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1.
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
2.
Emily C. Bouck Jiyoon Park Kennedy Levy Katie Cwiakala Abbey Whorley 《Exceptionality》2020,28(1):45-59
ABSTRACTIn theory, both virtual manipulatives and explicit instruction are viable options to support students with disabilities as they learn mathematics. This study explored the effect of a treatment package—an app-based virtual manipulative (Cuisenaire® Rods) in conjunction with explicit instruction—on students’ acquisition and generalization of solving problems involving division of whole numbers with remainders. Three middle school students with disabilities participated in this multiple baseline, multiple probe across participants single case design study. Each of the students acquired the mathematical behavior of being able to solve division with remainders problems. In other words, a functional relation existed between the intervention package of explicit instruction and the Cuisenaire® Rods app-based manipulative and students’ accuracy in solving division with remainders problems. Yet, two students failed to generalize the skill without the explicit instruction and use of the app-based manipulative. 相似文献
3.
Ricardo Lopes Coelho 《Science & Education》2013,22(5):1043-1068
It is generally accepted nowadays that History and Philosophy of Science (HPS) is useful in understanding scientific concepts, theories and even some experiments. Problem-solving strategies are a significant topic, since students’ careers depend on their skill to solve problems. These are the reasons for addressing the question of whether problem solving could be improved by means of HPS. Three typical problems in introductory courses of mechanics—the inclined plane, the simple pendulum and the Atwood machine—are taken as the object of the present study. The solving strategies of these problems in the eighteenth and nineteenth century constitute the historical component of the study. Its philosophical component stems from the foundations of mechanics research literature. The use of HPS leads us to see those problems in a different way. These different ways can be tested, for which experiments are proposed. The traditional solving strategies for the incline and pendulum problems are adequate for some situations but not in general. The recourse to apparent weights in the Atwood machine problem leads us to a new insight and a solving strategy for composed Atwood machines. Educational implications also concern the development of logical thinking by means of the variety of lines of thought provided by HPS. 相似文献
4.
Jeremy Roschelle Ken Rafanan Ruchi Bhanot Gucci Estrella Bill Penuel Miguel Nussbaum Susana Claro 《Educational technology research and development : ETR & D》2010,58(4):399-419
Based on strong research literatures, we conjectured that social processing of feedback by cooperating in a small group setting—with social incentives to ask questions, give explanations and discuss disagreements—would increase learning. We compared group and individual feedback, using two technologies: (1) Technology-mediated, Peer-Assisted Learning (TechPALS), which uses wireless handheld technology to structure feedback in small groups as they solve fractions problems and (2) a popular desktop product, which provides feedback to individual students as they solve fractions problems individually. Three elementary schools participated in a randomized controlled experiment conducted in the 2007–2008 school year. Students in the TechPALS condition learned more than did the control group students, with effect sizes ranging from d = 0.14 to d = 0.44. Analysis of observational data confirmed that students in the TechPALS condition participated socially in questioning, explaining, and discussing disagreements, whereas students in the individual condition did not. We conclude that an integration of technology, cooperative activity designs and broader educational practices can lead to impact on students’ mathematics learning. 相似文献
5.
Stephanie J. Hathcock Daniel L. Dickerson Angela Eckhoff Petros Katsioloudis 《Research in Science Education》2015,45(5):727-748
Creativity can and should play a role in students’ science experiences. Beghetto (Roeper Review 29(4):265–270, 2007) suggested a framework for teachers to assist students in transforming their creative ideas into creative products. This framework involves taking time to listen to students’ ideas, helping them recognize the constraints of a task, and giving them multiple opportunities to think through and try their ideas. Ill-structured problems, such as those found in inquiry and engineering design activities, provide excellent opportunities for students to experience creative processing and express their creativity through product creation. These types of problems are typically challenging, but the use of appropriate questioning has been shown to assist students in solving problems. This multiple case study investigated the use of inquiry-based questioning as a means of supporting creativity within a design-based science, technology, engineering, and mathematics (STEM) activity. Findings suggest that groups facilitated by inquiry-based questioning strategies were better able to solve an ill-structured problem and achieved a more linear progression toward creative products than groups who were not facilitated by inquiry-based questions. 相似文献
6.
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
7.
