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1.
ABSTRACT

One aim of school science instruction is to help students become adaptive problem solvers. Though successful at structuring novice problem solving, step-by-step problem-solving frameworks may also constrain students’ thinking. This study utilises a paradigm established by Heckler [(2010). Some consequences of prompting novice physics students to construct force diagrams. International Journal of Science Education, 32(14), 1829–1851] to test how cuing the first step in a standard framework affects undergraduate students’ approaches and evaluation of solutions in physics problem solving. Specifically, prompting the construction of a standard diagram before problem solving increases the use of standard procedures, decreasing the use of a conceptual shortcut. Providing a diagram prompt also lowers students’ ratings of informal approaches to similar problems. These results suggest that reminding students to follow typical problem-solving frameworks limits their views of what counts as good problem solving.  相似文献   

2.
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3.
The purpose of this study was to investigate the relationship between both 9th-grade and 1st-year undergraduate students’ use of “look back” strategies and problem solving performance in multiple solution methods, the difference in their use of look back strategies and problem solving performance in multiple solution methods, and the role of look back strategies in problem solving in multiple solution methods. Data for this study were comprised of 30 9th-grade and 30 1st-year undergraduate students’ problem solving scores in multiple solution methods and their think-aloud protocols. Based on and expanded from Polya’s (1973) ideas, “look back” in the present study means “examination of what was done or learned previously.” The results of this study indicated that both the 9th-grade and 1st-year undergraduate students who looked back more frequently tended to perform better in multiple solution methods, the 1st-year undergraduate students tended to look back more frequently and perform better than the 9th-grade students in multiple solution methods, and both the 9th-grade and 1st-year undergraduate students tended to review and to compare multiple solution methods in their use of look back strategies.  相似文献   

4.
A study of the effects of explicitly teaching a problem‐solving strategy on problem‐solving ability, course average, course success, and student retention is reported. Two classes of microeconomics principles were involved in a quasi‐experiment. The experimental class was explicitly taught the problem‐solving strategy and this strategy was then used to solve microeconomic problems in class. The control class was assigned, solved, and discussed the same problems without being taught the problem‐solving strategy. Multiple regression and analysis of variance show that while teaching problem solving did not significantly affect course average, student success in passing the course or problem solving ability, it did result in significantly higher student retention. Results indicate that teaching problem solving only affects those students with low problem solving abilities who would have dropped out of class, and that teaching this strategy helps them remain in the class and succeed.  相似文献   

5.
Over the past decade, curricular reform in mathematics education has emphasized the use of problem solving at all levels of instruction for all students, but adaptations for students with unique needs have not been specified. This study investigated the nature of problem solving in deaf education, focusing in particular on the use of story problems in the primary-level curriculum. Approximately 90% of the K-3 teachers from five schools for the deaf were asked with what frequency and in which communication mode they presented story problems to their students. Most teachers reported presenting story problems 1-3 times per week, and presentation method tended to reflect school communication philosophy. We found trends in story problem presentation in accordance with the mathematics grade level taught. We discuss implications for curricular reform and teacher education.  相似文献   

6.
Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of constructivist-oriented mathematics instruction involving students with LD, the authors conducted a case study to analyze teacher–student interactions during constructivist-oriented small group instruction involving a student with LD. The student demonstrated, to a certain degree, the ability to reason mathematically when provided with appropriate opportunities and prompting. However, given the limited intervention time, his reasoning and problem solving did not seem to go beyond the semiconcrete level of operation, which may have inhibited his solving of complex word problems with large numbers. Findings indicate that more efforts are needed to support students, those with LD in particular, in their transitions from concrete or semiconcrete to abstract conceptual understanding and problem solving.  相似文献   

7.
The purpose of this study was to explore methods to enhance mathematical problem solving for students with mathematics disabilities (MD). A small‐group problem‐solving tutoring treatment incorporated explicit instruction on problem‐solution rules and on transfer. The transfer component was designed to increase awareness of the connections between novel and familiar problems by broadening the categories by which students group problems requiring the same solution methods and by prompting students to search novel problems for these broad categories. To create a stringent test of efficacy, we incorporated a computer‐assisted practice condition, which provided students with direct practice on real‐world problem‐solving tasks. We randomly assigned 40 students to problem‐solving tutoring, computer‐assisted practice, problem‐solving tutoring plus computer‐assisted practice, or control, and pre‐ and posttested students on three problem‐solving tasks. On story problems and transfer story problems, tutoring (with or without computer‐assisted practice) effected reliably stronger growth compared to control; effects on real‐world problem solving, although moderate to large, were not statistically significant. Computer‐assisted practice added little value beyond tutoring but, alone, yielded moderate effects on two measures.  相似文献   

8.
While the value of ‘schematic representations’ in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of ‘schematic representation’ (diagrams vs. schematic drawings) on the solving of arithmetical problems. The results show that the presence of schematic representations has a clear positive effect on overall student performance and that a non negligible proportion of students manage to reuse the representations encountered in order to solve new problems. While showing an effect slightly in favor of diagrams as opposed to schematic drawings, our results do not really permit us to draw any conclusions about the form that these representations should take, in particular since a differential effect was observed depending on the type of problem.  相似文献   

