ethanporcaro/eric-fulltext-meta huggingface dataset:
From Theory to Methodology: Guidance for Analyzing Students&apos; Covariational Reasoning
Author: Tyburski, Brady A.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Guidelines,Thinking Skills,Student Behavior,Calculus,Mathematics Instruction,Undergraduate Students,Problem Solving,Graphs,Lesson Plans,Theory Practice Relationship,Teaching Methods

The fields of quantitative and covariational reasoning boast a wide range of powerful theoretical tools, which are described carefully in the literature. Less frequent and explicit attention, however, has been paid to writing down detailed, practical guidance for operationalizing these theoretical constructs. Some guidance is provided by covariational reasoning frameworks, but much is left unsaid concerning the inherent complexities and ambiguities involved in analyzing students' moment-by-moment behaviors and what these behaviors convey about their covariational reasoning. In an effort to more clearly link theory to analytic methodology, we share three lessons about analyzing students' covariational reasoning to make research more accessible to newcomers and better address what is often left unsaid in the covariational reasoning literature. [For the complete proceedings, see ED630060.]
A Conceptual Synthesis on Approximations of Practice
Author: Sapkota, Bima
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Teacher Education Programs,Learning Processes,Research Reports,Mathematics Instruction,Mathematics Teachers,Teacher Educators,Educational Practices,Futures (of Society),Preservice Teacher Education,Authentic Learning,Scaffolding (Teaching Technique)

Approximations of practice create valuable opportunities for preservice teachers (PSTs) by engaging them in components of teaching. By reviewing the literature, this study explored PSTs' learning through approximations and the extent approximated practices preserve the complexity -- or authenticity -- of teaching. A review of 25 empirical studies related to approximations of mathematics teaching indicated that mathematics teacher educators are currently exploring an expansion of opportunities through approximations wherein PSTs could experience a higher degree of authenticity. The existing conceptualization of authenticity emphasizes the complexity of practices but overlooks how approximated practices prepare PSTs for their future teaching. An alternative definition is proposed for the emerging conceptualization of authenticity to highlight how PSTs' learning through approximations prepares them for their future teaching. [For the complete proceedings, see ED630060.]
Semantically Linked Syntactic Literacy Affordances in Secondary Mathematics
Author: Smith, Ethan P.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Semantics,Secondary School Students,Syntax,Teacher Student Relationship,Language Skills,Sociolinguistics,Mathematics Instruction,Mathematics Teachers,Guidelines,Literacy,Teaching Methods,Classroom Communication,Discourse Analysis,Technology Uses in Education

This report details a literacy affordance framework for describing and connecting the ways in which teachers focus their students on the syntactic structures of reading, writing, speaking, and listening in mathematics. This framework is intended to serve as a critical access point for connecting and moving broader research in secondary mathematics teaching towards a sociolinguistic perspective. The framework is applied to a sample of teachers from two U.S. states to indicate ways in which these secondary mathematics teachers currently attend to such literacies in otherwise dialogically orientated lessons. Findings indicate the applicability of the framework as well as the opportunities and shortfalls in how such teachers currently attend to language in secondary mathematics. [For the complete proceedings, see ED630060.]
Noticing for Equity in Written Work: Exploring One Teacher&apos;s Student Work Analysis Practices
Author: Leshin, Miriam
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Teachers,Writing (Composition),Equal Education,Teacher Student Relationship,Thinking Skills,Public Schools,Middle School Teachers,Grade 6,Mathematics Instruction,Attention

Attending to students' thinking and using it to inform instruction has been shown to be an effective teaching practice. Although research on teacher noticing has explored how teachers attend to and interpret thinking in the moment and through video, less is known about the ways in which teachers notice students' thinking in written work, as well as the cultural dimensions that shape noticing. While work on &quot;noticing for equity&quot; has begun to explore the latter, it focuses on noticing of participation. This qualitative case study asks if equitable noticing extends to students' work. Analysis of one equity-oriented math teacher's student work analysis practices revealed that she (a) attended to the details of students' strategies with a learner stance, (b) contextualized their understandings, (c) interpreted their understandings through a strengths-based lens, and (d) planned to respond by identifying aspects of work to share with the class. [For the complete proceedings, see ED630060.]
Moves Teachers Use to Respond to Students&apos; Non-Canonical Approaches for Solving Equations
Author: Milewski, Amanda
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Problem Solving,Teaching Methods,Equations (Mathematics),Secondary School Teachers,Mathematics Teachers,Item Analysis,Vignettes,Teacher Attitudes,Guidelines,Linguistics,Classroom Communication,Teacher Student Relationship,Algebra,Thinking Skills,Decision Making,Multimedia Materials,Discourse Analysis

