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1.
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   

2.
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   

3.
Abstract

This study examined the effect of schema-based instruction (SBI) on 7th-grade students’ mathematical problem-solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a pretest-intervention–posttest-retention test design, the study compared the learning outcomes for 1,163 students in 42 classrooms who were randomly assigned to treatment (SBI) or control condition. After 6 weeks of instruction, results of multilevel modeling indicated significant differences favoring the SBI condition in proportion problem solving involving ratios/rates and percents on an immediate posttest (g = 1.24) and on a 6-week retention test (g = 1.27). No significant difference between conditions was found for a test of transfer. These results demonstrate that SBI was more effective than students’ regular mathematics instruction.  相似文献   

4.
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   

5.
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   

6.
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   

7.
This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic‐based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe across participants design, results suggested a functional relation between explicit instruction in the SOLVE strategy and increase in strategy use and computation scores on grade level mathematical word problems for all participants. Additionally, all participants generalized the SOLVE Strategy to other mathematic topics and concepts, and the teacher and students felt the intervention was socially acceptable. Finally, limitations, implications for practice, and suggestions for future research are discussed.  相似文献   

8.
Often mathematical instruction for students with disabilities, especially those with learning disabilities, includes an overabundance of instruction on mathematical computation and does not include high-quality instruction on mathematical reasoning and problem solving. In fact, it is a common misconception that students with learning disabilities are not strong problem solvers in general. This article highlights the inherent problem solving strengths that students with learning disabilities possess; how they use those skills to address everyday barriers and challenges, and how teachers can relate these skills to academic mathematical instruction. Additionally, practical classroom examples, suggested teaching strategies, and questions for further examinations are discussed.  相似文献   

9.
This study investigated the effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of six middle school students with learning disabilities. Conditions of the multiple baseline, across-subjects design included baseline, two levels of treatment, setting and temporal generalization, and retraining. For Treatment 1, subjects received either cognitive or metacognitive strategy instruction. Treatment 2 consisted of instruction in the complementary component of the instructional program so that all subjects eventually received both cognitive and metacognitive strategy instruction. This design allowed a componential analysis of the content as well as sequence of instruction. Generally, subjects improved their mathematical problem solving as measured by performance on one-, two-, and three-step word problems. Discussion focused on effectiveness of treatment, acquisition and application of strategic knowledge, error pattern analysis, and the need to tailor instruction to the learner's individual characteristics.  相似文献   

10.
This study explores the effects of the presence of external representations of a mathematical object (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric figures. Performance was evaluated according to the reaction time (RT) required for solving the problem and the accuracy of the answer. Thirty high school students studying at high and regular levels of instruction in mathematics (HL and RL) were asked to solve half of the problems with ERs and half of the problems without ERs. Each task was solved by half of the students with ERs and by half of the students without ERs. We found main effects of the representation mode with particular effect on the RT and the main effects of the level of mathematical instruction and mathematical subject with particular influence on the accuracy of students’ responses. We explain our findings using the cognitive load theory and hypothesize that these findings are associated with the different cognitive processes related to geometry and algebra.  相似文献   

11.
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   

12.
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   

13.
ABSTRACT

The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a tool to relieve teachers from the time-consuming tasks of individual diagnosis, selection of problems, and immediate feedback, they developed adaptive training software. The authors evaluated the application of the software in 2 naturalistic studies with 9 third-grade classes. Results show that even a moderate amount of individualized practice was associated with large improvements of arithmetic skills and problem solving, even after a follow-up period of 3 months.  相似文献   

14.
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15.
Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate “real‐world” knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure [Learning and Instruction, 4(4), 273–294, 1994], two studies were designed to investigate (a) Chinese elementary school children’s ability to solve realistic word problems and (b) the different effects of two instructional interventions (warning vs. process‐oriented) on their performance. The results indicated that, contrasting to the standard problem solving, the participating children demonstrated a strong tendency to exclude real‐word knowledge and realistic considerations from their solution processes when solving the realistic problems. Process‐oriented instruction, calling for a deep‐level processing, was more likely than warning instruction to promote the activation of realistic considerations, but it was not effective at helping children arrive at realistic or correct answers. Finally, the results and their implications for mathematical teaching are discussed.  相似文献   