9.
Secondary 5 students from four schools in Hong Kong were required to classify 18 paper and pencil physics problems in terms of whether the problems contain necessary and sufficient, missing or irrelevant information for their solution. Students' ability to denote missing information correlated rather highly with the solution rates of the problems. In another test, students were asked to classify whether the problems in each of six pairs were similar to or different from each other according to students' self-determined criteria. Students who used a deep structure (i.e. used the underlying physics principles) to classify the problems have significantly higher scores in detecting missing and irrelevant information and in the solution rates than those who used surface structure or features for classification. It is argued that a student who is able to identify what information is sufficient, missing or irrelevant for solving a problem understands the problem structure and so is better able to solve it. Such a student is likely to adopt a deep structure in categorizing physics problems. This latter result corroborates with the findings of the expert-novice research paradigm. Specializations: physics education, alternative conceptions of science, computer-assisted learning, problem solving.  相似文献   

10.
What strategies do high school students use when solving chemistry problems? The purpose for conducting this study was to determine the general problem-solving skills that students use in solving problems involving moles, stoichiometry, the gas laws, and molarity. The strategies were examined for success in problem solving for 266 students of varying proportional reasoning ability, using interviews incorporating the think-aloud technique. Data were coded using a scheme based on Polya's heuristics. Results indicated that successful students and those with high proportional reasoning ability tended to use algorithmic reasoning strategies more frequently than nonsuccessful and low proportional reasoning students. However, the majority of all students solved the chemistry problems using only algorithmic methods, and did not understand the chemical concepts on which the problems were based.  相似文献   

11.
ABSTRACT

This study explores first-year university students’ reasoning as they learn to draw Lewis structures. We also present a theoretical account of the formal procedure commonly taught for drawing these structures. Students’ discussions during problem-solving activities were video recorded and detailed analyses of the discussions were made through the use of practical epistemology analysis (PEA). Our results show that the formal procedure was central for drawing Lewis structures, but its use varied depending on situational aspects. Commonly, the use of individual steps of the formal procedure was contingent on experiences of chemical structures, and other information such as the characteristics of the problem given. The analysis revealed a number of patterns in how students constructed, checked and modified the structure in relation to the formal procedure and the situational aspects. We suggest that explicitly teaching the formal procedure as a process of constructing, checking and modifying might be helpful for students learning to draw Lewis structures. By doing so, the students may learn to check the accuracy of the generated structure not only in relation to the octet rule and formal charge, but also to other experiences that are not explicitly included in the formal procedure.  相似文献   

12.
Graduate teaching assistants (GTAs) constitute a valuable and economical teaching force in many higher education undergraduate programmes. However, student satisfaction with their teaching has attracted little attention in the research literature. This study aimed at examining students’ evaluation of teaching of GTAs in discussion groups, as well as exploring the effects of group and GTA variables on these ratings. Data were collected using a questionnaire administered online and completed by 7078 undergraduate students. Participants were enrolled in classes taught by 278 GTAs from four faculties in a major Israeli university. Results indicated that ratings assigned to clarity of instruction were the most salient predictor of students’ overall evaluation. Generally, findings were consistent with those reported in the literature for other categories of instructors. Groups taught by GTAs in exact sciences and engineering were rated higher than those in social sciences and business management. Group size and the percentage of men students were inversely correlated with student ratings, while student attendance rate was positively correlated. Women GTAs and GTAs who taught more than one group tended to receive higher ratings. Overall student attendance rate was the most prominent predictor of student ratings. The implications of the findings are discussed.  相似文献   

13.
Problem solving is an important yet neglected mathematical skill for students with autism spectrum disorder and intellectual disability (ASD/ID). In addition, the terminology and vocabulary used in mathematical tasks may be unfamiliar to students with ASD/ID. The current study evaluated the effects of modified schema-based instruction (SBI) on the algebra problem solving skills of three middle school students with ASD/ID. Mathematics vocabulary terms were taught using constant time delay. Participants were then taught how to use an iPad that displayed a task analysis with embedded prompts to complete each step of solving the word problems. This study also examined participant’s ability to generalize skills when supports were faded. Results of the multiple probe across participants design showed a functional relation between modified SBI and mathematical problem solving as well as constant time delay and acquisition of mathematics vocabulary terms. Implications for practice and future research are discussed.  相似文献   

14.
Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a Southeastern State University over multiple semesters (six semesters, seven classes). PSTs’ solution methods for one intentionally misleading mathematics problem were analyzed using a convergent parallel mixed methods content analysis. Two-thirds of PSTs misunderstood the problem scenario and directly translated numbers from the problem text. PSTs who answered correctly used a problem model strategy to comprehend the scenario and were more likely to use multiple models, draw a diagram, and draw a diagram before using another model. However, a large number of PSTs who answered incorrectly also used multiple models and drew diagrams. Self-correction was not common (8 of 121), because their equations did not provide feedback or support comprehension. Three kinds of imprecision also affected problem comprehension and were evident in both correct and incorrect solutions. Intentionally misleading problems helped PSTs see consequences of their mathematical habits and highlighted the importance of sense making and precision when creating problem models.  相似文献   

