ethanporcaro/eric-fulltext-meta huggingface dataset:
Examining the Nature of Pedagogical Content Knowledge (PCK) with a Validation Argument for the PCK-Fractions Measure
Author: Zolfaghari, Maryam
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Fractions,Mathematics Instruction,Pedagogical Content Knowledge,Validity,Elementary School Students,Teaching Methods,Teacher Effectiveness,Thinking Skills,Education Majors,Nonmajors,Comparative Analysis,Scores,Preservice Teachers,Field Experience Programs,Measures (Individuals)

This study presents an extension of the validity argument for the PCK-Fractions measure. PCK-Fractions is designed to assess the effectiveness of professional experiences in facilitating teachers' pedagogical content knowledge (PCK) for children's fraction reasoning in grades 3-5. We examined data across 101 participants from two Midwest universities including noneducation majors, education majors, and education majors with grade 3 to 5 math field experiences. Results provide additional validity evidence for the PCK-Fractions. Namely, evidence indicates differences in scores between groups of participants--preservice teachers grade 3 to 5 field experience had higher scores than those without, and all preservice teachers had higher scores than non-education majors. [For the complete proceedings, see ED630210.]
Educating Teachers in California: What Matters for Teacher Preparedness?
Author: Patrick, Susan Kemper
Date: 2023-05-12
Type: Reports - Research
Subjects: Teacher Education,Career Readiness,Credentials,Student Attitudes,Blacks,American Indian Students,Special Education Teachers,Access to Education,Educational Policy,Clinical Supervision (of Teachers),Student Surveys,Beginning Teachers,Employers,Program Effectiveness

High-quality teacher preparation is a critical building block of an effective and stable teacher workforce. In California, the Commission on Teacher Credentialing (CTC) currently oversees teacher preparation programs (TPPs) at more than 100 institutions, and these programs graduate more than 10,000 teacher candidates per year. Over the past decade, California has considerably revised its statewide licensing and accreditation systems that set standards for teacher preparation and performance expectations for beginning teachers. These new teaching standards emphasize teachers' abilities to teach to the more ambitious student learning standards the state adopted in 2010. Given policy changes and financial investments, what is the state of teacher preparation in California? Based on survey responses from almost 60,000 completers of TPPs across California from 2016-17 to 2020-21, this report describes changes in the pool of newly credentialed teachers over this period of time, how well prepared completers of TPPs feel in different domains of practice, what kind of learning opportunities they encountered, what aspects of preparation explain how prepared completers feel to enter the profession, and how access to preparation experiences varies among different groups of teachers. This analysis also examines the extent to which perceptions of TPP completers align with survey responses from more than 5,000 cooperating teachers working with student teachers and more than 1,500 employers hiring these new teachers. This report begins by describing the landscape of teacher preparation in California. The authors then explain the data and methods used in this report and outline how the composition of the pool of newly credentialed teachers has changed between 2016-17 and 2020-21. They then detail the findings from the analysis of CTC surveys. These findings are organized into three sections: (1) overall perceptions of preparation effectiveness, (2) differences in perceptions of effectiveness by characteristics of preparation, and (3) differential access to highly rated preparation. The report concludes with policy considerations for California and implications for other states. [For the Research Brief, see ED630346.]
Educating Teachers in California: What Matters for Teacher Preparedness? Research Brief
Author: Patrick, Susan Kemper
Date: 2023-05-12
Type: Reports - Descriptive
Subjects: Teacher Education,Career Readiness,Credentials,Student Attitudes,Blacks,Preservice Teachers,American Indian Students,Special Education Teachers,Access to Education,Educational Policy,Clinical Supervision (of Teachers),Student Surveys,Educational Research

Over the past decade, California has revised its standards for teacher preparation and credentialing and invested in high-retention pathways for entering teaching. As part of its new accreditation system, the California Commission on Teacher Credentialing (CTC) administers surveys to program completers who apply for their preliminary teaching credentials. This analysis examines survey responses of almost 60,000 completers from 2016-17 to 2020-21. California has a growing and increasingly diverse pool of teacher preparation graduates, and more than 90% rated their programs positively. Clinical support and access to subject-area preparation are strong predictors of overall feelings of preparedness. Graduates of new preservice residencies and student teaching programs report feeling better prepared than those entering as interns or on emergency-style permits. However, access to higher-rated programs offering more clinical support varies, with half of Black and Native American candidates, as well as most special education candidates, entering without access to student teaching. [Report originally published March 2, 2023, last revised May 12, 2023. For the full report, see ED630345.]
Equitable Teaching Practices: Developing Emergent Bilinguals&apos; Positive Mathematical Identities = Prácticas Equitativas De Enseñanza: Desarrollando Identidades Matemáticas Positivas en Los Bilingües Emergentes
Author: Castellón, Libni B.
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Equal Education,Teaching Methods,Bilingualism,Mathematics Education,Self Concept,Grade 5,Elementary School Students,Elementary School Teachers,Mathematics Instruction,Teacher Student Relationship,Mathematics Skills,Cognitive Ability,Language Usage,Native Language,Classroom Communication,Inclusion,Diversity,Problem Solving,Bilingual Teachers,Spanish,English (Second Language),Second Language Learning,Second Language Instruction,Language Teachers,Lesson Plans,Video Technology,Teacher Characteristics,Instructional Effectiveness

