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1.
Low mathematics achievement is a persistent problem in the United States, and multiplication is a fundamental area in which many students manifest learning difficulties. This study examined the strategic developmental levels of multiplication problem solving among 121 elementary school students in Grades 3 through 5. A latent class analysis modeling was used to identify three valid groups representing different patterns of strategy choices for each of three types of multiplication problems. Findings indicated intra-group variability for problem-solving accuracy, for frequency of using different strategies, and for accuracy of executing direct retrieval/algorithm (DR/AG) strategies. Students demonstrated relative consistency in their strategy choices for solving the three problem types. Students who used DR/AG strategies most frequently showed the highest problem-solving accuracy and the highest accuracy of executing the DR/AG strategies. Students who most frequently relied on incorrect operations or who indicated they did not know how to solve problems demonstrated the lowest problem-solving accuracy among the three groups; the number of students in this group increased with problem difficulty levels. Implications are discussed in terms of identifying students' strategic developmental levels and providing differentiated instruction based on the identified levels.  相似文献   

2.
This study evaluated whether schema-based instruction (SBI), a promising method for teaching students to represent and solve mathematical word problems, impacted the learning of percent word problems. Of particular interest was the extent that SBI improved high- and low-achieving students' learning and to a lesser degree on the indirect effect of SBI on transfer to novel problems, as compared to a business as usual control condition. Seventy 7th grade students in four classrooms (one high- and one low-achieving class in both the SBI and control conditions) participated in the study. Results indicate a significant treatment by achievement level interaction, such that SBI had a greater impact on high-achieving students' problem solving scores. However, findings did not support transfer effects of SBI for high-achieving students. Implications for improving the problem-solving performance of low achievers are discussed.  相似文献   

3.
In Singapore, 6–12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13–17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is correlated with the ability to inhibit intrusions from the earlier arithmetic strategies. Similar to typical school practice in Singapore, we asked 14 year-old students (N = 157) to use only letter-symbolic algebra to solve 9 algebra word problems. After having controlled for algebraic knowledge, working memory, and intelligence, better inhibitory ability still predicted fewer arithmetic intrusions and higher problem solving accuracy. Path analysis revealed 2 types of inhibition. Inhibition-of-reified-processes predicted accuracy through arithmetic intrusions. Inhibition-of-recently-learned-associations predicted accuracy through intelligence. Findings suggest establishing pedagogical links between arithmetic and algebraic methods may facilitate students' transition to letter-symbolic algebra.  相似文献   

4.
Background:?Cooperative learning may help students elaborate upon problem information through interpersonal discourse, and this may provoke a higher level of thinking. Interaction stimulates students to put forward and order their thoughts, and to understand the ideas or questions of their peer learner. However, partner gender is an important variable in cooperative learning. Previous research indicates that female students profit less than male students from mixed-gender cooperative learning in physics, especially where problem-solving is involved. Female and male students have different communication styles. For example, male students tend to give their opinions and explanations directly, while females tend to avoid presenting their opinion and are more likely to initiate cooperative problem-solving by asking questions.

Purpose:?The main aim of this study was to ascertain whether partner gender influences female students' learning to solve science problems and the role female communication style plays in the cooperative learning process.

Sample:?A total of 62 high schools students (31 female, 31 male) from three schools in the Netherlands participated in the study. Students were selected from three physics classes in grade 10, with a mean age of 15.6. Students came from various family backgrounds.

Design and methods:?An experiment was carried out to test the effect of group composition on female and male students' cooperative problem-solving in science. The students were randomly assigned to dyads and three research conditions: 15 mixed-gender pairs (MG); eight female–female pairs (FF) and eight male–male pairs (MM). Students were given training in how to solve a problem as a team, and how to complete the answer sheet. All students solved the same problems in four 50-minute sessions. In each session, students were asked to solve three new and moderately structured problems working together. Each dyad had a university student as an observer. The observer's task was to log the students' time on task and to document the interactions between the students. The observers did not interfere with the communication between the students during problem-solving.