A historical review of mathematics textbooks suggests a canonical method to solving equations that teachers often see as &quot;the&quot; way to solve equations. In this paper, we examine data from a nationally-distributed sample of 524 secondary mathematics teachers who responded to scenario-based survey items that represent the instructional situation of solving equations. The items featured scenarios in which students presented non-canonical solution methods and asked participants to share how they would respond. Using a framework that draws on systemic functional linguistics, we describe the linguistic resources teachers used. While closed moves are frequently used to avoid discussion of non-canonical solutions, our results suggest that teachers find ways to make regular use of: (1) closed moves for accommodating non-canonical solutions; and (2) open moves when steering the conversation back to the canonical method. [For the complete proceedings, see ED630060.]
The Informal Covariational Statistical Reasoning: Focus on the Notion of Aggregate Using Digital Technology
Author: Morgado Hernández, Cindy Nathalia
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Statistics Education,Teaching Methods,Thinking Skills,Task Analysis,Misconceptions,Educational Technology,Student Attitudes,Algebra,Computer Software,High School Students,Foreign Countries,Graphs

We report the results of a study on informal covariate statistical reasoning conducted with 22 students (aged 16 and 18 years). We designed and implemented a task in a digital technology environment to introduce the line of best fit. The task design having elements that foresee misconceptions reported in the literature, and by focusing on four statistical ideas that we consider being central to the development of informal reasoning about the line of best fit. After having used the digital technology environment, students transitioned from viewing points of a scatterplot as individual points or fragmented into subsets to viewing the scatterplot as an aggregate from a mathematical mechanism that links them through the notion of distance from a point set to a right line. [For the complete proceedings, see ED630060.]
The Relationship between Confidence, Accuracy, and Decision Making in a Calculus Skills Review Program
Author: van de Sande, Carla
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: College Students,Self Esteem,Accuracy,Decision Making,Relationship,Calculus,Skills,Intervention,Program Implementation,Knowledge Level,Vacation Programs,Program Effectiveness,Skill Development,Thinking Skills

Just like physical skills, cognitive skills grow rusty over time unless they are regularly used and practiced so academic breaks can have negative consequences on student learning and success. The Keeping in School Shape (KiSS) program is an engaging, innovative, and cost-effective intervention that harnesses the benefits of retrieval practice by using technology to help students maintain proficiency over breaks from school by delivering a daily review problem via text message or email. A growth mindset is promoted through feedback messages encouraging students to try again if they get a problem wrong and to take on a challenge problem if they get a problem correct. This paper reports on the relationship between confidence, accuracy, and decision making during the implementation of the KiSS Program at a large university during winter break for students enrolled in an engineering introductory Calculus course sequence. [For the complete proceedings, see ED630060.]
Opportunities for Mathematics Engagement in Secondary Teachers&apos; Practice: Validating an Observation Tool
Author: Jansen, Amanda
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Secondary School Teachers,High School Teachers,Scoring Rubrics,Equal Education,Validity,Reliability,Classroom Observation Techniques,Teaching Methods,Learner Engagement,Evaluators,Mathematics Teachers,Teacher Student Relationship,Teacher Evaluation

The purpose of this report is to present our process and results for establishing validity and reliability of an observation tool used to investigate teaching practices that high school mathematics teachers use to engage students. We developed our tool using established practices, such as reviewing literature to develop a framework for instruction and piloting the tool to design descriptive levels for rubrics. After validating externally by consulting experts, additional rubrics regarding teaching mathematics for equity were added to the tool. We conducted a reliability study of 149 episodes of classroom instruction (equivalent to 447 10-minute segments of instruction in all), two raters per episode, to investigate the nature of coding disagreements. Most disagreements occurred due to raters noticing different evidence rather than different interpretations of rubrics, which suggested the value of two raters and resolution meetings. [For the complete proceedings, see ED630060.]
Identifying Graphical Forms Used by Students in Creating and Interpreting Graphs
Author: Rodriguez, Jon-Marc G.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Graphs,Mathematical Logic,College Students,Calculus,Identification,Mathematics Education

