and SMSE) were administered to 62 classes (62 teachers and 1283 fifth-graders) for gathering data, associated with SMA scores in school. Corresponding statistical analyses were applied to the obtained data. The findings revealed that mathematics teachers' efficacy beliefs were significantly influential to both SMSE and SMA. It also showed that MTE ratings could effectively predict SMA. Consequently, suggestions derived from findings and discussions were proposed for further improvement of these mathematics teachers' efficacy and, in turn, for enhancing fifth-graders' mathematics self-efficacy and mathematical achievement in the future. [For the complete proceedings, see ED597799.]
Supporting the Introduction to Formal Proof
Author: Cirillo, Michelle
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Validity,Mathematical Logic,Geometry,Teaching Methods,Secondary School Mathematics,High Schools,Faculty Development,Mathematical Concepts,Concept Formation,Scaffolding (Teaching Technique)

In this study, a tool that worked to support teachers with the introduction to formal proof in geometry is discussed. The tool helped teachers navigate the &quot;shallow end&quot; of proof. More specifically, the tool was shown to support teachers with introducing and scaffolding proof. Findings from this study suggest that the tool may be useful for supporting formal reasoning in geometry as well as other areas. [This project is supported by a grant from the Knowles Science Teaching Foundation. For the complete proceedings, see ED597799.]
The Teaching Activity and the Generation of Mathematical Learning Opportunities
Author: Ferrer, Miquel
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Secondary School Mathematics,Secondary School Teachers,Educational Opportunities,Mathematics Education,Geometry,Grade 8,Urban Schools,Group Discussion,Secondary School Students,Intervention,Teaching Methods,Learning Activities

We present a case study that has been developed to inform about the teaching activity of a secondary mathematics teacher in a whole group discussion and the mathematical learning opportunities generated for the students in this classroom context. For data of one lesson we determine the episodes that shape the whole group discussion. For each episode we then examine the effects of the observed actions on the type of learning that can be encouraged. Our research reveals significant relationships between the teaching activity of the teacher and the creation and potential exploitation of mathematical learning opportunities on the part of the students. [For the complete proceedings, see ED597799.]
Using ICT in Teaching a Specific Mathematics Concept: Graphs of Logarithmic Functions
Author: Getenet, Seyum Tekeher
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Concepts,Computer Software,Graphs,Teaching Methods,Teacher Education Programs,Teacher Educators,Preservice Teachers,Mathematics Teachers,Educational Technology,Technology Uses in Education,Concept Formation,Foreign Countries

This paper describes the use of the free software, to teach graphs of logarithmic functions at an Ethiopian College of Teacher Education. Data comprised two video-recorded lessons and interview data provided by a mathematics teacher educator, and three primary school mathematics pre-service teachers who were in the class of learners. Pre-service teachers using Microsoft Mathematics readily understood and described properties of logarithmic functions as the bases varied. The study highlights the importance of illustrating the use of particular software to teach specific mathematics concepts. [For the complete proceedings, see ED597799.]
Algebraic Expressions of Deaf Students: Connecting Visuo-Gestural and Dynamic Digital Representations
Author: Fernandes, Solange Hassan Ahmad Ali
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Deafness,Algebra,Mathematics Instruction,Educational Technology,Technology Uses in Education,Teaching Methods,Mathematical Logic,Learning Activities,Cognitive Processes,Foreign Countries,Grade 9,Visual Aids,Sign Language

This paper explores the algebraic expressions of deaf learners as they explore and construct sequences using the digital microworld Mathsticks. More specifically, it attempts to identify how the deaf students coordinated bodily, discursive and digital resources in order to attribute their own personal senses to the notion of variable. Examples of their interactions with the tasks and tools are analysed to identify evidence of the presence of the three conditions of algebraic thinking, indeterminacy, denotation and analyticity. Our findings suggest that the creation of a shared sign &quot;secret number&quot; to represent the idea of variable was central in facilitating the students to adopt algebraic rather than arithmetic approaches and to appropriate the idea of a general term. [For the complete proceedings, see ED597799.]
Why Lectures in Advanced Mathematics Often Fail
Author: Fukawa-Connelly, Tim
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Lecture Method,Teaching Methods,Mathematics Teachers,Course Content,Student Attitudes,Comprehension,College Faculty,College Students,Mathematical Logic,Validity,Notetaking,College Mathematics

