ethanporcaro/eric-fulltext-meta huggingface dataset:
Icelandic 5th-Grade Girls' Developmental Trajectories in Proportional Reasoning
Author: Steinthorsdottir, Olof B.
Date: 2009-00-00
Type: Journal Articles
Subjects: Females,Learning Strategies,Mathematical Concepts,Teaching Methods,Grade 5,Elementary School Students,Mathematical Logic,Logical Thinking,Problem Solving,Algebra,Instructional Effectiveness,Foreign Countries

Understanding of ratio and proportion is critical to the development of higher level mathematical skills. Following Carpenter, Gomez, et al.'s (1999) proposal of a four-level trajectory in the development of proportional reasoning, a 12-week investigation was undertaken of the developmental trajectory of proportional reasoning of girls in two 5th-grade classes in Iceland. Students in these classes were accustomed to instructional practices that encouraged them to devise and explain their own solutions to mathematical problems. Results of the study confirm the learning trajectory with the addition of a further distinct level of development between Level 2 and Level 3. Results showed that girls moved easily, with minimum scaffolding, from Level 1 to 2 and from Level 2 to 3. The transition to Level 4, which involves explicit awareness of &quot;within&quot; and &quot;between&quot; multiplicative relationships, took greater time and effort. Teacher awareness of the four-level learning strategy, with the new emerging Level 3, assists in the design of appropriate problems, class structure, and teaching strategies. Building on Lamon's notions of unitizing and norming as by Carpenter et al.'s (1999) developmental model, this study contributes to our comprehension of students' understanding of proportionality and how it develops. (Contains 10 figures and 1 table.)
Growth Points in Students' Developing Understanding of Function in Equation Form
Author: Ronda, Erlina R.
Date: 2009-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Secondary School Mathematics,Equations (Mathematics),Mathematical Concepts,Comprehension,Thinking Skills,Mathematical Logic,Foreign Countries,Interviews,Age Differences,Concept Formation

This paper presents a research-based framework for analyzing and monitoring students' understanding of functions in equation form. The framework consists of &quot;growth points&quot; which describe &quot;big ideas&quot; of students' understanding of the concept. The data were collected from Grades 8, 9, and 10 students using a set of tasks involving linear and quadratic relationships, and were used in order to identify and describe &quot;big ideas&quot; in students' understanding of function in equation form. The framework also shows a typical learning path leading towards generality and abstraction in students' thinking about function. (Contains 2 tables and 1 figure.)
Reasoning with Paper and Pencil: The Role of Inscriptions in Student Learning of Geometric Series
Author: Carlsen, Martin
Date: 2009-00-00
Type: Journal Articles
Subjects: Foreign Countries,Geometric Concepts,Problem Solving,Thinking Skills,Visual Aids,Student Behavior

The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students made use of inscriptions, self-made as well as those provided by text books and teachers, and the role these inscriptions played in the coordination of students' learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students externalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significant as anchor points for arguments in the ongoing discussions. Three main issues are highlighted: (a) how the inscriptions used contribute to the process of appropriation, (b) how the students use inscriptions to externalise and clarify their ideas and attempts at meaning-making, and (c) how the inscriptions are conducive to closing the gap between the original problem as given in the text book and the mathematisation necessary. It is argued that inscriptions, through their material nature, play a decisive role in learning mathematical reasoning. (Contains 3 figures and 5 notes.)
Converting Mathematics Tasks to Learning Opportunities: An Important Aspect of Knowledge for Mathematics Teaching
Author: Sullivan, Peter
Date: 2009-00-00
Type: Journal Articles
Subjects: Foreign Countries,Mathematics Education,Mathematics Teachers,Elementary Secondary Education,Mathematics Instruction,Professional Development,Pedagogical Content Knowledge,Learning Experience,Mathematics

As part of a research and professional development project that focused on the opportunities and constraints provided by different kinds of mathematical tasks, a group of 67 primary and 40 secondary practising teachers of mathematics were asked to complete a survey focusing on their use of tasks. In this article, we discuss responses to one particular item which sought teachers' ideas on taking a fraction comparison task (which is larger: 2/3 or 201/301?) and converting it into a mathematics lesson in the middle years of schooling. Drawing upon a number of components of &quot;mathematical knowledge for teaching&quot; as a framework, we attempt to examine those aspects of mathematical knowledge which are involved in making such a conversion. Our recommendation following this analysis is that greater emphasis is necessary in professional development settings on taking a potentially useful task and converting it into a worthwhile mathematics learning experience for students. Knowing the relevant mathematics also seems necessary even if not sufficient to make this conversion. (Contains 4 tables and 1 note.)
Appreciating Mathematical Structure for All
Author: Mason, John
Date: 2009-00-00
Type: Journal Articles
Subjects: Foreign Countries,Mathematics Instruction,Teaching Methods,Mathematical Concepts

