ethanporcaro/eric-fulltext-meta huggingface dataset:
Forms of Nascent Political Conocimiento Leveraged in a Content Course for Preservice Elementary Teachers
Author: Lee-Hassan, Alexa W. C.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Course Content,Preservice Teachers,Teacher Education Programs,Elementary School Teachers,Political Attitudes,Critical Thinking,Grading,Student Attitudes,Teacher Student Relationship,College Faculty,Reflection,Social Justice,Advocacy,Urban Schools,Introductory Courses,Literacy,Decision Making,Student Characteristics,Pedagogical Content Knowledge,Cultural Differences

This study examines the nascent forms of political conocimiento demonstrated by elementary preservice teachers before and after a series of activities designed to engage them in thinking critically and quantitatively about the impacts of different grading systems. In reflections about their learning, the preservice teachers most frequently raised considerations related to knowledge with students and communities, followed by political knowledge. Many of the preservice teachers anticipated using their new knowledge in the near future to understand the implications of their professors' grading systems and in the more distant future to design grading scales in their own classrooms. A few reflections showed awareness of the tensions involved in grading systems, potentially a sign of developing Nepantla, while others evidenced more binary thinking. [For the complete proceedings, see ED630060.]
Opportunities to Learn in Cycles of Enactment and Investigation
Author: Arbaugh, Fran
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Pedagogical Content Knowledge,Teaching Methods,Secondary School Teachers,Mathematics Teachers,Mathematics Instruction,Methods Courses,Teacher Education Programs,Lesson Plans,Educational Objectives,Student Attitudes,Learning Processes

In recent decades, scholars of teacher education have suggested that teacher educators (TEs) should integrate the development of prospective teachers' (PTs') knowledge with their skills for enacting teaching, characterized in the literature as pedagogies of practice. One way to operationalize pedagogies of practice is through engaging PTs in cycles of enactment and investigation (CEIs). Using an opportunity to learn (OTL) lens, this study investigated one CEI enacted in a secondary mathematics methods course. Analyzing course artifacts and final interviews, we found that the PTs had OTL in all six nodes of the CEI, that OTL differed across the nodes, and that OTL in later nodes depended on knowledge built in previous nodes. Implications include the importance of PTs engaging in all nodes of a CEI to maximize OTL about mathematics teaching practices, mathematics, students, and learning. [For the complete proceedings, see ED630060.]
The Evolution from Linear to Exponential Models When Solving a Model Development Sequence = Evolución de Modelos Lineales a Exponenciales al Resolver una Secuencia de Desarrollo de Modelos
Author: Montero-Moguel, Luis E.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Models,College Students,Mathematics,Numbers,Mathematical Logic,College Mathematics,Mathematics Instruction

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified, expanded, and refined, as they developed different iterations of their models. Students' models evolved by creating, first, linear models that required direction; second, models where there was no dissociation between linear and exponential behavior; then, situated exponential models; and finally, sharable, and reusable exponential models. [For the complete proceedings, see ED630060.]
Image of Mathematics In- and Out-of-School: A Case Study of Two Original Participants in an Afterschool STEM Club--Girls Excelling in Math And Science (GEMS)
Author: Zhou, Lili
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Relevance (Education),Clubs,After School Programs,STEM Education,Females,Student Attitudes,Mathematics,Learning Experience,Mathematics Education,Grade 5,Grade 6,Attitudes,Womens Education,Elementary School Students,Developmental Continuity

People often view mathematics as abstract, cold, and irrelevant to real-life, and their school experiences influence such views. In this case study, we investigated the mathematics learning experiences of two women who participated in an afterschool girls STEM club 26 years ago. We explored their experiences in and out of school and how such experiences informed their images of mathematics. Data were collected from a survey, focus group interviews, and individual interviews. Using qualitative analysis, we learned that their school mathematics experiences influenced the participants' images of mathematics. The findings also revealed the participants' continuous and discontinuous learning experiences between school and out-of-school mathematics. This study suggests creating spaces to develop curricula that bridge the gap between school and out-of-school learning experiences. [For the complete proceedings, see ED630060.]
Differential Backward Transfer Effects for Students with Different Levels of Linear Function Reasoning Abilities
Author: Hohensee, Charles
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Logic,Thinking Skills,Mathematical Concepts,Mathematics Education,Transfer of Training,Algebra,Grade 9,Grade 10,Grade 11,Minority Group Students,Summer Programs

