ethanporcaro/eric-fulltext-meta huggingface dataset:
Structured Participation Promotes Access and Accountability during Cooperative Learning in Mathematics Education
Author: Kim, Nicholas
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Student Participation,STEM Education,Geometry,Group Activities,Cooperative Learning,Student Projects,Grade 9,Learning Processes,Program Effectiveness,Large Group Instruction,Small Group Instruction,Student Role,Public Speaking

This study investigated how the use of structured participation, specifically group presentation roles, supported more equitable participation in doing and learning mathematics. We analyzed videos of two lessons focused on radius, diameter, circumference, and area of circles in which students worked in small groups in a STEM project-based geometry class. Students' mathematics learning was assessed by the teacher through a group presentation where students were assigned individual presentation roles. We identified themes related to access and participation in small group and whole class interactions during this problem-focused lesson and found nuanced differences in both access and participation when compared to students' typical involvement in the more common unit-wide project-based tasks. Findings provide insights into effective uses of structured participation for both group work and whole class interactions to support more equitable doing and learning of mathematics in high school classrooms. [For the complete proceedings, see ED606556.]
Four Attentional Motions Involved in the Construction of Angularity
Author: Hardison, Hamilton L.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Grade 9,Concept Formation,Geometric Concepts,Spatial Ability,Attention,Motion,Mathematical Logic

Quantifying angularity is critical for the study of K-12 school mathematics and beyond; yet, quantifying angularity is challenging for individuals across these grade levels. Using data from a yearlong teaching experiment with ninth-grade students, I address the role of attentional motion in quantifying angularity and present four such motions involved in the construction of angularity. Additionally, I consider implications of these motions for teaching and research. [For the complete proceedings, see ED606556.]
Secondary Mathematics Teachers&apos; Efforts to Engage Students through Academic and Social Support
Author: Jansen, Amanda
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: High School Teachers,Mathematics Teachers,Learner Engagement,Teacher Student Relationship,Self Efficacy,Mathematics Instruction,Educational Practices,Social Support Groups,Grade 9,High School Students,Mathematics Activities,Teaching Methods,Feedback (Response)

Teachers' efforts to support students, both academically and socially, can play a role in how high school students productively engage with mathematics in the moment. To examine the connection between teacher support and student engagement, we conducted an exploratory mixed-methods study combining data from 20 high school classroom observations with student self-reports taken during the observed activity. Our findings indicate that when teachers provide academic support to their students during a lesson, they are also likely to provide social support. Higher teacher support of both kinds correlates with higher student self-efficacy, as well as social and cognitive engagement. Investigating relationships between observations of teaching and students' self-reports of engagement in-the-moment is a potentially revealing approach for uncovering engaging instructional strategies in secondary mathematics classrooms. [For the complete proceedings, see ED606556.]
Jumping into Modeling: Elementary Mathematical Modeling with School and Community Contexts
Author: Turner, Erin E.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Models,Culturally Relevant Education,Elementary School Students,Elementary School Mathematics,Grade 5,Teaching Methods,Student Experience,Knowledge Level,Teacher Role,Elementary School Teachers,Social Justice,STEM Education,Relevance (Education)

Mathematical modeling is a high-leverage topic, critical STEM education and civic engagement. This study investigates culturally responsive, school and community-based approaches that support mathematical modeling with elementary students. Specifically, we analyzed two modeling lessons in one fifth grade classroom, with a focus on how students drew upon their experiences and funds of knowledge as they engaged in the mathematical modeling process. Our findings illustrate different ways that students' experiences and situational knowledge informed and guided their modeling activity, including the quantities that they deemed relevant, and how they interpreted and refined their solutions. We also attend to the teacher's role in supporting such connections. Implications for mathematics teacher educators and research are included. [For the complete proceedings, see ED606556.]
Rethinking Mathematics Classroom Participation: Student and Teacher Perspectives
Author: Martínez, José Manuel
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Student Participation,Mathematics Instruction,Student Attitudes,Teacher Attitudes,Grade 3,Immersion Programs,Spanish,Elementary School Teachers,Elementary School Students,Elementary School Mathematics

