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1.
Nurit Hadas Rina Hershkowitz Baruch B. Schwarz 《Educational Studies in Mathematics》2000,44(1-3):127-150
In many geometrical problems, students can feel that the universalityof a conjectured attribute of a figure is validated by their action in adynamic geometry environment. In contrast, students generally do not feelthat deductive explanations strengthen their conviction that a geometricalfigure has a given attribute. In order to cope with students' convictionbased on empirical experience only and to create a need for deductiveexplanations, we developed a collection of innovative activities intended tocause surprise and uncertainty. In this paper we describe two activities, thatled students to contradictions between conjectures and findings. We analyzethe conjectures, working methods, and explanations given by the studentswhen faced with the contradictions that arose.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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Naomi Prusak Rina Hershkowitz Baruch B. Schwarz 《Educational Studies in Mathematics》2012,79(1):19-40
Our main goal in this study is to exemplify that a meticulous design can lead pre-service teachers to engage in productive
unguided peer argumentation. By productivity, we mean here a shift from reasoning based on intuitions to reasoning moved by
logical necessity. As a subsidiary goal, we aimed at identifying the kinds of reasoning processes (visual, inquiry-based,
and deductive) pre-service teacher's students adopt, and how these reasoning processes are interwoven in peer-unguided argumentation.
We report on a case study in which one dyad participating in a pre-service teachers program solved a mathematical task. We
relied on three principles to design an activity: (a) creating a situation of conflict, (b) creating a collaborative situation,
and (c) providing a device for checking hypotheses/conjectures. We show how the design afforded productive argumentation.
We show that the design of the task entailed argumentation which first relied on intuition, then intertwined the activities
of conjecturing and checking conjectures by means of various hypotheses-testing devices (measurement, manipulations, and dynamic
change of figures with Dynamic Geometry software), leading to a conflict between conjectures and the outcome of the manipulation
of DG software. Peer argumentation then shifted to abductive and deductive considerations towards the solution of the mathematical
task. These beneficial outcomes resulted from collaborative rather than adversarial interactions as the students tried to
accommodate their divergent views through the co-elaboration of new explanations. 相似文献
3.
Suzanne Ingrid Dorée 《PRIMUS》2017,27(2):179-188
AbstractHow can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable, but false, conjectures. 相似文献
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Tami S. Martin Sharon M. Soucy McCrone Michelle L. Wallace Bower Jaguthsing Dindyal 《Educational Studies in Mathematics》2005,60(1):95-124
Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage
in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results
from a classroom-based interpretive study of teaching and learning proof in geometry. The goal of this research was to identify
factors that may be related to the development of proof understanding. In this paper, we identify and interpret students'
actions, teacher's actions, and social aspects that are evident in a classroom in which students discuss mathematical conjectures,
justification processes and student-generated proofs. We conclude that pedagogical choices made by the teacher, as manifested
in the teacher's actions, are key to the type of classroom environment that is established and, hence, to students' opportunities
to hone their proof and reasoning skills. More specifically, the teacher's choice to pose open-ended tasks (tasks which are
not limited to one specific solution or solution strategy), engage in dialogue that places responsibility for reasoning on
the students, analyze student arguments, and coach students as they reason, creates an environment in which participating
students make conjectures, provide justifications, and build chains of reasoning. In this environment, students who actively
participate in the classroom discourse are supported as they engage in proof development activities. By examining connections
between teacher and student actions within a social context, we offer a first step in linking teachers' practice to students'
understanding of proof. 相似文献
6.
This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger their thinking processes, to promote their ability to investigate and to support them in learning numerical analysis' concepts and procedures. The results show that the investigations provided opportunities for students to experience mathematical processes, including posing questions, formulating and testing conjectures and, to some extent, proving results. They also provide some understanding about the role of problem posing in these processes. Posing questions occurred mainly in an implicit way, in the interpretation of tasks and in identifying regularities, analysing graphs and testing cases. The conjectures were often based on pattern identification or data manipulation, and the students tended to accept them without testing or proving. The students also proposed alternative formulations for the initial questions and posed new problems from their explorations and attempts to refine previous conjectures. 相似文献
7.
