ethanporcaro/eric-fulltext-meta huggingface dataset:
The Use of the History of Mathematics in the Teaching Pre-Service Mathematics Teachers
Author: Galante, Dianna
Date: 2014-06-00
Type: Journal Articles
Subjects: History,Mathematics,Preservice Teachers,Preservice Teacher Education,Mathematics Teachers,Pedagogical Content Knowledge,Accreditation (Institutions),Reflection,Journal Writing,Student Teacher Attitudes,Grounded Theory,Content Analysis,Discourse Analysis,Case Studies

Many scholars have written about using the history of mathematics in the teaching of pre-service mathematics teachers. For this study, pre-service mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the &quot;Mathematics History Journal&quot; was to help measure the mathematics content knowledge and pedagogical content knowledge of the pre-service mathematics teachers for accreditation purposes. Results of the study indicated that by allowing pre-service teachers to investigate and present topics in the history of mathematics, pre-service teachers believed they strengthened their mathematics content knowledge and were introduced to a new avenue for teaching secondary students about mathematics.
Predictors of Achievement When Virtual Manipulatives Are Used for Mathematics Instruction
Author: Moyer-Packenham, Patricia S.
Date: 2014-06-00
Type: Journal Articles
Subjects: Mathematics Instruction,Teaching Methods,Educational Technology,Technology Uses in Education,Manipulative Materials,Grade 3,Grade 4,Elementary School Students,Comparative Analysis,Fractions,Pretests Posttests,Observation,Predictor Variables,Student Characteristics,Quasiexperimental Design,Regression (Statistics),Statistical Analysis

The purpose of this study was to determine variables that predict performance when virtual manipulatives are used for mathematics instruction. This study used a quasi-experimental design. This design was used to determine variables that predict student performance on tests of fraction knowledge for third- and fourth-grade students in two treatment groups: classroom instruction using texts and physical manipulatives (CI), and computer lab instruction using virtual fraction applets (VM). The Pre-test, Post-test 1, and Post-test 2 measured learning and retention of fraction concepts. Observation ethograms documented representation use. The results revealed that fewer demographic predictors of student performance (e.g., socio-economic status, English language learner status, and gender) exist during fraction instruction when virtual manipulatives were used. When instructors used virtual manipulatives, there was an equalizing effect on achievement in third and fourth grade classrooms, in that fewer demographic factors were influential for VM groups compared to CI groups.
Observatório da Educação: An Investigation of Teacher Professional Development of Mathematics Teachers
Author: Garcia Silva, Angélica F.
Date: 2014-06-00
Type: Journal Articles
Subjects: Faculty Development,Mathematics Teachers,Qualitative Research,Observation,Questionnaires,Interviews,Reflection,Elementary School Teachers,Teacher Competencies,Teaching Methods,Knowledge Base for Teaching

This paper aims to present the results of an investigation regarding the professional development of teachers who worked in the early years of basic education. The qualitative research involved teachers who participated in the &quot;Observatório da Educação&quot; project (MEC/CAPES). Because of the data amount, we choose to present the data analysis based on the work of only one teacher, who is considered as a legitimate representative of the whole group. All data were collected through direct observations, recordings, questionnaires, interviews and reflective &quot;relatorios&quot; on the implementation of the activities to their students. Data analysis was based on Ponte, Garcia, Shulman and Serrazina' studies, researchers that study the development and professional knowledge or reflection. This study reveals that the experiences during the training process favoured the redefinition process of mathematical content and teaching beyond reflection on practice.
Students' Equation Understanding and Solving in Iran
Author: Barahmand, Ali
Date: 2014-06-00
Type: Journal Articles
Subjects: Foreign Countries,High School Students,Secondary School Mathematics,Mathematics Education,Equations (Mathematics),Problem Solving,Mathematics Skills,Data Analysis,Prior Learning,Mathematical Concepts,Mixed Methods Research,Correlation,Regression (Statistics),Questionnaires

The purpose of the present article is to investigate how 15-year-old Iranian students interpret the concept of equation, its solution, and studying the relation between the students' equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between understanding and solving equation. The results indicate that students' understanding of equation has, basically, been shaped by their experiences in arithmetic and students usually have not any perception of equations and real world problems. Moreover, the study shows that students rarely paid any attention to the equality sign and the use of operators in both sides of the equation.
Understanding the Knowledge and Practices of Mathematics Teacher Educators Who Focus on Developing Teachers' Equitable Mathematics Pedagogy
Author: McLeman, Laura
Date: 2012-10-00
Type: Journal Articles
Subjects: Teacher Educators,Mathematics Teachers,Mathematics Instruction,Teaching Methods,Teacher Education,Mathematics Education,Teacher Education Programs,Preservice Teachers,Knowledge Base for Teaching