This paper focuses on Emergent bilinguals (EBs) who traditionally face unequal opportunities to learn mathematics, harming their identities. The purpose of this paper is to illustrate how a fifth grade teacher cultivated the development of her EBs' mathematical identities by giving them opportunities to participate in cognitively demanding activities. Drawing on a conception of mathematical identity as something that changes in response to different situations, we illustrate how a fifth-grade teacher positively impacted her students' mathematical identities. The results reveal that when teachers use instructional strategies such as distributing mathematical authority, positioning students as mathematically capable, and incorporating students' languages as a resource for instruction, their EBs have multiple opportunities to build positive mathematical identities. [For the complete proceedings, see ED630210.]
&quot;Mirror Logic&quot;: A Preservice Mathematics Teacher&apos;s Thinking about Radian in the Context of Light Reflection
Author: Alyami, Hanan
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Mathematics Teachers,Mathematics Instruction,Light,Geometry,Mathematical Concepts,Thinking Skills,STEM Education,Mathematics Curriculum,Teaching Methods,Measurement,Teacher Education Programs,Spatial Ability,Logical Thinking

Integrated science, technology, engineering, and mathematics (iSTEM) education allow learners to utilize multiple disciplinary perspectives. However, the discipline of mathematics remains underrepresented in iSTEM curriculum. To explore the nature of mathematical thinking with an iSTEM curricular approach that emphasizes mathematics, we investigated the thinking of a preservice mathematics teacher, Alex (pseudonym), who engaged in a task-based digital activity involving radian angle measure in the context of light reflection. Findings suggest that Alex's ways of thinking comprise mathematical terminology, concepts, and processes, including mathematical ways of thinking about light reflection. The findings in this report suggest that emphasizing mathematics in this iSTEM context provided an opportunity for new ways of thinking about radian angle measure, and about how angle measure relates to light reflection. [For the complete proceedings, see ED630210.]
Collective Curricular Noticing within a Mathematics Professional Learning Community
Author: Barno, Erin
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematics Teachers,Communities of Practice,Decision Making,Educational Change,High School Students,Learning Processes,Lesson Plans,Teacher Attitudes,Teacher Student Relationship,Algebra,Teaching Methods,Intuition

This paper explores how a professional learning community (PLC) redesigns high school mathematics lessons towards a shared commitment. We describe the nature of a PLC's collective curricular vision to illuminate how teachers can come to new understandings as a group in order to shift the ways students experience mathematics. Using the curricular noticing framework (attending, interpreting, and responding), we analyzed the meetings of a PLC with six teachers as they individually presented lessons to be redesigned with a focus on the group's shared commitment. Findings indicate three ways ideas were introduced that led to expansive responses, which suggests this analytic approach could identify ways in which a PLC can work towards new curricular decisions. [For the complete proceedings, see ED630210.]
Tensions of Knowledge and Authority: Challenges of Teaching SJM
Author: Warburton, Trevor T.
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Knowledge Level,Power Structure,Social Justice,Preservice Teachers,Mathematics Teachers,Teaching Methods,Mathematics Education,Graduate Students,Student Attitudes,Teacher Student Relationship

This study seeks to demonstrate how knowledge and authority are linked for preservice mathematic teachers and how this link may pose a challenge for teaching mathematics for social justice. A CDA of multiple preservice class discussions is presented. [For the complete proceedings, see ED630210.]
Leveraging Equity and Civic Empathy through Community-Based Mathematical Modeling
Author: Aguirre, Julia M.
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Models,Mathematics Instruction,Teaching Methods,Equal Education,Empathy,Elementary School Students,Guidelines,Learner Engagement,Justice,Academic Standards,Educational Objectives,Faculty Development,Culturally Relevant Education,Ethics,Vignettes,Elementary School Teachers,Library Materials,Ethnic Groups,Cultural Pluralism,Graphs,Diversity,Water Quality,Educational Environment,Charts,Community Involvement