Inquiry instruction often neglects graphing. It gives students few opportunities to develop the knowledge and skills necessary to take advantage of graphs, and which are called for by current science education standards. Yet, it is not well known how to support graphing skills, particularly within middle school science inquiry contexts. Using qualitative graphs is a promising, but underexplored approach. In contrast to quantitative graphs, which can lead students to focus too narrowly on the mechanics of plotting points, qualitative graphs can encourage students to relate graphical representations to their conceptual meaning. Guided by the Knowledge Integration framework, which recognizes and guides students in integrating their diverse ideas about science, we incorporated qualitative graphing activities into a seventh grade web-based inquiry unit about cell division and cancer treatment. In Study 1, we characterized the kinds of graphs students generated in terms of their integration of graphical and scientific knowledge. We also found that students (n = 30) using the unit made significant learning gains based on their pretest to post-test scores. In Study 2, we compared students' performance in two versions of the same unit: One that had students construct, and second that had them critique qualitative graphs. Results showed that both activities had distinct benefits, and improved students' (n = 117) integrated understanding of graphs and science. Specifically, critiquing graphs helped students improve their scientific explanations within the unit, while constructing graphs led students to link key science ideas within both their in-unit and post-unit explanations. We discuss the relative affordances and constraints of critique and construction activities, and observe students' common misunderstandings of graphs. In all, this study offers a critical exploration of how to design instruction that simultaneously supports students' science and graph understanding within complex inquiry contexts. 相似文献
8.
Jiun‐Liang Ke Martin Monk Richard Duschl 《International Journal of Science Education》2013,35(13):1571-1594
This paper reports a cross‐sectional study of Taiwanese physics students’ understanding of subatomic phenomena that are explained by quantum mechanics. The study uses students’ explanations of their answers to items in a questionnaire as a proxy for students’ thinking. The variation in students’ explanations is discussed as is the development in the way in which students link different concepts. A discussion of the source of students’ ideas turns to the way schema contain mental models that derive from sensori‐experiences. The principal recommendation for teaching is the need to include practical activities on a range of precursor phenomena so as to extend the students repertoires of mental models. This advice is different from that given in previous studies. 相似文献
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This study explores interactions with diagrams that are involved in geometrical reasoning; more specifically, how students publicly make and justify conjectures through multimodal representations of diagrams. We describe how students interact with diagrams using both gestural and verbal modalities, and examine how such multimodal interactions with diagrams reveal their reasoning. We argue that when limited information is given in a diagram, students make use of gestural and verbal expressions to compensate for those limitations as they engage in making and proving conjectures. The constraints of a diagram, gestures and linguistic systems are semiotic resources that students may use to engage in geometrical reasoning. 相似文献
10.
This study aims to characterize a group of students’ preliminary oral explanations of a scientific phenomenon produced as part of their learning process. The students were encouraged to use their own wordings to test out their own interpretation of observations when conducting practical activities. They presented their explanations orally in the whole class after having discussed and written down an explanation in a small group. The data consists of transcribed video recordings of the presented explanations, observation notes, and interviews. A genre perspective was used to characterize the students’ explanations together with analysis of the students use of scientific terms, gestures, and the language markers “sort of” and “like.” Based on the analysis we argue to separate between event-focused explanations, where the students describe how objects move, and object-focused explanations, where the students describe object properties and interactions. The first type uses observable events and few scientific terms, while the latter contains object properties and tentative use of scientific terms. Both types are accompanied by an extensive use of language markers and gestures. A third category, term-focused explanations, is used when the students only provide superficial explanations by expressing scientific terms. Here, the students’ use of language markers and gestures are low. The analyses shows how students’ explanations can be understood as tentative attempts to build on their current understanding and observations while trying to reach out for a deeper and scientific way of identifying observations and building explanations and new ways of talking. 相似文献
11.