Participation in mathematics classrooms has received considerable attention in previous research. Scholars have emphasized researchers' and teachers' perspectives on what it means to participate. I draw on sociocultural theories of learning to explore both students' and a teacher's perspectives on participation. I describe a participatory research study where a Spanish immersion third-grade teacher and I collaborated to elicit students' perspectives on mathematics class participation. Data generation included multi-method focus groups with the students, and an interview with the teacher. Drawing on social semiotics as an analytical framework, findings suggest that there were two connotations of participation in this classroom: While the teacher's connotation characterized participation mainly as quantifiable, observable student talk attributable to individual children, students' connotation characterized participation mainly as qualifiable, amorphous, diverse and focused on the social. I argue that developing mathematics teaching that is inclusive of diverse ways of participating involves learning about students' perspectives on participation. [For the complete proceedings, see ED606556.]
STEM Ways of Thinking
Author: Slavit, David
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: STEM Education,Teaching Methods,Mathematics,Mathematical Logic,Validity,Interdisciplinary Approach,Cognitive Processes,Learning Theories,21st Century Skills,Epistemology,Elementary Schools,Middle Schools,High Schools,Student Projects,Elementary School Students,Middle School Students,High School Students

We explore the epistemological issues that arise when considering STEM as a curricular and instructional construct. Our approach is somewhat unique in that we are not focused on the curricular or instructional boundaries of STEM education, but consider the nature of the cognitive activity at play during STEM-focused activity, with an emphasis on mathematical thinking. We focus specifically on the epistemological underpinnings of mathematics and other STEM disciplines, and the possibility of an epistemology of STEM as a curricular construct. The implications on students' STEM ways of thinking (SWoT) are discussed in detail from a theoretical and empirical lens. Future research directions are identified. [For the complete proceedings, see ED606556.]
Framework to Analyze and Promote the Development of Functional Reasoning in High-School Students
Author: Miranda, César Briseño
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: High School Students,Mathematical Logic,Thinking Skills,Spatial Ability,Algebra,Geometry,Mathematical Concepts,Calculus,Models

The research this report belongs to aims at exploring the functional reasoning of high-school students from a covariation approach and proposing a framework to describe and predict the student's responses to modeling tasks in Dynamic Geometrical Situations. Items were designed for the students to build/construct the corresponding function guided by questions that allowed for the analysis of covariation. The results are shown in a framework consisting of five components, which describe the student's response patterns based on examples of each component. The framework will provide a basis for the design of tasks involving learning and evaluation of the concept of function for high-school students. It can be an instrument to analyze the students' covariational and functional reasoning. [For the complete proceedings, see ED606556.]
The Conceptual and Practical Challenges of Taking Learning Trajectories to Scale in Middle School Math
Author: Confrey, Jere
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Middle School Students,Mathematics Instruction,Barriers,Diagnostic Tests,Educational Change,Student Evaluation,Data Analysis,Constructivism (Learning),Sociocultural Patterns,Teacher Student Relationship,Test Content,Test Items,Computer Assisted Testing,Computer Software,Mathematics Tests

This paper reports on a design-based implementation study of the use of a diagnostic classroom assessment tool framed on learning trajectories (LTs) for middle grades mathematics, where teachers and students are provided immediate data on students' progress along LTs. The study answers the question: &quot;How can one characterize the challenges encountered when a school implements a diagnostic assessment system around learning trajectories at scale?&quot; by identifying three explanatory themes: shifting to classroom assessment, understanding the concept and content of the LT, and seeing the results as a call to action. Each theme is discussed with references to observed activities and discussions with participants and related to the challenges connected with taking the concept of LTs to scale. [For the complete proceedings, see ED606556.]
Cases of Learning to Respond to Errors through Approximations of Leading Whole-Class Discussions
Author: Baldinger, Erin E.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Discussion (Teaching Technique),Preservice Teacher Education,Secondary School Mathematics,Error Correction,Methods Courses,Research Universities,Coaching (Performance),Teacher Response,Vignettes,Preservice Teachers

The emerging use of approximations of practice in teacher education calls for ways to document teacher candidates' (TCs') skill from their enactments and to determine how TCs' skill develops through such pedagogies. We highlight two cases of secondary mathematics TC development, connecting analyses of two types of approximations--coached rehearsals and scripting tasks--with a focus on the practice of responding to errors in whole-class discussion. Each case illustrates a distinct example of TC development. This work contributes to the research on pedagogies of practice in teacher education by offering approaches for understanding TC practice and development through multiple data sources. [For the complete proceedings, see ED606556.]
Interacting with Dynamic Computer Activities Impacts College Algebra Students&apos; Math Attitudes and Performance
Author: Johnson, Heather Lynn
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Computer Assisted Instruction,Computer Uses in Education,College Students,Algebra,Student Attitudes,Mathematics Achievement,College Mathematics,Intervention,Mathematics Activities,Attitude Change

