ethanporcaro/eric-fulltext-meta huggingface dataset:
Exploring How Understandings from Abstract Algebra Can Influence the Teaching of Structure in Early Algebra
Author: Wasserman, Nicholas H.
Date: 2017-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Algebra,Case Studies,Elementary School Mathematics,Elementary School Teachers,Teaching Methods,Mathematical Logic,Mathematics Skills,Knowledge Base for Teaching,Pedagogical Content Knowledge,Lesson Plans,Video Technology,Interviews

Empirical work that connects content knowledge to teaching practice has become increasingly important in discussions around a professional knowledge base for teaching. This paper aims to continue that work, reporting a single exploratory case study of one elementary mathematics teacher. The purpose of the study was to investigate how introducing teachers to advanced mathematics, particularly ideas in abstract algebra, might inform and influence their instructional practices for teaching early algebra topics about arithmetic structure. The findings indicate that instructional practices did change, especially in ways that more explicitly incorporated structure in early algebra with students, and fostered increased reasoning and sense-making about these ideas. Implications for mathematics teacher education are discussed.
A Case Study of Teachers&apos; Development of Well-Structured Mathematical Modelling Activities
Author: Stohlmann, Micah
Date: 2017-00-00
Type: Journal Articles
Subjects: Case Studies,Mathematical Models,Mathematics Instruction,Learning Activities,Elementary School Teachers,Mathematics Activities,Graduate Study,Documentation,Teacher Attitudes

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about mathematical modelling activities, and in-class discussion and feedback. We describe the teachers' development process and how well structured the activities were based on six principles of mathematical modelling activities. We also describe the teachers' interpretations of the six principles connected to their modelling activity. Two of the teachers were able to develop modelling activities that met the six principles while one teacher did not meet the generalizability and self-assessment principles. Developing mathematical modelling activities is a difficult task and the class activities allowed the teachers to go through revisions with their mathematical modelling activities to allow the opportunity for the activities to be properly structured.
Equity and Adequacy in Ohio School Funding
Author: Johnson, Justin L.
Date: 2017-00-00
Type: Journal Articles
Subjects: Educational Equity (Finance),Educational Finance,State Aid,Resource Allocation,Educational Policy,Funding Formulas,Court Litigation,Public Schools,School Districts

This article explores state school funding in Ohio and examines the concepts of equity and adequacy. This is accomplished not by conducting an empirical study but through a thorough review of the current environment of school funding in the state. For Ohio, the concepts of equity and adequacy are especially pertinent when considering that Ohio's funding methods for public education have been found unconstitutional more than once. Recent trends in policy as well as current research are used in determining if Ohio is funding education at necessary levels to provide an adequate and equitable education for all students. Because current education reforms provide a more relevant context for equity and adequacy concerns to policy makers, a review of these reforms, their implications, and how the state ensures that education funding is both equitable and adequate is addressed.
Preservice and Novice Teachers&apos; Knowledge on Preformal Proofs: Triangle Postulate as an Example
Author: Leung, Kui Chiu Issic
Date: 2017-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Preservice Teachers,Beginning Teachers,Knowledge Level,Teacher Competencies,Validity,Mathematical Logic,Foreign Countries,Questionnaires,College Students,Geometric Concepts,Geometry,Qualitative Research,Statistical Analysis

By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers' knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful tool for connecting abstract geometrical concepts with concrete meanings. We conclude by providing strategies for teachers to use preformal proofs effectively in their teaching of geometric propositions.
Orchestrating Productive Whole Class Discussions: The Role of Designed Student Responses
Author: Evans, Sheila
Date: 2017-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Group Discussion,Teaching Methods,Responses,Problem Solving,Large Group Instruction,Secondary School Students,Secondary School Mathematics,Early Adolescents,Video Technology,Mixed Methods Research,Questioning Techniques,Foreign Countries,Intervention,Interviews

