ethanporcaro/eric-fulltext-meta huggingface dataset:
From Computational Strategies to a Kind of Relational Thinking Based on Structure Sense
Author: Martínez-Hernández, Cesar
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Elementary School Students,Elementary School Mathematics,Mathematics Skills,Computation,Thinking Skills,Learning Strategies,Number Concepts,Algebra

This paper provides evidence on how elementary school students from a Mexican public school move from using an operational sense, expressed in computational strategies, to a kind of relational thinking based on structure sense ideas and expressed by number decomposition. Even though the results are somewhat preliminary, they illustrate how students can leave behind their computational strategies and develop a more sophisticated mathematical reasoning regarding equivalence of numerical expressions and equalities; however the strategies they developed tended to be based on &quot;ad hoc decomposition of one side and comparison with the initial form of the other side,&quot; rather than on compensation [For the complete proceedings, see ED606556.]
What Does It Take to Be a Fox? New Horizons for Mathematics Communities of Practice
Author: Wessman-Enzinger, Nicole M.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Communities of Practice,Computer Simulation,Barriers,Comparative Analysis,College Faculty,Instructional Leadership,Educational Change,Mathematics Teachers,Academic Rank (Professional),Research,Access to Information,Computer Mediated Communication,Educational Environment,Scholarship

In this theoretical research report we reflect on the challenges of becoming more fox-like in mathematics education work. Using a communities of practice motivating theoretical lens, we compare and discuss the differences in defining, creating, and accessing knowledge between virtual and scholarly communities of practice in mathematics education. We present four claims that virtual communities of practice in mathematics education are inherently foxy work. As part of our claims, we discuss how scholarly communities of practices are inherently hedgehog work. We conclude with a list of recommendations of those within the scholarly communities of practice in mathematics education. These recommendations include looking toward the successful fox-like attributes of the virtual communities in mathematics education. [For the complete proceedings, see ED606556.]
Examining Obstacles to Mathematics Graduate Students Development as Teachers
Author: Beisiegel, Mary
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Barriers,Graduate Students,Mathematics Education,Student Attitudes,Guidelines,Mathematics Teachers,Teaching Experience,Teaching Assistants,Higher Education,Teaching Skills,Professional Development,Program Descriptions,Faculty Development

As the field of professional development for mathematics graduate students evolves, there is a need for research studies that examine how mathematics graduate students develop as teachers. This study aims to fill this gap in the research by studying mathematics graduate students' experiences with teaching as they progress through their graduate programs. Mathematics graduate students were recruited from a large university mathematics department. They were responded to surveys and were interviewed semi-annually for two or more years. We analyzed their responses using thematic analysis and a framework that captured their development as teachers. In this report, we describe a framework for teachers' development and context and methods of the study. We present findings on how the framework elucidated mathematics graduate students' development as teachers and illustrate obstacles to their development. [For the complete proceedings, see ED606556.]
Acquiring a Stance on Equity and Social Justice within an Online Mathematics Specialist Program
Author: Baker, Courtney K.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Equal Education,Social Justice,Online Courses,Mathematics Instruction,Specialists,Masters Programs,Teacher Competencies,Mathematics Teachers,Elementary Secondary Education,Student Attitudes,Teacher Responsibility

This research report will discuss mathematics specialists and the way in which they communicate ideas of equity and social justice within a master's program that leads to a state endorsement in mathematics education leadership. Many mathematics specialist programs focus on developing their mathematical content knowledge for teaching, but these specialized leaders also need to learn about curriculum, assessment, pedagogy, and leadership for school change. This research describes one mathematics specialist program's initial efforts in developing mathematics teacher leaders who take action within their K-12 school contexts. Preliminary findings suggest that the mathematics specialists within this program are aligning their views of equitable mathematics instruction with Principles to Actions (National Council of Teachers of Mathematics, 2014) and the Teaching for Robust Understanding Framework (Schoenfeld, 2015). Implications for the program are that we are still exploring how to incorporate these ideas and facilitate critical conversations as teacher educators within our classrooms. [For the complete proceedings, see ED606556.]
Characterizing Evolution of Mathematical Models
Author: Czocher, Jennifer A.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Models,Mathematics Instruction,Teaching Methods,Thinking Skills,Undergraduate Students,Problem Solving,Cognitive Processes,Symbols (Mathematics)

Formulating a mathematical model is a dynamic process, and attending to changes in students' models as they engage in modeling tasks is critical for informing pedagogical interventions. In this report, we coordinate constructs from literature on mathematical modeling, quantitative and covariational reasoning, and semiotics to characterize changes in mathematical models. We illustrate the application of these constructs using data from an undergraduate solving a modeling task. [For the complete proceedings, see ED606556.]
Covariational Reasoning Supporting Preservice Teachers&apos; Mathematization of an Energy Balance Model for Global Warming
Author: Gonzalez, Dario A.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Mathematics Teachers,Mathematical Logic,Climate,Pollution,Ecology,Logical Thinking,Mathematical Models,Energy,Environment,Comprehension