Results:?Analyses of pre- and post-test performance revealed that female students in the MG condition did not learn to solve physics problems as well as male partners or as female students in all-female dyads. Analyses of interactive behaviours showed that female students in the MG condition devoted less time to actively seeking solutions and spent more time asking questions than their male partners.

Conclusions:?Difference in solution-seeking behaviour could explain an important part of the difference in problem-solving performance between the female and male students in this study. Female students in the all-female dyads did not differ in interactive behaviour or post-test performance from males. They had a more balanced interactive style than females in the mixed-gender dyads. Suggestions for further research are discussed. It would be interesting to examine if the findings of this study carried over to areas in which females are traditionally more comfortable, such as biology.  相似文献   

5.
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   

6.
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7.
This study examined the effects of a research-based intervention, schema-based instruction (SBI), implemented by experienced- (taught SBI in previous study; Jitendra et al., 2015) and novice-teacher implementers (taught SBI for the first time with professional development) on the mathematics outcomes of seventh-grade students. SBI is a multicomponent intervention that emphasizes the mathematical structure of problems through the use of schematic diagrams and incorporates problem solving and metacognitive strategy instruction. Results indicated that both experienced- and novice-teacher implementers delivered SBI with similar levels of fidelity; there was no SBI experience effect on the immediate and 10-week retention tests of proportional problem-solving, on a general measure of problem solving, or on the end of the year state mathematics achievement test. These results provide evidence that the effectiveness of SBI generalizes over time to different cohorts of teachers and that the impact of SBI on student mathematics outcomes is maintained over time without additional PD.  相似文献   

8.
The solving of reasoning problems in first language (L1) education can produce an understanding of language, and student autonomy in language problem solving, both of which are contemporary goals in senior high school education. The purpose of this study was to obtain a better understanding of senior high school students' knowledge of the language problem-solving process. Fifty-three 11th-grade high school students solved standard, comprehension, and linguistic reasoning problems. Before solving the problems, the participants had filled in open-ended questions inquiring about their knowledge regarding the effectiveness of a chosen problem-solving strategy. Content analysis of the responses indicated four categories and nine subcategories. The implications of the relatively few responses in the category of explicit knowledge of the language problem-solving process are discussed in the light of the changing needs of L1 students.  相似文献   

9.
If we carefully observe the spatial and temporal organization of students' pen strokes as they solve an engineering problem, can we predict their ability to achieve the correct answer? To address this question, 122 college students were asked to solve exam problems in an engineering course using a smartpen that recorded their writing as digitized timestamped pen strokes. The pen stroke data was used to compute a collection of 10 metrics characterizing various elements of problem-solving fluency including the tendency to progress down the page without revisions, the amount of time with no activity, and the frequency of constructing and using equations. The primary finding is that, on average across 13 different exam problems, these elements of problem-solving process explained 40% of the variance in scores of the correctness of the problem solution. In short, success on generating correct solutions was related to the fluency of the student's problem-solving process (i.e., working sequentially from the top to the bottom of the page, working without detours or long pauses, and working by constructing equations). This work is consistent with the idea that expertise in solving common engineering problems involves being able to treat them like routine rather than non-routine problems.  相似文献   

10.
Guided design is a systematic approach to instruction which is centered upon the learner's ability to solve open-ended problems that typify the situations he or she will experience as a professional in the field. The content is taught by self-instructional materials that have been systematically developed. The problem-solving process is taught using group projects that are designed to afford maximum utilization of the content in solving the problem presented by the case.  相似文献   

