ethanporcaro/eric-fulltext-meta huggingface dataset:
The Role of Pictures in Reading Mathematical Proofs: An Eye Movement Study
Author: Beitlich, Jana T.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: College Students,Mathematical Concepts,Concept Formation,Validity,Mathematical Logic,Pictorial Stimuli,Textbooks,Illustrations,Eye Movements,Adults,Attention,Expertise,Professional Personnel,College Mathematics,Visualization,Reading,Foreign Countries,College Faculty,Majors (Students)

To support university students' understanding of mathematical proofs, pictures accompanying text are frequently used in textbooks as well as in lectures. However, it is unclear if such pictures influence the individual's reading behaviour. By recording the eye movements of eight mathematicians, we investigated whether and how adults with high expertise in mathematics pay attention to additional pictures when reading a written mathematical proof. We found that all participants paid attention to the pictures. As expected, in two out of three items, the text was fixated upon significantly longer than the picture. The data suggest that the participants tried to integrate information from text and picture by alternating between these representations. [For the complete proceedings, see ED597799.]
A New Approach to Measuring Pre-Service Teachers&apos; Attitudes towards Mathematics
Author: Barmby, Patrick
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Student Attitudes,Mathematics Instruction,Elementary School Teachers,Evaluation Methods,Measurement Techniques,Foreign Countries,Graduate Students,Mixed Methods Research

Research (for example Ball, 1988; Philippou &amp; Christou, 1998) have linked teachers' attitudes with classroom practice in teaching mathematics. Previous studies have identified and examined the relationships between different components of teachers' attitudes (Nisbet, 1991). However, a particular criticism of these studies is the lack of content validity of the measures used. In the present study, in line with the conference theme for PME 38, we developed an innovative approach to examining the attitudes of pre-service elementary teachers. The study utilised a mixed methods approach, firstly eliciting qualitative statements from teachers, then using these statements in Likert-scale questionnaire items. We argue that this provides a more valid assessment of attitudes, and a method that can be applied across differing contexts for teachers. [For the complete proceedings, see ED597799.]
Fostering the Argumentative Competence by Means of a Structured Training
Author: Brockmann-Behnsen, Dirk
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Secondary School Students,Grade 8,Persuasive Discourse,Competence,Geometry,Mathematics Instruction,Validity,Mathematical Logic,Problem Solving

We report on a long-term study which was executed in a German secondary school with 128 eights graders (ages 14 to 15) in four different classes. Two of these classes served as control groups. The mathematics lessons of the other two classes (treatment groups) were frequently enriched by distinguished phases in which structured argumentation and the use of heuristics was trained. The study aimed at investigating the development of the argumentation competence of the students over that period. For this report, the products of four different geometry tasks of 15 students from one of the treatment groups and 15 from one of the control groups respectively were evaluated. [For the complete proceedings, see ED597799.]
Primary School Teachers Learn Modeling: How Deep Should Their Mathematics Knowledge Be?
Author: Barabash, Marita
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Elementary School Teachers,Mathematics Instruction,Pedagogical Content Knowledge,Preservice Teachers,Mathematical Models,Interdisciplinary Approach,Teaching Methods,Foreign Countries

We taught a group of experienced in-service primary school mathematics teachers the notion of mathematical model, in order to foster the interdisciplinary mathematics teaching in primary school. In particular, we developed an exercise in which they were supposed to construct a mathematical model on the basis of primary school mathematics. We found out that the formal mathematical knowledge needed to perform the exercise was not sufficient to successfully cope with it. The main factor that influences the ability of the teachers to cope with this type of activity is the depth of their mathematical knowledge which we identify with a person's mathematical insight. [For the complete proceedings, see ED597799.]
Competencies Developed by University Students in Microworld-Type Core Mathematics Courses
Author: Buteau, Chantal
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Undergraduate Students,College Mathematics,Mathematics Skills,Competence,Computer Uses in Education,Design,Programming,Student Projects,Coding,Mathematical Applications

We report on an empirical study grounded in our sustained implementation over ten years of a sequence of three-term undergraduate core mathematics courses centred on microworlds. The survey study investigates students' views on 15 competencies potentially developed as they, individually or in pairs, create 12 Exploratory Objects, i.e., microworld-type environments, on diverse mathematical topics as part of their workload. Results suggest that students develop further the competencies as they repeat designing, programming, and using microworlds to learn and do mathematics, and that original projects in which students start by selecting their own topic, is key to the development of these competencies. No gender differences were found. [For the complete proceedings, see ED597799.]
Semiotic and Theoretic Control within and across Conceptual Frames
Author: Bikner-Ahsbahs, Angelika
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Semiotics,Epistemology,Cognitive Processes,Decision Making,Persuasive Discourse,Problem Solving,Mathematics Skills,Mathematics Activities,Geometric Concepts,Geometry,High School Students,Grade 10,Foreign Countries,Equations (Mathematics),Mathematical Logic,Logical Thinking