I discuss how three preservice mathematics teachers' (PSTs') covariational reasoning supported the mathematization of a simple energy balance model (EBM) for global warming, and how such mathematization shaped PSTs' understanding of the link CO2 pollution and global warming. I use Thompson &amp; Carlson's (2017) levels of covariational reasoning and Thompson, Carlson, Byerley, and Hatfield (2014) descriptions of understanding and meaning to inform the discussion of results. The PST completed the EBM Task during an individual, task-based interview. The analysis revealed that Chunky Continuous Covariation level supports the mathematization of the EBM in terms of a covariation's rapidity of change. The analysis also revealed that particular mathematizations resulted in particular meanings for radiative equilibrium, which in turn have implications for understanding the link between CO2 pollution and global warming.
Against the Epistemic Horizon toward Powerful Discourse
Author: Byun, Sunghwan
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Student Centered Learning,Mathematics Teachers,Teacher Student Relationship,Power Structure,Epistemology,Discourse Analysis,Interaction

In mathematics classrooms, teachers are often the authority as a knower of mathematics. To support students to develop their identity as doers of mathematics, teachers need to decenter the authority and to place students in a more powerful position as autonomous thinkers. Building on the work of Herbel-Eisenmann and colleagues (2013), this paper aims to expand the notion of powerful discourse from a conversation analytic approach. By examining the fine-grain epistemic characteristics of interactional sequences, I argue for the significance of the interactional knowledge domain, in which positioning of students as more or less knowledgeable takes place. Further, I discuss the need for examining the discursive dimension of knowledge and discursive practices that can redistribute the epistemic authority in mathematics classrooms. [For the complete proceedings, see ED606556.]
Maintaining the Mathematical Focus of Whole-Class Discussions: Dilemmas and Instructional Decisions
Author: Gilbertson, Nicholas J.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Instructional Effectiveness,Discussion (Teaching Technique),Decision Making,Classroom Techniques,Experienced Teachers,Attention Control,Middle School Teachers,Grade 7,Educational Objectives,Common Core State Standards,Middle School Mathematics,Facilitators (Individuals)

As teachers shift their practice from traditional student-to-teacher interaction patterns to collaborative discussions around rich mathematics, they often encounter instructional challenges. One such challenge is deciding when to pursue interesting and productive ideas that run contrary to the particular mathematical goal of the lesson. In this research summary, I report results from a study involving one experienced teacher's instructional decisions and how she maintained attention to the lesson-specific content goal given possible alternative pathways. [For the complete proceedings, see ED606556.]
Components of High-Quality Mathematics Classrooms: Attending to Learning Opportunities for English Language Learners
Author: Sorto, M. Alejandra
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Educational Quality,English Language Learners,Teaching Methods,Barriers,Teacher Student Relationship,Educational Opportunities,Inclusion,Classroom Communication,Video Technology,Kindergarten,Elementary School Students,Middle School Students,Mathematics Achievement,Access to Education,Pedagogical Content Knowledge,Scores,Instructional Effectiveness

In response to the call for research on integrating best general practices in teaching with those that promote equity and access, we present a two-part study focused on instructional strategies that may remove learning barriers for English Language Learners. We theoretical developed and empirically explored supplemental components for traditional quality of instruction measures (MQI, Hill, 2014, Math Habits Tool, Melhuish &amp; Thanheiser, 2017). We share results from a quantitative study empirically verifying the effect of suggested ELL-focused instructional strategies (Chval &amp; Chávez, 2011) on ELL learning via the creation of an additional MQI dimension. Based on these results, we then provide theoretical operationalizations of these strategies to integrate into the student-and-teacher interaction tool: the Math Habits Tool (Melhuish &amp; Thanheiser, 2017) as means to concretize these strategies for researchers and practitioners. [For the complete proceedings, see ED606556.]
Flipped Instruction in Algebra 1: Is It an Old Idea in New Clothes?
Author: Zhao, Wenmin
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Blended Learning,Video Technology,Homework,Algebra,Mathematics Activities,Mathematics Instruction,Secondary School Mathematics