11.
Undergraduate students tend to struggle with probability in their introductory statistics course. Probability problem solving requires several steps. First, students must make sense of the probability scenario, then determine the appropriate probability rules, and finally, execute the procedures to solve the problem. With no previous exposure to probability, this presents too great a cognitive load for many students. Using worked‐out problems then transitioning to partially worked‐out problems in an introductory statistics course at a large university helped students succeed at solving probability problems. The worked‐out problems included writing prompts to encourage self‐explanation of students' thinking through studying the worked‐out examples. This paper explains the use of these instructional principles and their implementation in an introductory statistics course for non‐STEM majors, resulting in higher student achievement and understanding.  相似文献   

12.
The purpose of this study is to assess students’ conceptual learning of electricity and magnetism and examine how these conceptions, beliefs about physics, and quantitative problem-solving skills would change after peer instruction (PI). The Conceptual Survey of Electricity and Magnetism (CSEM), Colorado Learning Attitudes about Science Survey (CLASS), multiple-choice test was administered as a pre- and posttest with Solomon 4 group design to students (N  =  138) enrolled on freshman level physics course. The number of chapter taught to the students was 14. Problem-solving strategy steps were asked to students in the exam. The analyses of CSEM showed that the treatment group (g  =  0.62) obtained significantly higher conceptual learning gain than the control group (g  =  0.36). The conceptual understanding and problem-solving skills of the students on magnetism considerably enhanced when PI was conducted (37% and 20%, respectively). CLASS results for 5 subscales (conceptual understanding, applied conceptual understanding, problem solving general, problem solving confidence, and problem solving sophistication) supported the findings of CSEM.  相似文献   

13.
Knowledge representations that result from practicing problem solving can be expected to differ from knowledge representations that emerge from explicit verbalizing of principles and rules. We examined the degree to which the two types of learning improve problem-solving knowledge and verbal explanation knowledge in classroom instruction. We presented algebraic addition and multiplication problems to 153 sixth graders randomly assigned to two conditions. Students in the explicit learning condition had to verbally compare contrasted algebra problems. Students in the implicit learning condition had to generate and solve new problems. On three follow-up tests over 10 weeks, students in the explicit learning condition exhibited better problem-solving knowledge than students in the implicit learning condition, as well as some advantages in verbal concept knowledge. Implicit learning showed some advantages on not directly taught but incidentally learned aspects. Overall, this outcome favors the explicit learning of concepts. Explicit comparison fostered student performance on non-verbal and verbal measures, indicating that verbalization facilitates effective comparison.  相似文献   

14.
The purpose of this study was to explore relationships among school students' (N = 189) meaningful learning orientation, reasoning ability and acquisition of meaningful understandings of genetics topics, and ability to solve genetics problems. This research first obtained measures of students' meaningful learning orientation (meaningful and rote) and reasoning ability (preformal and formal). Students were tested before and after laboratory-based learning cycle genetics instruction using a multiple choice assessment format and an open-ended assessment format (mental model). The assessment instruments were designed to measure students' interrelated understandings of genetics and their ability to solve and interpret problems using Punnett square diagrams. Regression analyses were conducted to examine the predictive influence of meaningful learning orientation, reasoning ability, and the interaction of these variables on students' performance on the different tests. Meaningful learning orientation best predicted students' understanding of genetics interrelationships, whereas reasoning ability best predicted their achievement in solving genetics problems. The interaction of meaningful learning orientation and reasoning ability did not significantly predict students' genetics understanding or problem solving. Meaningful learning orientation best predicted students' performance on all except one of the open-ended test questions. Examination of students' mental model explanations of meiosis, Punnett square diagrams, and relationships between meiosis and the use of Punnett square diagrams revealed unique patterns in students' understandings of these topics. This research provides information for educators on students' acquisition of meaningful understandings of genetics. © 1996 John Wiley & Sons, Inc.  相似文献   

