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1.
Educators often use manipulatives when teaching mathematics because manipulatives are assumed to promote learning. However, research indicates that instructional variables impact the effectiveness of manipulatives. In this article, the authors consider the relations between two instructional characteristics: (a) level of instructional guidance and (b) perceptual qualities of manipulatives. Results from the randomized experiment with preschoolers (N = 72) suggest that learning is improved when instruction is conducted with high levels of instructional guidance and is impacted by the perceptual qualities of manipulatives. Perceptually rich manipulatives decreased learner performance on outcomes associated with conceptual knowledge and improved performance on transfer of learning. In addition, transfer was positively affected by perceptually rich manipulatives when low levels of instructional guidance were present. 相似文献
2.
Wang Jue Zhang Yi Hung Cheng-Yu Wang Qiyun Zheng Ying 《Educational technology research and development : ETR & D》2022,70(3):849-880
Existing computational thinking (CT) research focuses on programming in K-12 education; however, there are challenges in introducing it into the formal disciplines. Therefore, we propose the introduction of non-programming plugged learning in mathematics to develop students’ CT. The research and teaching teams collaborated to develop an instructional design for primary school students. The participants were 112 third- and fourth-grade students (aged 9–10) who took part in three rounds of experiments. In this paper, we present an iterative problem-solving process in design-based implementation research, focusing on the implementation issues that lead to the design principles in the mathematics classroom. The computational tasks, environment, tools, and practices were iteratively improved over three rounds to incorporate CT effectively into mathematics. Results from the CT questionnaire demonstrated that the new program could significantly improve students’ CT abilities and compound thinking. The results of the post-test revealed that CT, including the sub-dimensions of decomposition, algorithmic thinking, and problem-solving improved threefold compared to the pre-test between the three rounds, indicating that strengthened CT design enhanced CT perceptions. Similarly, the students’ and teacher’ interviews confirmed their positive experiences with CT. Based on empirical research, we summarize design characteristics from computational tasks, computational environment and tools, and computational practices and propose design principles. We demonstrate the potential of non-programming plugged learning for developing primary school students’ CT in mathematics.
相似文献3.
This study explored gender differences in the relationship between young people's mathematics attitudes and their perceptions
toward virtual manipulatives. Seven hundred eighty junior high school adolescents who participated in the problem-solving
activity using virtual manipulatives were selected for examination. The study found the male adolescents' views on motivation
and enjoyment of mathematics could explain many aspects of their perceptions toward virtual manipulatives. The female adolescents'
views on the importance of mathematics and freedom from fear of mathematics could explain many aspects of their perceptions
toward virtual manipulatives. However, motivation, enjoyment, and importance of mathematics were more prominent than freedom
from fear of mathematics in predicting male adolescents' perceptions toward virtual manipulatives, and freedom from fear and
importance of mathematics were more prominent than enjoyment and motivation of mathematics in predicting female adolescents'
perceptions toward virtual manipulatives. Two implications can be drawn from this study. First, teachers could provide males
with appealing problem contexts not only to be used to remove the fear of mathematics, but also to be used for enjoyment and
as motivation to see the importance of mathematics. Then male students could be encouraged to have more confirmed positive
perceptions toward virtual manipulatives when engaging in the activities of computer-based mathematics. Second, teachers could
provide females with interesting teaching activities, not only to be used for motivation and the enjoyment of mathematics,
but also to be used to remove the fear of mathematics and for experiencing the importance of mathematics. Then female students
could have positive perceptions toward virtual manipulatives when technology was integrated into the classroom to enhance
learning and to support effective mathematics teaching. 相似文献
4.
