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1.
Effects of consistency and adequacy of language information on understanding elementary mathematics word problems 总被引：3，自引：0，他引：3
Two types of elementary mathematics word problems involving different linguistic structures were devised to examine the understanding
and solution of these problems by 91 Grade 3, 4, and 5 children divided into “more able” and “less able” subgroups. One task
consisted of 12 consistent and 12 inconsistent language problems on the basic processes of addition, subtraction, multiplication
and division. Another task consisted of a total of 36 word problems with 12 items each containing adequate, inadequate, and
redundant information, respectively, for problem solution. Subsidiary tasks of general ability, vocabulary, reading comprehension,
mathematics concepts, reflection on mathematics learning, and working memory were also administered to provide estimates of
the contribution of these “nonmathematics” tasks to the solution of elementary mathematics problems. Analyses of variance
and covariance of group data showed significant main effects of grade, consistency, and adequacy of linguistic information
in problem solution. Word problems containing inconsistent information were more difficult than those with consistent information.
Further, word problems containing inadequate and redundant information were more difficult to classify, and for the children
to explain, than those items with just enough information. Interviews with 12 individual children provided further insight
into their strategies for problem solutions. Both cognitive and developmental perspectives are important for mathematics learning
and teaching for children with or without learning disabilities. 相似文献
2.
The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students?? knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment involved five experimental and six control classes (N?=?106 and 138, respectively) of third-grade students. The experiment comprised 20 lessons with 73 word problems, providing a systematic overview of the basic word problem types. Teachers of the experimental classes received a booklet containing lesson plans and overhead transparencies with different types of visual representations attached to the word problems. Students themselves were invited to make drawings for each task, and group work and teacher-led discussion shaped their beliefs about the role of visual representations in word problem solving. The effect sizes of the experiment were calculated from the results of two tests: an arithmetic skill and a word problem test, and the unbiased estimates for Cohen??s d proved to be 0.20 and 0.62. There were significant changes also in experimental group students?? beliefs about mathematics. The experiment pointed to the possibility, feasibility, and importance of learning about visual representations in mathematical word problem solving as early as in grade?3 (around age 9?C10). 相似文献
3.
van Garderen D 《Journal of learning disabilities》2007,40(6):540-553
This study examined the effectiveness of instruction focused on teaching students with learning disabilities (LD) to solve 1- and 2-step word problems of varying types. Three students with LD in Grade 8 participated in the study. During the treatment, students received instruction in diagram generation and a strategy that incorporates diagrams as a part of the procedure to solve word problems. The results indicated that all students improved in the number of diagrams they used and in their ability to generate diagrams. Their word problem solving performance increased. Moreover, the students generated and used diagrams to solve other types of problems. Overall, the students were very satisfied with the instruction and would continue to use the diagrams and the strategy to solve word problems in other classroom settings. 相似文献
4.
Esther Ziegler Peter A. Edelsbrunner Elsbeth Stern 《Educational Psychology Review》2018,30(2):531-558
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
5.
加强培养学生的数学建模能力具有十分重要的意义.在高职数学教学中溶入数学建模思想,有利于提高学生的学习兴趣,提高教学效果,促进教学方式的创新.数学建模思想在高职数学教学中的应用:用“数学的抽象性”特征,启发学生对数学公式、定义的理解与认识;用“数学的普遍性”特征,启发学生思考所遇到的实际问题;运用高等数学中的“变换观点”,培养学生联想能力. 相似文献
6.
Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had little application to errors in word problems. Using an error analysis approach, this study aimed to investigate in depth the various types and frequency of errors made by students with LD and their AA peers during math problem solving. The resulting similarities and differences between the two groups of students are discussed with insight into underlying cognitive processes, and implications for future research. 相似文献
7.
The present study examined the possibility that spelling fulfils a self‐teaching function in the acquisition of orthographic knowledge because, like decoding, it requires close attention to letter order and identity as well as to word‐specific spelling–sound mapping. We hypothesised that: (i) spelling would lead to significant (i.e. above‐chance) levels of orthographic learning; (ii) spelling would actually result in superior learning relative to reading owing to the additional processing demands invoked when spelling; (iii) there would be stronger outcomes for post‐test spelling production compared with spelling recognition; and (iv) relative to reading, spelling would produce superior orthographic learning in the case of later‐occurring orthographic detail compared with information appearing earlier in the letter string. In a fully within‐subjects design, third grade Hebrew readers were exposed to novel letter strings presented in three conditions: spelling, reading and an unseen control condition. With the exception of the position by condition interaction (our fourth hypothesis), which, although in the expected direction, failed to attain significance, all hypotheses were supported. These data highlight yet another dimension of reading–writing reciprocity by suggesting that spelling offers a powerful self‐teaching tool in the compilation of word‐specific orthographic representations. 相似文献
8.