15.
We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students’ ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were 130 eighth-grade students in two classes with a comparable background that were taught by the same teacher. A two-week intervention was implemented in the experimental class aiming to help students learn how to use geometric transformations to draw auxiliary lines in solving geometric problems. The data were collected from a teacher interview, video-recordings of the intervention, and pre- and post-tests. The results revealed that there was a positive impact of using geometric transformations on the experimental students’ ability in solving high-level cognitive problems by adding auxiliary lines, though the impact on the students’ ability in solving general geometric problems as measured using the overall average scores was not statistically significant. Recommendations for future research are provided at the end of the article.  相似文献   

16.
It has been shown previously that manipulation of the M demand (amount of information needed for processing) of chemistry problems affects student performance, which suggests that manipulation of logical structure of chemistry problems could also lead to significant changes in performance. The objective of this study is to investigate the following: Given the opportunity for training, what is the effect of increasing (manipulation) the complexity of logical structure of chemistry problems on student performance, and to what extent can cognitive variables explain changes in performance. Results obtained show that (a) even a small increase in the logical structure of a problem can change the role of cognitive variables (mental capacity and formal reasoning) to the extent that increase in logical complexity outweighs the advantage students may have gained through training on a similar problem; (b) the use of algorithms and training on particular types of chemistry problems could lead to a situation in which formal reasoning is the only cognitive variable that explains variance in performance significantly; and (c) after having solved very similar problems on two different occasions with improving performance, the improvement is not retained if the logical structure of a third problem increases considerably. It is concluded that when dealing with significant changes in logical complexity of chemistry problems, developmental level of students is the most consistent predictor of success. A model for the qualitative analysis of logical complexity of chemistry problems is presented.  相似文献   

17.
Physics is often seen as an excellent introduction to science because it allows students to learn not only the laws governing the world around them, but also, through the problems students solve, a way of thinking which is conducive to solving problems outside of physics and even outside of science. In this article, we contest this latter idea and argue that in physics classes, students do not learn widely applicable problem-solving skills because physics education almost exclusively requires students to solve well-defined problems rather than the less-defined problems which better model problem solving outside of a formal class. Using personal, constructed, and the historical accounts of Schrödinger’s development of the wave equation and Feynman’s development of path integrals, we argue that what is missing in problem-solving education is practice in identifying gaps in knowledge and in framing these knowledge gaps as questions of the kind answerable using techniques students have learned. We discuss why these elements are typically not taught as part of the problem-solving curriculum and end with suggestions on how to incorporate these missing elements into physics classes.  相似文献   

18.
Overprompting students by providing them with strong hints to answers of questions can do learners more instructional harm than good. The selective attention model was used to explain the effects of overprompting students provided with study questions adjunct to a complex flow diagram describing scientific cyclical schema. Tenth-grade students were randomly assigned to an unprompted-question, no-question, prompted-question, and a placebo control group. Analysis showed that strongly prompting students to the answers of such questions was less effective than an unprompted question treatment, p < 0.05. The no-question treatment did not significantly outperform the prompted treatment. The information presented in the flow diagram was operationally related to comprehension study and posttest questions. The theoretical discussion and the present findings suggested that science teachers should use prompting techniques with extreme caution.  相似文献   

19.
The heuristic value of the concept ofzone of proximal development in the field of scientific instruction is demonstrated by means of a study on the construction of the concept offorce by students aged 14 and 15. Based on an analysis of the differences between the students’ intuitive concepts and those taught in school, a sequence of learning steps are proposed to allow students to achieve the “shifts” needed to receive the concept of force, defined as an interaction between systems. Acting on the zone of proximal development means taking advantage of what students already know in order to help them construct precursory concepts in preparation for new conceptual propositions. The original teaching sequence presented is based on experimental problem situations designed to promote modelling skills. Students are asked to make predictions about measurement variations. To perform these prediction tasks, they must construct new concepts and use specific representation techniques. The study enabled us to show that it is possible in ten sessions to lead students to construct a precursor for the formal concept of force.  相似文献   

20.
While Physics Education Research has a rich tradition of problem-solving scholarship, most of the work has focused on more traditional, well-defined problems. Less work has been done with ill-structured problems, problems that are better aligned with the engineering and design-based scenarios promoted by the Next Generation Science Standards. This study explored the relationship between physics content knowledge and ill-structured problem solving for two groups of high school students with different levels of content knowledge. Both groups of students completed an ill-structured problem set, using a talk-aloud procedure to narrate their thought process as they worked. Analysis of the data focused on identifying students’ solution pathways, as well as the obstacles that prevented them from reaching “reasonable” solutions. Students with more content knowledge were more successful reaching reasonable solutions for each of the problems, experiencing fewer obstacles. These students also employed a greater variety of solution pathways than those with less content knowledge. Results suggest that a student’s solution pathway choice may depend on how she perceives the problem.  相似文献   

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