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Descriptors:
Bilingual Education; Comparative Analysis; Bilingualism; Language of Instruction; Bilingual Education Programs; Mathematics Education; High School Students; German; French; Problem Solving; Cognitive Ability; Code Switching (Language); Second Language Learning

Abstract:
Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations. (Contains 4 figures and 1 table.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Learning Problems; Learning Disabilities; Evaluation Criteria; Elementary School Students; Foreign Countries; Incidence; Clinical Diagnosis; Mathematics Education; Gender Differences; Mathematics Tests; Reading Tests; Mathematics Achievement

Abstract:
Developmental dyscalculia (DD) is a learning difficulty specific to mathematics learning. The prevalence of DD may be equivalent to that of dyslexia, posing an important challenge for effective educational provision. Nevertheless, there is no agreed definition of DD and there are controversies surrounding cutoff decisions, specificity and gender differences. In the current study, 1004 British primary school children completed mathematics and reading assessments. The prevalence of DD and gender ratio were estimated in this sample using different criteria. When using absolute thresholds, the prevalence of DD was the same for both genders regardless of the cutoff criteria applied, however gender differences emerged when using a mathematics-reading discrepancy definition. Correlations between mathematics performance and the control measures selected to identify a specific learning difficulty affect both prevalence estimates and whether a gender difference is in fact identified. Educational implications are discussed. (Contains 5 figures and 2 tables.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
College Mathematics; College Students; Cooperative Learning; Problem Solving; Video Technology; Mathematics Education; Teaching Methods; Validity; Mathematical Logic; Symbols (Mathematics); Mathematical Concepts; Learning Strategies

Abstract:
We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of situations in which example generation seems to play a positive role in proving. These aspects integrate qualities of students and of problems: "experience of utility of examples in proving," "personal example spaces and technical tools," "formulation of the problem," and "relational necessity." Our analysis led to integrating two theoretical ideas: the alignment of "conceptual insight" and "technical handle" when trying to prove; and "manipulating," "getting-a-sense-of," and "articulating" as phases of work associated with example construction. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Mathematics Education; Mathematical Concepts; Mathematics; Mathematics Instruction; Mathematical Logic; Mathematics Skills; Curriculum

Abstract:
In this paper we study the mathematical body as an assemblage of human and non-human mathematical concepts. We argue that learners' bodies are always in the process of becoming assemblages of diverse and dynamic materialities. Following the work of the historian of science Karen Barad, we argue that mathematical concepts must be considered dynamic material, and we suggest a "pedagogy of the concept" that animates concepts as both logical and ontological. We draw on the philosopher of mathematics Gilles Chatelet in order to pursue this argument, elaborating on the way that mathematical concepts partake of the mobility of the virtual, while learners, in engaging with this mobility, enter a material process of becoming. We show how the concept of virtuality allows us to look at mathematical concepts in school curriculum in new ways. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Equations (Mathematics); Novices; Mathematics Instruction; Expertise; Algebra; Mathematics Education; Secondary School Teachers; Secondary School Students; Mathematical Formulas; Mathematics; Interviews

Abstract:
While an algebraic expression is typically assigned a regular structure, this article introduces the concept of personal structure ("Strukturierung"); here, the structuring of an algebraic expression is understood as the act of forming relationships between its parts. This concept is used for the analysis of interviews in which experts and novices talk about the personal structures they produced when looking at fractional expressions and equations. The results show, firstly, that experts will structure a given fractional expression in various different ways. Secondly, four categories have been identified: structuring can mean that an expression is made more visually straightforward, changed, reinterpreted or classified. This is meaningful for negotiating the appropriateness of the personal structures in teaching algebra. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
College Students; Mathematics Education; Mathematics Instruction; Higher Education; Mathematical Models; Mathematics

Abstract:
This paper describes university students' grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four erroneous images of inflection points: (1) f ' (x) = 0 as a necessary condition, (2) f ' (x) is not equal to 0 as a necessary condition, (3) f " (x) = 0 as a sufficient condition, and (4) the location of "a peak point, where the graph bends" as an inflection point. We use the lenses of Fischbein, Tall, and Vinner and Duval's frameworks to analyze students' errors that were rooted in mathematical and in real-life contexts. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Childrens Literature; Science Activities; Books; Science Education; Science Instruction; Literacy; Mathematics Education; Mathematics Instruction; Learning Modules; Teaching Methods; Parent Participation

