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Eric.ed.gov – Math Extra. Final Report.

eric.ed.gov har udgivet: A project adapted an existing problem-solving curriculum to help unemployed or underemployed displaced homemakers and single parents qualify for job placement and training. Forty-five adult learners from the New Choice program participated. Handouts adapted from a prior Math Employment project and instructor-created materials were used. Handouts from level 1 of the previous project were simplified even further. Instruction was supplemented with self-help groups. Findings indicated the following: 43 of 45 participants increased their math scores; 15 raised their scores 1-2 grade levels; and 28 raised their scores 3-5 grade levels using the Test of Adult Basic Education. Test scores from completion of teacher-generated word problems were substantially increased. Of the 45 participants, 28 entered training and 2 entered full-time employment. (Appendixes to the 11-page report include sample… Continue Reading

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Eric.ed.gov – Visualizing the Olympic Didactic Situation (ODS): Teaching Mathematics with Support of the GeoGebra Software

eric.ed.gov har udgivet: The teaching of Mathematics in the context of the Mathematical Olympiads in Brazil constitutes a context of research still little considered, with particular interest in the teaching and the learning phenomena. In Brazil, we identified a large number of teachers and students who do not participate in official math competitions, such as the Brazilian Olympiads of Mathematics of Public Schools (OBMEP). On the other hand, it is important to implement didactic resources that allow other forms of didactic transposition to the mathematical knowledge addressed for the Olympic Problems (OP). In this way, the present work presents and introduces the notion of Olympic Didactical Situation (ODS), from a perspective of didactic transposition necessary for the teacher, who must transmit the mathematical knowledge characteristic of the Mathematical Olympiads to… Continue Reading

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Eric.ed.gov – Meaningful Mathematics: Networking Theories on Multiple Representations and Quantitative Reasoning

eric.ed.gov har udgivet: This paper articulates a stance on the study of students’ meaningful mathematics understanding with multiple representations. We integrate Thompson’s theory of quantitative reasoning and Dreyfus’ theory of multiple representations in our approach to frame and conduct empirical investigations of the study of meaningful understanding of function. We provide empirical data to support our approach to examining representational fluency and functional thinking from this networked stance. Our research articulates how the coordination of theories can be productive in informing the design, conduct, and analysis of contexts aimed to understand students’ meaningful math learning with a focus on functional thinking. [For the complete proceedings, see ED606556.] Link til kilde

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Eric.ed.gov – Instructional Scaffolds in Mathematics Instruction for English Learners with Learning Disabilities: An Exploratory Case Study

eric.ed.gov har udgivet: As today’s classrooms become more and more diverse, there is a growing need to explore the intersection between English Learners (ELs) and students with learning disabilities (LD) in the content-specific instruction of mathematics problem solving. The aim of this study was to determine which types of instructional scaffolds may be used by math teachers to effectively support ELs with LD learning multiplicative reasoning. To this end, we employed an exploratory case study based on a frequency count analysis of four scaffold types used by the students and the teacher in their sessions. The results showed that kinesthetic and linguistic scaffolds were the most beneficial for helping ELs with LD to cultivate mathematical thinking with both concrete and abstract units, while also helping to increase the sophistication of… Continue Reading

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Eric.ed.gov – Razonamiento digital: Representar, explorar y resolver problemas verbales con el uso de GeoGebra = Digital Reasoning: Representing, Exploring and Solving Word Problems through the Use of GeoGebra

eric.ed.gov har udgivet: In this study we analyze and contrast approaches that future high school math teachers show when solving word problems with the use of pencil and paper and later, with the use of a Dynamic Geometry System (DGS). The resources, representations, strategies and forms of mathematical reasoning that the participants exhibit when they use GeoGebra in the process of problem solving are analyzed. The results show that the use of the tool favors the dynamic exploration of the concepts involved, the formulation of conjectures and the search for different arguments to validate the solution. [This paper is provided in both Spanish and English. For the complete proceedings, see ED606531.] Link til kilde

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Eric.ed.gov – Preservice Education of Math Teachers Using Paradoxes.

eric.ed.gov har udgivet: Teacher preparation curriculum at Technion–Israel Institute of Technology (Israel) includes courses intended to bridge the gap between the pure mathematics courses and those in psychology. The focus of this paper is an experimental program for one of these courses and data collected while implementing it. This is a second report on a naturalistic study in which mathematical paradoxes were used in the preservice education of high school mathematics teachers. The potential of paradoxes was tested for improving student-teachers’ mathematical concepts and raising students pedagogical awareness of the role of falacious reasoning in the development of mathematical knowledge. Discussions include the psychological and mathematical background, the experimental courses and data collection procedures, the students, and findings. Examples of paradoxes are given. Included are 36 references. (DC) Link til… Continue Reading

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Eric.ed.gov – Algebraic Thinking in Adult Education

eric.ed.gov har udgivet: In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic exercise. This paper recommends two significant and necessary changes in the concept of algebra and the ways the authors approach it in education: a shift from thinking of algebra as one course to thinking of it as a content strand integrated into arithmetic instruction and a shift from thinking of algebra as merely manipulation skills to thinking of it as a means of representing and analyzing real situations. This fresh look at algebra and mathematics… Continue Reading

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Eric.ed.gov – Math Education Practices for Students with Disabilities and Other Struggling Learners: Case Studies of Six Schools in Two Northeast and Islands Region States. Issues & Answers. REL 2008-No. 053

eric.ed.gov har udgivet: The No Child Left Behind (NCLB) Act of 2001 requires states to ensure that all students make adequate yearly progress in achieving proficiency in English language arts and math. This study examines how six diverse schools have responded to the challenge of educating their students in math, particularly students with disabilities and other struggling learners. The report intends to help educators by providing examples and ideas to consider for their own school or district efforts to improve math teaching and learning. This report describes in-depth practices at six schools (3 in Massachusetts and 3 in New York) that are making targeted efforts to improve math education for students with disabilities and other struggling learners. It examines each school’s practices for improving the math learning of all students… Continue Reading

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Eric.ed.gov – Mathematics Education as a Science and a Profession

eric.ed.gov har udgivet: The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six chapters. In the first chapter, the author studies the relation between the surface approach and the strategic approach to learning outcomes according to the results of research conducted with a group of university students in Denmark. This chapter presents the results of research carried out with the students who were required to recognise and interpret mathematical concepts that could be interpreted from the graphs in different contexts. It also provides an insight into a detailed analysis… Continue Reading

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Eric.ed.gov – Math and Science Reform. Local Education Fund Issue Brief. Volume 1, Number 1

eric.ed.gov har udgivet: Politicians, academics, and business and community members all seem to be raising concerns that America is not as globally competitive as it once was. This is due, in part, to the fact that public schools in America are not producing high school graduates with the math, science, and technical skills to succeed in higher education or be employed in a knowledge-based, global marketplace. According to the Bureau of Labor Statistics, jobs requiring science, engineering or technical training will increase 24 percent between 2004 and 2014 to 6.3 million. However, less than half of high school graduates in the United States are academically prepared for college-level math and science. Between 1970 and 2010, America’s proportion of science and engineering doctorates will fall from 50 percent to 15 percent.… Continue Reading