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1.
The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.  相似文献   

2.
This study examines students’ use of proportional reasoning in high school physics problem‐solving in a West African school setting. An in‐depth, constructivist, and interpretive case study was carried out with six physics students from a co‐educational senior secondary school in Nigeria over a period of five months. The study aimed to elicit students’ meanings, claims, concerns, constructions, and interpretations of their difficulty with proportional reasoning as they worked on a series of 18 high school physics tasks. Multiple qualitative research techniques were employed to generate, analyse, and interpret data. Results indicated that several socio‐cultural, psychosocial, cognitive, and mathematical issues were associated with students’ use of proportional reasoning in physics. Students’ capacity to reason proportionally was not only linked to their difficulty with the concept, structure, and strategies of proportional reasoning as a learning and problem‐solving skill, but was also embedded in the social, cultural, cognitive, and contextual elements involved in the learning of physics. The study concludes with a discussion of the implications for teaching high school physics.  相似文献   

3.
The importance of students’ problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students’ mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students’ mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students’ mathematical content knowledge and their problem-posing abilities in mathematics.  相似文献   

4.
Upper secondary students’ task solving reasoning was analysed with a focus on arguments for strategy choices and conclusions. Passages in their arguments for reasoning that indicated the students’ beliefs were identified and, by using a thematic analysis, categorized. The results stress three themes of beliefs used as arguments for central decisions: safety, expectations and motivation. Arguments such as ‘I don’t trust my own reasoning’, ‘mathematical tasks should be solved in a specific way’ and ‘using this specific algorithm is the only way for me to solve this problem’ exemplify these three themes. These themes of beliefs seem to interplay with each other, for instance in students’ strategy choices when solving mathematical tasks.  相似文献   

5.
This study examined the effectiveness of 3 curriculum interventions focused on strengthening children’s ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional geometry. Participants were 131 fourth graders, recruited from a city in northern Taiwan, and 1 instructor. The results confirmed the effectiveness of an enriched curriculum integrating knowledge of 2-dimensional geometry in enhancing children’s conceptual understanding of area measurement. The group that received the enriched curriculum outperformed the other groups that received the curricula stressing only 2-dimensional geometry or numerical calculations for area measurement in solving the area problems requiring mathematical judgments and explanations. The curriculum also facilitated children’s reasoning in distinguishing between the perimeter and area of a rectangle, which required higher-order mathematical thinking. Interview data revealed that approximately all children from the 3 intervention groups could identify the mathematical subject-matter components highlighted in the curricula. Interviewees tended to consider the use of formulae to solve area measurement problems to be important, despite some differences in learning gains among the 3 groups. In interviews, the participating instructor revealed a change of perspective regarding the importance of offering students opportunities for manipulation and geometric operations when teaching area measurement, prompted by curriculum enactment.  相似文献   

6.
A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students’ mathematical reasoning, we conduct design research where whole-class mathematical discussions triggered by exploratory tasks play a key role. We take mathematical reasoning as making justified inferences and we consider generalizing and justifying central reasoning processes. Regarding teacher actions, we consider inviting, informing/suggesting, supporting/guiding and challenging actions can be identified in whole-class discussions. This paper presents design principles for an intervention geared to tackle such reasoning processes and focuses on a whole-class discussion on a grade 7 lesson about linear equations and functions. Data analysis concerns teacher actions in relation to design principles and to the sought mathematical reasoning processes. The conclusions highlight teacher actions that lead students to generalize and justify. Generalizations may arise from a central challenging action or from several guiding actions. Regarding justifications, a main challenging action seems to be essential, while follow-up guiding actions may promote a further development of this reasoning process. Thus, this paper provides a set of design principles and a characterization of teacher actions which enhance students’ mathematical reasoning processes such as generalization and justification.  相似文献   