Abstract:
In the following article, Dr. Seuss's children's books are creatively integrated with science activities through the creation of take-home activity kits. The kits provide families an opportunity to read at home while connecting the enjoyable experience to science content and skill development through associated activities. The kits should be constructed using easy-reading books and aligned to developmentally appropriate academic science standards. Most importantly, they should be designed in a manner so that all family members are participants rather than expecting the adults to teach the expected outcomes. The activity kits can be completed as stand-alone experiences for interested students, used by students who are ready for an additional challenge, or adapted for an entire classroom of students as part of a teacher's normal curriculum. (Contains 1 table, 6 figures, and 3 resources.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Elementary Schools; Foreign Countries; Teaching Assistants; Mathematics; Mathematics Education; Mathematics Instruction; Interviews; Elementary School Mathematics

Abstract:
Teaching Assistants (TAs) in primary schools in England have a growing pedagogic role. For some, this sometimes includes responsibility for the whole class instead of the teacher. This article draws on 24 interview transcripts to examine the practice in the context of primary mathematics lessons and from TAs' viewpoints. Emergency cover is often seen as reasonable where good working relationships exist. The practice of being regularly responsible for mathematics lessons evokes more diverse reactions. Some TAs initially appear to support the "official" view that it is unproblematic to run a lesson from pre-prepared plans, though close inspection reveals a different picture. Others acknowledge that the interactions involved in such lessons are not necessarily susceptible to planning. The findings raise considerable doubt about current policy and question its presentation as a way to raise standards. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Talent; Gifted; Identification; Intervention; Small Group Instruction; Gender Differences; Academic Ability; Instructional Program Divisions; Talent Development; Acceleration (Education); Language Arts; Mathematics Education; Science Education; Student Attitudes; Individualized Instruction; Mathematics Instruction

Abstract:
Established in the early 1970s, the talent search model has garnered strong theoretical and programming support for addressing the academic needs of highly able students. The two main components of the talent search model are discovery (identification) and development (programming) of academic talent. Discovery of academically talented elementary and middle school students occurs via the process of above-level testing, usually offered through university-based centers. The essence of talent search program intervention is acceleration, which has robust research support as the most effective intervention for high-ability students. Whereas talent search identification and programming are university based, talent search participants receive nearly all of their instruction in K-12 settings, where academic acceleration is less likely to be implemented. In this investigation, a large sample of talent search participants (n = 5,844) were asked questions designed to measure the various ways in which the students study mathematics, science, and language arts (writing and reading) in the K-12 setting. More than two thirds of the study sample reported that they were taught in the regular classroom, learning the same material, at the same level and pace as nongifted peers. The type of curriculum differentiation or program delivery model (e.g., small-group instruction) reported by the students varied according to subject area, with the greatest percentage of reports of differentiated delivery in mathematics. Main effects were found for gender, grade, and ability. Implications for school-based accelerative interventions are presented. (Contains 5 tables and 1 figure.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Reading Achievement; At Risk Students; Tutoring; Problem Solving; Mathematics Education; Pretests Posttests; Word Problems (Mathematics); Intervention; Small Group Instruction; Intermode Differences; Teaching Methods; Achievement Gains; Aptitude Treatment Interaction; Grade 3; Mathematical Enrichment; Mathematics Achievement; Learning Disabilities

Abstract:
This intervention study compared the efficacy of small-group tutoring on the mathematics learning of third-grade students at risk for mathematics difficulty using either a school-provided standards-based curriculum (SBC) or a schema-based instruction (SBI) curriculum. The SBI curriculum placed particular emphasis on the underlying mathematical structure of additive problems to represent and solve word problems. At-risk students (N = 136) from 35 classrooms scoring below a proficiency level on their district accountability assessment were assigned randomly to treatment groups. Results indicated interaction effects on the word problem-solving (WPS) posttest and retention tests such that SBI students with higher incoming (pretest) WPS scores outperformed SBC students with higher pretest scores, whereas SBC students with lower pretest scores outperformed SBI students with lower pretest scores. No effects were found on number combinations automaticity, and mathematics and reading achievement. Implications to improve the problem-solving performance of at-risk students are discussed. (Contains 4 tables and 2 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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