Backward transfer is when learning about a new topic influences an individual's prior ways of reasoning about a topic they previously learned about. This study looked at how quadratic functions instruction differentially influenced students' prior ways of reasoning about linear functions. Specifically, we compared students at three levels of reasoning about linear functions, low-, mid-, and high-level, using a pre/posttest design that bracketed a two-week quadratic functions math program. Results showed that students at different reasoning levels experienced different backward transfer effects, that particular mathematical reasoning processes were most involved in the effects, and that the effects spanned two dimensions of productiveness of mathematical reasoning. Results from this study are significant for better understanding the construct of backward transfer, and have implications for teaching quadratic functions. [For the complete proceedings, see ED630060.]
Using Teacher and Student Noticing to Understand Engagement during Secondary Mathematics Lessons
Author: Mirzaei, Amanda Mohammad
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: High School Teachers,Mathematics Teachers,High School Students,Learner Engagement,Attention,Mathematics Instruction,Student Participation

The purpose of this paper is to present a framework that illustrates teachers' and students' ways of noticing mathematical engagement. This framework offers clarity about the complexity of engagement, and it includes three elements: evaluations of the presence of engagement, descriptions of the nature of engagement, and features of the classroom that support or constrain engagement. We interviewed 30 sets of high school math teachers and focus groups of their students and asked them to reflect on students' engagement during a videotaped lesson from their classrooms. Results illustrate cases of how noticing of engagement between teachers and students can be shared. Cases of partially and minimally shared noticing of engagement suggest opportunities for teachers to learn about students' perspectives or how to communicate with students about their intentions to engage them. [For the complete proceedings, see ED630060.]
Exploring Connections between Prospective Teachers&apos; Views of Authority and Experiences in Justification
Author: Rosencrans, Brenda
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Student Attitudes,Problem Solving,Mathematics Instruction,Empowerment,Mathematical Logic,Power Structure,Elementary School Teachers

The purpose of this project was to understand how implicit views of authority support or limit prospective elementary teachers' (PTs) mathematical activity of justifying and to understand how the experience of justifying might support a development of an internal source of authority. In this case study of 18 PTs, we coordinate an analysis of (1) their responses to two justification tasks and (2) interview transcripts in which they discuss their experiences in learning to justify. Preliminary results indicate ways in which their views of authority limited their reasoning about mathematics by not recognizing their own sense-making and supported a sense-making exploration of mathematics that was freeing and empowering. These results provide mathematics teacher educators with insight to help them identify and address limiting views of authority and leverage productive views of authority. [For the complete proceedings, see ED630060.]
Characterizing Opportunities for Mathematical and Social Participation: A Micro-Analysis of Equity in Small-Group Zoom Interactions
Author: Fink, Heather
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Small Group Instruction,Mathematics Instruction,Self Concept,Equal Education,Distance Education,Calculus,Student Participation,Educational Opportunities,Videoconferencing,Computer Mediated Communication,Inclusion,Classroom Communication,Grade 12,High School Students,Advanced Placement,Discourse Analysis,Urban Schools

This study focused on issues of equity related to small-group participation in a distance learning calculus class. Equity is defined as the fair distribution of opportunities for students to participate and learn. I examined how opportunities for mathematical and social participation were constructed through acts of positioning for four students. Findings suggest that creating fair opportunities requires: (1) conceptualizing opportunities for participation as connected to students' positionings and developing identities, (2) acknowledging that what counts as an opportunity for one student does not necessarily count as an opportunity for another student, and (3) leveraging both mathematical and social contributions in creating equitable, supportive, and intellectually rich learning communities. [For the complete proceedings, see ED630060.]
Circular Reasoning: Shifting Epistemological Frames across Mathematics and Coding Activities = Razonamiento Circular: Cambios del Marco Epistemológico en Actividades en la Intersección de Matemáticas y Codificación
Author: Brady, Corey
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Computer Science Education,STEM Education,Coding,Interdisciplinary Approach,Epistemology,Geometry,Thinking Skills,Spatial Ability,Grade 8,Middle School Students,Learning Activities,Teaching Methods,Urban Schools,Art Education