The value of students publicly sharing and discussing their solutions to unstructured problems is widely recognized. This can, however, be pedagogically challenging. The solutions may be partial, unclear and unpredictable. For many teachers, particularly those new to working with such problems with their students, the improvisation needed to orchestrate productive discussions can be unmanageably high. In this paper we present a pedagogical tool to help teachers. Specifically, teachers orchestrate discussions of &quot;designed, worked-out solutions&quot; to unstructured problems. The worked-out solutions have been carefully pre-designed for teachers to use in lessons. Knowing the range of distinct solutions students are to work with supports teachers' planning. The reduced need for improvisation means they are better placed to learn and practice new ways of probing students' reasoning. These acquired practices may then be applied to discussions of students' own responses to a problem. In the study we explore the question: for a teacher new to working with unstructured problems, how do discussions of worked-out solutions (called in this paper designed student responses) differ from discussions of students' own solutions? Our findings indicate that discussions of authentic student solutions tend to focus on procedural descriptions, whereas the discussions of designed solutions stimulated student explanation and evaluation. The work reported here represents the initial part of an on-going study.
Becoming a Reader: Significant Social Influences on Avid Book Readers
Author: Merga, Margaret K.
Date: 2017-00-00
Type: Journal Articles
Subjects: Reading Habits,Social Influences,Influences,Authors,Recreational Reading,Mixed Methods Research,Foreign Countries,Individual Characteristics,Reading Instruction,Family Influence,Libraries,Parent Role,Books,Librarians

Understanding how social influences can foster avid book reader identification is a key research goal that warrants further investigation beyond a limited early-years lens. The author's 2015 International Study of Avid Book Readers (ISABR) explored, as one of its key research questions, the influence positive social agents can have on avid book readers, relying on the retrospective reflections of respondents from a range of countries and supporting quantitative data to explore this research focus. Early influences were examined, with data suggesting that maternal instruction is the most prevalent source of early reading teaching. Most respondents (64.3 percent) were the recipients of positive influence from a social agent. Indirect avid reader influence, author influence, fostering access, shared social habit, reading for approval, recommendations and supporting choice, and exposure to reading aloud were recurring mechanisms of influence. The multiple mechanisms of influence identified constitute opportunities for engagement and subsequent intervention by literacy advocates, including librarians.
Making and Mentors: What It Takes to Make Them Better Together
Author: Kekelis, Linda
Date: 2017-00-00
Type: Journal Articles
Subjects: Mentors,STEM Education,Partnerships in Education,Secondary School Students,Females,Research and Development,Theory Practice Relationship,After School Programs,Science Instruction,Student Interests,Science Interests,Science Careers,Role Models

&quot;Making&quot; as an educational approach holds promise both for introducing mentors into STEM programming and for showing girls new pathways into STEM (Wittemyer &amp; Gill, 2014). With its merger of cutting-edge technology and traditional arts and crafts, &quot;Making&quot; can help girls learn about electronics, robotics, metalwork, woodwork, sewing, and many other fabrication techniques. It can also attract mentors who have both technical expertise and personal interest in the creative aspects of &quot;Making.&quot; This research-practice partnership focused on an afterschool &quot;Making&quot; program for high school girls. The article reveals promising practices for supporting mentors in STEM-oriented &quot;Making&quot; programs.
Equity and Inclusion: An Action Agenda for Youth Development Professionals
Author: Curry, Jennifer Siaca
Date: 2017-00-00
Type: Journal Articles
Subjects: Equal Education,Inclusion,Culturally Relevant Education,Identification (Psychology),Student Diversity,Social Justice,After School Programs,Youth Programs,Social Bias,Language Usage,Bullying,Student Behavior,Evidence Based Practice

After the push of No Child Left Behind to focus on academic preparation, the field has moved to yet another phase: an expanding commitment to social and emotional learning. Fortunately, this out-of-school time (OST) trend is paralleled in formal education. The Every Student Succeeds Act of 2015, for example, uses a broad definition of student success that includes safety, communication skills, and healthy relationships. This new emphasis is an important one, but it cannot be fully implemented without attention to basic principles of respect and safety or to the need to value all children and youth. In recent years, American youth have witnessed a surge in racially charged violence and discriminatory rhetoric. The OST field can and should respond with an explicit commitment to equity, inclusion, and culturally responsive practice. OST professionals must actively value and respect the identities of the young people they serve, including their race, religion, ethnicity, gender, socioeconomic status, sexual orientation, appearance, and ability. This essay proposes significant yet simple changes--grant funding not required--to support youth while embracing their diverse assets. There are not enough pages in this journal to do full justice to every aspect of this sensitive topic. As one contribution, this article provides both immediate action steps and food for further thought and exploration. The author offers a theory- and practice-based model for how OST professionals can approach their work using &quot;critical social pedagogy.&quot; This new pairing of existing frameworks, building on a tradition widely used in Europe, views OST professionals as caregivers and protectors of children's rights. Framing OST professionals as critical social pedagogues, this article challenges educators to take action both by attending to their own beliefs, attitudes, and behaviors and by designing programs with an antidiscrimination framework.
Fear, Loathing and Ambivalence toward Learning and Teaching Mathematics: Preservice Teachers&apos; Perspectives
Author: Itter, Diane
Date: 2017-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Preservice Teachers,Negative Attitudes,Student Attitudes,Mathematics Anxiety,Foreign Countries,Beliefs,Preservice Teacher Education,Case Studies,Qualitative Research