7.
Separate tests of mathematics skills, proportions and translations between words, and mathematical expression given the first week of class were correlated with performance for students who completed a college physics course (completes) and students who dropped the course (drops). None of the measures used discriminated between completes and drops as groups. However, the correlations between score on the test of math skills and on both of the measures involving mathematical reasoning (proportions, and translations) were dramatically different for the two groups. For the completes, these correlations were slightly negative, but not significant. For the drops, the correlation was positive and signficant at the p < 0.01 level. This suggests the possibility that the students who complete the course tend to have independent cognitive skills for the “mechanical” mathematical operations and for questions requiring some degree of reasoning, while, in contrast, the same skills for students at high risk for dropping overlap significantly. The study also found that when students are given the results of mathematics skills tests in a diagnostic mode, with feedback on specific areas of weakness and time to remediate with self study, the correlation between mathematics and physics is lower than previously reported values.  相似文献   

8.
数学推理有两种截然不同的推理方式:原创性推理和模仿性推理.数学推理的认知成分和结构包括:阅读、分析、探索、计划、实施、验证等6个环节.原创性推理和模仿性推理的差异主要体现在阅读、分析、探索、计划这4个认知成分上,前者更注重深层理解、内在比较、再结构化、适时调整目标,后者更多采用记忆、类比、联结方式作推理动力.换句话说,原创性推理更强调思维的自主性、发散性.教师在教学中应注重学生的原创性自主思维.  相似文献   

9.
In this paper, we focus on the efforts of educators at nine different research sites within the United States, funded by a grant from the National Institute of Environmental Health Sciences (NIEHS), to develop and implement innovative, interdisciplinary curriculum on the relationship of the environment and human health. The NIEHS correctly maintained that the interdisciplinary nature of learning about environmental health would improve students’ learning across several subject areas and should, therefore, contribute to students scoring higher on state’s subject area based standardized tests. However, these goals were undermined by state polices linking standardized tests with student promotion and graduation, and the federal No Child Left Behind Act (NCLB) that required public schools and districts to aggregate test scores which might have negative consequences, such as reducing school funding or privatizing school administration and state policies. These policies resulted in deleterious effects that undermined implementing environmental health curricula.  相似文献   

10.

Whilst spatial reasoning skills have been found to predict mathematical achievement, little is known about how primary (elementary) students’ conceptual understanding of three-dimensional objects develops. In this article, we report a qualitative study and the impact of rich learning experiences on 48 Years 3–6 students’ geometric reasoning relating to prisms. A one-to-one task-based interview, refined by the researchers, was used to assess student learning. Coding and data analysis were informed by our previous research. The findings reveal noticeable shifts in students’ knowledge of and reasoning about prisms, their ability to construct and describe prisms with geometric language, and their visualisation and spatial structuring skills. The implications of these findings highlight the importance of teachers’ choice of tasks that require students to compose and decompose three-dimensional (3D) objects; compare 3D objects through physical and mental transformations; take different perspectives; and visualise and reason geometrically.

  相似文献   

11.
Students at the junior high school (JHS) level often cannot use their knowledge of physics for explaining and predicting phenomena. We claim that this difficulty stems from the fact that explanations are multi‐step reasoning tasks, and students often lack the qualitative problem‐solving strategies needed to guide them. This article describes a new instructional approach for teaching mechanics at the JHS level that explicitly teaches such a strategy. The strategy involves easy to use visual representations and leads from characterizing the system in terms of interactions to the design of free‐body force diagrams. These diagrams are used for explaining and predicting phenomena based on Newton's laws. The findings show that 9th grade students who studied by the approach advanced significantly from pretests to post‐tests on items of the Force Concept Inventory—FCI and on other items examining specific basic and complex understanding performances. These items focused on the major learning goals of the program. In the post‐tests the JHS students performed on the FCI items better than advanced high‐school and college students. In addition, interviews conducted before, during, and after instruction indicated that the students had an improved ability to explain and predict phenomena using physics ideas and that they showed retention after 6 months. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 1094–1115, 2010  相似文献   