We take &quot;mathematical structure&quot; to mean the identification of general properties which are instantiated in particular situations as relationships between elements or subsets of elements of a set. Because we take the view that appreciating structure is powerfully productive, attention to structure should be an essential part of mathematical teaching and learning. This is not to be confused with teaching children mathematical structure. We observe that children from quite early ages are able to appreciate structure to a greater extent than some authors have imagined. Initiating students to appreciate structure implies, of course, that their appreciation of it needs to be cultivated in order to deepen and to become more mature. We first consider some recent research that supports this view and then go on to argue that unless students are encouraged to attend to structure and to engage in structural thinking they will be blocked from thinking productively and deeply about mathematics. We provide several illustrative cases in which structural thinking helps to bridge the mythical chasm between conceptual and procedural approaches to teaching and learning mathematics. Finally we place our proposals in the context of how several writers in the past have attempted to explore the importance of structure in mathematics teaching and learning. (Contains 1 figure and 3 footnotes.)
Awareness of Pattern and Structure in Early Mathematical Development
Author: Mulligan, Joanne
Date: 2009-00-00
Type: Journal Articles
Subjects: Mathematics Education,Mathematical Concepts,Grade 1,Concept Formation,Algebra,Mathematical Logic,Spatial Ability,Elementary School Mathematics,Elementary School Students,Pattern Recognition

Recent educational research has turned increasing attention to the structural development of young students' mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of mathematical structure is crucial to mathematical competence among young children. The purpose of this paper is to propose a new construct, Awareness of Mathematical Pattern and Structure (AMPS), which generalises across mathematical concepts, can be reliably measured, and is correlated with general mathematical understanding. We provide supporting evidence drawn from a study of 103 Grade 1 students. (Contains 3 figures and 1 table.)
Structuring Numbers 1 to 20: Developing Facile Addition and Subtraction
Author: Ellemor-Collins, David
Date: 2009-00-00
Type: Journal Articles
Subjects: Foreign Countries,Numeracy,Mathematics Achievement,Elementary School Mathematics,Grade 3,Grade 4,Mathematics Instruction,Instructional Materials,Mathematical Concepts,Numbers,Arithmetic,Intervention

The Numeracy Intervention Research Project (NIRP) aims to develop assessment and instructional tools for use with low-attaining 3rd- and 4th-graders. The NIRP approach to instruction in addition and subtraction in the range 1 to 20 is described. The approach is based on a notion of structuring numbers, which draws on the work of Freudenthal and the Realistic Mathematics Education program. NIRP involved 25 teachers and 300 students, 200 of whom participated in an intervention program of approximately thirty 25-minute lessons over 10 weeks. Data is drawn from case studies of two intervention students who made significant progress toward facile addition and subtraction. Pre- and post-assessment interviews and five lesson episodes are described, and data drawn from the activity of the students during the episodes are analysed. The discussion develops a detailed account of the progression of students' learning of structuring numbers, and how this can result in significant level-raising of students' arithmetical knowledge as it becomes more formalised and less context-dependent. (Contains 1 footnote.)
Developing Mathematics Understanding and Abstraction: The Case of Equivalence in the Elementary Years
Author: Warren, Elizabeth
Date: 2009-00-00
Type: Journal Articles
Subjects: Foreign Countries,Elementary School Mathematics,Learning Theories,Mathematical Concepts,Readiness,Algebra,Arithmetic,Longitudinal Studies,Models

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data was gathered from multiple sources including interviews, videos of classroom teaching, and pre- and post- tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory. (Contains 9 figures.)
Structuring Variability by Negotiating Its Measure
Author: Lehrer, Richard
Date: 2009-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Grade 5,Grade 6,Models,Mathematical Concepts,Urban Schools,Statistics,Measurement Techniques,Teaching Methods