15.
Fourth graders with differing achievement records participated in a specially designed two week unit on decimal fractions. Students were encouraged to connect meaningful referents with decimal fraction symbols and use these meanings to develop procedures for adding and subtracting decimal numbers. One year later these students and a matched set of fifth graders were interviewed and given paper-and-pencil tests. Three questions were of interest: (1) Do short term changes in the processes students use to solve problems remain stable over time; (2) Do students who have been instructed in conceptually-based processes exhibit a higher level of performance one year later than their conventionally taught peers; and (3) What is the relationship between entry achievement level and the year-long effects of conceptually-based instruction? The results suggest that: (1) If students used the meanings of written symbols as a basis for solving problems immediately after instruction, they used these processes to solve problems one year later, regardless of entering achievement; (2) Compared to their conventionally taught peers, students in the lower achievement group benefitted relatively more from the conceptually-based instruction than students in the higher achievement group; (3) However, higher achieving students were more likely to exhibit use of conceptually-oriented processes one year later than the lower achieving students.  相似文献   

16.
ABSTRACT

The aim of this study was to characterise thoroughly the differences between Physics Olympiad competitors' and regular students' successes and approaches in relation to counterintuitive dynamics problems (CDPs) in order to discover some of the differences between skilled problem-solvers and those with fewer such skills. A total of 23 Physics Olympiad competitors were found by snowball sampling, while 40 regular students were selected by means of convenience sampling to participate in this study. To compare the students' solutions, we ran through six CDP of low, medium, and high difficulty. Students' responses were analysed by means of both qualitative and quantitative methods. The findings indicate that Olympians are much more successful and careful in handling CDP than regular students. On the other hand, regular students' challenges were often associated with a superficial problem-solving approach and with inadequate analysis of the problem. It can be concluded that, when compared to regular students, expert students' in-depth analysis resulted in greater successes and more efficient approaches in solving counterintuitive problems. Hence, it may be claimed that, with the use of counterintuitive problems, teaching and assessment practices may be developed to help students advance to higher hierarchical categories of problem-solving.  相似文献   

17.
《Learning and Instruction》2000,10(3):203-220
Explanations students provide themselves (self-explanations) in the course of learning or problem-solving have been shown to be positively associated with performance. However, the role self-explanation plays in problem solving has not been fully elaborated. This study aims to analyze the role of self-explanation in solving algebra word problems. We argue that self-explanation may function as verbal mediation that supports the transformation between different external representations of the problem. Our analysis of the problem solving protocols aims to illustrate this point through a multiple case studies design. Specifically we illustrate the way a particular kind of self-explanation (categorical explanation) mediates students' transformation from the sentential representation of the problem to the tabular one.  相似文献   

18.
In this study a two-sample, pre/posttest, quasi-experimental design was used to investigate the effect of explicit problem-solving instruction on high school students' conceptual understanding of physics. Eight physics classes, with a total of 145 students, were randomly assigned to either a treatment or comparison group. The four treatment classes were taught how to use an explicit problem-solving strategy, while the four comparison classes were taught how to use a textbook problem-solving strategy. Students' problem-solving performance and conceptual understanding were assessed both before and after instruction. The results indicated that the explicit strategy improved the quality and completeness of students' physics representations more than the textbook strategy, but there was no difference between the two strategies on match of equations with representations, organization, or mathematical execution. In terms of conceptual understanding, there was no overall difference between the two groups; however, there was a significant interaction between the sex of the students and group. The explicit strategy appeared to benefit female students, while the textbook strategy appeared to benefit male students. The implications of these results for physics instruction are discussed. © 1997 John Wiley & Sons, Inc. J Res Sci Teach 34: 551–570, 1997.  相似文献   

19.
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   

20.
许明明 《天津教育》2021,(11):142-143
提高学生的解题能力是初中数学教学的重点。初中数学习题灵活多变,解题方法多种多样,为促进学生解题能力更好地提升,教师会为学生讲解相关的解题思维。其中侧向思维是一种迂回思维,既能帮助学生更好地破题,又能简化解题步骤,提高解题效率,因此,教学中应结合具体例题,为学生讲解侧向思维的具体应用,给其以后的解题带来良好的指引。  相似文献   

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