In this paper, we describe a framework for characterizing students' graphical reasoning, focusing on providing an empirically-based list of students' graphical resources. The graphical forms framework builds on the knowledge-in-pieces perspective of cognitive structure to describe the intuitive ideas, called &quot;graphical forms&quot;, that are activated and used to interpret and construct graphs. In this study, we expand on the current knowledge base related to the specific graphical forms used by students. Based on data involving pairs of students interpreting and constructing graphs we present a list of empirically documented graphical forms and organize them according to similarity. We end with implications regarding graphical forms' utility in understanding how students construct graphical meanings and how instructors can support students in graphical reasoning. [For the complete proceedings, see ED630060.]
Investigating What Makes Beginning Teachers&apos; Enactment of Number Talks More or Less Ambitious
Author: Cavanna, Jillian M.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Elementary School Mathematics,Beginning Teachers,Elementary School Teachers,Numbers,Teaching Methods,Language Arts

Number talks, a popular mathematics teaching routine in the United States, may offer supports for beginning teachers (BTs) to engage in ambitious instruction. BTs' enactments of number talks, however, are varied, and there are few empirical studies that explore how BTs' enactment of number talks could be more (or less) ambitious. This paper draws on classroom observation data from a large investigation of BTs' enactment of ambitious instruction in elementary mathematics across five teacher preparation programs. We analyzed 19 transcripts of number talks enacted by seven BTs to investigate what makes number talks more or less ambitious. Findings illustrate three patterns among number talks that were categorized as approaching ambitious using the M-Scan (Berry et al., 2013) instrument. Discussions and implications are offered in relation to mathematics teacher education and research. [For the complete proceedings, see ED630060.]
Instructors&apos; Facilitation of Student Participation in Advanced Mathematics Lectures: A Case Study of Two Instructors
Author: Zarkh, Anna
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Student Participation,Mathematics Education,Teacher Attitudes,Lecture Method,Teaching Methods,Student Experience,Undergraduate Study

Literature portrays advanced mathematics lecturing as a uniform teaching style, often criticized for offering minimal opportunities for student participation. In this paper we present results from a comparative case study of two instructors' facilitation of student participation in Real Analysis lectures. Analyzing fieldnotes from several observed lectures of each instructor, we found that the two instructors' facilitation of student participation during lectures consistently differed in (1) the participation structures were used, (2) the types of questions asked, and (3) how instruction responded to students' contributions. Our findings show that lecturing in advanced mathematics is not a uniform style and that active student participation in lectures is possible. We interpret the potential impact of observed differences on students' learning and experiences in terms of the Teaching for Robust Understanding (TRU) framework (Schoenfeld, 2018). [For the complete proceedings, see ED630060.]
Classroom Supports for Generalizing
Author: Ellis, Amy
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Generalization,Teaching Methods,Mathematics Instruction,Instructional Effectiveness,Learner Engagement,Classroom Communication,Algebra,Thinking Skills,Middle School Students,High School Students,Mathematics Teachers,Video Technology,Teacher Student Relationship

Generalization is a critical component of mathematics learning, but it can be challenging to foster generalization in classroom settings. Teachers need access to better tools and resources to teach for generalization, including an understanding of what tasks and pedagogical moves are most effective. This study identifies the types of instruction, student engagement, and enacted tasks that support generalizing in the classroom. We identified three categories of Classroom Supports for Generalizing (CSGs): Interactional Moves, Structuring Actions, and Instructional Routines. The three categories operate at different levels to show how teachers, students, tasks, and artifacts work in interaction to mutually support classroom generalizing. [For the complete proceedings, see ED630060.]
Examining the Impact of Restorative Justice on Teacher Retention in K-12 Public Education
Author: Whitlock, Melvin D.
Date: 2023-00-00
Type: Reports - Evaluative
Subjects: School Safety,School Violence,Faculty Mobility,Decision Making,Justice,Elementary Secondary Education,Models,Public School Teachers,High School Teachers