What are the substantive differences between flipped and non-flipped instruction? This study examined the instruction of two teachers who have worked together within the same school using the same Algebra 1 curriculum for years. One teacher flipped his instruction (creating lecture videos assigned as homework), while the other teacher continued with non-flipped instruction. Data from classroom observations were analyzed qualitatively using the Flipped Mathematics Instruction Framework. Results show that although there were clear differences in the format of flipped and non-flipped lessons, there were also substantial similarities with regard to features of instruction (e.g., procedural mathematical development, teacher authority, and tasks with low cognitive demand). Our analysis indicates that flipped instruction is not necessarily an innovative model when compared with non-flipped. [For the complete proceedings, see ED606556.]
Backward Transfer Effects on Action and Process Views of Functions
Author: Hohensee, Charles
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics,Algebra,High School Students,Transfer of Training,Mathematics Instruction,Influences,Secondary School Mathematics,Logical Thinking,Pretests Posttests

This study was conducted to gain understanding about potential influences that learning about quadratic functions has on high school algebra students' action versus process views of linear functions. Pre/post linear functions tests were given to two classrooms of Algebra II students (N=57) immediately before and immediately after they participated in a multi-day unit on quadratic functions. The purpose was to identify ways that their views of linear functions had changed. Results showed that on some measures, students across both classes shifted their views of linear functions similarly. However, on other measures, the results were different across the classes. These findings suggest that learning about quadratic functions can influence students' action or process views of linear. Furthermore, the instructional differences between classes provide insights into how to promote those influences that are productive for students' views. [For the complete proceedings, see ED606556.]
Preservice Teachers&apos; Use of Noticing Practices to Evaluate Technological Resources
Author: Yeo, Sheunghyun
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Classroom Techniques,Perception,Elementary School Teachers,Mathematics Skills,Thinking Skills,Educational Technology,Mathematics Activities,Computer Software Evaluation

This study examines how elementary preservice teachers notice children's mathematical thinking and how this noticing influences the evaluation of technological resources. In particular, we explore the aspects of thinking to which preservice teachers attend and how they interpret evidence about children's thinking when using the Spatial-Temporal Math (ST Math) program. Data collection included a group survey administered after an initial exploration of a set of ST Math activities, screencast recordings during which children used and talked about the program, and a reflective writing assignment. The findings of this study show how preservice teachers used their noticing skills (attending and interpreting) in their evaluations of the tool, in some cases prompting them to shift their evaluation on the basis of student thinking. [For the complete proceedings, see ED606556.]
Examining the Tensions between High Quality Discourse and Sharing Mathematical Authority with Students
Author: Sullivan, Patrick
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Teaching Methods,Student Centered Learning,Classroom Communication,Mathematics Instruction,Secondary School Teachers,Grade 7,Grade 8,Grade 9,Grade 10,Grade 11,Grade 12,Discussion (Teaching Technique),Faculty Development,Teacher Attitudes,Mathematics Teachers,Secondary School Mathematics,Power Structure,Student Participation

Current reform efforts challenge teachers to create more student-centered classrooms focused on high quality classroom discourse (NCTM, 2014). There are difficulties, however, teachers face in bringing this vision to fruition. Over the past three years, we have worked with a group of 7-12 teachers supporting their efforts to implement high quality classroom discourse. Although their espoused beliefs aligned with our vision of high-quality discourse, their enacted practices did not align with those espoused beliefs. Further analysis suggested that many of these challenges are related to sharing mathematical authority with their students. We intend to share a set of &quot;Look Fors&quot; to build awareness of features of sharing mathematical authority that might be inhibiting the quality of teachers' classroom discourse. A set of questions will also be shared to help teachers decide upon a plan of action to overcome those challenges. [For the complete proceedings, see ED606556.]
&quot;Getting Better at Sticking with It&quot;: Examining Perseverance Improvement in Secondary Mathematics Students
Author: DiNapoli, Joseph
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Secondary School Students,Secondary School Mathematics,Persistence,Student Improvement,Thinking Skills,Problem Solving,Grade 9,Mathematics Activities,Scaffolding (Teaching Technique),Mathematics Instruction,Educational Practices

Supporting students' in-the-moment perseverance is a vital objective in mathematics education because it promotes learning with understanding. Yet, little is written about if and how student perseverance can improve over time. I examine the specific ways in which secondary students improved their perseverance as they engaged with challenging mathematical tasks over six weeks. The results show that encouraging students to initially attend to their conceptual thinking can prolong productive effort upon impasse and explicitly improve selection of problem-solving strategies and affect regulation. These findings suggest learning environment designs that provide consistent opportunities for students to practice (and improve) their perseverance. [For the complete proceedings, see ED606556.]
A Transformative Learning Experience for the Concept of Function
Author: Meagher, Michael S.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Concepts,Transformative Learning,Difficulty Level,Concept Formation,Preservice Teachers,Secondary School Mathematics,Educational Technology,Instructional Effectiveness,Undergraduate Students

