ethanporcaro/eric-fulltext-meta huggingface dataset:
Prior to School Mathematical Skills and Knowledge of Children Low-Achieving at the End of Grade 1
Author: Kollhoff, Sebastian
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Skills,Prior Learning,Mathematics Achievement,Numeracy,Elementary School Students,Concept Formation,Low Achievement,Grade 1,Grade 2,Preschool Children,Foreign Countries,Elementary School Mathematics

Recent psychological studies as well as research findings in mathematics education highlight the significance of early number skills for the child's achievement in mathematics at the end of primary school. In this context, first results from an ongoing four-year longitudinal study are reported. The study investigates the development of early numeracy understanding of 408 children from one year to school entry until the end of grade 2. The study seeks to identify children that struggle with respect to their mathematics learning after the first year of school mathematics and compare their performance with their number concept development one year prior to school as well as immediately prior to school entry. [For the complete proceedings, see ED597799.]
Flexible Use and Understanding of Place Value via Traditional and Digital Tools
Author: Kortenkamp, Ulrich
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Number Concepts,Concept Formation,Foreign Countries,Elementary School Mathematics,Elementary School Students,Grade 3,Mathematics Skills,Teaching Methods,Misconceptions,Manipulative Materials,Educational Technology,Technology Uses in Education

Place value is a key concept for numbers that is introduced in early mathematics. It is necessary to have a flexible understanding of place value for efficient arithmetic strategies and success in written algorithmic arithmetic. In our research we explore typical mistakes and misconceptions that occur with 3rd graders in German elementary school and investigate the various underlying actions when manipulating numbers in a place value chart. We also report on a follow-up quantitative study that compares real and virtual manipulatives for place value and their effect on learning of place value. [For the complete proceedings, see ED597799.]
Young Learners&apos; Understandings about Mass Measurement: Insights from an Open-Ended Task
Author: McDonough, Andrea
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Measurement,Comprehension,Elementary School Students,Foreign Countries,Mathematical Concepts,Knowledge Level,Self Evaluation (Individuals)

In response to an open-ended assessment task, 282 children of 6 to 8 years of age revealed their understandings of mass measurement. Each of the Year 1 and 2 children in 13 classes from 3 schools represented their knowledge of mass measurement in drawing and / or writing. Responses ranged from portrayals of activities they had undertaken or materials they had used in classes, to the more explicit articulation of key mathematical ideas. This paper presents samples of children's responses that illustrate a range of thinking and conceptual development about mass measurement revealed by the assessment tool. [For the complete proceedings, see ED597799.]
Looking for Goldin: Can Adopting Student &quot;Engagement Structures&quot; Reveal Engagement Structures for Teachers? The Case of Adam
Author: Lake, Elizabeth
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Learner Engagement,Mathematics Teachers,Secondary School Teachers,Teacher Attitudes,Classroom Communication,Teacher Student Relationship,Foreign Countries,Rural Schools,Psychological Patterns,Behavior Standards

Goldin et al. (2011) suggest nine 'engagement structures' for describing complex, 'in-the-moment' affective and social interactions as well as student beliefs. The study we report here examines the conjecture whether the 'engagement structures' construct can be appropriately adapted to allow such descriptions for secondary mathematics teachers. If this can be the case then linking teacher and student engagement structures could support detailed examination of classroom interactions. The aim of this paper is to consider one such adaptation and demonstrate some of its parts through the case of one teacher. We draw on this case study to indicate that such an approach has value, in particular in the ways in which it reveals relationships between engagement structures and norms in classroom interactions. [For the complete proceedings, see ED597799.]
Principles of Acquiring Invariant in Mathematics Task Design: A Dynamic Geometry Example
Author: Leung, Allen
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Educational Technology,Technology Uses in Education,Mathematics Instruction,Geometry,Geometric Concepts,Concept Formation,Teaching Methods,Differences

This paper is a theoretical discussion on a pedagogic task design model based on using variation as an epistemic tool. A set of four Principles of Acquiring Invariant is put forward that is complementary to the patterns of variation in Marton's Theory of Variation. These principles are then used as adhesive to tie together the epistemic modes in a model of task design in dynamic geometry environment that the author proposed in earlier research literature. A dynamic geometry task sequence is used to illustrate how the Principles of Acquiring Invariant can be used in mathematics task design. [For the complete proceedings, see ED597799.]
Explaining Mathematical Meaning in &quot;Practical Terms&quot; and Access to Advanced Mathematics
Author: le Roux, Kate
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Advanced Courses,Mathematics Instruction,College Students,Small Group Instruction,Video Technology,Discourse Analysis,Correlation,Introductory Courses,Group Discussion,Foreign Countries,Teaching Methods