This case study investigates the effectiveness of a lecture in advanced mathematics. We video recorded a lecture delivered by an experienced professor. Using video recall, we then interviewed the professor to determine the content he intended to convey and we analyzed his lecture to see if and how this content was conveyed. We also interviewed six students to see what they understood from this lecture. The students did not comprehend much of the content that the professor intended to cover in his lecture. We propose three reasons for why students failed to grasp much of the content that the professor intended to convey. [For the complete proceedings, see ED597799.]
Mathematical Activities in a Social Learning Framework: How Multimodality Works in a Community of Practice
Author: Ferrara, Francesca
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Communities of Practice,High School Students,Calculus,Student Experience,Social Development,Geometry,Grade 12,Advanced Placement Programs,Foreign Countries,Mathematical Concepts,Handheld Devices,Technology Uses in Education,Educational Technology,Computer Software,Interaction,Mathematics Activities

In this paper, we explore an approach to understanding how multimodality works in a community of practice. Using a social learning framework, we show how a community of practice, involving a pair of high school students, engaged in perceptual, bodily, and imaginary experiences while discussing about calculus concepts in a dynamic geometry environment. Our findings suggest that learners' multimodal experiences emerge in both visible and invisible uses of the artefact and are situated in the mathematical activities. This study enriches our understanding about how students participate in the mathematical activities with dynamic geometry environments. [For the complete proceedings, see ED597799.]
Mathematical Knowledge for Teaching Problem Solving: Lessons from Lesson Study
Author: Foster, Colin
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Problem Solving,Communities of Practice,Knowledge Base for Teaching,Pedagogical Content Knowledge,Faculty Development,Teacher Collaboration,Teaching Methods,Grade 10,Secondary School Mathematics,Foreign Countries,Mathematical Concepts,Learning Processes

Although the importance of mathematical problem solving is now widely recognised, relatively little attention has been given to the conceptualisation of mathematical processes such as representing, analysing, interpreting and communicating. The construct of Mathematical Knowledge for Teaching (Hill, Ball &amp; Schilling, 2008) is generally interpreted in terms of mathematical content, and in this paper we describe our initial attempts to broaden MKT to include mathematical process knowledge (MPK) and pedagogical process knowledge (PPK). We draw on data from a problem-solving-focused lesson-study project to highlight and exemplify aspects of the teachers' PPK and the implications of this for our developing conceptualisation of the mathematical knowledge needed for teaching problem solving. [For the complete proceedings, see ED597799.]
Exploring Mathematics Together: Figuring the Worlds of Teachers and Prospective Teachers
Author: Fede, Bryan
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Teacher Attitudes,Preservice Teachers,Teacher Education Programs,Theory Practice Relationship,Mentors,Power Structure,Cooperating Teachers,Expertise,Institutes (Training Programs),Summer Programs,Interprofessional Relationship,Elementary School Mathematics

This paper reports on an intentionally constructed hybrid space, the Odyssey, as an approach to address the gap between theory and practice in teacher education programs. In the Odyssey, prospective teachers and mentor teachers engaged in joint explorations of mathematics. We analyzed the interactions among participants using the concepts of figured worlds and positional identities (Holland, Lachicotte, Skinner, &amp; Cain, 1998). Findings point to the potential of experiences such as the Odyssey to challenge the power differential that often exists between mentor and prospective teachers. Furthermore the act of engaging in mathematical activities together may encourage prospective teachers to elaborate on their mathematical explanations as well as allow mentor teachers the opportunity to (re)visit mathematical ideas. [For the complete proceedings, see ED597799.]
Culture and Disadvantage in Learning Mathematics
Author: Gates, Peter
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Socioeconomic Status,Ethnicity,Predictor Variables,Mathematics Achievement,Family Income,Parent Background,Educational Attainment,Foreign Countries,Mathematics Curriculum,Poverty,Elementary Secondary Education

