ethanporcaro/eric-fulltext-meta huggingface dataset:
The Space between the Unknown and a Variable
Author: Hewitt, Dave
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Algebra,Symbols (Mathematics),Numbers,Bias,Fractions,Equations (Mathematics),Mathematical Concepts,Secondary School Students,Foreign Countries,Comprehension

The meaning given to letters is significant for students' ability to be successful with algebraic tasks. Recent studies have noted that even when students have a sense of generalised number, they often have a natural number bias in the values they think a letter can take. This study analyses interviews from 13 students across two schools to explore the meaning they had for letters. The responses supported the idea that some students have a natural number bias and also that the notion of a letter representing a fraction is problematic. In addition, three other factors emerged which affected the meaning given to a letter: what was mentally stressed; the desire to avoid &quot;messy&quot; calculations; and viewing an equation as an example of a wider class of equations. [For the complete proceedings, see ED597799.]
Students&apos; Understanding of Square Numbers and Square Roots
Author: Hiebert, Erica J. A.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Concepts,Concept Formation,Grade 11,High School Students,Mathematics Skills,Mathematics Instruction,Problem Solving,Secondary School Mathematics

Despite their apparent simplicity, the concepts of square numbers and square roots are problematic for high school students. I inquired into students' understanding of these concepts, focusing on obstacles that students face while attempting to solve square number problems. The study followed a modified analytic induction methodology that included a written questionnaire administered to 51 grade 11 students and follow up clinical interviews with 9 students. The study revealed significant obstacles relating to the representation of square numbers and confusion of concepts including both weak distinction between the concepts of square numbers and square roots and inconsistent evoking of their concept images. [For the complete proceedings, see ED597799.]
Interactive Construction of Attention Paths toward New Mathematical Content: Analysis of a Primary Mathematics Lesson
Author: Hino, Keiko
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Grade 6,Mathematics Instruction,Teaching Methods,Mathematical Concepts,Attention,Course Content,Classroom Communication,Lesson Plans,Foreign Countries,Elementary School Students,Concept Formation

On the basis of the construct of &quot;discursive focus&quot; by Sfard (2000), this study explores how students' attention is brought to new mathematical content in whole-class interaction between the teacher and the children. In a sixth-grade lesson introducing the concept of constancy of proportion, we analyzed the progression of social interaction in terms of how different foci were presented, problematized, or modified. The results show that the children's vague attention to the constant number was questioned and made an object of examination. The children's attention was then carefully controlled by involving them in building new perspectives, which became the basis for making sense of constancy of proportion. We also point out several significant teaching actions for making this process happen. [For the complete proceedings, see ED597799.]
Small Group Interactions: Opportunities for Mathematical Learning
Author: Hunter, Roberta
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Pacific Islanders,Group Activities,Small Group Instruction,Scaffolding (Teaching Technique),Cooperative Learning,Peer Relationship,Children,Early Adolescents,Low Income Students,Urban Schools,Elementary School Students,Verbal Communication,Problem Solving,Foreign Countries

Small group interactions can provide rich conceptual mathematical understandings. This paper reports on the mathematical talk of Maori and Pasifika students as they participated in small group activity. The findings illustrate that when the students were scaffolded to work collaboratively the talk shifted between focusing on mathematics (mathematizing) and people (subjectifying) and this supported their learning. [For the complete proceedings, see ED597799.]
Visual and Analytical Strategies in Spatial Visualization: Perspectives from Bilateral Symmetry and Reflection
Author: Ho, Siew Yin
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Spatial Ability,Geometry,Problem Solving,Grade 9,Grade 8,Visualization,Cognitive Processes,Problems,Secondary School Students

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative procedure. The inadequate criteria for reflection shaped the ninth grader's actions and equally served to validate her solutions, although in a flawed fashion. The visual strategy took over as a fallback measure. We attend to some of the well-known constraints that students encounter in dealing with symmetry, particular situations involving slanted line of symmetry. Importantly, we made an attempt to show how visual and analytical strategies interact in the production of a reflected image. [For the complete proceedings, see ED597799.]
U.S. Political Discourse on Math Achievement Gaps in Light of Foucault&apos;s Governmentality
Author: Indiogine, Salvatore Enrico
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Educational Philosophy,Mathematics Achievement,Achievement Gap,Discourse Analysis,Educational Policy,Political Attitudes,Government Role,Educational Legislation,Federal Legislation,Teaching Methods,Educational Equity (Finance),Economic Factors,Competition,Public Education,Educational Resources,Educational Quality,Academic Standards,Data Analysis,Elementary Secondary Education

