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1.
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   

2.
Miroslav Lovric 《PRIMUS》2018,28(7):683-698
We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs, etc.), offers simulation and experimentation, invites discussions about structure, requires logic and testing strategies, and handles mathematics objects with an added feeling of reality. Focusing on novice and inexperienced programmers, we look for answers to the practice-oriented question, “How do students reason through their difficulties when using programming to explore a mathematics problem?” Following literature review and methodology, we build the programming model, which we use to study students' experiences as they approach a mathematical problem by writing computer code. Our research is based on analyzing students' in-class work and class notes, author's observations of students working on their computers, and his interactions with students in class and elsewhere. In the four case studies that we present we touch upon students' difficulties in working with complex conditional statements and recurrence relations. As well, we discuss cases where resolving a programming issue demands posing and answering mathematical questions.  相似文献   

3.
Drawing on research that sought to explore the characteristics of ‘Possibility Thinking’ as central to creativity in young children's learning, this paper considers question‐posing and question‐responding as the driving features of ‘Possibility Thinking’ (PT). This qualitative study employed micro‐event analysis of peer and pupil–teacher interaction. Events were sampled from two early years settings in England, one a Reception classroom (4‐ to 5‐year olds) and the other a Year 2 classroom (6‐ to 7‐year olds). This article arises out of the second stage of an ongoing research programme (2004–2007) involving the children and practitioners in these settings. This phase considers the dimensions of question‐posing and the categories of question‐responding and their interrelationship within PT. Three dimensions of questioning were identified as characteristic of PT. These included: (i) question framing, reflecting the purpose inherent within questions for adults and children (including leading, service and follow‐through questions); (ii) question degree: manifestation of the degree of possibility inherent in children's questions (including possibility narrow, possibility moderate, possibility broad); (iii) question modality, manifestation of the modality inherent in children's questions (including verbal and non‐verbal forms). The fine‐grained data analysis offers insight into how children engage in PT to meet specific needs in responding to creative tasks and activities and reveals the crucial role that question‐posing and question‐responding play in creative learning. It also provides more detail about the nature of young children's thinking, made visible through question‐posing and responding in engaging playful contexts.  相似文献   

4.
An interesting aspect in the current literature about learning networks is the shift of focus from the understanding of the “whole network” of a course to the examination of the “personal networks” of individual students. This line of research is relatively new, based on small‐scale studies and diverse analysis techniques, which demands for more empirical research in order to contextualize the findings and to meta‐analyze the research methods. The main objective of this paper is to review two research questions posed by a previous British Journal of Educational Technology contribution by Shane Dawson in order to know whether the differences in personal network composition impact on the performance of students. The two questions were defined by Dawson as follows: (1) Are there significant differences in personal network composition between high‐ and low‐performing students? and (2) Do high‐performing students have larger personal networks than their low‐performing peers? In addition, the “clustered graphs” method used in this study allows the inclusion of the structural analysis of personal networks. In doing so, a new research question is addressed: (3) Are there significant differences in personal network structure between high‐ and low‐performing students? This paper tries to answer these questions in the context of two undergraduate, inter‐university and fully online courses, and two different technology‐enhanced learning environments (a virtual learning environment and a personal learning environment) where interactions took place indirectly through shared resources. The results show that the network behaviors of high‐ and low‐performing students' are strongly correlated, and that high‐performing students developed larger personal networks than low performers.  相似文献   

5.
Posing questions about an article might improve one’s knowledge—a cognitive function, or monitor one’s thought processes—a metacognitive function. This study focuses on guided question posing while using a metacognitive strategy by 12th grade honors chemistry students. We investigated the ways by which the metacognitive strategy affected students’ skills to pose complex questions and to analyze them according to a specially designed taxonomy. Our learning unit, Case-based computerized laboratories, emphasizes learning through chemical case studies, accompanied by tasks, that call for posing questions to which the answer cannot be found in the text. Teachers equipped their students with a metacognitive strategy for assessing the quality of their own questions and characterizing them according to a three-component taxonomy: content, thinking level, and chemistry understanding levels. The participants were 793 experimental and 138 comparison chemistry students. Research instruments included interviews and case-based-questionnaires. Interviews with students revealed that using the metacognitive strategy the students had been taught, they were capable of analyzing the questions they generated with the taxonomy. The questionnaires showed that students significantly improved their question posing skill, as well as the complexity level of the questions they posed. A significant difference was found in favor of the experimental group students. Stimulating students to generate complex questions with a metacognitive strategy in mind enabled them to be aware of their own cognitive process and to self-regulate it with respect to the learning task.  相似文献   