This theoretical paper describes how Community-based Mathematical Modeling can advance equity and cultivate civic empathy in elementary school settings. We provide a framework for community-based mathematical modeling instruction consisting of five goals: facilitating connections, fostering engagement, promoting rigor, cultivating civic empathy, and elevating justice. We illustrate how these goals work together to advance equity and cultivate civic empathy through classroom vignettes of community-based modeling lessons. Through this theoretical synthesis, implications for community-based mathematical modeling instruction will be discussed. [For the complete proceedings, see ED630210.]
A Study of the Consistency in New York State First Year Math Exams
Author: Schaefer, Stephanie
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Tests,High School Freshmen,Academic Standards,State Standards,Reliability,Educational Change,Academic Achievement,Test Content,State Departments of Education,Leaders,Measurement

As standards documents have been introduced over the past 20 years, many states have seen an evolution in both the standards and related high stakes exams. For many teachers across the U.S., the rollout of standards and exams has not been an experience that builds trust in state education leaders. In this study, we consider three major changes in the first-year high school math exams in New York State since 2002, looking at consistency in item types, topics addressed, and student performance. Shifts in all were noted, but the changes in topics, especially when not obvious by the names given to standards, are suggested as the mostly likely to misinform or misguide teachers. We consider how state educational leaders are working to build trust for the next iteration of standards. While this study is particular to one state, the methods and findings should be of interest to others who study curriculum and testing in high schools. [For the complete proceedings, see ED630210.]
Teacher Language and Gesture in an Intervention Focused on Developing Kindergarteners&apos; Understandings of the Equal Sign
Author: Sung, Yewon
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Kindergarten,Mathematics Instruction,Teaching Methods,Symbols (Mathematics),Nonverbal Communication,Language Usage,Equations (Mathematics),Thinking Skills,Algebra,Early Intervention,Correlation,Classroom Communication

This research reports on the teacher language and gesture that contributed to shifts in thinking about the equal sign and equations observed in twenty kindergarteners who took part in an early algebra intervention. Our analysis revealed ways in which the teacher used language and gesture to support students in moving from describing and working with the equal sign operationally (i.e., as a signal to compute) to describing the symbol as indicating the equivalence of two amounts and successfully working with equations of various forms. We detail four kinds of language and two kinds of gesture specifically related to mathematical equivalence that we believe contributed to students' growth. [For the complete proceedings, see ED630210.]
Building towards Harmony between Identity and Mathematics Synthesizing Figured Worlds and Rightful Presence
Author: Stringer, Brinley Poulsen
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Teaching Methods,Self Concept,Disadvantaged,Personal Autonomy,Psychological Patterns,Power Structure,Social Justice,Classroom Techniques,Access to Education,Equal Education

As identity becomes more discussed within education, it becomes crucial to understand identity in relation to power and social justice. In this paper, we discuss the identity frameworks of figured worlds and rightful presence to operationalize the critical consideration of identity within mathematics learning environments. We argue that by themselves, figured worlds and rightful presence have shortcomings that make it difficult to attend to power, and contextualize change, respectively. When considered in tandem, however, these two frameworks complement one another and build a stronger attention to identity that mobilizes student agency in the classroom. We call on educators and researchers to combine and utilize these frameworks to address the dissonance of identity that often occurs for marginalized students, thus building towards a greater harmony of identity and mathematics. [For the complete proceedings, see ED630210.]
Faculty and Student Perceptions of Instructional Servingness in Gateway Mathematics Courses at a Hispanic-Serving Institution
Author: Leyva, Luis A.
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: College Faculty,Teacher Attitudes,Undergraduate Students,Student Attitudes,Minority Serving Institutions,Hispanic American Students,Mathematics Education,Teaching Methods,Educational Experience,Mathematics Teachers,Introductory Courses,Statistics Education,Mathematics Skills,Teacher Student Relationship,Equal Education,Student Diversity,Inclusion,Faculty Development,State Universities

Research exploring how Hispanic-Serving Institutions (HSIs) serve Latin* STEM students has largely focused on features of organizational structures (e.g., support programs), but minimally examined instruction and classroom experiences. This is an important gap to fill, especially in gateway mathematics courses, where faculty relationships and quality of instruction impact Latin* students' persistence and identities in STEM. To advance such research, this report presents findings from an analysis of how perspectives from HSI mathematics faculty and students about instruction in introductory statistics converged and diverged in terms of serving Latin* populations. We present two illustrative cases of dissonant and resonant perspectives on serving Latin* students through instruction that frames mathematical ability expansively (e.g., not limited to being fast or correct). We conclude with research and practice implications. [For the complete proceedings, see ED630210.]
&quot;I Watched as He Put Things on the Paper&quot;: A Feminist View of Mathematical Discourse
Author: Theobold, Allison S.
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Feminism,Mathematics Education,Discourse Analysis,Cooperative Learning,Language Usage,Problem Solving,College Students,Peer Relationship