Elena Polotskaia Annie Savard Viktor Freiman 《European Journal of Psychology of Education - EJPE》2016,31(2):135-153
According to numerous studies (Barrouillet & Camos 2002; Brousseau 1988; Chevallard 1988; Riley et al. 1984; Schubauer-Leoni & Ntamakiliro, Revue Des Sciences de L’éducation, 20(1): 87–113, 1994; Vergnaud 1982; Xin, The Journal of Educational Research, 100(6):347–360, 2007), a combination of many factors, including curriculum, didactic contract and task design, can potentially lead to students experiencing difficulties in developing of a full understanding of addition and subtraction and their relationship in problem solving. Few studies (Conne, Recheche En Didactique Des Mathématiques, 5, 269–332, 1985; DeBlois, Éducation et Francophonie, 25(1), 102–120, 1997; Giroux & Ste-Marie, European Jornal of Psychology of Education, 16(2), 141–161, 2001) describe the misinterpretations of problems as a factor related to learning difficulties. We have studied how and why elementary school students misinterpret the mathematical structure of a simple additive word problem and what kind of possible (hidden) misinterpretation may occur. We analysed possible mechanisms of misinterpretations in word problem solving, discussing various examples of correct and incorrect solutions resulting from the misinterpretation of a problem. We gave the elementary school students a word problem, which could potentially be misinterpreted, and observed their solving strategies. Our results show how the particular form of mathematical misinterpretation—structure substitution—may help students obtain a correct answer and thereby hinder the development of their mathematical reasoning. We further discuss different ways of addressing this phenomenon in teaching practice. 相似文献
8.
This study seeks to analyze how students apply a mathematical modeling skill that was previously learned by solving standard word problems to the solution of word problems with nonstandard contexts. During the course of an experiment involving 106 freshmen, we assessed how well they were able to transfer the mathematical modeling skill that is used to solve standard problems to the solution of nonstandard ones that had an analogous structure. The results of our research show that students had varying degrees of success applying the different stages of modeling depending on whether they were solving a familiar problem (involving near transfer) or one that had an unfamiliar context (involving far transfer): in cases of near transfer, students applied the template formally even though it did not align with the text of the new word problem, which complicated further interpretation. In cases of far transfer, students chose to solve the problem by using an ordinary method of selecting a solution by trial and error in preference to the use of modeling. Thus, the application of the modeling skill as a multistage process is complicated when solving nonstandard problems involving either near or far transfer. 相似文献
9.
Asha K. Jitendra Jon R. Star Kristin Starosta Jayne M. Leh Sheetal Sood Grace Caskie Cheyenne L. Hughes Toshi R. Mack 《Contemporary educational psychology》2009
The present study evaluated the effectiveness of an instructional intervention (schema-based instruction, SBI) that was designed to meet the diverse needs of middle school students by addressing the research literatures from both special education and mathematics education. Specifically, SBI emphasizes the role of the mathematical structure of problems and also provides students with a heuristic to aid and self-monitor problem solving. Further, SBI addresses well-articulated problem solving strategies and supports flexible use of the strategies based on the problem situation. One hundred forty eight seventh-grade students and their teachers participated in a 10-day intervention on learning to solve ratio and proportion word problems, with classrooms randomly assigned to SBI or a control condition. Results suggested that students in SBI treatment classes outperformed students in control classes on a problem solving measure, both at posttest and on a delayed posttest administered 4 months later. However, the two groups’ performance was comparable on a state standardized mathematics achievement test. 相似文献
10.
Kam-Wah Lee 《Research in Science Education》1986,16(1):21-30
Summary Some important results that relate to classroom learning and teaching of problem solving emerge from these case studies. These
are now summarized as follows.
In terms of the students' potential learning experiences of problem solving, it was found that the students were mainly witnessing
their teachers' demonstrations of using rules or algorithms for solution to problems. Repeated practice of solving the sorts
of problems that occur in examinations was also emphatically included as part of the learning experience. The students were
not exposed to a range of strategies that could possibly be used to solve the same problems. There was no explicit teaching
of important problem solving skills such as translation skills (comprehending, analyzing, interpreting, and defining a given
problem) and linkage skills (concept relatedness between two concepts or using cues from the problem statements to associate
ideas, concepts, diagrams, etc. from memory). When teachers solve problems they use, in general, several strategies to solve
the same class of problems and they are very careful and explicit about translating problem statements, making relevant linkages
and checking.
These absences in the teachers' teaching of problem solving (and hence in the students' range of learning experiences) are
particularly interesting because they are part of the teachers' own repertoire of skills. Accordingly, it may not be too difficult
to get teachers to include them in their teaching. This would mean that the students' range of learning experiences for problem
solving would be very much strengthened. 相似文献
11.
This study was conducted to determine which skills and concepts students have that are prerequisites for solving moles problems through the use of analog tasks. Two analogous tests with four forms of each were prepared that corresponded to a conventional moles test. The analogs used were oranges and granules of sugar. Slight variations between test items on various forms permitted comparisons that would indicate specific conceptual and mathematical difficulties that students might have in solving moles problems. Different forms of the two tests were randomly assigned to 332 high school chemistry students of five teachers in four schools in central Indiana. Comparisons of total test score, subtest scores, and the number of students answering an item correctly using appropriate t-test and chi square tests resulted in the following conclusions: (1) the size of the object makes no difference in the problem difficulty; (2) students understand the concepts of mass, volume, and particles equally well; (3) problems requiring two steps are harder than those requiring one step; (4) problems involving scientific notation are more difficult than those that do not; (5) problems involving the multiplication concept are easier than those involving the division concept; (6) problems involving the collective word “bag” are easier to solve than those using the word “billion”; (7) the use of the word “a(n)” makes the problem more difficult than using the number “1”. 相似文献
12.