Preservice teachers graduate from an education system that shapes their mathematical understandings, beliefs and attitudes, and then re-enter that system to shape their own students' mathematical understandings, beliefs, and attitudes. Unfortunately, many of our future teachers have developed negative attitudes symptomatic of a self-perpetuating cycle of inter-generational fear, loathing, and ambivalence to mathematics. We investigated the mathematical attitudes of 152 third year preservice teachers (PST) using their written reflections about their categorisation of, and catalysts for, their attitudes towards mathematics. To understand better the genesis and consequences of negative mathematical attitudes and beliefs, we focus on the responses of 111 preservice teachers (nearly three-quarters of our sample) who acknowledged their negative or neutral attitudes towards mathematics. Our findings confirm the complex relationship between attitudes, beliefs, and emotions that impact on learners' motivation, engagement, and learning approaches, and, for our sample of preservice teachers, that will shape how they teach.
Learning Mathematics for Teaching Mathematics: Non-Specialist Teachers&apos; Mathematics Teacher Identity
Author: Crisan, Cosette
Date: 2017-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Mathematics Teachers,Professional Identity,Expertise,Secondary School Teachers,Inservice Teacher Education,Faculty Development,Questionnaires,Interviews,Lesson Observation Criteria,Instructional Materials,Case Studies,Foreign Countries

A non-specialist teacher of mathematics is a school teacher who qualified to teach in a subject other than mathematics yet teaches mathematics to students in secondary school. There is an emerging interest internationally in this population, a brief report of which is given in the paper. Because of concerns about the quality of non-specialists' mathematics teaching, in-service courses for these teachers have been provided by some educational jurisdictions, including within the United Kingdom (UK). This paper reports on a research project based on designing and teaching such courses in London. The paper operationalises &quot;Mathematics Teacher Identity&quot; by adapting Wenger's (1998) social ecology of identity to give a framework of &quot;Modes of Belonging&quot; for a teacher of mathematics, which is then used to analyse qualitative data of different types. Analysis of the data identifies (1) aspects of non-specialists' mathematics teacher identity in terms of indicators and (2) through two case studies, &quot;trajectories&quot; towards development of a mathematics teacher identity.
K-8 Pre-Service Teachers&apos; Algebraic Thinking: Exploring the Habit of Mind &quot;Building Rules to Represent Functions&quot;
Author: Magiera, Marta T.
Date: 2017-00-00
Type: Journal Articles
Subjects: Preservice Teachers,Preservice Teacher Education,Algebra,Thinking Skills,Theory of Mind,Knowledge Base for Teaching,Undergraduate Students,Problem Solving,Formative Evaluation,Summative Evaluation,Task Analysis,Scoring Rubrics,Correlation,Elementary School Mathematics,Middle Schools,Statistical Analysis

In this study, we examined the ability of grades 1-8 pre-service teachers (PSTs) to engage in thinking about patterns, relationships, and functional rules. Using the algebraic habit of mind Building Rules to Represent Functions as a framework, we examined whether and how well our PSTs (n = 18) used seven features of this habit of mind: organize information, predict patterns, chunk information, use different representations, describe a rule, describe change, and justify a rule. The data revealed distinct and significant differences among our PSTs' demonstrated abilities to justify a rule, organize information, predict a pattern, and describe a rule. Their ability to justify a rule was the weakest of the seven features, and it was correlated with the ability to predict patterns and the ability to chunk information. Our analysis reveals the complexity of the relationships among the seven features and provides a tentative grouping of features that together might support one another. Attention to these relationships has the potential to enhance instruction aimed at helping students learn to analyse problem situations that focus on writing rules to represent functional relationships.
Prospective Elementary Teachers&apos; Beliefs about Collaborative Problem Solving and Dialogue in Mathematics
Author: Xenofontos, Constantinos
Date: 2017-00-00
Type: Journal Articles
Subjects: Preservice Teachers,Elementary School Teachers,Student Attitudes,Beliefs,Teacher Collaboration,Problem Solving,Mathematics Instruction,Foreign Countries,Undergraduate Students,Questionnaires,Preservice Teacher Education,Qualitative Research,Workshops