Patrick McGuire Mable B. Kinzie Daniel B. Berch 《Early Childhood Education Journal》2012,40(4):213-222
Teachers in early childhood and elementary classrooms (grades K-5) have been using ten-frames as an instructional tool to support students’ mathematics skill development for many years. Use of the similar five-frame has been limited, however, despite its apparent potential as an instructional scaffold in the early elementary grades. Due to scant evidence of teacher use and a lack of systematic research we know little to nothing about both the developmental and pedagogical implications of using five frames and related instructional manipulatives in early childhood mathematics classrooms. In this paper, we provide an overview of five-frames and specifically demonstrate ways that five-frames, if used in conjunction with concrete manipulatives, can support pre-kindergarten (pre-K) children’s development of Gelman and Gallistel’s (1978) three basic counting principles: the stable-order principle, one-to-one correspondence, and cardinality. We conclude by discussing the developmental and instructional implications of using five-frames, as well as offer a set of teaching tips designed to help teachers maximize the potential advantages of integrating five-frames in the pre-K classroom. 相似文献
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6.
Jeong-Im Choi Michael Hannafin 《Educational technology research and development : ETR & D》1997,45(3):43-55
The focus of this study was on the effects of relevance in instructional context and reasoning complexity on mathematics problem-solving
achievement, transfer, and attitude. Forty-six fifth graders participated in the five-day study. Students received either
contextualized or decontextualized instruction involving either simple or complex reasoning. Two types of achievement questions
were used, context-rich and context-poor, which required either single or multiple computational steps to solve. An interaction
was found between complexity of treatment and complexity of questions. Students who studied simple problems in decontextualized
contexts performed best on one-step questions, while students who studied complex problems in contextualized contexts performed
best on multi-step questions (p = .003). A complexity effect was also found for student attitudes toward perceived lesson
difficulty (p = .0001) as well as for perceived relevance of mathematics (p = .015). Students who studied simple problems
perceived lesson difficulty and mathematics relevance more favorably than those who studied complex problems. These findings
suggest that rich mathematical instructional contexts best support mathematics problem-solving, but simple, decontextualized
instruction yields the most favorable attitudes. 相似文献
7.
Nicole M. McNeil David H. Uttal Linda Jarvin Robert J. Sternberg 《Learning and Instruction》2009,19(2):171-184
How do concrete objects that cue real-world knowledge affect students' performance on mathematics word problems? In Experiment 1, fourth- and sixth-grade students (N = 229) solved word problems involving money. Students in the experimental condition were given bills and coins to help them solve the problems, and students in the control condition were not. Students in the experimental condition solved fewer problems correctly. Experiment 2 tested whether this effect was due to the perceptually rich nature of the materials. Fifth-grade students (N = 79) were given: perceptually rich bills and coins, bland bills and coins, or no bills and coins. Students in the perceptually rich condition made the most errors; however, their errors were least likely to be conceptual errors. Results suggest that the use of perceptually rich concrete objects conveys both advantages and disadvantages in children's performance in school mathematics. 相似文献
8.
Teaching Multistep Equations with Virtual Manipulatives to Secondary Students with Learning Disabilities 
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下载免费PDF全文 Rajiv Satsangi Rachel Hammer Anya S. Evmenova 《Learning disabilities research & practice》2018,33(2):99-111
Students with learning disabilities often struggle with the academic demands presented in secondary mathematics curricula. To combat these students’ struggles, researchers have studied various pedagogical practices and classroom technologies for teaching standards covered in subjects such as algebra and geometry. However, as the role of computer‐ and tablet‐based technologies in education grows, some areas of study, such as the use of virtual manipulatives, lack exploration. This study sought to assess the benefits of virtual manipulatives to teach secondary students with a learning disability in mathematics how to solve multistep algebraic equations. A multiple baseline design across three participants demonstrated a functional relation between the use of a virtual manipulative balance and teaching students to acquire, maintain, and generalize the skill of solving multistep algebraic equations. Results provide new evidence demonstrating virtual manipulatives as a beneficial age‐appropriate technology to teach higher order mathematical concepts to secondary students with a learning disability. 相似文献
9.