Most mathematics teacher educators (MTEs) would agree that teachers must be prepared to provide equitable mathematics instruction to all their students. However, to date, there is not a wide database regarding the practice ofMTEs who play an integral role in this preparation. In this paper we argue that additional information is needed about the approaches in which MTEs have addressed or incorporated equity issues such as race, identity, language, and culture as a core part of the preparation of teachers. We further argue for the importance of developing a research agenda that examines the practices of MTEs who teach through this lens of equity, the goal of which would be to build models of professional development that prepare and support other MTEs to develop this specialized knowledge.
Three Key Concepts of the Theory of Objectification: Knowledge, Knowing, and Learning
Author: Radford, Luis
Date: 2013-02-00
Type: Journal Articles
Subjects: Mathematics Instruction,Mathematics Education,Arithmetic,Algebra,Children,Mathematics,Mathematics Teachers,Elementary School Mathematics,Equations (Mathematics)

In this article I sketch three key concepts of a cultural-historical theory of mathematics teaching and learning--the theory of objectification. The concepts are: knowledge, knowing and learning. The philosophical underpinning of the theory revolves around the work of Georg W. F. Hegel and its further development in the philosophical works of K. Marx and the dialectic tradition (including Vygotsky and Leont'ev). Knowledge, I argue, is movement. More specifically, knowledge is a historically and culturally codified fluid form of thinking and doing. Knowledge is pure possibility and can only acquire reality through activity--the activity that mediates knowledge and knowing. The inherent mediated nature of knowing requires learning, which I theorize as social, sensuous and material processes of objectification. The ideas are illustrated through a detailed classroom example with 9-10-year-old students.
Agency as Inference: Toward a Critical Theory of Knowledge Objectification
Author: Gutiérrez, José Francisco
Date: 2013-02-00
Type: Journal Articles
Subjects: Knowledge Level,Critical Theory,Mathematics Education,Algebra,Mathematics Teachers,Equations (Mathematics),Teaching Methods,Problem Solving,Mathematics Instruction,Secondary School Mathematics,High School Students,Secondary School Teachers,Mathematical Concepts,Ethnography,Interviews

This article evaluates the plausibility of synthesizing theory of knowledge objectification (Radford, 2003) with equity research on mathematics education. I suggest the cognitive phenomenon of mathematical inference as a promising locus for investigating the types of agency that equity-driven scholars often care for. In particular, I conceptualize students' appropriation of semiotic-cultural artifacts (e.g., algebraic symbols and forms) to objectify their pre-symbolic inferences as conditional on their agency to carefully and incrementally construct personal meaning for these artifacts. To empirically ground this emerging approach, this study focuses on algebraic generalization (as a type of mathematical inference) and applies Radford's framework to video data of two iterations of an instructional intervention conducted in a high school program for academically at-risk youth. I analyze and compare students' acts of appropriation/objectification during whole-class conversations centered on pattern-finding tasks, in relation to the instructional mode adopted for each of the iterations--&quot;direct instruction&quot; vs. &quot;inquiry-based.&quot; The analysis shows that the implementation involving inquiry-based instruction enabled more equitable access to opportunities for agency-as-mathematical inference, whereas the implementation involving direct-instruction was ostensibly more productive. Implications for future equity research involving cognition-and-instruction analyses are discussed.
Mathematics Education and Ethnomathematics. A Connection in Need of Reinforcement
Author: Palhares, Pedro
Date: 2012-02-00
Type: Journal Articles
Subjects: Mathematics Education,Ethnology,Mathematics,Foreign Countries,Mathematical Logic,Thinking Skills,Mathematics Achievement,Mathematics Instruction

In this article we analyze Ethnomathematics research in Portugal in the recent past and the way it has been used in Education. We divide our reflection in three main parts. One is about people's discourse and actions and how to use them to uncover mathematical thinking. The second is about artifacts and how to use them to uncover mathematical thinking. The third is about how to use ethnomathematics research to improve mathematics education. In each of these sections we reflect on some of what has been made and we propose paths we think are worth pursuing.
From Human Activity to Conceptual Understanding of the Chain Rule
Author: Jojo, Zingiswa Mybert Monica
Date: 2013-02-00
Type: Journal Articles
Subjects: Foreign Countries,Calculus,Mathematics Education,Mathematics Teachers,Mathematics,Mathematical Concepts,Qualitative Research,Algebra,College Freshmen,Engineering Education,Higher Education