This paper refers to the concept of semiotic and theoretic control describing resources to conduct decisions in epistemic processes. We consider an argumentation process from a complex problem-solving activity involving different conceptual frames related to parabolas. Using a micro-analytical interpretative lens, we will show that, in order to carry out the argumentation activity, semiotic and theoretic control within conceptual frames (local control) needs to be co-ordinated with control across different conceptual frames (global control). [For the complete proceedings, see ED597799.]
Problem-Solving Strategies as a Measure of Longitudinal Curricular Effects on Student Learning
Author: Cai, Jinfa
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Middle School Students,Middle School Mathematics,Educational Change,Mathematics Curriculum,Problem Solving,Logical Thinking,Algebra,Mathematics Achievement,High School Students,Longitudinal Studies,Mathematics Tests,Multiple Choice Tests,Mathematics Skills,Outcomes of Education,Retention (Psychology),Problem Based Learning

This study examined the longitudinal effects of a middle school reform mathematics curriculum on students' open-ended problem solving in high school. Using assessment data from a large, longitudinal project, we compared the open-ended problem-solving performance and strategy use of high school students who had used the Connected Mathematics Program (CMP) in middle school with that of students who had used more traditional mathematics curricula. When controlling for sixth-grade state mathematics test performance, high school students who had used CMP in middle school had significantly higher scores on a multipart open-ended problem. In addition, high school students who had used CMP appeared to have greater success algebraically abstracting the relationship in the task. [For the complete proceedings, see ED597799.]
Effects of Prompting Students to Use Multiple Solution Methods While Solving Real-World Problems on Students&apos; Self-Regulation
Author: Achmetli, Kay
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Prompting,Instructional Effectiveness,Problem Solving,Self Management,Mathematics Instruction,Grade 9,Secondary School Students,Foreign Countries,Self Concept,Problem Based Learning

In the project MultiMa (Multiple solutions for mathematics teaching oriented toward students' self-regulation), we investigated the effects of prompting students to use multiple solution methods while solving real-world problems on their learning. In this quasi-experimental study, we compared three treatment conditions. In one condition, students solved real-world problems by using multiple solution methods. These solution methods consisted of a solution using a table and a solution using differences. In the other two conditions, the same real-world problems were solved using only one of the methods. About 307 ninth graders from twelve middle track classes took part in this study during four lessons. Before and after a teaching unit, students' self-regulation was tested. [For the complete proceedings, see ED597799.]
Analogizing during Mathematical Problem Solving -- Theoretical and Empirical Considerations
Author: Assmus, Daniela
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Mathematics Skills,Problem Solving,Logical Thinking,Models,Cognitive Processes,Student Evaluation

The aim of the paper is to provide a process model to evaluate mathematical problem solving by analogy, in order to better determine at which point and under what conditions a learner is prompted to use analogies. The model is a theoretical construct. Qualitative results of an empirical study are used to underline and illustrate core aspects of the model. [For the complete proceedings, see ED597799.]
Using Interviews to Explore Teacher Knowledge Profiles in the Area of Permutations
Author: Caddle, Mary C.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Knowledge Base for Teaching,Mathematics Teachers,Profiles,Faculty Development,Teacher Attitudes,Educational Needs,Guidelines,Teacher Workshops,Secondary School Teachers

This paper illustrates consideration of multiple facets of mathematics teacher knowledge through interviews, demonstrates how teachers have different knowledge profiles, and discusses the implications for professional development. This study focuses on interviews with eight teachers, which were analyzed using Ball, Thames, and Phelps' (2008) framework of teacher knowledge, assigning knowledge types to statements made during the interview. All teachers exhibited multifaceted knowledge, but different profiles emerged. The implication is that teacher profiles should be considered in designing professional development. In addition, this analysis supports the use of teacher interviews as a tool to consider professional development needs. [For the complete proceedings, see ED597799.]
Mathematical Competencies in a Role-Play Activity
Author: Albano, Giovannina
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Role Playing,Mathematical Concepts,Concept Formation,Engineering Education,College Freshmen,Program Effectiveness,Teacher Role,Competence,Mathematics Skills,Validity,Mathematical Logic

This paper concerns a competencies-based analysis of the outcomes of a role-play activity aimed to foster conceptual understanding of mathematics for first year engineering students. The teacher role has been considered in order to investigate the competencies addressed by the questions created by the students and their matching with the activity's educational goal. The analysis shows that the quality of the posed questions made by the students highlights the moving from the instrumental approach, the students are used to, towards a relational one. [For the complete proceedings, see ED597799.]
Linking Children&apos;s Knowledge of Length Measurement to Their Use of Double Number Lines
Author: Beck, Pamela S.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Elementary School Students,Grade 6,Elementary School Mathematics,Mathematics Education,Mathematics Skills,Knowledge Level,Measurement,Number Concepts,Problem Solving,Logical Thinking