16.
Science as inquiry and mathematics as problem solving are conjoined fraternal twins attached by their similarities but with distinct differences. Inquiry and problem solving are promoted in contemporary science and mathematics education reforms as a critical attribute of the nature of disciplines, teaching methods, and learning outcomes involving understandings, attitudes, and processes. The investigative and quantitative processes involved in scientific inquiry include seeking problems, identifying researchable questions, proposing hypotheses, designing fair tests, collecting and interpreting data as evidence for claims, constructing evidence-based arguments, and communicating knowledge claims. Within this empirical context, science and mathematics come together to solve problems with evidence, construct knowledge claims, communicate claims, and persuade others that the claims are valid and useful. This study examined the intersection of inquiry and problem solving and the use of mathematics in 26 extracurricular open science inquiries. The category and the appropriateness of the mathematical procedures revealed these students used measurement, numeracy skills of counting and calculation, and tables and graphs in their science inquiries. It was found that most measurements in the science inquiries were used appropriately, but there is room for improvement with other mathematical procedures that involve higher-level thinking skills, such as analyzing and calculating numerical data and interpreting graphs and tables. The findings imply that mathematics and science are connected in inquiry and should be extended to solve real-life problems and that instruction should emphasize comprehending and interpreting data.  相似文献   

17.
Summaries

English

We describe a systematic study of skills for solving problems in basic physics, a domain of practical significance for instruction, but not of prohibitive complexity. Our studies show that an inexperienced student tends to solve a problem by assembling individual equations. By contrast, an expert solves a problem by a process of successive refinements, first describing the main problem features by seemingly vague words or pictures, and only later considering the problem in greater detail in more mathematical language. We have formulated explicit theoretical models with such features and have supported them by some detailed observations of individuals. In addition, experimental instruction incorporating such features seems to improve problem‐solving performance significantly. These investigations yield thus some basic insights into thinking processes effective for problem‐solving. Furthermore, they offer the prospect that these insights can be used to teach students improved problem‐solving skills and to modify common teaching practices which inhibit the development of such skills.  相似文献   

18.
This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9–10 (Grade 4). The children’s text comprehension and mathematical word problem‐solving performance was tested. Technical reading skills were investigated in order to categorise participants as good or poor readers. The results showed that performance on maths word problems was strongly related to performance in reading comprehension. Fluent technical reading abilities increased the aforementioned skills. However, even after controlling for the level of technical reading involved, performance in maths word problems was still related to reading comprehension, suggesting that both of these skills require overall reasoning abilities. There were no gender differences in maths word problem‐solving performance, but the girls were better in technical reading and in reading comprehension. Parental levels of education positively predicted children’s maths word problem‐solving performance and reading comprehension skills.  相似文献   

19.
This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nature of young students’ spontaneous mathematical problem solving with technology. The empirical data comprise digital records of her approaches to two problems from a web-based mathematical competition where she resorted to GeoGebra and an interview where she explains and describes her usual problem solving activity with this tool. Based on a proposed model for describing the processes of mathematical problem solving with technologies (MPST), the main results show that this student’s solving and expressing the solution are held from the early and continuing interplay between mathematical skills and the perception of the affordances of the tool. The analytical model offers a clear picture of the type of actions that lead to the solution of each problem, revealing the student’s ability to deal with mathematics and technology in problem solving. By acknowledging this as a case of a human-with-media in solving mathematical problems, the students’ efficient way of merging technological and mathematical knowledge is portrayed in terms of her techno-mathematical fluency.  相似文献   

20.
The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and the extent to which students' language level plays a differential role in these abilities. Data from a sample of over 2,000 students from first, second, and third grade in the Netherlands were analyzed in a multidimensional item response theory (IRT) framework. The latent correlation between the two ability dimensions (computational skills and applied mathematics problem solving) ranged from .81 in grade 1 to .87 in grade 3, indicating that the ability dimensions are highly correlated but still distinct. Moreover, students' language level had differential effects on the two mathematical abilities: Effects were larger on applied problem solving than on computational skills. The implications of these findings for measurement practices in the field of elementary mathematics are discussed.  相似文献   

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