Opportunities matter when it comes to students' math attitudes and performance. Over two semesters, across treatment sections of college algebra students, we implemented a set of dynamic computer activities linking animations and graphs. Across all sections, we administered a fully online survey of students' attitudes toward math. Using mixed methods, we analyzed students' attitudes toward math and their performance on a course final exam. At the end of each semester, we found statistically significant differences between treatment and comparison students' perceived competence toward math. Furthermore, treatment students outperformed comparison students on the course final exam, with statistically significant differences on an item linked to the dynamic computer activities. When students have opportunities to interact with dynamic computer activities, it can impact their math attitudes and course performance. [For the complete proceedings, see ED606556.]
Infrastructure to Support Students Exercising Conceptual Agency
Author: Nichols-Paez, Isaac
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Learning Activities,Mathematical Concepts,Concept Formation,Group Activities,Group Dynamics,Inquiry,Educational Technology,Technology Uses in Education,Computer Networks,Grade 5,Middle School Students,Fractions,Learner Engagement

Generative activities have been shown to support students to engage in space-creating play and exercise their conceptual agency to generate a mathematical space (e.g. Stroup et al. 2004), yet these studies implement generative activities only with their resonating counterpart, classroom networks, technological infrastructures that connect multiple, co-present students into a shared, digital representation. Because these technologies are in continuous redesign and still inaccessible to many classrooms, we need to understand the crucial features their infrastructure provides to the classroom system. By analyzing the strains on the classroom without classroom networks and how they relieved that pressure and revive the system, we found that the collective public displays provided students with a collective orientation and a sense of connection and individualism. [For the complete proceedings, see ED606556.]
Dissecting Curricular Reasoning: An Examination of Middle Grade Teachers&apos; Reasoning behind Their Instructional Decisions
Author: Dingman, Shannon W.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Teachers,Middle School Teachers,Mathematics Instruction,Decision Making,Course Content,Teaching Methods,Learning Activities,Planning,Educational Resources,Mathematics Curriculum,Instructional Materials

Mathematics teachers are vital components in determining what mathematics students have the opportunity to learn. There are a vast number of factors and reasons that influence a teacher's instructional decisions. As such, teachers rely heavily on their curricular reasoning (CR) to make decisions about what content to teach, how that content is taught, and the tasks to use to facilitate student learning. In this paper, we outline five strands of CR gleaned from research with middle grades mathematics teachers as they plan and implement instruction with unfamiliar curricular resources. These strands lay the foundation for our Instructional Pyramid model of CR and provide a lens through which teacher decision-making can be further understood and enhanced. [For the complete proceedings, see ED606556.]
Using Interpersonal Discourse in Small Group Development of Mathematical Arguments
Author: King, Shande
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Persuasive Discourse,Mathematics Instruction,Peer Relationship,Thinking Skills,Validity,Mathematical Logic,Mathematical Concepts,Discourse Analysis,Small Group Instruction,Classroom Communication,Cooperative Learning,Middle School Students,Audio Equipment,Teaching Methods,Instructional Effectiveness,Algebra

The development of proofs and argumentation is one of the major standards for mathematical practices in K-12 education that researchers and practitioners alike are continuing to improve. Further, the use of discourse is considered essential in the learning of mathematical concepts at these levels. However, K-12 educators continue to confound how best to utilize student interpersonal discourse to advance the development of mathematical arguments. This qualitative study examines the nature of student discourse in small-group interactions as students create collective arguments based on mathematical evidence. In examining the patterns of discourse in small groups, the study concludes the effectiveness of various types of discourse in peer-to-peer interaction as students develop more analytical thoughts through the support of their discourse with one another in creating proofs and arguments. [For the complete proceedings, see ED606556.]
What Role Does Professional Noticing Play? Exploring Connections to Affect and Pedagogical Content Knowledge
Author: Jong, Cindy
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Attention,Affective Behavior,Pedagogical Content Knowledge,Mathematics Skills,Thinking Skills,Preservice Teachers,Elementary School Teachers,Preservice Teacher Education,Predictor Variables,Teaching Methods

This research report describes a study that explored the intersections of professional noticing of children's mathematical thinking (PN), pedagogical content knowledge (PCK), and affective domains with preservice elementary teachers (PSETs). An instructional module on professional noticing, as defined by Jacobs, Lamb, and Philipp (2010), included three components: attending, interpreting, and deciding, was implemented with 170 PSETs. A comparison group of 121 PSETs were enrolled in mathematics methods courses but the PN module was not implemented. PSETs who participated in the module showed significant positive growth in attending, interpreting, and attitudes toward mathematics. While there was no significant change in dispositions toward teaching mathematics, a decrease was observed in PSET deciding and pedagogical content knowledge. However, findings showed promising connections among the constructs. [For the complete proceedings, see ED606556.]
Teachers&apos; Engagement with a Competing Models Informal Inference Task
Author: Lovett, Jennifer N.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Inferences,Teaching Methods,Mathematics Instruction,Statistics,Pedagogical Content Knowledge,Faculty Development,Mathematical Logic,Mathematics Teachers,Secondary School Mathematics,Middle School Teachers,Educational Technology,Cooperative Learning,Probability