In this paper we report on five Grade 6 students' responses to a proportional reasoning task. We conducted pair interviews within a longitudinal study focused on extending a hypothetical learning trajectory for length measurement. Results suggest that there exists a link between children's level of conceptual and procedural knowledge for length measurement and their ways of using the double number line representation when solving problems involving proportional reasoning. [For the complete proceedings, see ED597799.]
Juggling Reference Frames in the Microworld Mak-Trace: The Case of a Student with MLD
Author: Baccaglini-Frank, Anna
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Dyslexia,Learning Disabilities,Mathematics Skills,Cognitive Processes,Perspective Taking,Teaching Methods,Cognitive Development,Mathematics Education,Educational Technology,Technology Uses in Education,Computer Oriented Programs,Mathematical Concepts,Concept Formation,Program Effectiveness,Adolescents,Foreign Countries

This study gives insights into how Logo-like microworlds can affect cognitive development related to mathematics education of students with math learning difficulties. In particular, we analyse the case of a 15-year-old student with dyslexia and severe dyscalculia. Among the various cognitive aspects involved, here we delve into the development of his perspective-taking ability, seen in terms of becoming aware of and juggling two different allocentric frames of reference. [For the complete proceedings, see ED597799.]
&apos;I Sense&apos; and &apos;I Can&apos;: Framing Intuitions in Social Interactions
Author: Andrà, Chiara
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Intuition,Class Activities,Interpersonal Relationship,Secondary School Students,Grade 9,Cooperative Learning,Mathematics Activities,Problem Solving,Persuasive Discourse,Power Structure,Group Dynamics,Interpersonal Communication,Nonverbal Communication,Interaction,Affective Behavior,Motivation

In this article we examine intuitions as they emerge in groupwork activities. We provide a framework and a methodology to code various aspects of the activity, social and mathematical. Focusing mostly on students' gazes, we explore how affective moves give rise to, and determine, students' interactions and thoughts. We argue that intuition does not take place in the mind of the individual, it is not a matter of 'I think', but it arises from actions and reactions, in relationships with others and with artefacts. Data from a 50 minutes groupwork activity of four grade-9 students allows us to further discuss our framework. [For the complete proceedings, see ED597799.]
Using the Patterns-of-Participation Approach to Understand High School Mathematics Teachers&apos; Classroom Practice in Saudi Arabia
Author: Alsalim, Lyla
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Mathematics Teachers,Mathematics Instruction,High School Teachers,Secondary School Mathematics,Teaching Methods,Textbooks,Educational Change,Teacher Attitudes

In this paper, patterns-of-participation theory serves as a lens to interpret and understand Saudi high school mathematics teachers' practices during the current reform movement and the role the new textbooks play in influencing teachers practice. The data presented is about Haya and Nora, two experienced, high school mathematics teachers. Generally, Nora's and Haya's practice as high school mathematics teachers reveals patterns of tension and confusion with regards to understanding the current reform movement in Saudi Arabia. [For the complete proceedings, see ED597799.]
Learning Negative Integer Concepts: Benefits of Playing Linear Board Games
Author: Bofferding, Laura
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Elementary School Students,Grade 1,Elementary School Mathematics,Number Concepts,Mathematics Instruction,Teaching Methods,Educational Games,Mathematics Activities,Mathematics Achievement,Achievement Gains,Young Children,Outcomes of Education,Low Income Students,Hispanic American Students,Computation

Linear board games have shown great promise as tools to teach whole number concepts (Ramani &amp; Siegler, 2008), but little is known about their utility for supporting negative integer concepts. This study sought to extend the use of linear board games to teach integer concepts. Forty-eight first graders (ages 6-7) counted along an integer board game with negative numbers or did control activities with integers. Students who played the board game made significant gains on several measures related to identifying and ordering integers. Findings suggest that even young children can benefit from games with negative integers, and we provide implications for instruction. [For the complete proceedings, see ED597799.]
Effects of a Holistic versus an Atomistic Modelling Approach on Students&apos; Mathematical Modelling Competencies
Author: Brand, Susanne
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Skills,Mathematical Models,Holistic Approach,Secondary School Mathematics,Secondary School Students,Grade 9,Foreign Countries,Mathematics Tests,Student Evaluation