Functions form a central part of the U.S. mathematics curriculum. A large body of research shows that students at all levels, including preservice secondary mathematics teachers, have difficulties with defining function as a correspondence between two sets with a univalence condition. Those difficulties include privileging algebraic representations and reductive interpretations of the univalence condition in the form of the vertical line test. In our research study, 47 pre-service mathematics teachers provided definitions of function, engaged with an interactive applet that had a non-standard representation of function. The interaction with the applet was effective in initiating a series of dilemmas in their conception of function that resulted in the majority of the participants transforming and/or refining their conception of function. [For the complete proceedings, see ED606556.]
Using Number Sequences to Model Middle-Grades Students&apos; Algebric Representations of Multiplicative Relationships
Author: Zwanch, Karen
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Middle School Students,Mathematics Instruction,Algebra,Thinking Skills,Mathematical Concepts,Cognitive Structures,Multiplication,Correlation,Concept Formation,Numbers,Task Analysis,Problem Solving

The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results indicate that students who have constructed a tacitly nested number sequence (TNS), second in the hierarchy, do not represent multiplicative relationships algebraically. Students who have constructed an advanced tacitly nested number sequence (aTNS), third in the hierarchy, do so inconsistently, and students who have constructed an explicitly nested number sequence (ENS), fourth in the hierarchy, do so consistently. Coordinating three levels of units in activity advantages aTNS and ENS students, while splitting further advantages ENS students' algebraic reasoning. [For the complete proceedings, see ED606556.]
Connections between Feedback and Student Happiness and Engagement in High Achievement Classrooms
Author: Anthony, Monica
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Feedback (Response),Psychological Patterns,Correlation,Learner Engagement,Classroom Environment,High Achievement,Teacher Student Relationship,Mathematics Instruction,Verbal Communication,Positive Reinforcement,Student Attitudes,Elementary School Teachers,Elementary School Students,Grade 4,Grade 5,Error Correction

Researchers have investigated how teacher feedback contributes to students' learning, yet there is insufficient research into the connection between teacher feedback and student happiness, which is linked to engagement, socio-emotional well-being, and ultimately academic achievement. We coded lesson transcripts from elementary teachers to determine emergent patterns between types of teacher feedback and average student self-reports of happiness in mathematics. We found teachers to employ specific feedback more than general feedback. In addition, feedback for effort and ability accounted for a small percentage of feedback. Findings suggest that student happiness is linked to specific combinations of feedback dimensions. [For the complete proceedings, see ED606556.]
Bob&apos;s Additive Reasoning: Implications for Knowing Fractions as Quantities
Author: Martin, Kristi
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Fractions,Learning Disabilities,Numbers,Mathematics Instruction,Elementary School Students,Grade 5,Logical Thinking,Elementary School Mathematics

Fractions are one of the most difficult areas of mathematics for all students and especially for students with learning disabilities (LD). An incomplete understanding of fractions during the elementary and middle school may be why some students view fractions as &quot;really small&quot; or &quot;less than 1&quot; compared to others who view them as multiplicative magnitudes. We analyzed how one student with LD worked on tasks involving both whole numbers and fractions using the framework of units coordination. Through our analyses of 14 teaching experiment sessions, we determined that he was operating on two levels of units with whole numbers, but only one level of units with fractions. We argue that this limited his ability to operate multiplicatively with fractions. However, his identified LD did not appear to impact his work with the fractions tasks he was given. Implications for future research and instruction are shared. [For the complete proceedings, see ED606556.]
Pass the &quot;Idea&quot;: Following Bilingual Mathematics Discussions = Pásame la &quot;Idea&quot;: Siguiendo Discusiones Matemáticas Bilingües
Author: Krause, Gladys
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Bilingual Education,Classroom Communication,Mathematics Instruction,Teaching Methods,Thinking Skills,Coaching (Performance),Team Sports,Teacher Student Relationship,Elementary School Students,Discussion (Teaching Technique),Problem Solving,Spanish,English (Second Language),Second Language Learning,Language Usage,Grade 2,Code Switching (Language),Logical Thinking

In this study we document how a mathematical idea, shared by a student, changes the development of the class discussion. Our work characterizes the flexible and open dynamics in mathematics instruction that a teacher adopts to give her students control of their own mathematical ideas. Our work argues that this flexibility is necessary for teachers to engage in instructional practices that respond to students' mathematical thinking. To demonstrate the teacher's flexibility we use the analogy of soccer, relying on the literature of Game Sense coaching approach, which suggests that the coach (the teacher in our context) is positioned to manipulate the practice environment with the purpose of facilitating learning. [This paper is provided in both Spanish and English. For the complete proceedings, see ED606556.]