ethanporcaro/eric-fulltext-meta huggingface dataset:
Development and Use of a Conjecture Map for Online Professional Development Model
Author: Choppin, Jeffrey
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Program Implementation,Online Courses,Educational Technology,Faculty Development,Rural Schools,Access to Education,Program Design,Maps,Collegiality,Teacher Competencies,Teaching Methods,Reflection,Discussion,Observation,Thinking Skills,Educational Environment,Mathematics Instruction

In this paper we discuss our development and use of a conjecture map for a large research project on the design and implementation of an online professional development model. Following Sandoval's (2014) model, we built the conjecture map to reflect our high-level conjectures (overarching goals of the project), the embodiment of the learning design, the mediating processes, and the outcomes. After roughly half a dozen iterations to ensure that we accurately and fully captured the features of the learning environment and the mediating processes, we used the conjecture map as an anchor for a number of our data analysis activities, particularly of our online course modules, and for initiating theory-building processes. We also found that it was an expedient way to communicate internally and externally the core assumptions and learning principles of our multifaceted online professional development model. [For the complete proceedings, see ED606531.]
Navigating Dilemmas of Studying Mathematics Engagement in Secondary Classrooms
Author: Jansen, Amanda
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Learner Engagement,High School Students,Mathematics Instruction,Teaching Methods,Educational Experience,Student Attitudes

To better understand how to support high school students' engagement, advancements in research methods that provide greater understandings of malleable factors of engagement and conditions that affect students' engagement are needed. In this conceptual paper, we introduce four dilemmas that researchers need to navigate to study secondary students' engagement with mathematics: How can we concurrently capture engagement in-the-moment and at scale? What counts as a moment or experience? What sorts of experiences could be engaging? Whose perspectives on the experience should be privileged? We propose approaches for navigating these dilemmas in the context of a current research project. [For the complete proceedings, see ED606531.]
Probability and Independence: A Comparison of Undergraduates
Author: Zwanch, Karen
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Undergraduate Students,Statistics,Probability,Mathematical Logic,Concept Formation,Problem Solving,Mathematical Formulas,Schemata (Cognition),Logical Thinking

Probability and independence are difficult concepts, as they require the coordination of multiple ideas. This qualitative research study used clinical interviews to understand how three undergraduate students conceptualize probability and probabilistic independence within the theoretical framework of APOS theory. One student's reasoning was consistent with a process conception, one student with at least an object conception, and one with a schema conception of probability and independence. Differences in students' thinking are analyzed, with a specific focus on intuition and simultaneously occurring events. [For the complete proceedings, see ED606531.]
Uses of Coordinate Systems: A Conceptual Analysis with Pedagogical Implications
Author: Lee, Hwa Young
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Teaching Methods,Mathematics Instruction,Mathematical Concepts,Abstract Reasoning,Difficulty Level,Textbooks,Guidelines,Curriculum Design,Learning Processes,Task Analysis,Geometry,Graphs

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of coordinate systems. We discuss the implications of the framework for student learning, curriculum design, and teaching. [For the complete proceedings, see ED606531.]
Analysis of Teachers&apos; Questioning in Supporting Mathematical Argumentation by Integrating Habermas&apos; Rationality and Toulmin&apos;s Model
Author: Zhuang, Yuling
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Teaching Methods,Questioning Techniques,Persuasive Discourse,Secondary School Teachers,Student Teaching,Student Teachers,Intention,Mathematical Logic

Teachers' questioning is a pivotal contributing factor to support students' engagement in productive mathematical collective argumentation. Following Habermas' (1998) construct of rational behavior, we attempted to demonstrate how teachers' questioning can be framed based on this construct. Adapting Habermas' construct with Toulmin's (1958/2003) model for argumentation, we conducted a case study to analyze how a prospective secondary teacher used questions to support collective argumentation in one of her student teaching classrooms. We also explored how the prospective teacher's interpretations of argumentation related to her use of rational questioning. The results suggested that this theoretical integration can be a useful tool to frame teacher questioning based on teachers' intentions and organizations of argumentation. Some educational implications for teacher professional development are provided. [For the complete proceedings, see ED606531.]
Expanding Students&apos; Role When Doing Proofs in High School Geometry
Author: Herbst, Patricio
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Student Role,Mathematical Logic,Geometry,Mathematics Instruction,Difficulty Level,Vignettes,High School Teachers,High School Students,Instructional Effectiveness,Teacher Attitudes