This paper uses a socio-political practice perspective of mathematics to investigate the action of first year university students as they work in small groups to explain the meaning of mathematical objects in &quot;practical terms&quot;. Written transcripts representing video recordings of the action were analysed using critical discourse analysis and focal analysis. I present a description of the micro-level action and locate this action relative to the mathematical discourses in the university space. This analysis raises questions about the relationship between problems requiring the use of the practical terms genre and access to advanced mathematics at university. [For the complete proceedings, see ED597799.]
The Incidence of Disaffection with School Mathematics
Author: Lewis, Gareth
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Incidence,Negative Attitudes,Secondary School Students,Adolescents,Foreign Countries,Psychological Patterns,Ability Grouping,Self Efficacy,Beliefs,Classroom Environment,Mathematics Education

This paper reports the results of a study of affect and school mathematics, conducted with a whole cohort of pupils in year 9 (pupils aged 15 to 16 years) in a typical UK secondary school. This preliminary study provided contextual data for a larger mixed methods investigation into disaffection. The study offers interesting insights into the incidence of affection/disaffection within this group. Further, since the school grouped pupils by ability, the study offered the opportunity to look at the distribution of aspects of affect and disaffection across the ability range. Results not only provide contextual data on the incidence of disaffection with mathematics amongst school pupils of this age, it also suggests some interesting tentative conclusions. [For the complete proceedings, see ED597799.]
How the Knowledge of Algebraic Operation Relates to Prospective Teachers&apos; Teaching Competency: An Example of Teaching the Topic of Square Root
Author: Leung, Issic Kui Chiu
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Algebra,Teacher Competencies,Preservice Teachers,Mathematics Instruction,Knowledge Base for Teaching,Pedagogical Content Knowledge,Mathematical Concepts,Concept Formation,Secondary School Teachers,Secondary School Mathematics,Grade 8,Teaching Methods,Misconceptions

This study is the part of a larger study on investigating Hong Kong (HK) prospective teachers' (PTs) subject matter knowledge (SMK) and Pedagogical Content Knowledge (PCK). In this paper, five HK PTs' and PC on teaching one topic regarding square root were investigated. The results suggest that insufficient understanding on the concept of algebraic operation is the major obstacle to limit those student teachers from teaching students with mathematical understanding. The results further echo with the viewpoint that SMK and PCK are two interrelated constructs and rich SMK leads to high quality of PCK. [For the complete proceedings, see ED597799.]
Exploring the Relationship between Explanations and Examples: Parity and Equivalent Fractions
Author: Levenson, Esther S.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Grade 5,Elementary School Mathematics,Fractions,Mathematical Logic,Models,Concept Formation,Mathematical Concepts,Teaching Methods

Examples and explanations are inherent elements of mathematics learning and teaching. This study explores the relationship between examples and explanations given for the same concept. Results indicated that for the concept of parity, fifth grade students offer different explanations for different examples. However, for the concept of equivalent fractions, algorithmic explanations were most preferred. [For the complete proceedings, see ED597799.]
The Effect of an Intelligent Tutor on Math Problem-Solving of Students with Learning Disabilities
Author: Ma, Xiaojun
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Educational Technology,Technology Uses in Education,Learning Disabilities,Problem Solving,Mathematics Instruction,Mathematics Skills,Intelligent Tutoring Systems,Special Education,Word Problems (Mathematics),Grade 3,Elementary School Students,Urban Schools

Reform-based math instruction calls for students' construction of conceptual understanding, solving challenging problems and explanation of reasoning. However, existing literature shows that students with learning disabilities (LD) easily get lost in reform-based instruction. As an outcome of collaborative work between math education and special education in instructing students with LD, we have developed an intelligent tutor (PGBM-COMPS) to nurture multiplicative reasoning of students with LD. The intelligent tutor dynamically models individual student's evolving conceptions and recommends tasks to promote her/his advancement to a higher level in the learning trajectory and solve complex word problems using mathematical model equations. This study evaluated the effect of this intelligent tutor on improving multiplicative reasoning and problem solving of students with LD. [For the complete proceedings, see ED597799.]
Invention of New Statements For Counterexamples
Author: Komatsu, Kotaro
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Skills,Problem Solving,Mathematical Logic,Middle School Students,Middle School Mathematics,Grade 8,Logical Thinking,Foreign Countries,Geometry