The objective of the study was to document and analyze the justifications given by federal institutions of the United States for governmental control of mathematics education as function of the achievement gaps (AGs) in mathematics. We wanted to shed light on the discourses made in the public arena that have legitimized this control and firmly established in the national conscience that the knowledge of mathematics is essential to the prosperity and survival of the nation. The research question can be briefly stated as &quot;what insights and understandings of the national education policy discourse on the achievement gaps in mathematics does Foucault's (2009) governmentality offer?&quot; [For the complete proceedings, see ED597799.]
How Is the Function Concept Introduced in Textbooks?: A Comparative Analysis
Author: Hong, Dae S.
Date: 2014-00-00
Type: Reports - Evaluative
Subjects: Mathematics Instruction,Textbooks,Textbook Content,Foreign Countries,Mathematical Concepts,Cultural Differences,Difficulty Level,Cognitive Processes

This study compared sections of functions and linear functions from four Korean textbooks and Core Plus Mathematics Project (CPMP). To understand differences and similarities among these textbooks, both horizontal and vertical analyses were conducted. The horizontal analysis results revealed that topics related to functions and linear functions are introduced relatively earlier in Korean textbooks than in CPMP. The vertical analysis results confirmed the findings of previous study (Hong &amp; Choi, 2014), which can be interpreted as &quot;textbook signature&quot;. [For the complete proceedings, see ED597799.]
Relating Student Meaning-Making in Mathematics to the Aims for and Design of Teaching in Small Group Tutorials at University Level
Author: Jaworski, Barbara
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: College Mathematics,Mathematics Instruction,Small Group Instruction,Tutoring,College Freshmen,Calculus,Epistemology,Mathematical Concepts,Foreign Countries,Teaching Methods

In a developmental research approach, from a sociocultural position, we address the meanings students make of mathematics in teaching sessions and how this relates to the intentions of the teacher and approaches to teaching. Analyses of data come from small group tutorials of one tutor with first year university mathematics students (n=5). We exemplify using data from one tutorial which addressed concepts in calculus that first year students encounter in their lectures. We explain teaching design and an approach to implementing it, and address issues that arise in practice and how these are related to students' meaning-making of mathematical concepts. Development of 'knowledge in practice' is seen alongside that of knowledge in the public domain. [For the complete proceedings, see ED597799.]
Preparing Principals for Pre-K in Illinois: The Prairie State&apos;s Story of Reform and Implementation
Author: Lieberman, Abbie
Date: 2019-10-00
Type: Reports - Evaluative
Subjects: Principals,Management Development,Preschool Education,Administrator Qualifications,Educational Change,State Policy,Educational Policy,Program Implementation,Internship Programs,Institutional Characteristics,Stakeholders,Progress Monitoring

This paper explores Illinois's shift from a general administrative license, called a &quot;Type 75&quot; license, to a &quot;PK-12 Principal Endorsement.&quot; It includes both a history of the reform efforts and a look at how implementation has fared nearly a decade after the legislation was signed into law. It also offers lessons and recommendations for other states looking to ensure principals are equipped to lead pre-K and early grade classrooms. [For an overview of this report, see ED599867.]
Preparing Principals for Pre-K in Illinois: The Prairie State&apos;s Story of Reform and Implementation. Education Policy. [Overview]
Author: Lieberman, Abbie
Date: 2019-00-00
Type: Reports - Descriptive
Subjects: Principals,Management Development,Preschool Education,Administrator Qualifications,Educational Change,State Policy,Educational Policy,Program Implementation,Progress Monitoring,Stakeholders,Internship Programs

In 2010, Illinois passed legislation making significant changes to its principal preparation and licensure policies. With the goal of improving student outcomes and closing achievement gaps, the state updated standards for principal preparation programs with a focus on instructional leadership. Illinois's reforms were ambitious, requiring all programs to reapply for approval from the state board of education under the new standards. Included in the legislation was something unique to Illinois-- a call to prepare all principals to lead pre-K students. This overview of the report, &quot;Preparing Principals for Pre-K in Illinois: The Prairie State's Story of Reform and Implementation&quot; includes both a history of the reform efforts and a look at how implementation has fared nearly a decade after the legislation was signed into law. It also offers lessons and recommendations for other states looking to follow Illinois's lead and ensure principals are equipped to lead pre-K and early grade classrooms. [For the full report, see ED599865.]
IQ-Achievement Discrepancy for Identification of Disabilities in Spanish-Speaking English Learners
Author: Santi, Kristi L.
Date: 2019-00-00
Type: Reports - Research
Subjects: Intelligence Quotient,Spanish Speaking,English Language Learners,Disability Identification,Validity,Grade 1,Grade 2,Elementary School Students,Longitudinal Studies,Language of Instruction,Classification,Low Achievement,Cutting Scores,Language Minorities,Evaluation Methods,Evaluation Criteria,Intelligence Tests