9.
Charles Perfetti 《Scientific Studies of Reading》2013,17(4):357-383
The lexical quality hypothesis (LQH) claims that variation in the quality of word representations has consequences for reading skill, including comprehension. High lexical quality includes well-specified and partly redundant representations of form (orthography and phonology) and flexible representations of meaning, allowing for rapid and reliable meaning retrieval. Low-quality representations lead to specific word-related problems in comprehension. Six lines of research on adult readers demonstrate some of the implications of the LQH. First, large-scale correlational results show the general interdependence of comprehension and lexical skill while identifying disassociations that allow focus on comprehension-specific skill. Second, word-level semantic processing studies show comprehension skill differences in the time course of form-meaning confusions. Studies of rare vocabulary learning using event-related potentials (ERPs) show that, third, skilled comprehenders learn new words more effectively and show stronger ERP indicators for memory of the word learning event and, fourth, suggest skill differences in the stability of orthographic representations. Fifth, ERP markers show comprehension skill differences in meaning processing of ordinary words. Finally, in text reading, ERP results demonstrate momentary difficulties for low-skill comprehenders in integrating a word with the prior text. The studies provide evidence that word-level knowledge has consequences for word meaning processes in comprehension. 相似文献
10.
Rajiv Satsangi Rachel Hammer Christina D. Hogan 《Learning disabilities research & practice》2019,34(1):35-46
As classrooms begin to adopt a greater number of digital technologies such as computers and tablets, it is important for educators to understand how effective such tools can be in aiding in the delivery of instruction to students who struggle in mathematics, such as those identified with a learning disability in mathematics. One digital‐based instructional strategy with a limited research base for students with a learning disability is video modeling. Through a single subject alternating treatments design, this study compared the use of video modeling to face‐to‐face explicit instruction for teaching geometry word problems to three secondary students with a learning disability in mathematics. Across 10 sessions of intervention, all three students demonstrated improved performance on all dependent variables with both interventions, while the explicit instruction condition produced slightly greater accuracy scores for two of the three students. The results and their implications for the field of mathematics are discussed. 相似文献
11.
“几何画板”在数学解题变式中的应用和体现 总被引：1，自引：0，他引：1
为了揭示问题的本质和规律,人们可以从不同侧面对数学题目进行研究。这就用到解题变式的三种形式：一题多解、一题多变和多题归一。作为一种现代教育技术手段,“几何画板”具有追踪轨迹、实时计算等功能,因此,为了降低认知负荷,它可以用以实施解题变式。同时,在数学解题变式中应用“几何画板”,能够增加学生的内在驱动力和学习主动性,能够培养学生的学习兴趣和创新能力。 相似文献
12.
Andreja Istenic Starcic Mara Cotic Matej Zajc 《British journal of educational technology : journal of the Council for Educational Technology》2013,44(5):729-744
This design‐based research study was conducted to identify what importance of a tangible user interface (TUI) can add to teaching and learning. Over a 2‐year period, teachers (n = 39) and students (n = 145) participated in the study. The identified problem for investigation was how students, including those with low fine motor skills and those with learning difficulties, develop geometry concepts combining cognitive and physical activity. A didactical application was designed during the first iteration and implemented in inclusive classrooms during the second and third iterations. Qualitative research methods were applied. A relationship between diverse students’ needs and geometry concept learning in relation to computer‐supported learning by TUI was discovered. Two dimensions were identified: (1) TUIs support concept development, with physical and virtual representations based on dynamic geometry assisted by TUI; (2) TUI manipulative properties support students who have low motor skills and difficulties in their geometry learning as well as in their inclusion in classroom activities. The study outcomes contributed to the design process of the TUI didactical application and its implementation in inclusive classrooms, and to the body of knowledge in teaching and learning geometry concepts applied for computer‐assisted learning environments supported by TUI. 相似文献
13.