12.
This study examined the Swedish national tests in chemistry for implicit and explicit values. The chemistry subject is understudied compared to biology and physics and students view chemistry as their least interesting science subject. The Swedish national science assessments aim to support equitable and fair evaluation of students, to concretize the goals in the chemistry syllabus and to increase student achievement. Discourse and multimodal analyses, based on feminist and critical didactic theories, were used to examine the test’s norms and values. The results revealed that the chemistry discourse presented in the tests showed a traditional view of science from the topics discussed (for example, oil and metal), in the way women, men and youth are portrayed, and how their science interests are highlighted or neglected. An elitist view of science emerges from the test, with distinct gender and age biases. Students could interpret these biases as a message that only “the right type” of person may come into the chemistry epistemological community, that is, into this special sociocultural group that harbours a common view about this knowledge. This perspective may have an impact on students’ achievement and thereby prevent support for an equitable and fair evaluation. Understanding the underlying evaluative meanings that come with science teaching is a question of democracy since it may affect students’ feelings of inclusion or exclusion. The norms and values harboured in the tests will also affect teaching since the teachers are given examples of how the goals in the syllabus can be concretized.  相似文献   

13.
Several studies show that university students in Germany still have problems in reasoning mathematically although this already should be fostered at high school since the implementation of standards for school mathematics. Mathematical argumentation is a core competence and highly important, especially in academic mathematics. To foster mathematical argumentation at the beginning of university studies, competence models are needed which give more detailed insights in the skills that are necessary for reasoning. As mathematical argumentation is a complex process, especially at the higher secondary level or at university, many little steps are needed to complete a competence model for argumentation at the secondary–tertiary transition gradually. A possible step can be to initially identify several aspects of mathematical argumentation competence that influence the reasoning quality. The empirical basis for identifying those aspects is a cross-sectional study with 439 engineering students who participate in a transition course in mathematics. We address the following questions: (1) how is the quality of student’s reasoning? (2) Which kind of arguments do students use? (3) What resources do students who reasoned correctly use for solving the problems? (4) Does the content of the tasks play an important role? The results show a great influence of the content on the reasoning quality, especially if the content is abstract or concrete. Argumentation quality of students decreases with an increasing level of abstraction of the content. Furthermore, the results reveal that students often use routines for solving the problems. That indicates that procedural approaches still play an important role in school mathematics. If procedures could be used for solving the tasks, students are more successful. Competence models for mathematical argumentation at the beginning of the tertiary level should, therefore, include these factors.  相似文献   

14.
ABSTRACT

Many science curricula and standards emphasise that students should learn both scientific knowledge and the skills associated with the construction of this knowledge. One way to achieve this goal is to use inquiry-learning activities that embed the use of science process skills. We investigated the influence of scientific reasoning skills (i.e. conceptual and procedural knowledge of the control-of-variables strategy) on students’ conceptual learning gains in physics during an inquiry-learning activity. Eighth graders (n?=?189) answered research questions about variables that influence the force of electromagnets and the brightness of light bulbs by designing, running, and interpreting experiments. We measured knowledge of electricity and electromagnets, scientific reasoning skills, and cognitive skills (analogical reasoning and reading ability). Using structural equation modelling we found no direct effects of cognitive skills on students’ content knowledge learning gains; however, there were direct effects of scientific reasoning skills on content knowledge learning gains. Our results show that cognitive skills are not sufficient; students require specific scientific reasoning skills to learn science content from inquiry activities. Furthermore, our findings illustrate that what students learn during guided inquiry activities becomes visible when we examine both the skills used during inquiry learning and the process of knowledge construction. The implications of these findings for science teaching and research are discussed.  相似文献   

15.
The teleological bias, a major learning obstacle, involves explaining biological phenomena in terms of purposes and goals. To probe the teleological bias, researchers have used acceptance judgement tasks and preference judgement tasks. In the present study, such tasks were used with German high school students (N?=?353) for 10 phenomena from human biology, that were explained both teleologically and causally. A sub-sample (n?=?26) was interviewed about the reasons for their preferences. The results showed that the students favoured teleological explanations over causal explanations. Although the students explained their preference judgements etiologically (i.e. teleologically and causally), they also referred to a wide range of non-etiological criteria (i.e. familiarity, complexity, relevance and five more criteria). When elaborating on their preference for causal explanations, the students often focused not on the causality of the phenomenon, but on mechanisms whose complexity they found attractive. When explaining their preference for teleological explanations, they often focused not teleologically on purposes and goals, but rather on functions, which they found familiar and relevant. Generally, students’ preference judgements rarely allowed for making inferences about causal reasoning and teleological reasoning, an issue that is controversial in the literature. Given that students were largely unaware of causality and teleology, their attention must be directed towards distinguishing between etiological and non-etiological reasoning. Implications for educational practice as well as for future research are discussed.  相似文献   