This article examines the validity of IQ-achievement discrepancy and low-achievement as criteria for the identification of disabilities in Spanish-speaking ELs and the factors that moderate the validity of these approaches as bases for identification. While there has been a long history of examining the validity of different approaches to disability identification in monolinguals, there are no systematic approaches taken for ELs. Data from Grades 1 and 2 of a large longitudinal data set consisting of young Spanish-speaking students attending schools in the U.S. were used to empirically examine criteria for disability identification among language minority children - one of the first large-scale attempts. Findings indicated significant overidentification when the language of assessment was not matched to the language of the instruction, although effects varied predictably over time and by language of instruction. Validation of classifications using measures external to the classification found that low achieving and discrepant children differ from typically developing children, and from one another in predictable ways based on differences in IQ. The study highlights the importance of taking into account the language of instruction and the severity of the cut-off to reduce misidentification of typically developing children. [This paper was published in &quot;New Directions for Child and Adolescent Development&quot; n166 p111-143 2019 (EJ1221827).]
School Day Classroom-Based Physical Activity and Sedentary Behavior
Author: Calvert, Hannah G.
Date: 2019-09-01
Type: Reports - Research
Subjects: Physical Activities,Physical Activity Level,Life Style,Program Effectiveness,Student Behavior,Recess Breaks,Physical Education,Intervention,Elementary School Students,Grade 2,Grade 3,Grade 4,Health Promotion,Teacher Role

Objectives: Many school-aged children do not meet the daily minimum recommendations for accruing moderate to vigorous physical activity (MVPA), and spend much of their day sedentary. The purpose of this study was to investigate the effects of teacher-delivered classroom-based physical activity (CBPA) on students' MVPA and sedentary behaviors. Methods: Participants included 157 students across seven classrooms and 500 student-days of observation. Students wore accelerometers for one week during fall of 2017, and teachers recorded their CBPA offerings daily. Minutes of scheduled recess and physical education (PE) were also recorded. Results: Overall, students spent the majority of the school day engaged in sedentary behavior, and accrued an average of 20 and 28 minutes of MVPA on non-PE and PE days, respectively. Students did not engage in lengthy bouts of sedentary behavior, and spent approximately 30 minutes each day in sedentary bouts. Mixed effects regressions revealed that offering any CBPA was associated with greater percent time in MVPA and less in sedentary behavior. Conclusions: CBPA is an important contributor to the 30 minutes of school day MVPA that students should accrue, especially since PE and recess are often not sufficient. [This paper was published in &quot;Health Behavior Policy Review&quot; Sep 2019.]
A Governor&apos;s Action Guide to Achieving Good Jobs for All Americans
Author: National Governors Association
Date: 2019-00-00
Type: Guides - Non-Classroom
Subjects: Job Development,Employment Opportunities,Labor Force Development,Education Work Relationship,Career Development,Job Training,Job Skills,Rural Development,Labor Market,Occupational Information,Talent Development,Retraining,Lifelong Learning,Employment Programs,State Programs,Recognition (Achievement),Employment Services,Certification,Holistic Approach,Best Practices

This guide is a result of the 2018-2019 National Governors Association (NGA) Chair's initiative, &quot;Good Jobs for All Americans,&quot; led by Montana Governor Steve Bullock. This initiative aimed to understand the changing world of work and the factors that affect an individual's ability to connect to a good job and for businesses to access the talent they need to thrive in today's global economy. Based on this understanding of the changes in the working world, this guide offers a toolbox of high-impact strategies that governors can take to connect workers to good jobs today and in the future. It outlines opportunities that governors have to create responsive, nimble training and workforce systems to better prepare Americans for the jobs of the future. These opportunities fall into three focus areas: (1) the workforce of the future -- aligning education and work; (2) second acts -- helping midcareer workers achieve success; and (3) rural resurgence -- empowering the rural workforce. [This guide was prepared by the NGA Solutions: The Center for Best Practices (NGA Solutions) team of Kimberly Hauge, Mike Bartlett, Dana Westgren and Meghan Wills.]
How a Professor Uses Diagrams in a Mathematics Lecture and How Students Understand Them
Author: Lew, Kristen
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: College Faculty,Mathematics Teachers,Mathematics Instruction,College Mathematics,Teaching Methods,Visual Aids,Undergraduate Students,Case Studies,Comprehension,Mathematical Logic

Mathematics education literature suggests that diagrams should be included in mathematics lectures, however few studies have empirically studied the use of diagrams in the undergraduate classroom. We present a case study investigating the use of diagrams in a university lecture and how students in the class understood them. Three archetypes of student understanding of diagrams are described and illustrated. [For the complete proceedings, see ED597799.]
Characteristics of University Mathematics Teaching: Use of Generic Examples in Tutoring
Author: Mali, Angeliki
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: College Mathematics,Mathematics Instruction,Tutoring,Teaching Methods,Mathematical Concepts,Mathematics Teachers,College Faculty,Foreign Countries,Small Group Instruction