6.
Our goals in this study were to explore the type of written questions students ask after reading one or more chapters from their textbook, and to investigate the ability of students to improve their questions during the course of a single semester. In order to classify student's questions we used a taxonomy that we have developed specifically for this purpose. Two comparable populations were examined: Undergraduate students in a large, introductory biology class who were taught in traditional lecture format, and students in a similar class who were taught in cooperative/active learning style. After the taxonomy was presented to the active learning class, more students were able to pose better, written questions. Their questions became more insightful, thoughtful, and content‐related, and were not easily answered by consulting the textbook or another readily available source. The best questions could be recast as scientific research questions (i.e., hypotheses). In contrast, when the taxonomy was presented to students in the traditionally taught class, the quality of student‐posed questions was largely unchanged. Various explanations for the difference in outcomes are discussed, and methods are suggested about how generally to encourage students' questions and to improve their question‐asking skills regardless of overall teaching style. © 2000 John Wiley & Sons, Inc. J Res Sci Teach 37: 854–870, 2000  相似文献   

7.
Recently, the importance of an everyday context in physics learning, teaching, and problem‐solving has been emphasized. However, do students or physics educators really want to learn or teach physics problem‐solving in an everyday context? Are there not any obstructive factors to be considered in solving the everyday context physics problems? To obtain the answer to these questions, 93 high school students, 36 physics teachers, and nine university physics educators participated in this study. Using two types of physics problems—everyday contextual problems (E‐problems) and decontextualized problems (D‐problems)—it was found that even though there was no difference in the actual performance between E‐problems and D‐problems, subjects predicted that E‐problems were more difficult to solve. Subjects preferred E‐problems on a school physics test because they thought E‐problems were better problems. Based on the observations of students' problem‐solving processes and interviews with them, six factors were identified that could impede the successful solution of E‐problems. We also found that many physics teachers agreed that students should be able to cope with those factors; however, teachers' perceptions regarding the need for teaching those factors were low. Therefore, we suggested teacher reform through in‐service training courses to enhance skills for teaching problem‐solving in an everyday context.  相似文献   

8.
The purpose of this study was to investigate the effects of the Common Knowledge Construction Model (CKCM) lesson sequence, an intervention based both in conceptual change theory and in Phenomenography, a subset of conceptual change theory. A mixed approach was used to investigate whether this model had a significant effect on 7th grade students' science achievement and conceptual change. The Excretion Unit Achievement Test (EUAT) indicated that students (N = 33) in the experimental group achieved significantly higher scores (p < 0.001) than students in the control group (N = 35) taught by traditional teaching methods. Qualitative analysis of students' pre‐ and post‐teaching conceptions of excretion revealed (1) the addition and deletion of ideas from pre‐ to post‐teaching; (2) the change in the number of students within categories of ideas; (3) the replacement of everyday language with scientific labels; and (4) the difference in the complexity of students' responses from pre‐ to post‐teaching. These findings contribute to the literature on teaching that incorporates students' conceptions and conceptual change. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 47: 25–46, 2010  相似文献   

9.
Field dependence/independence cognitive style was found to relate to general academic achievement and specific areas of mathematics; in the majority of studies, field-independent students were found to be superior to field-dependent students. The present study investigated the relationship between field dependence/independence cognitive style and problem-posing ability among sixth grade students. The 94 students’ sample was clustered into three groups, according to the cognitive-style field dependence/independence (field dependents, field mixed and field independents). The results suggest that field-independent participants outperformed field-mixed and field-dependent ones in both problem-posing ability and the complexity of the problems posed. It was also found that the content of the task influenced the differences between the three groups of students as regards the ability in problem posing and the complexity of the problems posed; while in the first (informal context), second and fourth task differences were found between the groups, in the third task (formal context), no differences were evident. The results are interpreted in consideration to the relevant literature findings. Some educational implications are discussed and directions for future research are drawn.  相似文献   