The paper deals with the question of the practicability and the effectiveness of different approaches to foster students' mathematical modelling competencies. Within the modelling project ERMO (Acquirement of modelling competencies) a holistic and an atomistic approach of mathematical modelling were compared in order to find out which approach is more effective in fostering the students' modelling competencies. The results of modelling tests with three measurement points show that both approaches foster students' modelling competencies, but both approaches have strengths and weaknesses. The data indicates that the holistic approach is more effectively for students with weaker performance in mathematics. [For the complete proceedings, see ED597799.]
Collective Problem Posing as an Emergent Phenomenon in Middle School Mathematics Group Discourse
Author: Armstrong, Alayne
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Group Discussion,Problem Solving,Secondary School Mathematics,Middle School Students,Behavior Patterns,Early Adolescents,Foreign Countries,Cooperative Learning,Suburban Schools,Mathematics Activities,Group Behavior

This naturalistic case study investigates the problem posing patterns that emerge as four small groups of 12 year old students in Western Canada work collectively on a structured mathematics task. A method of data analysis is introduced that blurs the data to create transcript &quot;tapestries&quot; providing visual evidence of collective patterns of posed problems that emerge over time. Results in progress suggest that groups vary widely in terms of the problems posed, and in terms of the patterns in which these problems emerge in their discourse. The reposing of problems helps to structure each group's discussion, with the role that each problem plays in the conversation evolving as it reemerges in the discourse. [For the complete proceedings, see ED597799.]
An Analytic Framework for Describing Teachers&apos; Mathematics Discourse in Instruction
Author: Adler, Jill
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Discourse Analysis,Classroom Communication,Interaction,Teaching Methods,Sociocultural Patterns,Guidelines,Faculty Development,Foreign Countries,Grade 10,Algebra,Lesson Plans,Mathematics Teachers,High School Teachers

We illustrate an analytic framework for teachers' mathematics discourse in instruction (MDI). MDI is built on three interacting components of a mathematics lesson: a sequence of examples and related tasks; accompanying talk; patterns of interaction. Together these illuminate what is made available to learn. MDI is grounded empirically in mathematics teaching practices in South Africa, and theoretically in socio-cultural theoretical resources. The framework is responsive to the goals of a particular research and professional development project with potential for wider use. [For the complete proceedings, see ED597799.]
Revisiting Transfer of Learning in Mathematics: Insights from an Urban Low-Income Settlement
Author: Bose, Arindam
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Transfer of Training,Low Income Students,Middle School Students,Foreign Countries,Problem Solving,Context Effect,Relevance (Education),Fractions,Learning Activities,Job Skills

Debates on transfer of learning in mathematics are not new. Claims of situatedness of learning within tasks and non-transferability of knowledge between tasks are widely contested. Direct Application (DA) of learning is a common paradigm for characterising transfer which led to many instances of transfer failure (Bransford &amp; Schwartz, 2001). The alternative framework presented here shows that some of the transfer failures in mathematics can be considered as partial transfer by broadening the DA paradigm which can scaffold classroom pedagogy by drawing upon everyday mathematics. Claims are supported by data drawn from an economically active low income settlement where sample middle graders are engaged in house-hold based micro-enterprise, possess diverse opportunities for gaining mathematical knowledge. [For the complete proceedings, see ED597799.]
Parent-Child Mathematics: A Study of Mothers&apos; Choices
Author: Anderson, Ann
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Parent Child Relationship,Mothers,Mathematics Instruction,Parents as Teachers,Home Study,Preschool Children,Middle Class,Teaching Methods,Play,Parenting Styles,Teaching Styles,Learning Activities,Mathematics Activities

Research on mathematics found in 'everyday' interactions (e.g., Walkerdine, 1988) often relies on analysis of parent-child talk during studies of social interactions and/or literacy events more generally. In contrast, from the outset of the current study, parents were aware that mathematics was the focus of study and that each of them would determine the activities to be video-taped in their home. In this paper, we report on the types of activities six middle class mothers perceived as opportunities to engage their preschool child with mathematics. Analysis also included the patterns found within and across families. Overall, the mothers documented play-based events, many of which were common across four or more homes and entailed 'less conventional' mathematics. Parental styles of mathematical engagement are discussed. [For the complete proceedings, see ED597799.]
Variable Parts: A New Perspective on Proportional Relationships and Linear Functions
Author: Beckmann, Sybilla
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Concepts,Mathematics,Algebra

We present a mathematical analysis that distinguishes two quantitative perspectives on ratios and proportional relationships: Multiple Batches and Variable Parts. We argue that (a) existing research on proportional relationships has addressed Multiple Batches but has largely overlooked Variable Parts, (b) Multiple Batches makes the co-variation aspect of proportional relationships more explicit, while Variable Parts makes the fixed multiplicative relationship between two quantities more explicit, (c) the distinction between Multiple Batches and Variable Parts is orthogonal to the within-measure-space versus between-measure-space ratio distinction, and (d) Variable Parts affords promising new approaches for addressing linear relationships. [For the complete proceedings, see ED597799.]