共查询到20条相似文献，搜索用时 593 毫秒
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Sarah R. Powell Lynn S. Fuchs Doug Fuchs 《Learning disabilities research & practice》2013,28(1):38-48
The Common Core State Standards provide teachers with a framework of necessary mathematics skills across grades K‐12, which vary considerably from previous mathematics standards. In this article, we discuss concerns about the implications of the Common Core for students with mathematics difficulties (MD), given that students with MD, by definition, struggle with mathematical skills. We suggest that instruction centered on the Common Core will be challenging and may lead to problematic outcomes for this population. We propose that working on foundational skills related to the Common Core standards is a necessary component of mathematics instruction for students with MD, and we provide teachers with a framework for working on foundational skills concurrent with the Common Core standards. We caution, however, that implementation of the Common Core is in its infancy, and the implications of the Common Core for students with MD need to be monitored carefully. 相似文献
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The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this article, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for mathematics instruction and theories of epistemic cognition. 相似文献
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Matthew Inglis Juan Pablo Mejia-Ramos Adrian Simpson 《Educational Studies in Mathematics》2007,66(1):3-21
In recent years several mathematics education researchers have attempted to analyse students’ arguments using a restricted
form of Toulmin’s [The Uses of Argument, Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate
mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use
of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role
in mathematical argumentation, and that one of the goals of instruction should be to develop students’ abilities to appropriately
match up warrant-types with modal qualifiers. 相似文献
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In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for acceptable reasoning across domains. We further argue that students’ acceptance of these values may be integral to their apprenticeship into proving practice; students who do not perceive or accept these values will likely have difficulty adhering to the norms that uphold them and hence will find proof confusing and problematic. We discuss the implications of mathematical values and norms with respect to proof for investigating mathematical practice, conducting research in mathematics education, and teaching proof in mathematics classrooms. 相似文献
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Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms. 相似文献
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We identify a recent trend in school mathematics as well as in some of the research literature in mathematics education: an emphasis on the practical uses of mathematics and an increased emphasis on verbalizations as opposed to numerical and computational skills. With tools provided by John Dewey, an early advocate of contextual and practical knowledge, we analyse the common research framework for discussing mathematical knowledge in terms of the procedural and the conceptual. We argue that procedural and conceptual knowledge should not be seen as opposites, and that the tendency to treat them as such might be avoided by emphasising the notion of operational skill. We argue that this is important in order for the students to gain both the contextual knowledge and the computational skill entailed in mathematical knowledge. 相似文献
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Students with mathematics disabilities (MD) experience difficulties with both conceptual and procedural knowledge of different math concepts across grade levels. Research shows that concrete representational abstract framework of instruction helps to bridge this gap for students with MD. In this article, we provide an overview of this strategy embedded within the explicit instruction framework. We highlight effective practices for each component of the framework across different mathematical strands. Implications for practice are also discussed and a detailed case study is provided. 相似文献
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Reuven Babai Tali Brecher Ruth Stavy Dina Tirosh 《International Journal of Science and Mathematics Education》2006,4(4):627-639
One theoretical framework which addresses students’ conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students’ reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common external features. In this paper, we explore the cognitive processes related to the intuitive rule more A–more B and discuss issues related to overcoming its interference. We focused on the context of probability using a computerized “Probability Reasoning – Reaction Time Test.” We compared the accuracy and reaction times of responses that are in line with this intuitive rule to those that are counter-intuitive among high-school students. We also studied the effect of the level of mathematics instruction on participants’ responses. The results indicate that correct responses in line with the intuitive rule are more accurate and shorter than correct, counter-intuitive ones. Regarding the level of mathematics instruction, the only significant difference was in the percentage of correct responses to the counter-intuitive condition. Students with a high level of mathematics instruction had significantly more correct responses. These findings could contribute to designing innovative ways of assisting students in overcoming the interference of the intuitive rules. 相似文献
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In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article
is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's
own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic
framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic
reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means
for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling,
symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning
and communicating in mathematics classrooms. 相似文献
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In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics.