10.
Bloom's taxonomy was adopted to create a subject‐specific scoring tool for histology multiple‐choice questions (MCQs). This Bloom's Taxonomy Histology Tool (BTHT) was used to analyze teacher‐ and student‐generated quiz and examination questions from a graduate level histology course. Multiple‐choice questions using histological images were generally assigned a higher BTHT level than simple text questions. The type of microscopy technique (light or electron microscopy) used for these image‐based questions did not result in any significant differences in their Bloom's taxonomy scores. The BTHT levels for teacher‐generated MCQs correlated positively with higher discrimination indices and inversely with the percent of students answering these questions correctly (difficulty index), suggesting that higher‐level Bloom's taxonomy questions differentiate well between higher‐ and lower‐performing students. When examining BTHT scores for MCQs that were written by students in a Multiple‐Choice Item Development Assignment (MCIDA) there was no significant correlation between these scores and the students' ability to answer teacher‐generated MCQs. This suggests that the ability to answer histology MCQs relies on a different skill set than the aptitude to construct higher‐level Bloom's taxonomy questions. However, students significantly improved their average BTHT scores from the midterm to the final MCIDA task, which indicates that practice, experience and feedback increased their MCQ writing proficiency. Anat Sci Educ 10: 456–464. © 2017 American Association of Anatomists.  相似文献   

11.
This research investigated the effect of reflective discussions following inquiry‐based laboratory activities on students' views of the tentative, empirical, subjective, and social aspects of nature of science (NOS). Thirty‐eight grade six students from a Lebanese school participated in the study. The study used a pretest–posttest control‐group design and focused on collecting mainly qualitative data. During each laboratory session, students worked in groups of two. Later, experimental group students answered open‐ended questions about NOS then engaged in reflective discussions about NOS. Control group students answered open‐ended questions about the content of the laboratory activities then participated in discussions of results of these activities. Data sources included an open‐ended questionnaire used as pre‐ and posttest, answers to the open‐ended questions that experimental group students answered individually during every session, transcribed videotapes of the reflective discussions of the experimental group, and semi‐structured interviews. Results indicated that explicit and reflective discussions following inquiry‐based laboratory activities enhanced students' views of the target NOS aspects more than implicit inquiry‐based instruction. Moreover, implicit inquiry‐based instruction did not substantially enhance the students' target NOS views. This study also identified five major challenges that students faced in their attempts to change their NOS views. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 1229–1252, 2010  相似文献   

12.
This study compared the problem‐solving skills required for solving well‐structured problems and ill‐structured problems in the context of an open‐ended, multimedia problem‐solving environment in astronomy. Two sets of open‐ended questions assessed students' abilities for solving well‐structured and ill‐structured problems. Generalized, rubric scoring systems were developed for assessing problem‐solving skills. Instruments were also developed and administered to assess cognitive and affective predictors of problem‐solving performance. By regressing the scores on the cognitive and affective predictors onto students' scores on the well‐structured and ill‐structured problems, we concluded that solving well‐structured and ill‐structured problems require different component skills. Domain knowledge and justification skills were significant predictors of well‐structured problem‐solving scores, whereas ill‐structured problem‐solving scores were significantly predicted by domain knowledge, justification skills, science attitudes, and regulation of cognition. Implications for problem solving in science education are presented. © 2003 Wiley Periodicals, Inc. J Res Sci Teach 40: 6–33, 2003  相似文献   

13.
Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs are a good place to start the process of redesigning mathematics curricula so that school mathematics will pay more than lip service to problem posing. Data are presented and analyzed showing that teacher education students can recognize the need for problem posing both in their own programs and in school mathematics curricula. Examples of problems posed by teacher education students are presented and discussed. An active learning framework for interpreting the role of problem posing in mathematics classrooms is presented.  相似文献   