Using mixed-effects regression, we analyzed teachers' responses to a multimedia survey of instructional practices in posing proof problems in geometry. Teachers described and rated for appropriateness three different ways of involving students in deciding what to prove, including one in which the teacher chooses the givens and the conclusion to prove, and two others that expand the students' role in different degrees. While teachers recognized the former as normative, their ratings identified an alternative as more appropriate, having more positive value, and less negative value than the normative one. This alternative has students propose the givens or the conclusion to prove, and it allows the teacher to control the complexity of instruction by endorsing one proposal before students are to write the proof. [For the complete proceedings, see ED606531.]
Teachers&apos; Perception of Standardized Classroom Observation Tool
Author: Barrogo, Sheilla D.
Date: 2020-07-00
Type: Journal Articles
Subjects: Teacher Attitudes,Classroom Observation Techniques,Public School Teachers,Teacher Evaluation,Feedback (Response),Teacher Administrator Relationship,Anxiety,Teacher Improvement,Classroom Environment,Educational Technology,Technology Uses in Education,Teacher Effectiveness,Foreign Countries

Working as a public school teacher is a great challenge. There is a lot of task at hand to be done and accomplished. Doing paper works is just one thing, providing quality learning is another. This study analyzes the teachers' perception of the standardized classroom observation tool. The researcher used a descriptive type of design in the study with a survey as the primary instrument of gathering data. Using a simple random sampling technique, 200 public school teachers participated in the survey. For the instrument of the study, the researcher adopted the questionnaire constructed by Wairimu (2016). The study used the following statistical tools to analyze the teachers' perception: frequency, mean, percentage, and standard deviation with the help of Microsoft Excel. The result of the survey showed that eight out of the ten statements regarding the standardized classroom observation tool yielded an overall response of &quot;strongly agree&quot;. The study concluded that a standardized classroom observation tool serves as a guide for the teachers to assess their performance and plan for their improvement, thus, enhancement of teachers' preparation and competency. With the foregoing results, the researcher provided pertinent recommendations for professional and organizational development.
Investigating MTE Questioning as a Relational Teaching Practice
Author: Lischka, Alyson E.
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematics Teachers,Teaching Methods,Methods Courses,Teacher Educators,Questioning Techniques,Teacher Collaboration,Teacher Education Programs,Teacher Attitudes,Educational Improvement,Feedback (Response)

As mathematics teacher educators (MTEs), we enact teaching practices in our mathematics methods courses as instantiations of practice for PTs. Questioning is a core practice in teaching (and learning to teach) mathematics that interacts with relationships between MTEs and prospective teachers (PTs). We engaged in a collaborative self-study to interrogate our questioning practice as part of relational teacher education with a goal of improving our questioning to reach all PTs. Observation and recordings of our questions during mathematics methods classes, collaborative conversations, and narratives were analyzed to describe characteristics of our questioning practice (Dillon, 1990) and determine how it is relational (Kitchen 2005b). We found commonalities in our questioning practice and identified ways to improve it. This serves as an exemplar for MTEs to inquire about their own questioning practice. [For the complete proceedings, see ED606531.]
The In-the-Moment Noticing of the Novice Mathematics Teacher
Author: Jarry-Shore, Michael
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Public School Teachers,Elementary School Teachers,Secondary School Teachers,Beginning Teachers,Mathematics Teachers,Mathematics Instruction,Thinking Skills,Teacher Student Relationship,Observation,Attention

Recent reforms urge teachers to support students in pursuing their own mathematical strategies. Yet, to support a student in pursuing a strategy that they themselves devise, teachers must first notice details in the student's mathematical thinking, often in-the-midst of instruction. In this study, I examined four novice teachers' noticing of students' thinking in-the-moment, as well as the types of knowledge teachers called upon to support them with this noticing. Teachers took part in a post-lesson interview, in which they discussed moments from a preceding lesson of theirs caught on video. Findings indicate that novice teachers relied most on knowledge they developed in their own classrooms (e.g., knowledge of their individual students) to support their in-the-moment noticing. These findings align with calls to prepare teachers to view their classrooms as rich sources of knowledge supportive of their instructional practice. [For the complete proceedings, see ED606531.]
Capturing Variability in Flipped Mathematics Instruction
Author: Otten, Samuel
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Blended Learning,Teaching Methods,Mathematics Instruction,Comparative Analysis,Guidelines,Video Technology,Homework,Class Activities,Classroom Research,Multimedia Materials,Outcomes of Education