In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research
on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate
the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests
that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms
where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional
approaches that support the learning of mathematics through the process of guided reinvention. 相似文献
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A discipline apart: the challenges of ‘Fostering a Community of Learners’ in a mathematics classroom
This is the fifth in a series that examines the challenges that teachers in different domains face as they attempt to implement the pedagogical reform ‘Fostering a Community of Learners’ (FCL). Here we focus on the relationship between FCL and the teaching of mathematics. We argue that it is possible to teach mathematics through the FCL pedagogy, but that doing so requires some rethinking of both mathematics instruction and FCL. In particular, we describe three shifts that aided a teacher's implementation of FCL pedagogy with mathematics: the teacher developed a new perspective on mathematics that emphasized the importance of having students learn both mathematical concepts and processes; the teacher developed a new understanding of the role of the teacher in mathematics‐education reform; and the teacher modified his understanding of FCL, coming to believe that a discourse community could be the basis for FCL pedagogy in a mathematics classroom. 相似文献
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AbstractApplying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities from multiple courses in the program, we offer general principles of instruction for supporting mathematical inquiry at all grade levels. We contend that an awareness and application of the multiple facets of mathematical knowledge for teaching can be critical to supporting mathematical inquiry across the K-16 spectrum. 相似文献
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Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students' mathematical literacy. Explicit instruction about how to engage with each text type helps to build students' awareness of the function of mathematical texts and of how to leverage them to support the doing of mathematics. Teachers and leaders can use this discussion of mathematical text types to organize and conceptualize instruction within a disciplinary literacy orientation. 相似文献
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Cheryl Allendoerfer Denise Wilson Mee Joo Kim Elizabeth Burpee 《Teaching in Higher Education》2013,18(7):758-771
In this paper, we identify beliefs about teaching and patterns of instruction valued and emphasized by science, technology, engineering, and mathematics faculty in higher education in the USA. Drawing on the notion that effective teaching is student-centered rather than teacher-centered and must include a balance of knowledge-, learner-, community-, and assessment-centered learning environments; we use qualitative interview data to explore how faculty's reported beliefs about teaching are associated with their consideration of these four types of environments. Findings indicated that although a range of beliefs about teaching emerged, most were firmly located in knowledge-centered learning environments, with little or no focus on the remaining three learning environments. Furthermore, even patterns of instruction that were heavily student-centered were situated within a knowledge-centered learning framework. We argue that for student-centered instruction to be truly successful, faculty must consider all four learning environments in crafting and facilitating the classroom environment. 相似文献
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Cathy Smith 《British Journal of Sociology of Education》2020,41(2):160-177
AbstractThis paper examines how young people account for choosing mathematical subjects, and how these processes sustain, or not, their continued participation. It draws on a 2-year qualitative study of 24 young people’s accounts of following advanced mathematical pathways within a widening participation programme. Working within a post-structural framework, I combine two arguments: firstly, that local discourses of time, age and maturity position contemporary adolescence as a time of ‘becoming’ that aligns personal aspirations with mathematical progress, and secondly that students’ accounts of choice and aspiration require multiple imaginings of present and future selves. I identify distinct discourses –moving/improving and getting ahead - that structure the intelligibility of participation in mathematics and further mathematics respectively. I argue that tracing the alignments between students’ accounts of themselves and/ in mathematics offers potential to understand emergent practices in mathematics participation but also how exclusions are re-inscribed along classed and gendered lines. 相似文献
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AbstractIn this article, we share a model of flipped instruction that allowed us to gain a window into our students’ mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be used to design experiences that help students make sense of mathematics during class sessions. 相似文献
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Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding. 相似文献
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Christine Pauli Kurt ReusserUrs Grob 《International Journal of Educational Research》2007,46(5):294-305
In mathematics instruction, can a teacher implement surface features of instruction that foster self-regulated learning as well as achieve quality at the deeper level of instruction, that is, focus on higher-order thinking, problem-solving, and mathematical modeling? An educational reform effort in Switzerland, which is based on constructivist and sociocultural theories of mathematics learning, targets both these dimensions: self-regulated learning and conceptual understanding. We examined the realization of the two dimensions in classroom instruction in a video-based study of 79 eighth-grade math classes using three kinds of data: videotapes of mathematics lessons, student and teacher questionnaires, and achievement tests. As to the surface level of instruction, teachers reported how frequently they provided opportunities for self-regulated learning. With regard to the deeper level of instruction, teachers reported how frequently they provided opportunities for independent problem solving. In addition, we examined the extent to which teachers’ pedagogical beliefs reflected a constructivist orientation. The results showed that teachers implemented the two dimensions relatively independently of one another. Teachers’ constructivist-oriented beliefs influenced only opportunities provided for independent problem solving and did not affect opportunities for self-regulated learning. Opportunities for self-regulated learning had a positive effect on students’ learning experience. Professional development should encourage teachers to take greater account of both surface-level and deeper-level (quality) features of instruction. 相似文献