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1.
Limitations to teaching children 2 + 2 = 4: typical arithmetic problems can hinder learning of mathematical equivalence 总被引：1，自引：0，他引：1
McNeil NM 《Child development》2008,79(5):1524-1537
Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7–9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __), switched lesson conditions, and solved math equivalence problems again. Correct solutions were less common following instruction with typical arithmetic problems. In a supplemental experiment, fifth graders (10–11 years old; N= 19) gave fewer correct solutions after a brief intervention on mathematical equivalence that included typical arithmetic problems. Results suggest that learning is hindered when lessons activate inappropriate existing knowledge. 相似文献
2.
Irvin R. Katz Randy Elliot Bennett Aliza E. Berger 《Journal of Educational Measurement》2000,37(1):39-57
Problem-solving strategy is frequently cited as mediating the effects of response format (multiple-choice, constructed response) on item difficulty, yet there are few direct investigations of examinee solution procedures. Fifty-five high school students solved parallel constructed response and multiple-choice items that differed only in the presence of response options. Student performance was videotaped to assess solution strategies. Strategies were categorized as "traditional"–those associated with constructed response problem solving (e.g., writing and solving algebraic equations)–or "nontraditional"–those associated with multiple-choice problem solving (e.g., estimating a potential solution). Surprisingly, participants sometimes adopted nontraditional strategies to solve constructed response items. Furthermore, differences in difficulty between response formats did not correspond to differences in strategy choice: some items showed a format effect on strategy but no effect on difficulty; other items showed the reverse. We interpret these results in light of the relative comprehension challenges posed by the two groups of items. 相似文献
3.
Nicole M. McNeil Caroline Byrd Hornburg Brianna L. Devlin Cristina Carrazza Mary O. McKeever 《Child development》2019,90(3):940-956
Experts claim that individual differences in children's formal understanding of mathematical equivalence have consequences for mathematics achievement; however, evidence is lacking. A prospective, longitudinal study was conducted with a diverse sample of 112 children from a midsized city in the Midwestern United States (Mage [second grade] = 8:1). As hypothesized, understanding of mathematical equivalence in second grade predicted mathematics achievement in third grade, even after controlling for second-grade mathematics achievement, IQ, gender, and socioeconomic status. Most children exhibited poor understanding of mathematical equivalence, but results provide clues about which children are on the path to constructing an understanding and which may need extra support to overcome their misconceptions. Findings suggest that mathematical equivalence may deserve more attention from educators. 相似文献
4.
The Differentiated Child Behavior Observational System (DCB, Ross, 1971) which provides for systematic recording of children's interactions in ongoing classroom activities, was applied in 48 classrooms with children aged five to eight. Three groups were studied: the first, representing a nontraditional, open-classroom approach was drawn from the Bank Street School for Children (middle-income); the second, with a similar approach, from Bank Street Follow Through classes in public schools (low-income); and the third, from traditional classes in public schools (low-income).The groups showed striking differences in amount of children's interactions, with significantly greater amounts in the two nontraditional groups. Analysis of the content of the interactions revealed further important differences. The Bank Street School and Bank Street Follow Through groups totalled significantly more higher-order cognitive statements and questions, and more autonomous behavior. Results indicated that although in SES background, Follow Through classes were more like the traditional classes, the interactions of the Follow Through children were more like those of the (nontraditional) Bank Street School.1 This presentation is limited to the most salient points of definition. A comprehensive listing of examples for each subcategory component is presented in the Observer's Manual.2 The incidence of such behaviors is reflected by the following mean total frequencies for the three groups: Bank Street School = 1.9, Follow Through = 10, and Comparison = 10.More recent work with the DCB can be found in Sylvia Ross, Herbert Zimilies and David Gerstein, Children's Interaction in Traditional and Nontraditional Classrooms. New York: Bank Street College of education, 1975.Notes 相似文献
5.