A recent study conducted by the American Psychological Association (APA) on school violence observed an emerging trend of in-school violence committed by students on school faculty and staff (McMahon et al., 2022). As a result, educators have increasingly factored student-related violence on adult stakeholders in their decisions regarding teacher turnover in various schools throughout the United States (Acosta, 2023; Walker, 2022). Although the recent phenomenon on school safety tends to focus on mass-shootings, this paper will examine how effective restorative justice has been as a deterrent to daily student-led violence during school hours (Dukes, 2023; Walker, 2022). Additionally, this paper will cite the Colorado Department of Education (CDE) and Denver Public Schools (DPS) as a model to examine the success or challenges of restorative justice in k-12 public education.
Exploring Teachers&apos; Responsiveness to Children&apos;s Fraction Thinking and Relationships to Fraction Achievement
Author: Empson, Susan B.
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Fractions,Thinking Skills,Grade 3,Grade 4,Grade 5,Elementary School Teachers,Faculty Development,Elementary School Students,Mathematics Achievement,Correlation,Teacher Competencies,Expertise,Questioning Techniques,Attention,Word Problems (Mathematics)

Identifying components of teaching that make a difference in children's learning is an ongoing challenge in our field. Focusing on teaching that is responsive to children's fraction thinking, we decomposed responsiveness into the instructional practices of questioning to support and extend children's thinking, noticing children's thinking, and anticipating children's thinking. We worked with 49 teachers in grades 3-5 in multiyear professional development and assessed their expertise in each of the practices. We also assessed their students' fraction achievement at the beginning and end of the school year. Correlational analyses revealed significant moderate relationships among teachers' expertise in the three practices, and a multilevel regression analysis revealed significant positive relationships for both expertise in teacher questioning and years of professional development with children's fraction achievement. [For the complete proceedings, see ED630060.]
Tuition and Fees, Appropriations, and Financial Aid in the West, 2022-23: Trends and Implications. WICHE Insights
Author: Falkenstern, Colleen
Date: 2023-05-00
Type: Reports - Evaluative
Subjects: Higher Education,Tuition,Fees,Student Financial Aid,Educational Finance,Trend Analysis,State Aid,Two Year Colleges,Public Colleges,Federal Aid,Grants

The most recent data on tuition, appropriations, and state grant aid present an economic outlook that appears favorable in the West. Tuition rates remained relatively flat for the past decade, total state funding to higher education increased across the region in the past year, and state grant aid continued to increase since 2010-11. Despite these promising trends, higher education institutions and systems face considerable challenges such as declining enrollment, concerns about the value of a degree, rising costs for students and institutions, and a need to address critical workforce gaps. With potential for an economic slowdown in the near future, higher education leaders and policymakers must strategically align fiscal policy levers to address state priorities and concerns on the affordability and value of a postsecondary degree. This WICHE Insights looks at the trends and implications for tuition and fees, appropriations, and financial aid in the west for 2022-23. [For the 2021-22 report, see ED622567.]
Preservice Secondary Teachers&apos; Reasoning about Static and Dynamic Representations of Function
Author: Ozen, Demet Yalman
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Secondary School Teachers,Mathematics Teachers,Mathematical Logic,Mathematics,Graphs,Algebra,Mathematics Education

This study aims to describe how preservice secondary mathematics teachers (PSMTs) reason about different function representations. The study focuses on two PSMTs' reasonings across static and dynamic representations of functions. Sfard's (2008) Theory of Commognition guided our analysis. Findings indicate that while static representations restrict attention given to covariation, dynamic representations support PSMTs' reasoning about covariation including making connections to how covariation is represented in static graphs. [For the complete proceedings, see ED630060.]
Doing Math in the Digital Age: An Analysis of Online Mathematics Platforms
Author: Condon, Lara
Date: 2021-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Elementary School Mathematics,Elementary School Students,Electronic Learning,Learning Experience,Mathematics Instruction,Educational Games,Mathematics Activities,Mathematics Skills,Decision Making,Classification

We present a typology for characterizing online student-facing mathematics platforms that examines how they position students as learners, exemplified by 9 commonly used platforms. We identify three types of student learning experiences: instruction and practice, practice and support, and conceptual games and activities, and describe each one in terms of the relationships among instructional guidance, student agency, and the mathematical rigor of tasks. We find that within and across categories, there is substantial variation in cognitive demand and student agency, offering implications for further research, school decision makers and platform designers. [For the complete proceedings, see ED630060.]