In this study we present results of a discourse analysis of the interactions between two partners, Uma and Sean, through a feminist lens. During roughly five hours of small group work in a teaching experiment, how each partner used language to position each other's thinking as mathematically significant and establish a collaborative environment varied dramatically. Specifically, Uma shouldered the burden of continuously working to maintain collaboration, oftentimes at the expense of having her thinking positioned as mathematically significant. On the other hand, Sean regularly offered little opportunity for Uma to engage openly with his thinking, which ultimately constrained Uma's opportunities to learn. [For the complete proceedings, see ED630210.]
Obscuring Racial Inequities through Gender-Focused Discourse: An Analysis of Student Participation in a Calculus Class
Author: Fink, Heather
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Racial Differences,Gender Differences,Calculus,Mathematics Instruction,Equal Education,High School Students,Student Participation,White Students,Males,Minority Group Students,Inclusion,Diversity,Classroom Communication,Mathematics Teachers,Student Teachers,Discourse Analysis,Grade 12,Teacher Attitudes,Student Attitudes

Inequities in STEM participation for people of color and women are documented extensively, often highlighting issues of representation and/or achievement. This study adds to the literature by looking at participation inequities in a high school calculus class. Equity is conceptualized as a fair distribution of opportunities for students to engage in rich mathematical experiences. Analysis of participants' dialog revealed talk about student participation focused primarily on gender patterns, even when pertaining to only one race-gender group of students (i.e., White males). Analysis of whole-class participation showed White dominance superseded male dominance; White males had the most robust opportunities to participate followed by White females, females of color, and males of color. Findings suggest participants' gender-focused discourse obscured racial inequities in classroom participation. [For the complete proceedings, see ED630210.]
Invented Strategies Changing Teachers&apos; Pedagogical Content Knowledge
Author: Lunt, Jana
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Pedagogical Content Knowledge,Learning Strategies,Teaching Methods,Elementary School Teachers,Faculty Development,Teacher Attitudes,Algorithms,Cognitive Style,Misconceptions,Instructional Materials,Group Discussion,Textbooks,Critical Thinking,Educational Change

This study investigates how utilizing student-invented strategies in the classroom can inform teachers' pedagogical content knowledge. Two elementary school teachers participated in professional development discussing the benefits of invented strategies. Data was then gathered as the participants implemented this practice in their classrooms. Data was analyzed qualitatively to show the ways in which invented strategies can be useful in a teacher's development of their pedagogical content knowledge, including their Knowledge of Content and Students, Knowledge of Content and Teaching, as well as Knowledge of Content and Curriculum. [For the complete proceedings, see ED630210.]
K-2 Student&apos;s Composing of Lego Structures
Author: Kocabas, Sezai
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Toys,Learning Activities,Accuracy,Grade 2,Elementary School Students,Spatial Ability,Thinking Skills,Kindergarten,Grade 1,Color,Guides,Comparative Analysis,Decision Making,Illustrations,Teaching Methods,Difficulty Level,Geometry,Mathematics Skills,Montessori Method,After School Programs

Block building activities help develop students' spatial reasoning, but few studies focus on the development of block building skills beyond preschool. We worked with four kindergarten, four first grade, and four second grade students to learn more about their Lego block building. We compared students' accuracy, building strategies, and spatial language as they used manuals versus pictures of final Lego structures (presented in color versus grayscale) to build two Lego structures. On the first structure, students using color manuals or pictures had an easier time choosing correct bricks but had difficulty correctly placing them; students using grayscale manuals or pictures had difficulty picking the correct bricks but placed them more accurately. By the second design, students did better with the manuals, regardless of color. Students need more support to use specific spatial language and building with depth versus height. [For the complete proceedings, see ED630210.]
Conceptual Reorganization, from Count-Up-To to Break-Apart-Make-Ten: A Case of a 6th Grader Struggling in Mathematics
Author: Tzur, Ron
Date: 2022-00-00
Type: Speeches/Meeting Papers
Subjects: Grade 6,Mathematics Instruction,Learning Problems,Elementary School Students,Mathematical Concepts,Computation,Constructivism (Learning)

Through a constructivist teaching experiment, we studied how a 6th-grade student (Adam, pseudonym) struggling in mathematics may reorganize his available additive scheme (count-up-to) into a more advanced scheme involving the decomposition of composite units (break-apart-make-ten, or BAMT). First, we posed a task that led us to infer Adam was yet to construct the BAMT scheme at the anticipatory stage (solving a task without prompting). We thus turned to promote reorganization of his anticipatory, count-up-to scheme used to solve missing-addend tasks. Through reflection on the relationships between his goal, count-up-to actions, and effect of those actions, Adam independently brought forth what he called &quot;easy number-pairs&quot; (i.e., 10+X = X-teen). This seemed to afford his reorganization of count-up-to into the BAMT scheme. We discuss implications of this reorganization for theory building and practice. [For the complete proceedings, see ED630210.]