This article reports on a study which investigated first year university engineering students' construction of the definition of the concept of the chain rule in differential calculus at a University of Technology in South Africa. An APOS (Action-Process-Objects-Schema) approach was used to explore conceptual understanding displayed by students in learning the chain rule in calculus. Structured worksheets based on instruction designed to induce construction of conceptual understanding of the chain rule were used. A number of students used the straight form technique in differentiating complicated tasks while very few used either the link and Leibniz form techniques. In this manner differentiation of each function within the composite function was accomplished. Students either operated in the Inter- or Trans stages of the Triad. It was found that even students who had inadequate understanding of composition of functions, performed well in the application of the chain rule.
Empirical Taxonomies of Gameplay Enjoyment: Personality and Video Game Preference
Author: Quick, John M.
Date: 2012-00-00
Type: Journal Articles
Subjects: Video Games,Taxonomy,Personality Traits,Preferences,Holistic Approach,Individual Characteristics,Undergraduate Students,Questionnaires,Likert Scales,Correlation,Multivariate Analysis,Factor Analysis,Design

A survey study was conducted to better understand how gameplay enjoyment relates to players' personality traits and video game preferences. This study demonstrated that the core design elements of games that lead to enjoyment can be empirically identified. Similarly, it showed that considering personality, an individual characteristic, can produce informative insights about how players perceive gaming experiences. Whereas video game research has historically emphasized either games or players in isolation (Juul, 2010), this study is an initial effort towards a holistic approach that considers how design features and player characteristics combine to generate enjoyable video game experiences. Two empirical taxonomies for creating more enjoyable game experiences are presented.
Workplace Mathematics Research: Reflections on Personal Practical Experiences
Author: Naresh, Nirmala
Date: 2013-10-00
Type: Journal Articles
Subjects: Mathematics,Case Studies,Ethnology,Research Projects,Mathematics Activities,Mathematical Concepts,Mathematics Instruction,Mathematics Education,Foreign Countries,Semi Structured Interviews,Qualitative Research

This article describes our transitions through three phases of a reflective cycle as a journey from the past to the future. In the descriptive phase, we delve into our past research experiences and address questions such as: What is the role of mathematics at work? In doing so, we uncovered additional venues for exploration that called for a new mode of analysis. We transition into a theory-building phase where we share our learning experiences that occurred in-the-moment. We then shift to an action oriented (reflexive) phase during which we construe personal practical theories that enable us to negotiate broader understandings of the role of mathematics at work and identify areas for future inquiry. We document our lived experiences as informed and inspired by our work with two groups of workers--bus conductors and street vendors.
The Impact of Early Algebra: Results from a Longitudinal Intervention
Author: Brizuela, Bárbara M.
Date: 2013-06-00
Type: Journal Articles
Subjects: Algebra,Longitudinal Studies,Comparative Analysis,Statistical Analysis,Nonparametric Statistics,Grade 3,Grade 4,Grade 5,Experimental Groups,Control Groups,Mathematics Curriculum,Intervention,Elementary School Mathematics,Mathematics Education,Mathematics Instruction,Factor Analysis,Multivariate Analysis

In this paper, we provide evidence of the impact of early algebra (EA) over time. We document this impact in the following ways: (a) by showing the performance over time of an experimental group of 15 children on an algebra assessment, from 3rd to 5th grade; and (b) by showing how the performance on an algebra assessment of children from an experimental group differs from the performance of a group of comparison students from their same elementary school who did not receive EA instruction from 3rd to 5th grade. We compared students' scores through comparisons of means, corrspondence factorial analyses, and hierarchical analyses. Our results highlight the positive impact of an early access to algebra, indicating that this early access is associated, when we compare 3rd graders to 5th graders, with increased scores on items that involve inequalities and graphs. When comparing experimental to comparisongroup students we find increased scores on items that involve variables, functional relations, intra-mathematical contexts, tables, and algebraic expressions. The study adds to a body of literature that has been arguing for EA as well as a need to thread algebra throughout the mathematics curriculum, starting in the earliest grades
Montessori Practices: Options for a Digital Age
Author: Powell, Mark
Date: 2016-00-00
Type: Journal Articles
Subjects: Montessori Schools,Montessori Method,Technology Uses in Education,Educational Technology,Technological Literacy,Age Groups,Generational Differences,Student Empowerment

Mark Powell's plea for an open-minded view on the full scope of technology that is compatible with Montessori education enriches Maria Montessori's clear modernism of welcoming science into her educational vision. Growing up digital can be intelligently managed so that &quot;technology may offer an effective, adaptable, and easily available means … to gain independence … that may otherwise have intimidated them.&quot; Mark's enthusiasm for the right use of technology in history, writing, touch typing, information access and sharing, photography, place-based learning, and citizen science upholds technology as a supportive and educational tool for today's Montessori student. Mark offers a laundry list of technology resources to choose with commentary as to positive learning tendencies met by digital natives, millennials, and succeeding generations of young people who look to adapt to the onslaught of technological tools in carrying out life missions.
The Scientist in the Casa: The Child as Scientist in the Making
Author: Sackett, Ginni
Date: 2016-00-00
Type: Journal Articles
Subjects: STEM Education,Montessori Schools,Montessori Method,Technology Uses in Education,Educational Technology,Teaching Methods,Preschool Education

