ethanporcaro/eric-fulltext-meta huggingface dataset:
Teacher Feedback and Authority during Instances of Students&apos; Proving
Author: Wambua, Mitchelle M.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Teacher Role,Feedback (Response),Mathematical Logic,Validity,Mathematics Instruction,Geometry,Secondary School Teachers,Secondary School Mathematics,Knowledge Level,Questioning Techniques,Student Role,Secondary School Students

Teacher feedback during the process of students' proving is important to consider because proving is often challenging for students, requiring feedback and support. Additionally, feedback has implications for authority and agency, which are constantly being negotiated. We examined the authority dynamics evidenced in a teacher's feedback actions while students proved geometry claims. By analyzing audio and video recordings of classroom proving discussions, we found that various teacher feedback types position either the teacher or students as authorities with regard to providing and validating mathematical ideas. We provide suggestions for research and practice with respect to teacher feedback and authority in proof instruction. [For the complete proceedings, see ED630060.]
Slope across the Curriculum: A Textbook Case Analysis
Author: Fisher, Thomas
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Concepts,Textbooks,Mathematics Instruction,Textbook Content,Mathematical Logic,Secondary School Mathematics,Grade 6,Grade 7,Grade 8,Grade 9,Grade 10,Grade 11,Grade 12

This study reviews how slope is developed in expository materials across a seven-textbook series. Slope development is analyzed using a framework of five slope components to describe which components are used and connected, and by investigating accompanying levels of covariational reasoning. Findings suggest that the series describes slope from multiple components, and this development is grounded in various levels of covariational reasoning. While many connections were found between components, occurrences of both visual and nonvisual approaches within components were not prevalent. Suggestions include building connections between Behavior Indicator and Determining Property components through descriptions of covariation as well as more connections to the Steepness component. [For the complete proceedings, see ED630060.]
Elementary Patterning Problems: Visual and Numerical Structuring
Author: Frazee, Leah M.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Elementary School Students,Thinking Skills,Mathematical Concepts,Grade 4,Public Schools,Mathematics Education,Mathematics Instruction,Pictorial Stimuli,Spatial Ability

Research on elementary students' reasoning on patterning problems with pictorial representations has illustrated that students can visualize structure in patterns in different ways. In this paper, we offer a characterization of students' spatial structures and numerical structures and explain how the link between these two structures can support students' generalization of a pattern or prediction of a future value. [For the complete proceedings, see ED630060.]
Theo&apos;s Reinvention of the Logic of Conditional Statements&apos; Proofs Rooted in Set-Based Reasoning
Author: Dawkins, Paul Christian
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Validity,Mathematical Logic,Learning Trajectories,Teaching Methods,Instructional Design,Undergraduate Students,Comparative Analysis,Geometry,Concept Formation,Mathematical Concepts,Learning Processes,Inferences,Logical Thinking,Calculus,Minority Serving Institutions,Hispanic American Students

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in number theory and geometry). We document the progression of Theo's emergent set-based model from a model-of the truth of statements to a model-for logical relationships. This constitutes some of the first evidence for how such logical concepts can be abstracted in this way and provides evidence for the viability of the learning progression that guided the instructional design. [For the complete proceedings, see ED630060.]
Interpreting Worked Examples of Integer Subtraction
Author: Bofferding, Laura
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Grade 1,Grade 3,Elementary School Students,Elementary School Mathematics,Subtraction,Problem Solving,Number Concepts,Concept Formation,Mathematical Logic

Drawing on research around the utility of worked examples, we examine how 29 first- and 27 third-grade students made sense of integer subtraction worked examples and used those examples to solve similar problems. Students first chose which of three worked examples correctly represented an integer subtraction problem and used the example to solve a similar problem. Later, we presented only the correct worked example and had them solve another similar problem. Our results highlight how their initial ideas around which worked example was correct supported or constrained their later interpretation and use of the correct worked example. Students were attuned to the number of jumps shown in the examples; however, they sometimes misinterpreted the jumps' direction. Students' visual answers were correct more than their written answers, suggesting further attention to visuals could support students' reasoning. [For the complete proceedings, see ED630060.]
Isomorphism and Homomorphism as Types of Sameness
Author: Rupnow, Rachel
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Algebra,Mathematics,Professional Personnel,Attitudes,Mathematical Concepts