Children living in out-of-home care have experienced a multitude of adversities, often resulting in compromised functioning. The current study used Ontario Looking After Children (OnLAC) project data to estimate developmental trajectories of behavioral outcomes (i.e., conduct and emotional problems) over a 4-year period (i.e., ages 6–10 to 9–13) in 313 children living in out-of-home care. Predictors measured at baseline (e.g., sex) and across the subsequent 4-year period (e.g., parenting practices) were also investigated. Findings indicated that 64.2% and 58.6% followed resilient trajectories for conduct behaviors and emotional functioning, respectively. Predictors of resilient trajectories included internal developmental assets, number of children in the home, whether the child was receiving treatment, and positive parenting. Findings need to be interpreted with an understanding that children in out-of-home care have varying levels of functioning across various domains (e.g., educational, social) other than the ones measured here. Predictors were static and dynamic and cut across various contexts, emphasizing the importance of considering child functioning within an ecological model. 相似文献
6.
7.
Within mathematics education research, there has been a strong focus on students’ understanding of mathematical equivalence because of its key role in the development of mathematics skills. One of the most frequently used tools to assess students’ understanding of equivalence has been the Mathematical Equivalence Assessment (MEA) (Rittle-Johnson et al., 2011). In this study, we investigate for the first time the cross-cultural measurement invariance of an adaptation of the MEA. This included a sample (N = 2760) of students aged 8–12 years old from China, England, New Zealand, South Korea, Turkey, and US to examine whether the same construct is being measured across all countries. Configural and partial scalar invariance was established for a two-factor, 11-item version of the adapted MEA. There were significant mean differences across countries, with students from China performing better and students from New Zealand performing worse than the rest of the sample. 相似文献
8.
In mathematical word problem solving, a relatively well-established finding is that more errors are made on word problems in which the relational keyword is inconsistent instead of consistent with the required arithmetic operation. This study aimed at reducing this consistency effect. Children solved a set of compare word problems before and after receiving a verbal instruction focusing on the consistency effect (or a control verbal instruction). Additionally, we explored potential transfer of the verbal instruction to word problems containing other relational keywords (e.g., larger/smaller than) than those in the verbal instruction (e.g., more/less than). Results showed a significant pretest-to posttest reduction of the consistency effect (but also an unexpected decrement on marked consistent problems) after the experimental verbal instruction but not after the control verbal instruction. No significant effects were found regarding transfer. It is concluded that our verbal instruction was useful for reducing the consistency effect, but future research should address how this benefit can be maintained without hampering performance on marked consistent problems. 相似文献
9.
Researchers have speculated that children find it more difficult to acquire conceptual understanding of the inverse relation
between multiplication and division than that between addition and subtraction. We reviewed research on children and adults’
use of shortcut procedures that make use of the inverse relation on two kinds of problems: inversion problems (e.g., 9 ×24 ?24 {9} \times {24} \div {24} ) and associativity problems (e.g., 9 ×24 ?8 {9} \times {24} \div {8} ). Both can be solved more easily if the division of the second and third numbers is performed before the multiplication of
the first and second numbers. The findings we reviewed suggest that understanding and use of the inverse relation between
multiplication and division develops relatively slowly and is difficult for both children and adults to implement in shortcut
procedures if they are not flexible problem solvers. We use the findings to expand an existing model, highlight some similarities
and differences in solvers’ use of conceptual knowledge across operations, and discuss educational implications of the findings. 相似文献
10.
Constance A. Mara 《Journal of Experimental Education》2018,86(3):442-457
Researchers are often interested in establishing equivalence of population variances. Traditional difference-based procedures are appropriate to answer questions about differences in some statistic (e.g., variances, etc.). However, if a researcher is interested in evaluating the equivalence of population variances, it is more appropriate to use a procedure designed to determine equivalence. A simulation study was used to compare novel equivalence-based tests to traditional variance homogeneity tests under common data conditions. Results demonstrated that traditional difference-based tests assess equality of variances from the wrong perspective and that the proposed Levene-Wellek-Welch test for equivalence of group variances the best performing test for detecting equivalence. An R function is provided in order to facilitate use of this test for equivalence of population variances. 相似文献
11.
“Success stories,” i.e., cases in which mathematical problems posed in a controlled setting are perceived by the problem posers or other individuals as interesting, cognitively demanding, or surprising, are essential for understanding the nature of problem posing. This paper analyzes two success stories that occurred with individuals of different mathematical backgrounds and experience in the context of a problem-posing task known from past research as the Billiard Task. The analysis focuses on understanding the ways the participants develop their initial ideas into problems they evaluate as interesting ones. Three common traits were inferred from the participants' problem-posing actions, despite individual differences. First, the participants relied on particular sets of prototypical problems, but strived to make new problems not too similar to the prototypes. Second, exploration and problem solving were involved in posing the most interesting problems. Third, the participants' problem posing involved similar stages: warming-up, searching for an interesting mathematical phenomenon, hiding the problem-posing process in the problem's formulation, and reviewing. The paper concludes with remarks about possible implications of the findings for research and practice. 相似文献
12.