Although variability and structure are often considered as antonyms in many everyday settings, a mathematically disciplined view contradicts this opposition. To initiate fifth- (10 years old) and sixth-grade (11 years old) students in this disciplinary view, we engaged students in practices of modeling data. These practices included inventing and revising data displays, inventing and revising measures of centre and variability, and inventing and revising models of chance to account for variability. Here we focus on prospective correspondences between students' invented measures (statistics) of variability and those favoured by the discipline. We suggest that inventing measures positions students to transform their vision of variability from mere difference to more structured forms, some of which coordinate centre and spread. By tracing interactions among an inventor, her classmates, and the teacher, we trace how structuring variability and constituting its measure co-originated during the course of negotiations about the meaning of the measure. Consideration of the coherency, transparency and generalisability of a statistic, all of which are valued by the discipline of statistics, emerged during the course of invention. (Contains 5 figures.)
Learning to Reason in an Informal Math After-School Program
Author: Mueller, Mary
Date: 2009-00-00
Type: Journal Articles
Subjects: After School Programs,Urban Areas,Mathematics Instruction,Informal Education,College School Cooperation,Disadvantaged Youth,Poverty,African Americans,Hispanic Americans,Cooperative Learning,Problem Solving,Mathematical Concepts,Peer Teaching,Persuasive Discourse,Thinking Skills,Mathematical Logic,Models

This research was conducted during an after-school partnership between a University and school district in an economically depressed, urban area. The school population consists of 99% African American and Latino students. During the informal after-school math program, a group of 24 6th-grade students from a low socioeconomic community worked collaboratively on open-ended problems involving fractions. The students, in their problem solving discussions, coconstructed arguments and provided justifications for their solutions. In the process, they questioned, corrected, and built on each other's ideas. This paper describes the types of student reasoning that emerged in the process of justifying solutions to the problems posed. It illustrates how the students' arguments developed over time. The findings of this study indicate that, within an environment that invites exploration and collaboration, students can be engaged in defending their reasoning in both their small groups and within the larger community. In the process of justifying, they naturally build arguments that take the form of proof. (Contains 10 figures, 1 table, and 3 footnotes.)
Bilingual Students Using Their Languages in the Learning of Mathematics
Author: Planas, Nuria
Date: 2009-00-00
Type: Journal Articles
Subjects: Bilingual Students,Foreign Countries,Immigrants,Mathematics Instruction,Social Theories,Bilingualism,Learning Strategies,Language Usage,Spanish Speaking,Social Influences,Classroom Environment,Secondary School Students

This paper is about how immigrant bilingual students use their languages in the learning of mathematics. Our research has been with immigrant bilinguals in Catalonia, Spain, who arrived at a young age from South-American countries. We use a critical sociolinguistic approach, which draws on social theory in the analysis of how language is involved in the construction of teaching and learning opportunities. Our data point to the differences in the ways that the Spanish dominant bilingual students use their two languages during their engagement in mathematical activity. The shifts from Catalan to Spanish, and from Spanish to Catalan, coincide with shifts in the complexity of the students' mathematical practices. The students tend to use the two languages for different purposes, depending on the complexity of the mathematical practices, and in relation to different social settings that coexist within the classroom. (Contains 2 tables, 3 figures and 3 footnotes.)
Mathematics Anxiety in Preservice Teachers: Its Relationship to Their Conceptual and Procedural Knowledge of Fractions
Author: Rayner, Vanessa
Date: 2009-00-00
Type: Journal Articles
Subjects: Preservice Teachers,Methods Courses,Rating Scales,Mathematics Instruction,Mathematics Anxiety,Knowledge Base for Teaching,Mathematical Concepts,Correlation,Elementary School Mathematics,Scores,Foreign Countries

The objective of the present study was to examine the relationship between mathematics anxiety and the procedural and conceptual knowledge of fractions in prospective teachers. Thirty-two preservice teachers enrolled in an elementary mathematics methods course were administered the Revised Mathematics Anxiety Rating Scale (RMARS, Baloglu, 2002). Procedural and conceptual knowledge of fractions was assessed with a validated paper and pencil test (Saxe, Gearhart, &amp; Nasir, 2001) and with four additional problems created by the researchers. Results indicated that as mathematics anxiety scores increased, scores on the validated measure of procedural knowledge of fractions decreased. The same relationship was found between the RMARS and the validated measure of conceptual knowledge. The findings provide some insight on the cognitive and pedagogical factors associated with mathematics anxiety in the preservice teacher population, underscoring the importance of facilitating their proficiency in both mathematical procedures and concepts. (Contains 4 tables and 1 figure.)
Teacher Identification of Student Learned Helplessness in Mathematics
Author: Yates, Shirley
Date: 2009-00-00
Type: Journal Articles
Subjects: Foreign Countries,Mathematics Achievement,Helplessness,Student Behavior,Mathematics Instruction,Psychometrics,Measures (Individuals),Mathematics Teachers,Identification (Psychology)