Isomorphism and homomorphism are topics central to abstract algebra, but research on mathematicians' views of these topics, especially with respect to sameness, remains limited. This study examines 197 mathematicians' views of how sameness could be helpful or harmful when studying isomorphism and homomorphism. Instructors saw benefits to connecting isomorphism and sameness but expressed reservations about homomorphism. Pedagogical considerations and the dual function-structure nature of isomorphism and homomorphism are also explored. [For the complete proceedings, see ED630060.]
&quot;What Do You Believe Is True?&quot; A Routine for Proving Theorems in Secondary Geometry
Author: Cirillo, Michelle
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Geometry,Mathematical Logic,Secondary School Students,Mathematics Instruction,Grade 8,Honors Curriculum

We report findings from an investigation of one teacher's instruction as he guided students through the proofs of 21 theorems in a Grade 8 Honors Geometry course. We describe a routine involving four distinct phases, including Setting up the Proof and Concluding the Proof. Results from an end-of-course proof test are also presented to attest to the effectiveness of the teacher's approach. By engaging with descriptions of the theorem-proving routine, one can learn about different strategies that may support students to learn to prove theorems, such as asking students to put forth claims in the form of conjectures or other statements that they believe are true and seeking justifications for these claims as well as sanctioning a theorem once proven. [For the complete proceedings, see ED630060.]
Narratives of Raza in Mathematics Education Research Literature
Author: Jones, Stacy R.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Hispanic Americans,Educational Research,Mathematics Education,Racism,Power Structure,Whites,Acculturation,Language Usage

We present a finding from a literature analysis of Raza populations published in top-tiered peer reviewed mathematics education journals. We look at how narratives are perpetuated and resisted at the intersections of Raza, mathematics education, and research. The findings reveal the field of mathematics education research is perpetuating deficit narratives of Raza through (1) simplistic descriptions of Raza which perpetuate a racial hierarchy; (2) white institutional spaces group, order, and Americanize Raza populations; and (3) counter-stories of La Raza; however, we will only concentrate on the first finding for this manuscript. The examined literature continues to center Anglos' narratives and values while maintaining a social hierarchy and the assimilation and Americanization of La Raza. Finally, we provide implications for disseminating our research to go beyond simplistic demographics of social constructs. [For the complete proceedings, see ED630060.]
Operationalizing Authentic and Disciplinary Activity for the Undergraduate Context
Author: Melhuish, Kathleen
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Undergraduate Study,Learner Engagement,Mathematics Instruction,Mathematics Education,Teacher Student Relationship,Mathematical Concepts,Discussion,College Mathematics

Many educators and researchers advocate for student engagement in disciplinary activity. This is especially the case in advanced undergraduate courses taken by mathematics majors. In our respective design-based research projects, we found a need to better operationalize the activity of mathematicians in order to both plan for and document student engagement in disciplinary activity. In this report, we share our literature-based efforts to identify the tools and objects used by pure mathematicians in their work. We share the overarching framework we developed, Authentic Mathematical Proof Activities (AMPA), and illustrate the ways we have used this framework to analyze teacher-student activity using an activity theory lens. We conclude with reflections on how tensions between authenticity-to-the-discipline and authenticity-to-the-students shape the teacher-student activity system. [For the complete proceedings, see ED630060.]
Understanding Joint Exploration: The Epistemic Positioning in Collaborative Activity in a Secondary Mathematics Classroom
Author: Dyer, Elizabeth B.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Secondary School Students,Mathematics Instruction,Video Technology,Grounded Theory,Teacher Role,Epistemology,Cooperative Learning,Personal Autonomy,Classroom Communication,Problem Solving,Grade 10,Grade 11,Graphs,Concept Formation,Mathematical Concepts,Trigonometry

This study examines how joint exploration is established and maintained among students and the teacher in secondary mathematics classrooms. We use the theoretical perspective of positioning to conceptualize joint exploration as involving the negotiation and coordination among participants to position students with epistemic agency and authority. Using a constant comparative method, we use classroom video data of two episodes containing joint exploration and closely analyze the shifts in epistemic positioning within them. We find that shifts in epistemic positioning, especially when students position one another with epistemic authority, help to support continued joint exploration. We also find that the teacher can play an important role in decentering themselves as the epistemic authority. [For the complete proceedings, see ED630060.]
Storylines in News Media Texts: A Focus on Mathematics Education and Minoritized Groups
Author: Andersson, Annica
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: News Media,Mathematics Education,Minority Groups,Foreign Countries,Language Minorities,Indigenous Populations,Youth,Social Bias,Elementary Secondary Education,Mathematics Achievement,Cultural Influences

