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 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 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 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 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 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 →
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eric.ed.gov har udgivet: In partnership with the Consortium for Policy Research in Education, RFA has been studying Philadelphia schools’ take-up of an instructional reform that has demonstrated positive impacts on teacher knowledge and student learning in math. The Ongoing Assessment Project (OGAP) is designed to deepen teachers’ understanding of foundational concepts in math and engage them in regular formative assessment of their students’ problem-solving strategies. Implementing an ambitious educational reform such as this one is notoriously challenging, as project staff, district personnel, and school leaders struggle to move from initial professional development–where so much money is invested–to deep, routine engagement in schools and classrooms. Teachers’ instructional practices are difficult to change, and it is particularly hard to engender reform ownership in contexts full of competing demands. In our 2019 study… Continue Reading →
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eric.ed.gov har udgivet: The Program for International Assessment of Adult Competencies, better known as PIAAC, developed a numeracy assessment framework that was used internationally to assess adults’ numeracy skills. The assessment gauged adults’ (aged 16-65 years) numeracy skills across a full range, from adults with very low levels of numeracy to college level math ability. PIAAC’s assessment framework is based on two concepts: math as being use-oriented and math proficiency as a continuum. While this framework was designed to measure adults’ numeracy ability in a structured assessment environment (including adults’ home with trained evaluators), it is useful beyond its original intent. This framework can be used to help teachers better understand how to differentiate instruction while still focusing on a particular theme or topic in a classroom, ensuring rich discussions… Continue Reading →
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eric.ed.gov har udgivet: The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content and the pedagogy of problem solving. This study investigated problem solving process of in-service secondary school teachers in a non-routine problem context. Teachers? written responses were examined based on Polya?s problem solving theory to elucidate their disposition in relation to the problem context. Findings suggest that the in-service teachers exhibit (1) greater lack of understanding of the non-routine problem, (2) insufficient capacity to select appropriate heuristic strategies, and (3) total failure to reach the final “look back” stage.… Continue Reading →
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eric.ed.gov har udgivet: The impact of fixation in solving math problems and that of gender on divergent thinking has been studied in this paper. The study was made in the academic year of 2006-2007, Fall Semester, at Necatibey Faculty of Education, Balikesir University. 229 first and second-year students at the Dept of Primary Math Teaching have been participated in the study. 70% of the prospective mathematics teachers have been found to be fixed in problem solving. There is no meaningful difference between the scores of those with fixation and those without fixation but the scores of those who have fixation in solving problems are slightly higher than the others. The impact of gender has been studied as a factor on divergent thinking but it has not been found to have… Continue Reading →
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