Teachers frequently encounter students with learned helplessness who are discouraged, turned off, or have given up trying to learn mathematics. Although learned helplessness has a long history in psychology, there has been no reliable means by which mathematics teachers can identify students exhibiting these debilitating yet changeable characteristic behaviours in the classroom. The psychometrically robust Rasch calibrated &quot;Student Behaviour Scale&quot; consisting of ten items rated on a five point scale provides teachers with an efficient interval measure of student learned helplessness and an ordered hierarchy of these behaviours as they are manifest in mathematics classrooms. (Contains 3 tables and 1 figure.)
The Interaction between Multimedia Data Analysis and Theory Development in Design Research
Author: van Nes, Fenna
Date: 2010-00-00
Type: Journal Articles
Subjects: Mathematics Education,Educational Research,Research Methodology,Computer Software,Data Analysis,Researchers,Validity,Reliability,Case Studies,Research Design,Models,Mathematical Aptitude,Learning Processes,Experiments,Multimedia Materials

Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in design research. The software can (a) act as a type of mould for organising large amounts of data; (b) contribute to improving the trackability and reliability of the research; and (c) support theory generation and validation. We propose an integrated model that elucidates the complex process of data analysis by showing how each of the components that are involved in the data analysis procedures feeds into the emerging local instruction theory. The model combines the intricate cycles of coding and analysing raw video data with the cumulative cyclic process that characterises design research in mathematics education. Our experiences with this model may support other mathematics education researchers in the development of thorough and empirically supported local instruction theories from complex qualitative analyses. (Contains 5 figures and 1 footnote.)
Learning to Teach Mathematics with Technology: A Survey of Professional Development Needs, Experiences and Impacts
Author: Bennison, Anne
Date: 2010-00-00
Type: Journal Articles
Subjects: Foreign Countries,Secondary School Mathematics,Mathematics Curriculum,Technology Uses in Education,Graphing Calculators,Teacher Characteristics,Mathematics Teachers,Professional Development

The potential for digital technologies to enhance students' mathematics learning is widely recognised, and use of computers and graphics calculators is now encouraged or required by secondary school mathematics curriculum documents throughout Australia. However, previous research indicates that effective integration of technology into classroom practice remains patchy, with factors such as teacher knowledge, confidence, experience and beliefs, access to resources, and participation in professional development influencing uptake and implementation. This paper reports on a large-scale survey of technology-related professional development experiences and needs of Queensland secondary mathematics teachers. Teachers who had participated in professional development were found to be more confident in using technology and more convinced of its benefits in supporting students' learning of mathematics. Experienced, specialist mathematics teachers in large metropolitan schools were more likely than others to have attended technology-related professional development, with lack of time and limited access to resources acting as hindrances to many. Teachers expressed a clear preference for professional development that helps them meaningfully integrate technology into lessons to improve student learning of specific mathematical topics. These findings have implications for the design and delivery of professional development that improves teachers' knowledge, understanding, and skills in a diverse range of contexts. (Contains 8 tables and 1 figure.)
Streaming for Mathematics in Years 7-10 in Victoria: An Issue of Equity?
Author: Forgasz, Helen
Date: 2010-00-00
Type: Journal Articles
Subjects: Low Achievement,Mathematics Achievement,Mathematics Teachers,Teaching Methods,Secondary School Mathematics,Mathematics Instruction,Teacher Attitudes,Curriculum Development,Individualized Instruction,Educational Change,Disadvantaged Youth,Ability Grouping,Foreign Countries,Institutional Characteristics,Teacher Characteristics,School Policy,Age Differences

&quot;Streaming&quot; for mathematics remains a contentious issue and particular forms of the practice have been considered inequitable. In the study reported here, the focus was on the extent to which streaming is used for mathematics at years 7-10 in Victorian secondary schools. Also of interest were the forms of streaming adopted and the criteria for selection into class groups; and teachers' views on streaming, their beliefs on whether all students benefit equitably from the practices adopted, and if they modify the curriculum and/or pedagogy in streamed classes. The findings indicated that forms of streaming were fairly widespread, were supported by many mathematics teachers, and were more prevalent as year level increased. Curriculum differentiation and pedagogical change that appeared to support high achievers, but which might limit low achievers' future mathematics options, were reported. Some teachers recognised some of the limitations associated with streaming, and that particular students might be disadvantaged as a result. The teachers participating in the study did not identify students' gender, socioeconomic, or ethnic/Indigenous backgrounds as factors of disadvantage linked to streaming. The implications of the findings and recommendations for future research are discussed. (Contains 5 tables, 1 figure and 4 footnotes.)