From a fallibilist perspective, mathematics gradually develops with problems, conjectures, proofs, and refutations. To attain such authentic mathematical learning, it is important to intentionally treat refutation in mathematics classrooms, such as facing or proposing counterexamples and coping with them. In particular, analysing students' behaviour in response to counterexamples can lead to a design of teaching materials and instruction based on students' existing knowledge and strategies. In this paper, we construct a framework for capturing students' actions of inventing a new statement that holds for counterexamples to an original statement. We then illustrate a specific aspect of this framework with an episode that took place in an eighth grade classroom, and discuss two approaches to deductively generating a new statement. [For the complete proceedings, see ED597799.]
Mathematicians&apos; Example-Related Activity in Formulating Conjectures
Author: Lockwood, Elise
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Models,Professional Personnel,Mathematics,Teaching Methods,Validity,Mathematical Logic,Problem Solving,College Faculty

This paper explores the role examples play in mathematicians' conjecturing activity. While previous research has examined example-related activity during the act of proving, little is known about how examples arise during the formulation of conjectures. Thirteen mathematicians were interviewed as they explored tasks that required the development of conjectures. During the interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating systematic lists of examples that they examined for patterns. The results suggest pedagogical implications for explicitly targeting examples in conjecturing, and the study contributes to a body of literature that points to the benefits of exploring, identifying, and leveraging examples in proof-related activity. [For the complete proceedings, see ED597799.]
Perceptions and Reality: One Teacher&apos;s Use of Prompts in Mathematical Discussions
Author: Kosko, Karl W.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Elementary School Teachers,Elementary School Mathematics,Mathematics Instruction,Teaching Methods,Prompting,Cues,Mathematics Teachers,Questioning Techniques,Discussion (Teaching Technique),Vignettes,Instructional Effectiveness

We examined one primary teacher's knowledge for facilitating mathematical discussion (MKT-Disc) via approximations of practice and compared her use of certain questioning prompts in these vignettes with her facilitation of discussions in her actual mathematics teaching. Findings showed differences in what the teacher reported she knows and what she actually did in practice. Evidence suggests the teacher's institutional obligations to a mandated curriculum, as well as the nature of her MKT-Disc, were the primary reasons for the mismatch between approximations and actual practice. [For the complete proceedings, see ED597799.]
Students&apos; Manipulation of Algebraic Expressions as &apos;Recognizing Basic Structures&apos; and &apos;Giving Relevance&apos;
Author: Meyer, Alexander
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Algebra,Mathematics Instruction,Case Studies,Cognitive Processes,Guidelines,Teaching Methods,Grade 7,Learning Activities,Peer Relationship,Secondary School Students

Manipulating algebraic expressions is guided by students' structure sense and the individual process of relating subexpressions to each other. This paper presents a framework for identifying the underlying cognitive processes of manipulating algebraic expressions, based on 'basic structures' and 'giving relevance'. A design-research case study illustrates how different cognitive processes, related to each of these two constructs, lead to different activities of manipulating algebraic expressions. [For the complete proceedings, see ED597799.]
Making Sense of Word Problems: The Effect of Rewording and Dyadic Interaction
Author: Mellone, Maria
Date: 2014-00-00
Type: Reports - Research
Subjects: Word Problems (Mathematics),Mathematics Instruction,Grade 5,Elementary School Mathematics,Language Usage,Cooperative Learning,Teaching Methods

In this study we investigated the effect of the request to reword the text of problematic word problems on the occurrence of realistic answers. We proposed the activity of rewording word problems to fifth grade pupils either working individually or in dyads. We found that the rewording the problems while working individually had no effect, while rewording in dyads produced a strong increase of pupils' realistic answers. Moreover we analysed the pupils' reworded texts in order to characterize the kind of information added by pupils. [For the complete proceedings, see ED597799.]
Teachers&apos; Knowledge of Infinity, and Its Role in Classroom Practice
Author: Montes, Miguel
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Knowledge Base for Teaching,Mathematics Instruction,Pedagogical Content Knowledge,Numbers,Mathematical Concepts,Concept Formation,Teaching Methods

This paper considers infinity as an element of professional knowledge. We assume that teachers need a wider knowledge of the topic than that they possess as mathematics students. Using three models of professional knowledge, athematics Teacher's Specialised Knowledge (MTSK), Mathematical Knowledge for Teaching (MKT), and Knowledge Quartet (KQ), we discuss how the notions being proposed in these models, and on which they are constructed, might contribute to studying teachers' knowledge of infinity. [For the complete proceedings, see ED597799.]
Rethinking Special Education Certification in Texas. Texas Special Education Policy Forum Report
Author: Benz, Sarah
Date: 2019-04-00
Type: Reports - Research
Subjects: Special Education Teachers,Teacher Certification,Elementary Secondary Education,Licensing Examinations (Professions),Teacher Selection