This study aimed to explore secondary students’ explanations of evolutionary processes, and to determine how consistent these
were, after a specific evolution instruction. In a previous study it was found that before instruction students provided different
explanations for similar processes to tasks with different content. Hence, it seemed that the structure and the content of
the task may have had an effect on students’ explanations. The tasks given to students demanded evolutionary explanations,
in particular explanations for the origin of homologies and adaptations. Based on the conclusions from the previous study,
we developed a teaching sequence in order to overcome students’ preconceptions, as well as to achieve conceptual change and
explanatory coherence. Students were taught about fundamental biological concepts and the several levels of biological organization,
as well as about the mechanisms of heredity and of the origin of genetic variation. Then, all these concepts were used to
teach about evolution, by relating micro-concepts (e.g. genotypes) to macro-concepts (e.g. phenotypes). Moreover, during instruction
students were brought to a conceptual conflict situation, where their intuitive explanations were challenged as emphasis was
put on two concepts entirely opposed to their preconceptions: chance and unpredictability. From the explanations that students
provided in the post-test it is concluded that conceptual change and explanatory coherence in evolution can be achieved to
a certain degree by lower secondary school students through the suggested teaching sequence and the explanatory framework,
which may form a basis for teaching further about evolution. 相似文献
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Daniela Kênia B.S. Oliveira Paula Cristina Cardoso Mendonça 《International Journal of Science Education》2013,35(9):1402-1435
This paper discusses the use of non-verbal representations in a modelling-based science teaching context, in which argumentative and explanatory situations occur. More specifically, we analyse how the students and teacher use representations in their discourse in modelling activities, and we discuss the relationships between the functions of these representations and the demands of the explanatory and argumentative situations that exist in that classroom. The data were collected by video recording all the classes in which a teaching sequence about intermolecular interactions was used—a topic which the students had not previously studied. In the activities, the students had to create, express, test, and discuss models in order to understand the difference between intermolecular and interatomic interactions, as well as their influences on the properties of substances. Initially, we selected excerpts of the recorded classes in which a non-verbal representation was used. Then, we used criteria to identify the argumentative and explanatory situations (previously defined), and we created categories for the functions of the representations that were used in order to analyse all the identified situations. The analysis supports conclusions indicating the relevance of the use of non-verbal representations in the construction, use, and defence of explanations. As the defence of explanations was the main context in which argumentative situations occurred in this study, our conclusions also indicate the contribution that representations make towards changing the status of the students' explanations. 相似文献
13.
Although molecular-level details are part of the upper-secondary biology curriculum in most countries, many studies report that students fail to connect molecular knowledge to phenomena at the level of cells, organs and organisms. Recent studies suggest that students lack a framework to reason about complex systems to make this connection. In this paper, we present a framework that could help students to reason back and forth between cells and molecules. It represents both the general type of explanation in molecular biology and the research strategies scientists use to find these explanations. We base this framework on recent work in the philosophy of science that characterizes explanations in molecular biology as mechanistic explanations. Mechanistic explanations describe a phenomenon in terms of the entities involved, the activities displayed and the way these entities and activities are organized. We conclude that to describe cellular phenomena scientists use entities and activities at multiple levels between cells and molecules. In molecular biological research, scientists use heuristics based on these intermediate levels to construct mechanistic explanations. They subdivide a cellular activity into hypothetical lower-level activities (top-down approaches) and they predict and test the organization of macromolecules into functional modules that play a role in higher-level activities (bottom-up approaches). We suggest including molecular mechanistic reasoning in biology education and we identify criteria for designing such education. Education using molecular mechanistic reasoning can build on common intuitive reasoning about mechanisms. The heuristics that scientists use can help students to apply this intuitive notion to the levels in between molecules and cells. 相似文献
14.
Berry Billingsley Keith Taber Fran Riga Helen Newdick 《Research in Science Education》2013,43(4):1715-1732
A number of previous studies have shown that there is a widespread view among young people that science and religion are opposed. In this paper, we suggest that it requires a significant level of what can be termed “epistemic insight” to access the idea that some people see science and religion as compatible while others do not. To explore this further, we draw on previous work to devise a methodology to discover students’ thinking about apparent contradictions between scientific and religious explanations of the origins of the universe. In our discussion of the findings, we highlight that students’ epistemic insight in this context does seem in many cases to be limited and we outline some of the issues emerging from the study that seem to boost or limit students’ progress in this area. 相似文献
15.