16.
Contextual problems involving rational numbers and proportional reasoning were presented to seventh grade students with different curricular experiences. There is strong evidence that students in reform curricula, who are encouraged to construct their own conceptual and procedural knowledge of proportionality through collaborative problem solving activities, perform better than students with more traditional, teacher-directed instructional experiences. Seventh grade students, especially those who study the new curricula, are capable of developing their own repertoire of sense-making tools to help them to produce creative solutions and explanations. This is demonstrated through analysis of solution strategies applied by students to a variety of rate problems.  相似文献   

17.
The idea of causality is central in science and has long given rise to debate among philosophers and scientists. While the tendency to avoid causality seems to have become dominant in science and philosophy, research in science education has shown the strong presence in common reasoning of causal explanations, often conceived as a ‘mechanism’ capable of accounting for physical transformations. Some researchers have proposed using this common causal reasoning as a basis for teaching–learning sequences, especially in electricity and mechanics. This paper analyses some features of causal reasoning used in physics by students, using questionnaires and interviews involving students and teachers. This study has shown three aspects which are related to one another: a confusion between efficient and contingent causes, between the conditions of occurrence of a phenomenon and the cause actually producing it; a tendency to ‘displace’ causes, skipping intermediate objects; and a difficulty in connecting local causes and global effects. The paper highlights the differences between common reasoning and scientific usage, and their effect on learning. In fact, these trends of reasoning must be taken into account in teaching: they should be considered not only as creating an obstacle to learning physics, but also as resources at the learner’s disposal.  相似文献   

18.
Explaining appears to dominate primary teachers’ understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop mathematical reasoning. The task used in this study of children’s reasoning is a number commonality problem. We analysed written and verbal samples of reasoning gathered from children in grades 3 and 4 from three primary schools in Australia and one elementary school in Canada to map the variation in their reasoning. We found that comparing and contrasting was a critical aspect of forming conjectures when generalising in this context, an action not specified in frameworks for generalising in early algebra. The variance in children’s reasoning elicited through this task also illuminated the difference between explaining and justifying.  相似文献   

19.
《学习科学杂志》2013,22(1):35-67
Project-based curricula have the potential to engage students' interests. But how do students become interested in the goals of a project? This article documents how a group of 8th-grade students participated in an architectural design project called the Antarctica Project. The project is based on the imaginary premise that students need to design a research station in Antarctica. This premise is meant to provide a meaningful context for learning mathematics. Using ethnography and discourse analysis, the article investigates students' engagement with the imaginary premise and curricular tasks during the 7-week project. A case study consisting of scenes from main phases of the project shows how the students took on concerns and responsibilities associated with the figured world proposed by the Antarctica Project and how this shaped their approaches to mathematical tasks (Holland, Lachicotte, Skinner, & Cain, 1998). Participating in the figured world of Antarctica and evaluating situations within this world was important for how students used mathematics meaningfully to solve problems. Curricular tasks and classroom activities that facilitated students in assuming and shifting between roles relevant to multiple figured worlds (i.e., of the classroom, Antarctica, and mathematics) helped them engage in the diverse intentions of curricular activities.  相似文献   

20.
A 14-week course program was designed to investigate pre-service teachers’ noticing skills and scaffolding practices. Six pre-service teachers were matched with a pair of sixth grade students to observe and scaffold students’ mathematical understanding while they were working on the given tasks. Data was collected through pre-service teachers’ own recorded videos of implementation of tasks, their written reflections about the implementations, videos of group reflections before and after the implementations, and students’ written work. The analysis of data revealed that pre-service teachers mostly noticed students’ errors and strategies during their interactions with students, they attended important instances about students’ thinking and justified their reasoning for their comments in their written reflections. However, while interacting with students, they usually used low level scaffolding practices such as asking for clarification, explanation, and justification rather than attempting to elicit students’ thinking and improve their understanding.  相似文献   

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