Flipped instruction is being implemented in an increasing number of mathematics classes but the research base is not yet well developed. Many studies of flipped instruction involve a small number of flipped classes being compared to non-flipped classes, but this methodology fails to account for variations in implementations. To aid in the systematic attention to variation, this article presents a framework for flipped mathematics instruction that identifies key features of the videos assigned as homework as well as features of the in-class activities. The components of the framework are accompanied by proposed quality indicators to further distinguish between flipped implementations that are structurally similar but different in enactment. [For the complete proceedings, see ED606531.]
Design Principles for the Development of Professional Noticing of Students&apos; Technological Mathematical Practices
Author: McCulloch, Allison W.
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Pedagogical Content Knowledge,Technological Literacy,Video Technology,Case Method (Teaching Technique),Preservice Teachers,Secondary School Mathematics,Attention,Preservice Teacher Education,Instructional Materials,Curriculum Design,Statistics,Trigonometry

In support of standards for the learning and teaching of mathematics and statistics that advocate for the use of technology to promote reasoning and sense making, and to elicit student thinking, we draw on the use of authentic student work in the form of video case instruction to develop prospective secondary mathematics teachers' [PSMTs] knowledge of students' understanding, thinking, and learning with technology in mathematics. Specifically, we draw on the extant literature related to TPACK, video cases as learning objects, and noticing to propose a set of design principles intended to guide the development of materials to support PSMTs' acquisition of TPACK. Here we explicate six design principles situated in the literature, provide an example of a module designed based on these principles, and share findings from pilot studies utilizing the module. [For the complete proceedings, see ED606531.]
Static and Emergent Thinking in Spatial and Quantitative Coordinate Systems
Author: Paoletti, Teo
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: STEM Education,Graphs,Logical Thinking,Spatial Ability,Mathematical Concepts,Cognitive Processes,Visual Aids,Measurement

The body of research examining students' graphing understandings across STEM fields indicates students are not developing productive meanings for graphs. We conjecture such failings may, in part, be explainable by features of students' use of coordinate systems and graphing activity that are under examined. In this theoretical report, we present a conceptual analysis of different ways students may reason about graphs and coordinate systems. Specifically, we describe two different uses of coordinate systems--spatial and quantitative--students might leverage and two ways of reasoning--static and emergent--students might engage in as they construct or interpret graphs. We characterize how a student may engage in each kind of reasoning in each use of coordinate system. We intend this paper to serve as a theoretical lens for future empirical studies examining students' developing graphing understandings. [For the complete proceedings, see ED606531.]
Early Care and Education in Rural Communities. OPRE Research Brief 2020-62
Author: Paschall, Katherine
Date: 2020-06-00
Type: Reports - Descriptive
Subjects: Early Childhood Education,Child Care,Rural Areas,Child Care Centers,Access to Education,Urban Areas,Suburbs,Rural Urban Differences,Infants,Toddlers,Family Needs,Professional Development,Certification,Family Environment,Accreditation (Institutions),Labor Turnover,Access to Health Care,Transportation,Scheduling,Costs,Predictor Variables,Educational Quality,Preschool Teachers,Caregivers,Individual Characteristics

This report provides a descriptive comparison of the early care and education (ECE) landscape across rural, moderate-density urban (suburban), and high-density urban areas. The goal of this comparison was to understand whether ECE availability and characteristics in rural areas differ from those in more densely populated communities. We used nationally representative data on both households with young children and ECE providers to describe availability of care, use of and need for child care, and setting and workforce characteristics in rural, moderate-density urban, and high-density urban areas. Key findings from this report relate to the following: (1) Availability and use of care; (2) Families' need for and difficulties finding care; (3) Characteristics of ECE centers and homes by rurality; and (4) Characteristics of ECE center-based and home-based workforces by rurality. In terms of workforce characteristics, findings suggest that listed home-based teachers and caregivers in rural areas may benefit from additional professional supports such as involvement in quality initiatives and professional organizations. Although current findings are representative of ECE in communities of various population densities at a national level, the findings should be supplemented with research using regional or state data to better understand the supply and demand of rural ECE at a more local level.
Response to Intervention and Multi-Tiered Systems of Support in Maine Schools: Portraits of Promising Practices
Author: Hawes, Kathryn
Date: 2020-04-00
Type: Reports - Research
Subjects: Response to Intervention,Positive Behavior Supports,Students with Disabilities,Equal Education,Educational Legislation,Federal Legislation,Special Education,State Legislation,Program Implementation,Success,Barriers,Educational Benefits,Individualized Education Programs,High School Students,Middle School Students,Elementary School Students,Mental Health Programs,Parent Participation