There is concern internationally that socio-economic class and ethnicity remain the most significant predictors of outcomes in mathematics; performance is often largely dependent on family income and level of parental education. Consequently the influence of pupils' socio-economic backgrounds remains a major challenge to those of us in the field concerned with achieving equitable education. However, the ways in which socio-economic factors play out in different parts of the world subject to different political systems and structures, remains unclear. In this paper we present an analysis of mathematics achievement in Penang to offer a localized perspective on the ways in which socio-economic status and ethnicity affect achievement. [For the complete proceedings, see ED597799.]
The Case for Learning Trajectories Research
Author: Ellis, Amy B.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Learning Processes,Secondary School Mathematics,Secondary School Students,Academic Standards,Curriculum Development,Mathematics Curriculum,National Standards,Benchmarking,Affordances,Student Educational Objectives,Mathematical Concepts,Algebra

This paper addresses the role of learning progressions in informing many international standards documents, discussing the affordances and limitations of building standards and curricula from a learning progression model. An alternate model, the hypothetical learning trajectory, is introduced and contrasted with learning progressions. Using the example of exponential functions, learning progressions are compared to learning trajectories in terms of their theoretical origins and practical implications. Recommendations for further work building learning trajectories in secondary mathematics are discussed. [For the complete proceedings, see ED597799.]
Exploring Fraction Comparison in School Children
Author: Gómez, David M.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Fractions,Mathematics Instruction,Grade 5,Grade 6,Grade 7,Error Patterns,Foreign Countries,Mathematics Skills,Bias,Numbers,Mathematical Concepts,Mathematical Logic

The application to rational numbers of the procedures and intuitions proper of natural numbers is known as Natural Number Bias. Research on the cognitive foundations of this bias suggests that it stems not from a lack of understanding of rational numbers, but from the way the human mind represents them. In this work, we presented a fraction comparison questionnaire to 502 school children from 5th to 7th grade to investigate if the Natural Number Bias succeeds in explaining their error patterns. About 25% of children responded in a way perfectly consistent with the Bias, but good students committed many errors in items that the Bias predicts to be easy. We propose an explanation based on comparison strategies and wrong generalizations of a common remark used for teaching fraction magnitude. [For the complete proceedings, see ED597799.]
Personal Beliefs and Gender Gaps in Mathematics
Author: Gómez-Chacón, Inés Mª
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Gender Differences,Mathematics Achievement,Preservice Teachers,Elementary School Teachers,Attitude Measures,Sex Stereotypes,Social Influences,Adults,Beliefs

In this paper we report data, gathered in Madrid, Spain, from two groups aged 20-39: one group comprised pedestrians stopped in the City streets, the other consisted of university students, specifically prospective primary school teachers [PPST]. It was found that the PPST were generally more negative than members of the general public about mathematics and its importance. Overall, there was relatively little evidence of gender stereotyping, However, when found, the traditional male stereotype prevailed. [For the complete proceedings, see ED597799.]
Jamila&apos;s Story: Analysing Affective Behaviors through a Pragmatist Perspective of Identity
Author: Frade, Cristina
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Beginning Teachers,Mathematics Teachers,Affective Behavior,Professional Identity,Teacher Behavior,Foreign Countries

This paper presents the story of a novice mathematics teacher, through which we aim to explore the social nature of affective behaviours drawing on a pragmatist perspective of identity formation. Data was produced by interview and treated as narrative, allowing the teacher-participant to freely trace and trace back contextually relevant aspects of her/his life experience. Our analysis indicates that teachers' affective positionings towards others emerge from shared social scenarios, manifested in response/reaction to such scenarios, and reflect their attempts to redescribe themselves in the eyes of others. [For the complete proceedings, see ED597799.]