We identify storylines about youth from minoritized cultures and/or languages in Norwegian news media to identify positionings made available to migrated and Indigenous mathematics students in this public discourse. Our search from 2003-2020 in a Norwegian media database including newspapers, journals, tabloids, etc., identified 1896 articles, reduced to 96 for relevancy. These storylines were identified: 'The majority language and culture are keys to learning and knowing mathematics', 'Mathematics is language- and culture-neutral', 'Minoritized mathematics students are motivated by gratitude', 'Extraordinary measures are needed to teach students from minoritized groups mathematics', 'Students from minoritized groups must put in extraordinary effort to learn mathematics', 'Students from minoritized groups' mathematics achievements are linked to culture and gender', and 'Students from minoritized groups underachieve.' [For the complete proceedings, see ED630060.]
Analytic Equation Sense: A Conceptual Model to Investigate Students&apos; Algebraic Manipulation
Author: Ying, Yufeng
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Algebra,Mathematics Instruction,Models,Thinking Skills,Equations (Mathematics),Abstract Reasoning,Schemata (Cognition)

In this paper, I propose a new construct named &quot;analytic equation sense&quot; to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to explain the new model. [For the complete proceedings, see ED630060.]
Impact of Teachers&apos; Identification of Written Mathematical Points on Students&apos; Learning
Author: Atanga, Napthalin A.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Concepts,Identification,Teacher Influence,Mathematics Education,Elementary School Teachers,Mathematics Instruction,Grade 3,Grade 4,Grade 5

I examined the relationship between teachers' identification of mathematical points in written lessons and students' mathematical learning opportunities. Lessons in teachers' guides and classroom instruction were analyzed for written mathematical points and those articulated by teachers during instruction. Teachers who appropriately identified written mathematical points together with suggested curricular resources to realize them had a positive impact on students' mathematical learning opportunities. Positive impact was influenced by the teacher's ability to appropriately identify the role of available curricular resources in supporting the achievements of written mathematical points, recognize relationships between suggested activities and curricular resources toward written mathematical points, and develop a productive mathematical storyline. [For the complete proceedings, see ED630060.]
Impact of Mediated Field Experiences on Teacher Candidates&apos; Self-Reported Learning: A Multi-Institutional Descriptive Pilot Study
Author: Swartz, Barbara Ann
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Field Experience Programs,Preservice Teachers,Mathematics Instruction,Mathematics Teachers,Classroom Environment,Self Esteem,Student Attitudes,Preservice Teacher Education,Mathematics Education,Educational Practices

Mediated Field Experiences (MFEs) provide teacher candidates (TCs) structured opportunities to unpack and enact core teaching practices, gain mathematics content and pedagogical knowledge, and reflect critically on mathematics teaching and learning. In this paper we present findings from a multi-institutional descriptive pilot study that investigates the impact of MFEs on TC learning. TCs reported that they (1) deepened their understanding of the targeted core teaching practice(s), (2) developed a vision of ambitious mathematics teaching, (3) recognized the importance of cultivating a positive classroom learning community, and (4) increased their confidence when teaching after their completion of a one-term course implementing MFEs. [For the complete proceedings, see ED630060.]
Representing Proportional Reasoning Algebraically to Problem Solve
Author: Lamberg, Teruni
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Logic,Mathematical Concepts,Problem Solving,Elementary School Teachers,Middle School Teachers,Algebra,Faculty Development,Word Problems (Mathematics),Thinking Skills

Proportional reasoning problems can be solved using algebraic reasoning. Therefore, making connections between proportional reasoning and algebraic thinking is important for solving problems. This study examined K-8 teachers' problem-solving strategies as they worked out a real world multi-step problem that involved proportional reasoning and algebraic thinking. The findings revealed that many teachers found this problem challenging. Particularly, some teachers had difficulty figuring out how to translate the variables into an algebraic equation. Some teachers who used variables as labels tended to engage in additive reasoning. They had difficulty representing the proportional problem context algebraically and solving the problem for the unknown quantity. Implications for further research are discussed.
Prospective Mathematics Teachers&apos; Designed Manipulatives as Anchors for Their Pedagogical and Conceptual Knowledge
Author: Akuom, Denish
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Mathematics Teachers,Manipulative Materials,Teacher Role,Pedagogical Content Knowledge,Mathematics Instruction,Problem Solving,Mathematical Logic,Inquiry,Fractions