STEM integration holds significant promise for supporting students in making connections among ideas and ways of thinking that might otherwise remain &quot;siloed.&quot; Nevertheless, activities that integrate disciplines can present challenges to learners. In particular, they can require students to shift epistemological framing, demands that can be overlooked by designers and facilitators. We analyze how students in an 8th grade mathematics classroom reasoned about circles, across math and coding activities. One student showed evidence of shifting fluently between different frames as facilitators had expected. The dramatic change in his contributions gauge the demands of the activities, as do the contributions of other students, who appeared to work within different frames. Our findings have relevance for the design and facilitation of integrated STEM learning environments to support students in navigating such frame-shifts. [For the complete proceedings, see ED630060.]
Gesture Indicates Productive Struggle in Proof Writing: Case Studies from a Basic Topology Course
Author: Gallagher, Keith
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Undergraduate Students,Nonverbal Communication,Validity,Mathematical Logic,Mathematics Instruction,Learner Engagement,Case Studies,Task Analysis,Video Technology,Schemata (Cognition),Problem Solving,Topology,Thinking Skills

Many students struggle with proof writing. However, struggle is not universally bad: researchers have distinguished between productive and unproductive forms of struggle and have identified productive struggle as essential for learning mathematics. Yet, in practice, recognizing when learners are engaged in productive struggle or unproductive struggle can be challenging. In this report, I argue that students' gesture production may indicate engagement in productive struggle. I observed three undergraduate students from an introductory point-set topology course, collaborating in pairs to complete proof tasks. I present evidence from the students' work on two proof tasks that undergraduate students' gesture frequently when they are engaged in productive struggle and that gesture is rare during engagement in unproductive struggle. [For the complete proceedings, see ED630060.]
A Hypothetical Learning Trajectory for the Understanding of Number Density in High School Students = Una Trayectoria Hipotética de Aprendizaje para la Comprensión de Densidad Numérica con Estudiantes de Bachillerato
Author: Suárez-Rodríguez, Mayra
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,High School Students,Number Concepts,Semiotics,Concept Formation,Foreign Countries,Secondary School Mathematics

During their school life, students learn mathematical topics that can be considered essential for the understanding of the property of density in the set of real numbers. Therefore, we detected a need to design and elaborate a Hypothetical Learning Path to include topics to help promote the learning of this property. This report shows results of a first stage of an educational experiment as part of an ongoing research. It describes how through the trajectory, high school students are able to recognize ways of finding numbers in an interval using various semiotic representations. We also describe some difficulties that students had to recognize the non-existence of a successor in real numbers. [For the complete proceedings, see ED630060.]
Quantitative Reasoning and Covariational Reasoning as the Basis for Mathematical Structure for Real-World Situations
Author: Kularajan, Sindura Subanemy
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics,Thinking Skills,Concept Formation,Undergraduate Students,Mathematical Models,Decision Making,Mathematics Instruction,STEM Education,Majors (Students),Networks,Teaching Methods,Task Analysis,Problem Solving,English (Second Language),Second Language Learning,Second Language Instruction,Student Characteristics

In this paper we address the question, how do quantitative reasoning and covariational reasoning present as students build structural conceptions of real-world situations. We use data from an exploratory teaching experiment with an undergraduate STEM major to illustrate the explanatory roles quantitative reasoning and covariational reasoning play in, (a) coordinating more than two interdependent quantities, (b) conceiving of real-world situations in more than one way, (c) constructing networks of quantitative relationships, and (d) creating a mathematical expression. We make the case that looking at mathematical model construction through the lens of quantitative reasoning and covariational reasoning may provide insights into students' mathematical decisions as they structure complex real-world scenarios. [For the complete proceedings, see ED630060.]
Student Struggle during Collaborative Problem-Solving in One Mathematics Classroom
Author: Jarry-Shore, Michael
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Cooperative Learning,Problem Solving,Barriers,Middle School Students,Grade 7,Difficulty Level,Cognitive Processes,Video Technology,Group Dynamics

In solving mathematics problems in collaboration, students encounter a range of mathematical and social struggles. As teachers cannot possibly respond to every such struggle, they may need to respond to those with which students require most support. Yet, little is known about students' success in overcoming the various types of struggle they encounter. In this study, we examined the types of struggle students experienced as they worked together in solving a cognitively-demanding problem. We analyzed the relative proportions of the various types of struggle they encountered, their success in overcoming each type, and the resources they leveraged in doing so. While students overcame many mathematical struggles, they had less success overcoming struggles related to reaching consensus or having their questions answered by peers. We argue that teachers may merit from support in learning to attend to these latter, more social struggles. [For the complete proceedings, see ED630060.]
Enhancing K-12 Pre-Service Teachers&apos; Embodied Understanding of the Geometry Knowledge through Online Collaborative Design
Author: Sung, Hanall
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Geometry,Mathematics Instruction,Preservice Teachers,Teacher Education Programs,Thinking Skills,Geometric Concepts,Motion,Video Games,Kindergarten,Elementary Secondary Education,Pedagogical Content Knowledge,Intervention,Formative Evaluation,Transfer of Training,Teaching Methods,Instructional Design,COVID-19,Pandemics,Computer Mediated Communication,Cooperative Learning