Informal inference is a critical practice for students to engage in if they are to understand formal statistical methods. However, during informal inference students often utilize complex ideas that many in-service teachers are not prepared for as they have not had the opportunity to think deeply about statistics and develop statistical knowledge for teaching (Groth, 2013). Research shows that engaging teachers in authentic inquiry of content supports the development of that content knowledge, and there is an urgent need to do so through professional developments (PDs). However, there is limited literature concerning PDs in statistics education, and a dearth of research focusing on teachers' engagement with informal inference tasks. This paper describes in detail how two teachers engaged with a seminal informal inference task during a PD, including their reasoning about variability and sample size when making inferences. [For the complete proceedings, see ED606556.]
Measurement and Decomposition: Making Sense of the Area of a Circle
Author: Cox, Dana C.
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Geometry,Preservice Teacher Education,Elementary School Teachers,Geometric Concepts,Concept Formation,Teaching Methods,Preservice Teachers,Spatial Ability,Knowledge Base for Teaching,Mathematical Logic

As a component of a course on geometry for preservice elementary teachers (PSTs), we derive area formulas for a variety of polygons including triangles, quadrilaterals, and both regular and irregular shapes whose areas can be measured empirically using decomposition. Decomposing a circle to justify why its area can be measured using the standard formula is more challenging as it requires both empirical and deductive reasoning involving limits. In spite of the challenge, we expected decomposition strategies to transcend work with polygons and support PSTs when thinking about the area of circles. Results show that few PSTs utilized decomposition and instead focused on finding meaning in the symbolism of the formula. Concept images related to area will be discussed. [For the complete proceedings, see ED606556.]
Time Expressions and Elementary Students&apos; Reasoning with the Analog Clock
Author: Earnest, Darrell
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Elementary School Students,Grade 2,Grade 4,Time,Mathematical Concepts,Measurement,Mathematics Education,Vocabulary

This paper investigates the interplay of words and expressions with students' efforts to indicate times on a clock. We consider how elementary students interpret precise times (e.g., 2:30, 4:30) as compared to relative times (e.g., half past 11) as they describe this intangible quantity using a clock. Interviews with students in grades 2 and 4 (n = 42) revealed that precise times led to whole number descriptions whereas relative times led to descriptions of part-whole relations consistent with representations of measure. A subsequent analysis of assessment performance of students across elementary grades (N = 612) corroborates the differential performance based on expression used in the tasks. Findings suggest that elementary students need further support to treat this invisible quantity according to measurement properties. Implications for theory are discussed. [For the complete proceedings, see ED606556.]
Preservice Teachers&apos; Understanding of Two-Variable Inequalities: APOS Theory
Author: Moon, Kyunghee
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Secondary School Teachers,Mathematics Teachers,Knowledge Level,Graphs,Algebra,Visualization,Mathematical Concepts,Equations (Mathematics),Misconceptions,Mathematics Skills

This study investigated preservice secondary mathematics teachers' difficulties with and understanding of graphs of two-variable inequalities with the lens of the APOS theory. The analysis showed that most teachers understood inequality graphs as actions, at best, and used informal rules to construct graphs. They also had difficulty justifying graphs, such as overgeneralization of linear inequality graphs, lack of understanding of the meaning of solutions and the Cartesian Connection, and inability to transfer algebraic/verbal to geometric rays. This study suggests two methods for the visualization of inequality graphs, which uses the concepts of variable and parameter. [For the complete proceedings, see ED606556.]
Examining Mathematical Modeling of Fifth Graders: Use of Interactive Computer Simulations
Author: Manouchehri, Azita
Date: 2019-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Models,Grade 5,Elementary School Students,Computer Simulation,Computer Uses in Education,Student Attitudes,Mathematics Activities

We analyzed 5th grade students' interactions with one computer-based modeling simulation to examine how they defined and prioritized variables in a dynamically simulated environment. Results revealed that exposure to the simulation environment helped students visualize continuous motions, interpret the different quantities present in the model, and connect how variables related to each other. Additionally, students became more precise and systematic in adjusting the variables to explore the problem, test hypotheses, and achieve desired outcomes. [For the complete proceedings, see ED606556.]