Positioning teachers as designers of curricular resources invites opportunities for exploration at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for preparing teachers to maintain a commitment to their pedagogical vision in practice, this work seeks to cultivate the imagination of humanistic forms of mathematics teaching and learning by supporting these explorations. Toward that end, this paper reports on research that examines connections between the pedagogical/conceptual knowledge that prospective teachers embed in the designs of original manipulatives and how those designs mediate the pedagogical moves they make in teaching situations. The promise of this work is that these connections may reveal a viable means to support bolder connections between teacher preparation and practice. Implications of our findings for teacher preparation are considered. [For the complete proceedings, see ED630060.]
Eliciting Dispositions for Teaching in the Context of a Video-Based Intervention for Secondary Teacher Candidates
Author: Cavey, Laurie O.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Video Technology,Preservice Teachers,Secondary School Teachers,Preservice Teacher Education,Mathematics Instruction,Student Characteristics,Teacher Characteristics,Knowledge Level,Metacognition,Cognitive Processes,Thinking Skills,Attention,Empathy

For years, teacher education programs have focused considerable effort on teacher knowledge and how to develop the types of knowledge that matter in teacher education candidates. Meanwhile, candidate dispositions for teaching have received little attention, particularly in mathematics courses for candidates. As developers and practitioners of a curriculum intervention designed to support candidates' mathematical knowledge, we are beginning to see how much disposition towards teaching mathematics matters in a candidate's ability to attend to students' ideas. In this paper we share results from a pilot study investigating the dispositional characteristics elicited in an online video-based curriculum focused on students' ideas on a figural pattern task. Results indicate that efforts to cultivate secondary candidates' disposition for teaching may have payoffs with respect to both dispositions and knowledge. [For the complete proceedings, see ED630060.]
Using Proportional Tasks to Explore Teachers&apos; Ability to Make Sense of Student Thinking
Author: Brown, Rachael Eriksen
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Task Analysis,Thinking Skills,Middle School Teachers,Problem Solving,Mathematics Instruction,Protocol Analysis,Pedagogical Content Knowledge,Difficulty Level,Knowledge Base for Teaching,Teaching Methods

In this paper, we extend our previous work on challenges teachers face when engaging with proportional reasoning contexts to investigate two contexts that included four problems for middle grades teachers to solve as well as eight student solutions. Analysis included coding for correct solving of the problem as well as making sense of and determining reasonableness of the associated student work. Results indicate that making sense of student work was not dependent on correctly solving the problem. Determining reasonableness of student work was more challenging for our 32 participants. The think aloud interview, we argue, mimics responding to student thinking in a live setting. Implications for teacher knowledge as well as professional development and teaching will be discussed. [For the complete proceedings, see ED630060.]
Understanding Mathematics Teachers&apos; Collaborative Sensemaking in the Context of Teachers&apos; Learning Ecologies
Author: Ehrenfeld, Nadav
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Teachers,Professional Development,Teacher Collaboration,Teacher Education,Learning Processes,Educational Environment

Over the last two decades, researchers have portrayed quality professional development for mathematics teachers as collaborative and situated in teachers' instructional realities. However, empirical findings also point out various impediments to transforming teacher conversations into consequential learning. These findings illuminate the need to acknowledge additional resources that teachers bring to professional interactions and the need for ever more nuanced theories of teacher learning to inform teacher educators' work. Inspired by ecological models of learning, in this conceptual paper I work towards understanding teachers' collaborative sensemaking as part of broader teacher learning ecologies. I distinguish and name possible scopes and contexts for the study of teacher learning in conversations about instruction, and then identify directions for future research towards stronger connections between immediate and broader contexts. [For the complete proceedings, see ED630060.]
Mathematical Knowledge for Teaching Proof: Comparing Secondary Teachers, Pre-Service Teachers and Undergraduate STEM Majors
Author: Buchbinder, Orly
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,STEM Education,Mathematics Skills,Knowledge Level,Mathematical Logic,Validity,Knowledge Base for Teaching,Intervention,Secondary School Teachers,Mathematics Teachers,Undergraduate Students,Majors (Students),Capstone Experiences

It has been suggested that integrating reasoning and proof in mathematics teaching requires a special type of teacher knowledge -- Mathematical Knowledge for Teaching Proof (MKT-P). Yet, several important questions about the nature of MKT-P remain open, specifically, whether MKTP is a type of knowledge specific to teachers, and whether MKT-P can be improved through intervention. We explored these questions by comparing performance on an MKT-P questionnaire of in-service secondary mathematics teachers, undergraduate STEM majors, and pre-service secondary mathematics teachers. The latter group completed the questionnaire twice- before and after participating in a capstone course, Mathematical Reasoning and Proving for Secondary Teachers. Our data suggest that MKT-P is indeed a special kind of knowledge specific to teachers and it can be improved through interventions. [For the complete proceedings, see ED630060.]