Texas public schools provide special education services to almost 500,000 students. Despite these services, students with disabilities perform significantly lower on state assessments in reading and mathematics than their same-aged peers. While the numbers of students in special education increased by 5.7% from 2014 to 2017, the number of certified special educators decreased by 1% during the same period. The Texas Education Agency identified teacher preparation as a possible lever to increase student achievement. TEA, along with members of the Texas Comprehensive Center (TXCC) at the American Institutes for Research (AIR), conducted a series of forums with stakeholders in special education to examine the current certification requirements in Texas. The forum participants were charged with reconceptualizing special education certification to better serve students, better prepare teachers, and respond to the teacher shortage in special education. Overall, 31 participants were recruited and represented a diverse group of stakeholders, from superintendents to parents.
Cooperation Types Specific for Barriers
Author: Lange, Diemut
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Barriers,Cooperative Learning,Grade 5,Elementary School Students,Student Behavior,Problem Solving,Mathematics Instruction,Early Adolescents,Classification

We present the results of a study analysing the cooperative behaviour of fifth-grade student pairs when they have to overcome a difficulty (a barrier) in a mathematical problem task. As analysing method we used content analysis as well as frequency-tests (chi-squared test, CFA, Freeman-Halton-test). Our results help to confirm and elaborate the vague assumptions about cooperation types occurring at barriers based on the results of existing studies. In addition, our results suggest that 'presenting an idea of how or why to do sth.' could be relevant for overcoming the barrier in a pair. [For the complete proceedings, see ED597799.]
Influence of Early Repeating Patterning Ability on School Mathematics Learning
Author: Lüken, Miriam M.
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Numeracy,Early Childhood Education,Young Children,Mathematical Concepts,Mathematics Skills,Age Differences,Foreign Countries

Recent studies in early mathematics education highlight the importance of patterning abilities and their influence on mathematics learning and the development of mathematical reasoning in young children. This paper focuses on young children's repeating patterning abilities and reports results from an ongoing four-year longitudinal study that investigates the development of early numeracy understanding of 408 children from one year prior to school until the end of grade 2. The analyses in this paper reveal a significant influence of young children's repeating patterning abilities one year prior to school on their mathematical competencies at the end of grade one. [For the complete proceedings, see ED597799.]
A Comparative Study on Brain Activity Associated with Solving Short Problems in Algebra and Geometry
Author: Leikin, Mark
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Brain,Males,Adolescents,Problem Solving,Algebra,Geometry,Brain Hemisphere Functions,Foreign Countries,High School Students

This paper presents study that investigates brain activity (using ERP methodology) of male adolescents when solving short problems in algebra and geometry. The study design links mathematics education research with neuro-cognitive studies. We performed a comparative analysis of brain activity associated with the translation from visual to symbolic representations of mathematical objects in algebra and geometry. The findings demonstrate that electrical activity associated with the performance of geometrical tasks is stronger than that associated with solving algebraic tasks. Additionally, we found different scalp topography of the brain activity associated with algebraic and geometric tasks. Based on these results, we argue that problem solving in algebra and geometry are related to different patterns of brain activity. [For the complete proceedings, see ED597799.]
An Inferential View on Concept Formation
Author: Meyer, Michael
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Inferences,Mathematical Concepts,Concept Formation,Teaching Methods,Learning Processes,Educational Philosophy,Figurative Language,Language Usage,Classroom Communication,Educational Games,Problem Solving,Elementary School Students,Secondary School Students,Teacher Student Relationship,German,Foreign Countries

This paper focuses on an inferential view on introducing new concepts in mathematics classrooms. A theoretical framework is presented which helps to analyse and reflect on the processes of teaching and learning mathematical concepts. The framework is based on the philosophies by Ludwig Wittgenstein and Robert Brandom. Wittgenstein's language-game metaphor and especially its core, the primacy of the use of words, provide insight into the processes of giving meaning to words. Concerning the inferentialism by Brandom, the use of words in inferences can be regarded as an indicator of the understanding of a concept. The theoretical considerations are exemplified by the interpretation of a scene of real classroom communication. [For the complete proceedings, see ED597799.]
Children&apos;s Conceptual Knowledge of Triangles Manifested in Their Drawings
Author: Maier, Andrea Simone
Date: 2014-00-00
Type: Speeches/Meeting Papers
Subjects: Geometric Concepts,Freehand Drawing,Childrens Art,Concept Formation,Children,Foreign Countries,Kindergarten,Elementary School Students

When asked to draw different kinds of triangles, children reveal many creative ways to express variety. In this paper, the drawings of 81 children in the age between 4 and 6 will be examined and illustrated what kind of understanding of the concept &quot;triangle&quot; precedes the drawings. Therefore, different categories of the children's drawings were generated and also compared to their explanations of a triangle, which sometimes might not be in agreement with their drawings. [For the complete proceedings, see ED597799.]