Andrea Ibieta J. Enrique Hinostroza Christian Labbé 《Journal of Research on Technology in Education》2019,51(3):217-238
AbstractResearch shows that students face a range of difficulties when using the Internet to solve information problems. Using a quasi-experimental design, we tested a strategy to improve Chilean 10th graders’ skills for information problem solving using the Internet (IPS-I). The intervention was based on a workshop in which students learned IPS-I strategies and solved information problems using a customized Internet search software package. Results showed that members of the experimental group changed their search behavior and improved the quality of their products. However, no correlation between the number of search actions and product quality was found. Based on this, we highlight the potential of combining teaching strategies to improve specific search skills and the use of customized search tools with embedded functionalities that foster good search techniques. 相似文献
13.
M. Rosario Sánchez 《Cultura y Educación》2013,25(4):695-725
AbstractTextbooks are frequently used as a resource to teach children how to solve word problems in mathematics classes. The solving models explicitly proposed by textbooks, and the kind of problems they propose, can therefore have a decisive influence on the way in which students learn to solve them. This paper analyses the extent to which the problem solving models proposed by the books include reasoning as one of the steps needed to solve a problem. To do this, the processes and steps articulated in the models proposed in the books by Anaya, SM and Santillana are categorized according to data, reasoning, choice of operation, strategies, execution of operations, expression of results, checking and inventing. The results indicate that reasoning processes are hardly ever found in the models, especially in lower year courses. It is concluded that mathematical textbooks provide incomplete solving models that fail to promote reasoning. 相似文献
14.
Marina de Lima Tavares María-Pilar Jiménez-Aleixandre Eduardo F. Mortimer 《Science & Education》2010,19(6-8):573-598
The oral arguments of 12th grade students while solving tasks related to evolution are examined. Two groups (N = 45), taught by the same teacher, were studied during a complete teaching sequence. The paper focuses on data from the last sessions, devoted to solving problems in small groups, problems related to different dimensions of the evolutionary model. Data include video recordings, the students’ written productions and the researcher (first author) field notes. The objective is to examine the process of articulation of students’ argumentation practices with their use of evolutionary models. The results show that participants were able to apply notions such as common ancestors, radiation, or gradualism to different contexts. The arguments required the articulation of evolution notions with argumentative practices as coordinating evidence with claims at different epistemic levels. The influence of the teacher’s strategies in the students’ role is discussed. 相似文献
15.
16.
Strategies implemented by 12–13 year olds to solve electricity problems are examined. Three factors account for observed strategies:
- type of problem representation, itself dependent on the knowledge base;
- cognitive personality dimensions;
- form of problem statement.
- a strategy based on misconceptions such as the vanishing current model;
- a similar strategy but greater verbalization of doubt;
- rush to use formulas;
- sequential analysis of circuit;
- application of principles learned in class.
17.
Eric Kuo Nicole R. Hallinen Luke D. Conlin 《International Journal of Science Education》2013,35(7):814-839
ABSTRACTOne 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
18.
J. Anamuah-Mensah 《科学教学研究杂志》1986,23(9):759-769
The study investigated the strategies used by 47 high school students to solve volumetric analysis problems in chemistry. Using the talking-aloud technique, the students were required to calculate the concentration of hydrochloric acid used in a titration with NaOH after having performed the titration themselves. Students were met individually and their verbalization audiotaped. After making this calculation, each student was asked to use the same data to predict the concentration of acid in three situations involving different mole ratios. It was found that two main strategies, Formula Approach and Proportional Approach with their variants, were employed by the students during the problem solving process. The Formula Approach was found to be used mainly by the students in the high ability group while students in the low ability group used the Proportional Approach. It was also found that problems involving 2:1 stoichiometric ratios presented a number of conceptual problems to the students. These conceptual problems were found to be related to their inability to write balanced equations or write correct formulas, focusing on only the strength of acid, inability to use the mole ratios in the calulations and deriving the mole ratios from the formulas of reactants. 相似文献
19.
The research issue in this study is how to structure collaborative learning so that it improves solving physics problems more than individual learning. Structured collaborative learning has been compared with individual learning environments with Schoenfeld’s problem‐solving episodes. Students took a pre‐test and a post‐test and had the opportunity to solve six physics problems. Ninety‐nine students from a secondary school in Shanghai participated in the study. Students who learnt to solve problems in collaboration and students who learnt to solve problems individually with hints improved their problem‐solving skills compared with those who learnt to solve the problems individually without hints. However, it was hard to discern an extra effect for students working collaboratively with hints—although we observed these students working in a more structured way than those in the other groups. We discuss ways to further investigate effective collaborative processes for solving physics problems. 相似文献
20.
Gerald Noelting 《Educational Studies in Mathematics》1980,11(2):217-253
Two related problems have to be solved before we can have a clearer picture of cognitive development:
- Is development hierarchical, leading to higher-order systems controlling lower-order subsytems?
- If so, what are the mechanisms involved in a process of development?