In response to requirements of the federal Individuals with Disabilities Education Act (IDEA), Maine enacted a rule requiring all schools to have a multi-tiered system of supports (MTSS) in place by 2012 for a general education, pre-referral system of student support. The purpose of this system, generally termed Response to Intervention (RtI) by many practitioners, was to increase student achievement and decrease the growing number of students referred for special education services. It was anticipated that the system would also reduce overall costs for student support by providing early interventions. The Maine Education Policy Research Institute (MEPRI) was asked by the Maine Legislature to conduct a study of RtI or MTSS behavioral programs in Maine schools. The goal of the study is to improve the state's understanding of the current practices, challenges, and supports needed through descriptive portraits of Maine schools' MTSS programs. This can help to inform future policy changes that would help schools to implement robust programs, and also help Maine districts to learn from what others are doing. In early conversations to recruit schools for this study it became clear that curriculum leaders and superintendents in southern Maine also expressed an independent desire for more information about the ways in which districts are designing, implementing, and evaluating RtI or MTSS in their schools. Given the overlap with the purpose of the legislative study, the scope of the work was expanded to include more schools to allow a broader depiction.
Razonamiento digital: Representar, explorar y resolver problemas verbales con el uso de GeoGebra = Digital Reasoning: Representing, Exploring and Solving Word Problems through the Use of GeoGebra
Author: Gómez-Arciga, Adrián
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Computer Software,Geometry,Mathematics Instruction,Teaching Methods,High School Teachers,Problem Solving,Word Problems (Mathematics),Mathematical Concepts

In this study we analyze and contrast approaches that future high school math teachers show when solving word problems with the use of pencil and paper and later, with the use of a Dynamic Geometry System (DGS). The resources, representations, strategies and forms of mathematical reasoning that the participants exhibit when they use GeoGebra in the process of problem solving are analyzed. The results show that the use of the tool favors the dynamic exploration of the concepts involved, the formulation of conjectures and the search for different arguments to validate the solution. [This paper is provided in both Spanish and English. For the complete proceedings, see ED606531.]
How Do Undergraduate Students Make Sense of Points on Graphs in Calculus Contexts?
Author: David, Erika
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Calculus,Undergraduate Students,Mathematics Instruction,College Mathematics,Graphs,Mathematical Logic,Geometry,Validity

The purpose of this study is to examine the characteristics of students' thinking about graphs while evaluating statements from Calculus. We conducted clinical interviews in which undergraduate students evaluated mathematical statements using graphs to explain their reasoning. We report our classification of students' thinking about aspects of graphs in terms of value-thinking and location-thinking, which emerged from our data. These two ways of thinking were rooted in students' attention to different attributes of points on graphs we provided: either the input and output values represented by the points or the location of the points in space. Our findings indicate that students' thinking about aspects of graphs accounts for key differences in their understandings of mathematical statements. [For the complete proceedings, see ED606531.]
Computational and Inferential Orientations: Lessons from Observing Undergraduates Read Mathematical Proofs
Author: Dawkins, Paul Christian
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Logic,Validity,Mathematics Instruction,College Students,Learning Strategies,Inferences,Linguistics,Schemata (Cognition),Student Attitudes,Equations (Mathematics)

This paper presents selected findings from an assessment of university students' moment-by-moment reading of mathematical proof. This method, adapted from an assessment of narrative reading validated by psychologists, yields novel insights into the strategies students use to construct meaning for the equations in a proof text. In particular, we present evidence that novice readers constructed meanings for the equations using mathematical practices familiar from non-proof oriented courses -- substituting and solving for variables -- while more experienced readers drew upon practices native to proof-oriented mathematics -- inferring properties of quantities. We refer to these as computational and inferential orientations, respectively. We interpret this mismatch of practices in terms of Systemic Functional Linguistic's notion of textual metafunction and briefly discuss its implications for proof-oriented instruction. [For the complete proceedings, see ED606531.]
A Fine-Grained Analysis of Proof Summaries: A Case Study of Abstract Algebra Students
Author: Demeke, Eyob
Date: 2018-00-00
Type: Speeches/Meeting Papers
Subjects: Undergraduate Students,Validity,Mathematical Logic,Algebra,College Mathematics,Graduate Students,Comprehension,Mathematics Skills

In this paper I explore eleven undergraduate students' comprehension of a proof taken from an undergraduate abstract algebra course. My interpretation of what it means to understand a proof is based on a proof comprehension model developed by Mejia-Ramos, et al. (2012). This study in particular examines the extent to which undergraduate students are able to summarize a proof using the proof's higher-level ideas. Additionally, eleven doctoral students in mathematics were asked to provide a summary of the same proof that the undergraduate students received. Undergraduates' holistic comprehension of the proof was then analyzed in light of summaries that the doctoral students provided. The main finding of the study is that undergraduates' comprehension of the proof was overall inadequate--notably, they demonstrated limited skills in summarizing a proof via the proof's key ideas. Moreover, undergraduates failed to recognize the scope of the method used in the proof. [For the complete proceedings, see ED606531.]