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: National studies reveal that 50 percent to 70 percent of community college students are required to take developmental, or remedial, math courses upon enrollment, and only 20 percent of developmental math students ever successfully complete a college-level math course. Taking up the challenge is the “New Mathways Project” (NMP), developed by the Charles A. Dana Center at the University of Texas at Austin in partnership with the Texas Association of Community Colleges. This new initiative aims to change the standard pathways to and through colleges’ traditional math sequences. This report analyzes the development of the “New Mathways Project” (NMP) from spring 2012 through its first year of rollout at nine colleges in Texas in 2013-2014, as well as student outcomes at the colleges before and during the… Continue Reading →
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eric.ed.gov har udgivet: In this article we describe the results of a special final course, at the main teachers’ college in Mexico, which had two related main objectives: one was to find out the Mathematical Knowledge for Teaching (MKT) held by student teachers (ST) at the end of their instructional preparation. The other was to discern ways to improve this knowledge and to document the changes observed. In teachers’ colleges in Mexico, math contents and pedagogical ideas are taught separately, so we aimed to help student teachers to integrate these. The analysis showed that their knowledge is mainly instrumental but that through discussions and reflection about the main issues, they were able fairly quickly to attain a significant improvement in all the contents included. Moreover, they also showed changes on… Continue Reading →
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eric.ed.gov har udgivet: This action research project looks at what happened when a small group of adult numeracy teachers with widely different experiences of learning and teaching mathematics explored their own informal numeracy practices and undertook a series of collaborative mathematical tasks. Evidence from qualitative data collected during the enquiry suggests that “realistic” tasks can provoke a range of mathematical thinking and learning responses which allow us to identify ways in which “procedural” and “conceptual” thinking is being used, and to track learning journeys through different stages of problem-solving. Although more experienced numeracy teachers could move between and within their “real worlds” and “maths worlds” with intent and ease, others had less integrated experiences, often valuing perceived mathematical powers over their own intuitive powers, with mixed success. Link til kilde
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eric.ed.gov har udgivet: Ninety-seven education students majoring or minoring in mathematics had their math homework examined in a Number Theory or Abstract Algebra course. Each student’s homework was observed for the purpose of identifying common errors and misconceptions when writing mathematical proofs. The results showed that students collectively made four recurring errors: assuming the conclusion in order to prove the conclusion, proving general statements using specific examples, not proving both conditions in a biconditional statement, and misusing definitions. In the same courses taken subsequently by 91 new students, we informed them about these common errors prior to assigning their homework to see how the students’ proving processes would differ. The results showed that more exercises were left blank with comments such as “I’m not sure how to start the proof”,… Continue Reading →
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eric.ed.gov har udgivet: Parents, K-8 teachers, and 4th-8th grade children participated as equals in math-focused learning communities through the Math and Parent Partners (MAPPS) program. Pre/post testing and qualitative interviews revealed that the learning communities served as a platform for improvement in mathematical knowledge for teaching of participating teachers. Moreover, teachers learned about parents’ knowledge and strategies, a construct analogous to Knowledge of Content and Students that we describe as “Knowledge of Content and Parents.” [For the complete proceedings, see ED584829.] Link til kilde
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eric.ed.gov har udgivet: Limited Singapore research indicated a lack of exposure of modelling tasks at primary levels. Teacher reflection is used as a tool in design research cycles exploring the potentials of modelling tasks in a Singapore primary five classroom. Findings reveal that the teacher identified three potentials of a modelling task on children’s mathematisation process: the task provided a platform for children to (a) identify variables and form relationships between them, (b) relate school-based math learning to real-world experiences, and (c) justify their mathematical models. Implications on the promotion of modelling tasks at primary schools as well as teacher education are drawn. Link til kilde
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eric.ed.gov har udgivet: Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during which students build a strong foundation in fractions concepts. At the same time, the National Mathematics Advisory Panel (2008) cites limited understanding of fractions as the key reason for the high failure rate in algebra courses. Longitudinal data from both the United States and the United Kingdom have demonstrated that knowledge of fractions in the elementary grades plays a powerful role in subsequent success in algebra, the gateway to math achievement in high school. Members of… Continue Reading →
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eric.ed.gov har udgivet: Calls to advance students’ ability to engage in mathematical reasoning practices including conjecturing, generalising and justifying (CGJ) place significant new demands on teachers. This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote them in the classroom. Findings demonstrate how CGJ readings and focused discussions, coupled with repeated cycles of collaborative lesson planning, observation and debrief, supported the development of teacher knowledge, professional community, and teaching resources. In addition, this paper explores the role school leadership played in facilitating Math Studio to ensure these learning opportunities were realised. Documenting how Math Studio features and participants contributed to teachers’ ability to implement CGJ focused lessons not only provides insights into the difficulties… Continue Reading →
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eric.ed.gov har udgivet: Research about teacher noticing of students’ mathematical thinking has been an important and ongoing strand of research and practice in mathematics education. Our work extends this agenda by working collaboratively with teachers to learn together how to notice students’ mathematical strengths. The lens on strengths runs counter to the prevalent culture in U.S. schools to overemphasize gaps in students’ understandings. In this paper we describe a video club focused on identifying and naming students’ mathematical strengths and the protocols that support this focus. We illustrate and discuss the important shifts in teachers’ ways of noticing and talking about students’ mathematical activity. We also discuss implications for further research and professional development focused on teacher noticing of students’ math strengths. [For the complete proceedings, see ED583989.] Link til… Continue Reading →
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