Principle-oriented explanations have demonstrated to foster students’ mathematical understanding, as they integrate conceptual and procedural information to make the solution process tangible to novice students. Teachers, however, often omit conceptual information when explaining procedures. In two experimental studies, we tested the hypothesis that teachers’ tendency to omit conceptual information may have occurred, as teachers generally devalued the potential of principle-oriented explanations. In Study 1, we randomly provided two cohorts of secondary students (N = 129) with principle-oriented versus procedure-oriented explanations on four mathematical topics. Afterwards, students answered a knowledge test. We replicated previous findings that students with principle-oriented explanations outperformed students with procedure-oriented explanations on the knowledge test (application test, transfer test). In Study 2, we gave mathematics teachers (N = 69) these explanations as judgment materials. Teachers randomly rated a balanced set of four explanations of Study 1 which varied in their procedure- versus principle-orientation. We found no significant differences between teachers’ judgments of principle- versus procedure-oriented explanations. Content analyses of the justifications revealed that teachers were more concerned about students’ overload when judging principle-oriented explanations than procedure-oriented explanations. Our findings replicated the beneficial effects of principle-oriented explanations for novice students’ understanding. Furthermore, they highlight the need to sensitize teachers for potential effects of providing principle-oriented explanations. 相似文献
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确立现代教学与现代管理的观念，掌握基本的教学管理方法是形成课堂教学管理艺术的基础。现代教学管理观念包括学生是教学主体的观念、教学管理是服务的观念、教学管理创造与维护教学活动的观念等。教师应学会使用自我管理、分组控制、激励等现代管理方法。教学管理艺术形成的内容包括沟通与化解矛盾艺术的形成、表扬与批评艺术的形成等。在形成化解矛盾艺术的过程中。教师应学会使用分析问题。区分矛盾，“制造”矛盾，让学生解决矛盾的能力。为了形成表扬的艺术．教师应掌握表扬的方法，在教学实践中应学会表扬的设计。批评手段的有效使用对教学的顺利进行．学生学习任务的完成有十分重要的意义。掌握批评原则、学会批评设计有利于形成批评艺术。 相似文献
17.
《学习科学杂志》2013,22(1):49-94
To reap the benefits of natural language interaction, tutorial systems must be endowed with the properties that make human natural-language interaction so effective. One striking feature of naturally occurring interactions is that human tutors and students freely refer to the context created by prior explanations. In contrast, computer-generated utterances that do not draw on the previous discourse often seem awkward and unnatural and may even be incoherent. The explanations produced by such systems are frustrating to students because they repeat the same information over and over again. Perhaps more critical is that, by not referring to prior explanations, computer-based tutors are not pointing out similarities between problem-solving situations and therefore may be missing out on opportunities to help students form generalizations. In this article, we discuss several observations from an analysis of human-human tutorial interactions and provide examples of the ways in which tutors and students refer to previous explanations. We describe how we have used a case-based reasoning algorithm to enable a computational system to identify prior explanations that may be relevant to the explanation currently being generated. We then describe two computational systems that can exploit this knowledge about relevant prior explanations in constructing their subsequent explanations. 相似文献
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Explanations are used as indicators of understanding in mathematics, and conceptual explanations are often taken to signal deeper understanding of a domain than more superficial explanations. However, students who are able to produce a conceptual explanation in one problem or context may not be able to extend that understanding more generally. In this study we challenge the notion that conceptual explanations indicate general understanding by showing that – although conceptual explanations are strongly associated with correct answers – they are not employed equally across different contexts, and the highest performing students tend to use more general explanations, which may or may not be conceptual. Overall, our results suggest that explanations of fraction magnitudes follow a learning trajectory reflected in students’ accuracy and explanations: weak students focus on concrete, non-conceptual features, stronger students use concepts to explain their answers, and the highest performers tend to use general (but not necessarily conceptual) rules. 相似文献