This study is concerned with prospective elementary teachers' beliefs about collaborative problem solving and dialogue in mathematics classrooms. Participants (n = 16) attended an undergraduate module titled &quot;Problem Solving in Primary Mathematics&quot;, which was specifically designed to provide them with opportunities in collaborative problem solving and dialogic activities. Students were invited to answer an open-ended questionnaire at the beginning and end of the course. In addition, at the end of the semester, students wrote individual reflective reports commenting on their experiences. Qualitative analyses revealed three areas of beliefs for which positive changes were observed: (a) dialogue and its relation to school mathematics, (b) the characteristics of a &quot;good&quot; interlocutor, and (c) the importance of collaborative problem solving. This paper closes with a discussion concerning the implementations of our findings and suggestions for future research.
Using Video Game Design to Motivate Students
Author: Evans, Michael A.
Date: 2017-00-00
Type: Journal Articles
Subjects: Video Games,Student Motivation,After School Education,After School Programs,Learner Controlled Instruction,Learner Engagement,Motivation Techniques,Science Interests,Simulation,Participant Observation,Semi Structured Interviews,Biology,Evolution,Scientific Concepts,Scientific Methodology,Case Studies,Student Participation,Student Projects,Student Attitudes,Computer System Design

Because video games are so popular with young people, researchers have explored ways to use game play to engage students in school subjects (Peppler &amp; Kafai, 2007; Rockwell &amp; Kee, 2011; Small, 2011). Motivating students in science is especially important because of declines both in the number of young people who choose science careers and in the number of adults who have a sufficient grasp of science to make thoughtful decisions (Bell, Lewenstein, Shouse, &amp; Feder, 2009). To counter these trends, informal science educators have adopted video games and simulations as teaching tools and have called for research on how games can motivate youth to engage with science (Honey &amp; Hilton, 2011). Video games that provide level-building capabilities (Reiber, 2005) can be particularly useful in fostering informal science learning. To add to the knowledge base, the authors studied how students used level-based video game development in an out-of-school time (OST) setting to learn science content. Building on prior efforts (Evans &amp; Biedler, 2012; Evans, Norton, Chang, Deater-Deckard, &amp; Balci, 2013; Evans, Pruett, Chang, &amp; Nino, 2014), they explored how the project incorporated the video game to support learners' science motivation. This work with a commercial off-the-shelf video game is an example of how a learner-centered, technology-infused approach can advance the theory and practice of informal science learning (Honey &amp; Hilton, 2011).
Fostering Arts Education through a University-Afterschool Partnership
Author: Leonard, Alison E.
Date: 2017-00-00
Type: Journal Articles
Subjects: College School Cooperation,Partnerships in Education,Art Education,After School Programs,Public Schools,Art Activities,Teacher Education,Teacher Education Programs,Elementary School Students,Grade 2,Grade 3,Grade 4,Grade 5,Grade 6,Visual Arts,Theater Arts,Field Experience Programs

Regardless of the type of arts activity, the importance of the arts in afterschool programs cannot be overestimated. As the arts are increasingly marginalized in public school systems, afterschool arts education can be an alternative way to integrate the arts into children's academic experiences or build on their in-school arts experiences (Briggs &amp; McHenry, 2013; Charmaraman &amp; Hall, 2011; Eckhoff, Hallenbeck, &amp; Spearman, 2011; Stiegelbauer, 2008). However, logistical and resource constraints challenge afterschool programs looking to provide and maintain quality arts education (Montgomery et al., 2013). One solution to the challenge afterschool programs face in providing high-quality arts education is to partner with a university. In the model featured in this article, a university teacher education arts course brings its students into elementary afterschool programs at local Title I schools. These students participate in arts-oriented field experiences that both enhance their own education and provide quality arts activities in the afterschool programs. This ongoing university-afterschool partnership, now in its fifth year, is presented as a model partnership for enhancing arts education after school, one that presents unique opportunities and challenges and that suggests best practices in such partnerships.
An Unexpected Outcome: Afterschool STEM Enrichment Empowers Facilitators, Too!
Author: Masarik, Michelle
Date: 2017-00-00
Type: Journal Articles
Subjects: After School Programs,STEM Education,Empowerment,Self Efficacy,Teacher Effectiveness,Communication Skills,Middle School Students,Identification (Psychology),Critical Thinking

One of the goals of afterschool programming is to empower students by increasing their sense of autonomy and giving them room to chart their own course of discovery. Long before STEM (science, technology, engineering, and math) became part of the educational vernacular, afterschool practitioners were using science content and scientific practices as tools for youth empowerment. For that empowerment to happen, the youth themselves have to connect to the content and experience self-actualization. As educators work to increase their skills and knowledge to present the best experience for their students, an unexpected outcome can be an increase in their own self-efficacy and STEM identity.