If a parent were to ask what science and technology are offered in a Montessori preschool, Ginni Sackett provides a comprehensive reply. By precisely defining the words science and technology with an expansion of those definitions from renowned biologist E. O. Wilson, alongside the &quot;experiences we offer every day to the children in our Casas,&quot; we can honestly present the Casa as rich in science and technology. The hands, the senses, and the mind cultivate both interaction with the concrete world but also cultivate the imagination and clear judgment. In this way &quot;every material and activity…is preparing each child to follow the scientific process.&quot; [This paper was presented at the NAMTA conference titled &quot;A Montessori Integrated Approach to Science, Mathematics, Technology, and the Environment&quot; in Portland, OR, Mar 31-Apr 3, 2016.]
Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems
Author: Mokos, Evagelos
Date: 2013-06-00
Type: Journal Articles
Subjects: Metacognition,Elementary School Students,Elementary School Mathematics,Mathematics Education,Mathematics Activities,Problem Solving,Qualitative Research,Case Studies,Foreign Countries,Grade 5,Mathematics Instruction,Teaching Methods,Protocol Analysis

Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky &amp; Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity has been focused on the area of mathematics problem solving. This study investigates the spontaneous emergence of the metacognitive functions of control and monitoring, during the solving of different types of mathematical problems with fifth grade students. We used the &quot;think aloud&quot; method on a group of ten year old students and the results showed that metacognitive strategies were used by the students so as the metacognitive functions of control and monitoring to be achieved.
Biodiversity and Peace: Where Technology and Montessori Come Together in the Children's Eternal Rainforest, Costa Rica
Author: Norris, Jeff
Date: 2016-00-00
Type: Journal Articles
Subjects: Biodiversity,Peace,Technology Uses in Education,Science Education,Study Abroad,Foreign Countries,Ecology,Conservation (Environment),Conservation Education,Experiential Learning,Nongovernmental Organizations,Montessori Method

Jeff Norris, initially shocked by the Montessorians who are calling technology into question, states that technology can offer a means of development for the child who is concurrently supporting and learning from the rich and overpowering biodiversity of the rainforest. He speaks for the Children's Eternal Rainforest citizen's science as well as the combined visit to the United Nations' University for Peace offered by the Montessori Institute for the Science of Peace. He extols the three-period lesson and independent group research as useful, interpretive-learning approaches that awaken the interest of each student. A bibliography is included. [This paper was presented at the NAMTA conference titled &quot;A Montessori Integrated Approach to Science, Mathematics, Technology, and the Environment&quot; in Portland, OR, Mar 31-Apr 3, 2016.]
Algebra and Proof in High School: The Case of Algebraic Proof as Discovery
Author: Martinez, Mara V.
Date: 2014-02-00
Type: Journal Articles
Subjects: Algebra,Mathematical Logic,Validity,Secondary School Mathematics,Secondary School Students,Mathematics Instruction,Mathematics Education,Geometry,Secondary School Teachers,Mathematics Teachers,Grounded Theory,Mathematical Concepts,Problem Solving,Teaching Methods,Interviews

In the United States, students' learning experiences around proof is generally concentrated in the domain of high school geometry with a focus on its verification function. Thus, providing students with a limited conception of what proof entails and the role that it plays in performing mathematics. Moreover, there is a lack of U.S.-based studies addressing how to integrate proof into other mathematical domains within the high school curriculum. In this paper, the author reports results from an interview at the end of a teaching experiment which was designed to integrate algebra and proof into the high school curriculum. Algebraic proof was envisioned as the vehicle that would provide high school students the opportunity to learn about proof in a context other than geometry. Results indicate that most students were able to produce an algebraic proof involving variables and a parameter and its multiples. In doing so, students experienced the discovery function of proof.
Technology and the Prepared Environment for the Third-Plane Child
Author: Castiglione, Cynthia
Date: 2016-00-00
Type: Journal Articles
Subjects: Technology Uses in Education,Montessori Schools,Needs,Urban Schools,Montessori Method,Educational Environment,Adolescents

Cynthia Castiglione presents Near North Montessori School's (Chicago) adolescent community's approach to technology. Her framework begins with the needs of the adolescent for social independence, social acceptance, and social justice. Using that template, she defines seven keys or characteristics that make up the technological environment: adaptability, social, real, independent, structure, order, safety, beauty, and the role of the guide. Montessori's writings are interspersed with each area to support her orientation. A bibliography is included. [This paper was presented at the NAMTA conference titled &quot;A Montessori Integrated Approach to Science, Mathematics, Technology, and the Environment&quot; in Portland, OR, Mar 31-Apr 3, 2016.]