Sarah M. Bonner 《Journal of Experimental Education》2013,81(3):409-428
Although test scores from similar tests in multiple choice and constructed response formats are highly correlated, equivalence in rankings may mask differences in substantive strategy use. The author used an experimental design and participant think-alouds to explore cognitive processes in mathematical problem solving among undergraduate examinees (N = 64). The study examined the effect of format on mathematics performance and strategy use for male and female examinees given stem-equivalent items. A statistically significant main effect of format on performance was found, with constructed-response items more difficult. The multiple-choice format was associated with more varied strategies, backward strategies, and guessing. Format was found to moderate the effect of problem conceptualization on performance. Results suggest that while for purposes of ranking students on performance, the multiple-choice format may be adequate, for many contemporary educational purposes that seek to provide nuanced information about student cognition, the constructed response format should be preferred. 相似文献
13.
Héctor H. Rivera Hersh C. Waxman 《Journal of Education for Students Placed at Risk》2013,18(3):185-200
This study examines resilient and nonresilient characteristics in mathematics among Hispanic students in a major metropolitan city located in the south central region of the United States. The study examined data from semistructure interviews of 118 resilient and nonresilient English language learners (ELLs) in 4th and 5th grade. The interviews focused on a variety of factors including: (a) individual attributes (e.g., students’ motivation); (b) school and classroom factors (e.g., satisfaction, involvement, and affiliation); (c) family factors (e.g., parent involvement in academics); and (d) students’ use of time (e.g., doing homework). Additional indicators that were examined include help-seeking behaviors and skills that allow students to cope with academic difficulties. Overall, the findings indicate significant differences between resilient and nonresilient students on academic performance and their self-efficacy on perceived mathematical abilities. Significant differences were also found in the home learning environment, indicating that resilient students receive more assistance at home on academic tasks than non-resilient students. 相似文献
14.
Three Wechsler scales (the Wechsler Adult Intelligence Scale, Wechsler Intelligence Scale for Children, and Wechsler-Bellevue II) were administered in a counterbalanced design to 72 randomly selected 17 year-old high school Ss in order to investigate their comparability by testing the equality of ( a ) means, ( b ) variances, ( c ) reliability coefficients, and ( d ) validity coefficients based on scaled scores and IQs. Results indicated that the subtest scores and IQs for the given three scales were not equivalent. The present findings conform with most of the previous results regarding the comparability of Wechsler scales. Although the three scales investigated all evidence high similarity of item content and format, they clearly fail to meet the statistical criteria of equivalence for 17 year-old subjects. 相似文献
15.
Children's knowledge of concrete versions of additive composition, commutativity and associativity was investigated in two studies. In Study 1, 24 four- to five-year-olds and 25 five- to six-year-olds judged the equivalence of conceptually related addition problems presented using groups of objects. In Study 2, 45 five- to six-year-olds judged related problems and solved addition problems. Both studies indicated that concrete versions of principles were salient to most children although associativity was more difficult than commutativity and there were considerable individual differences in children's understanding. Study 1 results indicated that schoolchildren were more accurate at recognising additive composition than preschoolers and Study 2 results suggested that commutativity knowledge was related to using advanced counting strategies for solving addition problems. Overall, the research supports the claim that examining early knowledge of addition principles provides important insights into children's emerging part-whole knowledge and mathematical development. 相似文献
16.