14.
The literature provides confounding information with regard to questions about whether students in high school can engage in meaningful argumentation about socio‐scientific issues and whether this process improves their conceptual understanding of science. The purpose of this research was to explore the impact of classroom‐based argumentation on high school students' argumentation skills, informal reasoning, and conceptual understanding of genetics. The research was conducted as a case study in one school with an embedded quasi‐experimental design with two Grade 10 classes (n = 46) forming the argumentation group and two Grade 10 classes (n = 46) forming the comparison group. The teacher of the argumentation group participated in professional learning and explicitly taught argumentation skills to the students in his classes during one, 50‐minute lesson and involved them in whole‐class argumentation about socio‐scientific issues in a further two lessons. Data were generated through a detailed, written pre‐ and post‐instruction student survey. The findings showed that the argumentation group, but not the comparison group, improved significantly in the complexity and quality of their arguments and gave more explanations showing rational informal reasoning. Both groups improved significantly in their genetics understanding, but the improvement of the argumentation group was significantly better than the comparison group. The importance of the findings are that after only a short intervention of three lessons, improvements in the structure and complexity of students' arguments, the degree of rational informal reasoning, and students' conceptual understanding of science can occur. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 952–977, 2010  相似文献   

15.
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16.
In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students' responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed.  相似文献   

17.
This study evaluated metacognitive changes of three groups of 160 engineering students working on 60 different design projects. Two metacognitive features, cognitive self‐appraisal and cognitive self‐management, were used to indicate students' metacognitive level. The Engineering Design Project Inventory was used to assess students' metacognition. Students were asked to complete the instrument at the early and final stages of the project. Statistical results revealed a significant change in mechanical engineering students' metacognition while engaged in the project. Eighteen themes of responses that described the influencing factors for the change in students' self‐appraisal and 23 themes of responses that described the influencing factors for their self‐management change were identified from two open‐ended questions.  相似文献   

18.
Abstract

In this study we describe and examine the effectiveness of an instructional program designed to teach learning disabled adolescents to make better personal decisions. We presented problems in short narratives based on the types of problems these students must solve in their own lives. The program, conducted as part of the students' regular resource room curriculum, incorporated schema‐general questions for problem solving coupled with practice in generating problem‐specific questions to reach an appropriate decision. Participants were 70 resource room students in two large, urban high schools. We employed a pretest‐posttest comparison group design. On the posttest, instructed students performed significantly better on (1) identifying a general schema for making a personal decision and (2) applying the schema to reach appropriate decisions concerning novel problem narratives. The results support the view that application of a general schema to specific problems can be an effective instructional method to improve critical thinking and decision making.  相似文献   

19.
To enhance the learning outcomes achieved by students, learners undertook a computer‐simulated activity based on an acid–base titration prior to a university‐level chemistry laboratory activity. Students were categorized with respect to their attitudes toward learning. During the laboratory exercise, questions that students asked their assistant teachers were used as indicators of cognitive focus. During the interviews, students' frequency and level of “spontaneous” use of chemical knowledge served as an indicator of knowledge usability. Results suggest that the simulation influenced students toward posing more theoretical questions during their laboratory work and, regardless of attitudes, exhibiting a more complex, correct use of chemistry knowledge in their interviews. A more relativistic student attitude toward learning was positively correlated with interview performance in both the control and treatment groups. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 44: 1108–1133, 2007  相似文献   

20.
This study examined 10th‐grade students' use of theory and evidence in evaluating a socio‐scientific issue: the use of underground water, after students had received a Science, Technology and Society‐oriented instruction. Forty‐five male and 45 female students from two intact, single‐sex, classes participated in this study. A flow‐map method was used to assess the participants' conceptual knowledge. The reasoning mode was assessed using a questionnaire with open‐ended questions. Results showed that, although some weak to moderate associations were found between conceptual organization in memory and reasoning modes, the students' ability to incorporate theory and evidence was in general inadequate. It was also found that students' reasoning modes were consistent with their epistemological perspectives. Moreover, male and female students appear to have different reasoning approaches.  相似文献   

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