Sarah R. Powell 《Learning disabilities research & practice》2011,26(2):94-108
Solving word problems is a difficult task for students at‐risk for or with learning disabilities (LD). One instructional approach that has emerged as a valid method for helping students at‐risk for or with LD to become more proficient at word‐problem solving is using schemas. A schema is a framework for solving a problem. With a schema, students are taught to recognize problems as falling within word‐problem types and to apply a problem solution method that matches that problem type. This review highlights two schema approaches for second‐ and third‐grade students at‐risk for or with LD: schema‐based instruction and schema‐broadening instruction. A total of 12 schema studies were reviewed and synthesized. Both types of schema approaches enhanced the word‐problem skill of students at‐risk for or with LD. Based on the review, suggestions are provided for incorporating word‐problem instruction using schemas. 相似文献
14.
Torulf Palm 《Educational Studies in Mathematics》2008,67(1):37-58
The study presented in this paper seeks to investigate the impact of authenticity on the students’ disposition to make necessary
real world considerations in their word problem solving. The aim is also to gather information about the extent to which different
reasons for the students’ behaviors are responsible for not providing solutions that are consistent with the ‘real’ situations
described in the word problems. The study includes both written solutions to word problems and interview data from 161 5th
graders. The results show an impact of authenticity on both the presence of ‘real life’ considerations in the solution process
and on the proportion of written solutions that were really affected by these considerations. The students’ frequent use of
superficial solution strategies and their beliefs about mathematical word problem solving were found to be the main reasons
for providing solutions that are inconsistent with the situations described in the word problems. 相似文献
15.
林 《金华职业技术学院学报》2011,11(3):27-30
为了消除学生学习单片机的惧怕心理,课程组运用行动导向教学法对＂微控制器应用＂课程做了深入的改革实践,精心设计了教学项目,采用单人作业四步法教学。在教学实践过程中,存在教师和学生的交流不够,学生的参与度不高等不足之处,可以通过分阶段总结与归纳、个人考核为主、小组考核为辅等进行改进。 相似文献
16.
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
17.
The present study used multiple calibration indices to capture the complex picture of fifth graders' calibration of feeling of confidence in mathematics. Specifically, the effects of gender, type of mathematical problem, instruction method, and time of measurement (before and after problem solving) on calibration skills were investigated. Fourteen classes (N = 389 fifth graders) were randomly selected from two school mathematics programs, namely the gradual program design and the realistic program design. Students completed two different types of mathematical problems (a set of computation problems and a set of application problems) and reported their feeling of confidence (that they would find the right solution) when first reading the problem statement and again after they had produced the solution of each of the problems. Students' calibration skills were measured using three indices of calibration. Effects on the calibration of feeling of confidence due to gender, instruction method, type of mathematical problem, and time of measurement were found and are discussed. 相似文献
18.
This study examined the role of verbal counting skill as an early predictor of math performance and difficulties (at or below −1.5 standard deviation in basic math skills) in middle school. The role of fourth-grade level arithmetical skills (i.e., calculation fluency, multi-digit arithmetic i.e. procedural calculation, and word problem solving) as mediators was also investigated. The participants included 207 children in central Finland who were studied from kindergarten to the seventh grade. Path modeling showed that verbal counting in kindergarten is a strong predictor for basic math performance in seventh grade, explaining even 52% of the variance in these skills after controlling for the mothers’ education levels. This association between early verbal counting skill and basic math performance was partly mediated through fourth-grade procedural calculation and word problem solving skills. Furthermore, verbal counting had an unique predictive relation to middle school math performance above and beyond the basic arithmetical and problem solving skills in fourth grade. Poor kindergarten verbal counting skill was a significant indicator for later difficulties in mathematics. 相似文献
19.
This study explored the effectiveness of external representations presented together with compare word problems, and whether such effectiveness was moderated by working memory. Participants were 49 secondary school students. Each participant solved 48 problems presented in 4 presentation types that included 2 difficulty treatments (number of steps and language consistency). Data from errors and response times indicated that adding a graph to compare word problems helped accuracy (d =.60) and response time (d =.44). This effect was larger for difficult and cognitively demanding problems. Findings suggest that external representations might help problem-solvers build a mental model of the described problem situation. In addition, working memory was not found to moderate the effectiveness of external representations. 相似文献
20.
顾文 《上海师范大学学报(哲学社会科学版)》2010,(5):129-132
文章首先讨论在新授课中引入问题解决教学的价值,并基于校本实践的多个教学案例,分析小学数学新授课常用的问题设计策略和教学引导策略,即基于新知识设计多元开放的探究问题、引导学生灵活利用已有知识去解决新问题等,最后,对小学数学新授课中的问题解决教学进行初步定义。 相似文献