The aim of this paper is to report early findings from university mathematics teaching in the tutorial setting. The study addresses characteristics of the teaching of an experienced research mathematician and through interviews, her underlying considerations. An analysis of a teaching episode illuminates her use of generic examples to reveal aspects of a mathematical concept and links with the tutor's particular research practice, didactics and pedagogy emerge. [For the complete proceedings, see ED597799.]
The Influence of 3D Representations on Students&apos; Level of 3D Geometrical Thinking
Author: Kondo, Yutaka
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Geometric Concepts,Mathematics Instruction,Secondary School Mathematics,Grade 7,Middle School Students,Problem Solving,Spatial Ability,Mathematical Logic,Thinking Skills,Foreign Countries,Geometry

While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In this paper, we report findings from a classroom experiment in which Grade 7 students (aged 12-13) tackled a problem in 3D geometry that was, for them, quite challenging. To analyse students' reasoning about 3D shapes, we constructed a framework of levels of 3D geometrical thinking. We found that students at a lower level of 3D thinking could not manipulate representations effectively, while students operating at a higher level of 3D thinking controlled representations well and could reason correctly. [For the complete proceedings, see ED597799.]
A Model for Systemic Change in Rural Schools
Author: Knott, Libby
Date: 2014-00-00
Type: Reports - Descriptive
Subjects: Rural Schools,Educational Change,Elementary Secondary Education,Mathematics Education,Teachers,Administrators,Community,Models,School Community Relationship,Teacher Administrator Relationship

This paper describes a theoretical model for systemic change as it concerns the learning and teaching of mathematics in K-12 schools, with particular attention being paid to the rural context. Systemic change is the active process of establishing change in the community through lasting, long-term relationships, practices, and procedures (Adelman &amp; Taylor, 2003). Our purpose is to describe the mechanics of such change provided by the strategic, continuous, and monitored support of all three of the constituents: Teachers, administrators and community, and externally supported by a temporary catalyst. Systemic change is achieved when the removal of the external catalyst does not affect the rest of the model. Evidence to support this claim has been derived from our case studies. [For the complete proceedings, see ED597799.]
Mathematical Certainties in History and Distance Education
Author: Martínez Navarro, Benjamin
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Logic,Educational Technology,Technology Uses in Education,Mathematical Concepts,Concept Formation,History,Algebra,Secondary Education,Adult Education,Problem Solving,Equations (Mathematics)

An historical case is presented in which extra-mathematical certainties lead to invalid mathematics reasonings, and this is compared to a similar case that arose in the area of virtual education. A theoretical-methodological instrument is proposed for analysis of certainties. The article suggests the need for teachers to be aware that certainties of mathematics facts are not always based on mathematics understandings. [For the complete proceedings, see ED597799.]
Teachers&apos; Perceptions of Productive Use of Student Mathematical Thinking
Author: Leatham, Keith R.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Logic,Teacher Attitudes,Productivity,Mathematics Teachers,Student Participation,Mathematics Instruction,Thinking Skills

We argue that the teaching practice of productively using student mathematical thinking [PUMT] needs to be better conceptualized for the construct to gain greater traction in the classroom and in research. We report the results of a study wherein we explored teachers' perceptions of PU T. We interviewed mathematics teachers and analysed these interviews using and refining initial conjectures about the process teachers might go through in learning PUMT. We found that teachers' perceptions of PUMT ranged from valuing student participation, to valuing student mathematical thinking, to using that thinking in a variety of ways related to eliciting, interpreting and building on that thinking. [For the complete proceedings, see ED597799.]
High School Students&apos; Emotional Experiences in Mathematics Classes
Author: Martínez-Sierra, Gustavo
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: High School Students,Emotional Experience,Mathematics Education,Problem Solving,Fear,Psychological Patterns,Student Interests,Affective Behavior,Affective Measures,Cognitive Structures,Student Attitudes,Foreign Countries,Participant Satisfaction

The aim of this qualitative research is to identify Mexican high school students' emotional experiences in mathematics classes. In order to obtain the data, focus group interviews were carried out with 22 students. The data analysis is based on the theory of the cognitive structure of emotions (Ortony, Clore &amp; Collins, 1988) that specifies the eliciting conditions for each emotion and the variables that affect the intensity of each emotion. The participant students' emotional experiences are composed of (1) Satisfaction and disappointment while solving a problem, (2) Joy or distress emotions when submitting a test, (3) Fear and relief emotions in mathematics classes, (4) Pride and self-reproach emotions when grading a course and (5) Boredom and interest in mathematics classes. [The research reported in this article was supported by several research grants from Research and Graduate Department of National Polytechnic Institute of Mexico and the National Council of Science and Technology of Mexico (CONACYT, Basic Scientific Research 2012). For the complete proceedings, see ED597799. For a related article, see EJ1091418.]