It has been shown previously that many students solve chemistry problems using only algorithmic strategies and do not understand the chemical concepts on which the problems are based. It is plausible to suggest that if the information is presented in differing formats, the cognitive demand of a problem changes. The main objective of this study is to investigate the degree to which cognitive variables, such as developmental level, mental capacity, and disembedding ability explain student performance on problems which: (1) could be addressed by algorithms or (2) require conceptual understanding. All conceptual problems used in this study were based on a figurative format. The results obtained show that in all four problems requiring algorithmic strategies, developmental level of the students is the best predictor of success. This could be attributed to the fact that these are basically computational problems, requiring mathematical transformations. Although all three problems requiring conceptual understanding had an important aspect in common (the figurative format), in all three the best predictor of success is a different cognitive variable. It was concluded that: (1) the ability to solve computational problems (based on algorithms) is not the major factor in predicting success in solving problems that require conceptual understanding; (2) solving problems based on algorithmic strategies requires formal operational reasoning to a certain degree; and (3) student difficulty in solving problems that require conceptual understanding could be attributed to different cognitive variables. 相似文献
17.
Billie M. Cunningham 《Community College Journal of Research & Practice》2013,37(3):317-325
As the knowledge base in all disciplines continues to grow, professors face the problem of incorporating even more essential, difficult, technical material into their already content‐filled courses. Furthermore, companies are hiring more selectively than ever, requiring not only superior technical skills but also good writing skills of the people they hire. How can faculty add more technical material plus extra writing practice into already bulging courses? One solution may be to supplement typical homework problems with daily written journals. In using these journals, the students would think about and better understand difficult concepts that are not being fully understood through homework problems. Also, a byproduct of writing in daily journals would be extra writing practice and, presumably, better writing skills. The purpose of this paper is to describe the results of research done in the Collin County Community College District in which four Principles of Accounting classes were used in an experiment involving writing to learn. Two classes were conducted in the traditional accounting class format in which student participation was through homework problems. The other two classes also wrote in daily journals, using a few minutes of class time to individually summarize difficult concepts presented during that class. Final grades and attrition rates of the experimental groups were compared at the end of the semester with promising results. 相似文献
18.
Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The integrated theory of numerical development posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of the magnitudes to which they refer, and this magnitude understanding is central to general mathematical competence. We investigated relations among fraction magnitude understanding, arithmetic and general mathematical abilities in countries differing in educational practices: U.S., China and Belgium. Despite country-specific differences in absolute level of fraction knowledge, 6th and 8th graders' fraction magnitude understanding was positively related to their general mathematical achievement in all countries, and this relation remained significant after controlling for fraction arithmetic knowledge in almost all combinations of country and age group. These findings suggest that instructional interventions should target learners' interpretation of fractions as magnitudes, e.g., by practicing translating fractions into positions on number lines. 相似文献
19.
Louis Oppenheimer Adri Stet Eddie Versteeg 《European Journal of Psychology of Education - EJPE》1986,1(3):93-102
In total 131 children from fourth- and sixth-grades (mean ages 9.10 and 11.9 years) participated in this study with as its purpose to explore the relationships among conceptions of control and autonomy and various personality characteristics. To achieve this aim, the children were presented with questionnaires indexing their conceptions of control (CCQ), conceptions of autonomy (CAQ) and two diagnostic instruments: 1) the Amsterdam Biographical Questionnaire for Children (ABVK) and 2) the Achievement Motivation Test for Children (PMTK). The results reveal complex patterns of interrelated variables, indicating among others that children's conceived ability to cope with problems in the social environment does not relate to children's understanding of the variables affecting the outcomes of their behavior. 相似文献
20.
Young Children's Understanding of the Mind-Body Distinction 总被引：3，自引：0，他引：3
4 experiments investigated children's understanding of the mind-body distinction. Children of ages 4 and 5 recognized not only the differential modifiability of changeable versus unchangeable human properties and bodily versus mental properties, but also the independence of activities of bodily organs from a person's intention (Experiment 1). When presented 3 types of causal explanations (i.e., intentional, vitalistic, mechanical), 6-year-olds chose most often as most plausible for bodily functions vitalistic explanations (i.e., those ascribing the phenomena to a relevant bodily organ's initiative and effortful engagement in activity); 8-year-olds chose the vitalistic explanations second most often, following mechanical ones (Experiment 2). However, 6-year-olds, as well as 8-year-olds and adults, did not always choose vitalistic explanations over intentional explanations (Experiment 3); whereas they tended to prefer vitalistic explanations for biological phenomena, they predominantly accepted intentional ones for psychological phenomena (Experiment 3A). These results suggest that children as young as 6 years of age have acquired a form of biology as an autonomous domain which is separate from that of psychology. 相似文献