eric.ed.gov har udgivet: The universities and faculties which educate teachers of mathematics for teaching pupils/students of any age group from pre-school age to higher education carefully monitor and compare valuable results of this research, detect the areas in which the mathematical achievements of pupils should be improved at the national level and propose the ways to improve the quality of education and achieve better learning outcomes. We deem particularly valuable contributions of the researchers regarding the samples of poorer mathematical achievements at the “local level” in neighbouring countries, as well as the presentation of examples of good practice by means of which we pave the path towards better achievements of pupils and, consequently, the improvement in the quality of teaching mathematics at the “local,” as well as the global level.… Continue Reading →

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eric.ed.gov har udgivet: This article reports the findings of a study designed to examine the influence of multimodal writing on the communication of mathematical ideas. Elementary school students (ages 8-13) were required to write mathematics notes using two digital writing technologies, a personal digital notepad and a social mathematics blog, in the context of a formal intervention. Forty-two students participated, across three schools. The study showed that when students wrote notes that could be assessed for correctness, their answers were predominately right, indicating that mathematical sense-making was taking place. It also showed that the digital notepad and blog were used differently and that the type of technology influences the writing content. Moreover, students’ mathematical writing were understandable by their peers and students collaboratively explored solutions. Younger students were more likely… Continue Reading →

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eric.ed.gov har udgivet: This submission contains the Proceedings of the 2012 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Laval University in Québec City, Québec. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, a panel discussion, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc… Continue Reading →

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eric.ed.gov har udgivet: Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, “Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students”. The methods and examples included in the guide focus on helping students analyze solved problems, recognize structure, and utilize alternative approaches to solving algebra problems. Each recommendation includes the level of supporting research evidence behind it, examples to use in class, and solutions to potential implementation roadblocks. Teachers can implement these strategies in conjunction with existing standards or curricula. In addition, these strategies can be utilized for all students learning algebra in grades 6-12 and in diverse contexts, including during both formative and summative assessment. Administrators… Continue Reading →

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eric.ed.gov har udgivet: A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible solutions and evaluating and justifying their reasons for the results, thereby allowing students to become confident critical thinkers. Critical thinking and reasoning allows students to think about how they utilize their discipline of mathematical skills (i.e., they think about their method of thinking). Metacognition helps students to recognize that math is logical reasoning on solutions to problems. Students are taught how to: identify scenarios; evaluate; select problem-solving strategies; identify possible conclusions; select logical conclusions; describe how a solution was… Continue Reading →

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eric.ed.gov har udgivet: Recent reforms in mathematics education have led to an increased emphasis on proof and reasoning in mathematics curricula. The National Council of Teachers of Mathematics highlights the important role that teachers’ knowledge and beliefs play in shaping students’ understanding of mathematics, their confidence in and outlook on mathematics education, and their ability to use math to solve fundamental problems. It is crucial that teachers, especially the uninitiated, understand on a deep level the mathematical concepts that they are expected to teach to adolescents. Thus, it becomes critical for teacher educators to assess the understanding and abilities of student teachers in constructing mathematical proof. The analysis in this study is based on three factors: 1) meaning of proof, 2) ideas about teaching methods on proof, and 3) ideas… Continue Reading →

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eric.ed.gov har udgivet: This study documents and describes efforts to develop robust forms of pre-service teachers’ pedagogical content knowledge through a culturally responsive mathematics teaching approach. Embedded in a university K-8 mathematics methods course emphasising the connections among mathematics, children’s mathematical thinking, and children’s cultural/linguistic funds of knowledge, pre-service teachers (N = 40) were given an assignment to analyse their own mathematics lessons utilizing a rubric tool with categories about children’s mathematical thinking, academic language supports, cultural funds of knowledge, and critical math/social justice. Utilizing a mixed methods approach to analyse the pre-service teachers’ (PST) work, we found the highest average self-ratings across the categories associated with children’s mathematical thinking and high variability in the categories related to language, culture, and social justice. To understand the variation within the latter… Continue Reading →

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eric.ed.gov har udgivet: A design experiment with 18 students in a regular seventh grade math class was conducted to investigate how to differentiate instruction for students’ diverse ways of thinking during a 26-day unit on proportional reasoning. The class included students operating with three different multiplicative concepts that have been found to influence rational number knowledge and algebraic reasoning. The researchers and classroom teacher tiered instruction during a 5-day segment of the unit in which students worked on problems involving speed. Students were grouped relatively homogenously by multiplicative concept and experienced different number choices. Students operating at each multiplicative concept demonstrated evidence of learning, but all did not learn the same thing. We view this study as a step in supporting equitable approaches to students’ diverse ways of thinking, an… Continue Reading →

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eric.ed.gov har udgivet: In a study about pre-service secondary mathematics teachers’ (PSMTs) understanding about the nature of theorems in geometry, the researcher noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. Meanwhile, the use of the dragging feature of dynamic geometry environments (DGEs), such as the Geometer’s Sketchpad and GeoGebra, in teaching and learning proof and reasoning has been widely discussed and become an ongoing research trend. In this paper, the researcher and her colleague will present a research design aimed at investigating PSMTs’ conceptions of counterexamples in geometric reasoning when using the dragging feature of DGEs. Expected results of the study are potentially beneficial to pre-service/in-service secondary math teachers as well as teacher educators. Link til kilde

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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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