In this study, we devised research design that provides pre-service teachers to effectively experience embodied geometric thinking with the goal that it will impact teachers' instruction to students in their classrooms. Using a motion-capture video game and design tool, we offered opportunities for pre-service teachers to experience of performing mathematically related movements as well as creating their own directed actions for given conjectures. We hypothesize that these gameplay and co-design activity will reinforce not only teachers' understanding of the embodied nature of geometric thinking, but also their abilities to transfer their understanding to classrooms and the activities and assessments they design for their students. The results showed that after experiencing the interventions including embodied gameplay and co-design activity, teachers' awareness of students' 'sage of gestures was changed and they had better ability to understand and interpret students' gestures as a means of teachers' formative assessment practices. [For the complete proceedings, see ED630060.]
Establishing Student Mathematical Thinking as an Object of Class Discussion
Author: Leatham, Keith R.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Logic,Discussion (Teaching Technique),Secondary School Teachers,Mathematics Teachers,Mathematics Activities,Secondary School Mathematics

Productive use of student mathematical thinking is a critical yet incompletely understood dimension of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at its first element, establish. Based on an analysis of secondary mathematics teachers' enactments of building, we describe two critical aspects of establish--establish precision and establish an object--and the actions teachers take in association with these aspects. [For the complete proceedings, see ED630060.]
Conventions and Context: Graphing Related Objects onto the Same Set of Axes
Author: Jones, Steven R.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Graphs,Mathematics Instruction,Teaching Methods,Thinking Skills,Mathematics,High School Students,Undergraduate Students

Several researchers have promoted reimagining functions and graphs more quantitatively. One part of this research has examined graphing &quot;conventions&quot; that can at times conflict with quantitative reasoning about graphs. In this theoretical paper, we build on this work by considering a widespread convention in mathematics teaching: putting related, derived graphical objects (e.g., the graphs of a function and its inverse or the graphs of a function and its derivative) on the same set of axes. We show problems that arise from this convention in different mathematical content areas when considering contextualized functions and graphs. We discuss teaching implications about introducing such related graphical objects through context on separate axes, and eventually building the convention of placing them on the same axis in a way that this convention and its purposes become more transparent to students. [For the complete proceedings, see ED630060.]
Enacted Task Characteristics: Setting an Infrastructure for Students&apos; Quantitative Reasoning
Author: Altindis, Nigar
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Task Analysis,Mathematics Instruction,Thinking Skills,Generalization,Mathematics Skills,Middle School Students,High School Students,Vignettes,Video Technology,Teaching Methods

In this study, we explored enacted task characteristics (ETCs) that supported students' quantitative reasoning (QR). We employed a design-based methodology; we conducted a teaching experiment with eight secondary school students. Through ongoing and retrospective analyses, we identified ETCs which supported students' quantitative reasoning. The ETCs can set the infrastructure for students' QR when students are: (a) identifying changing attributes of the tasks or situations, (b) coordinating the change among quantities, and (c) making generalizations about quantitative relationships. ETCs play an important role in development of students' meaningful understanding when tasks are designed with focus on quantitative reasoning and representational fluency. [For the complete proceedings, see ED630060.]
Revealing Mathematical Activity in Non-Formal Learning Spaces
Author: Williams-Pierce, Caro
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Activities,Numbers,Prediction,Mathematics Instruction,Mathematics Education,Nonformal Education,Shared Resources and Services,Robotics,Grade 4,Elementary School Students,Feedback (Response)

We offer this synthesized framework as a tool to reveal mathematical activity in a non-formal makerspace. In particular, we connect research at different grain sizes to illustrate and explain how mathematics plays a crucial, if often implicit, role in this activity. We begin with describing the Approximate Number System and the Ratio-Processing System, explain how those systems connect to both embodied cognition and Thompson's (1994) conceptualization of quantities. We then examine how prediction and anticipation relate, with a particular emphasis on how social feedback guided the emergent mathematical activity. Finally, we synthesize across the two frameworks, in order to better reveal mathematical activity in low-notation environments, as the first step towards a framework for understanding mathematical learning in non-formal and low-notation contexts. [For the complete proceedings, see ED630060.]