Qingli Lei Rose A. Mason Yan Ping Xin John L. Davis Marie David Catharine Lory 《Learning disabilities research & practice》2020,35(4):201-217
This single-case meta-analysis is the first to provide a quantitative synthesis of the published literature on mathematics word problem-solving intervention studies for English learners with learning disabilities and mathematics difficulties. A total of ten single-subject studies were included for analysis. The current study investigated the magnitude of the effect of mathematics interventions targeting the improvement of students’ mathematics word problem-solving performance, and analyzed variables that moderated this effect. Results indicate a moderate overall effect size of 0.81 (95% CI [0.71, 0.90]) on word problem-solving performance for English learners with learning disabilities and mathematics difficulties. Moderator variables such as the implementer of the interventions, instructional focus, and word problem-solving content significantly moderated the mathematics intervention effects. 相似文献
10.
According to cognitive load theory, using worked examples is an effective and efficient instructional strategy for initial cognitive skill acquisition for novice learners, as it reduces cognitive load and frees up cognitive resources to build task competence. Contrary to this, productive failure (as well as invention learning, desirable difficulties and other problem-solving-first) frameworks suggest that scaffolded problem-solving activities (a generation phase) preceding explicit instruction enhance learners’ performance. The reported experimental study investigated the effectiveness of different levels of instructional guidance provided to students during the learning phase preceding explicit instruction in standard solution procedures in enhancing students’ engagement and transfer problem-solving skills. Specifically, the study compared partially-guided or unguided attempts at generating problem solutions as opposed to comprehensive guidance, in the form of a worked example. Levels of experienced cognitive load and learner motivation were evaluated in addition to delayed post-test performance scores. There were no differences between the three groups on the transfer post-test outcomes, even though the condition with fully-guided worked examples prior to the explicit instruction expectedly reduced cognitive load relative to the conditions without such guidance. There were also differences between the conditions on some sub-dimensions of the motivation scale. In general, the findings indicate that similar overall outcomes (delayed transfer performance) could be achieved by different sequences of instructional tasks aimed at achieving different sets of specific goals. 相似文献
11.
Sarah Guri‐Rozenblit 《Assessment & Evaluation in Higher Education》1990,15(2):105-114
This study purported to identify major factors which influence perseverance in studies at a distance teaching university with an open admission policy. The results indicate that: students who study in organised groups and get weekly tutorials have a higher perseverance rate as compared to students who study in the regular framework which provides tutorials every three weeks; veteran students have a greater chance to complete courses successfully as compared to novice students; and the success rate in liberal arts and social science courses is considerably higher as compared to natural science and mathematics courses. On the other hand, the factors of age, sex and previous level of education do not have an impact on perseverance and success in studies. 相似文献
12.
Qiang CHENG 《Frontiers of Education in China》2014,9(4):493-518
Although teaching quality is seen as crucial in affecting students’ performance, what types of instructional practices constitute quality teaching remains a question. With the theoretical assumptions of conceptual and procedural mathematics teaching as a guide, this study examined the types of quality mathematics instructional practices that affect students’ mathematics learning across five high-performing Asian education systems using the Trends in International Mathematics and Science Study (TIMSS) 2011 dataset. It found that no combinations of the components of conceptual and procedural mathematics teaching practices exist consistently across the five education systems. Results from the study provide important implications for practitioners and policy makers regarding how to improve mathematics teaching and learning in these Asian education systems as well as elsewhere. 相似文献
13.
Nicole A. Bannister 《学习科学杂志》2015,24(3):347-372
Using a case study design and ethnographic methods, this research investigated the interactions of a group of high school mathematics teachers who collaborated daily on issues related to curricular and pedagogical reforms. The members of the collaboration team implemented these reforms with the goal of supporting all students’ learning of 1st-year college preparatory mathematics. This study used conceptual tools from frame analysis (E. Goffman, 1974) alongside an analysis of teacher participation patterns to understand teacher learning within a community of practice (E. Wenger, 1998). This analysis documented development within the teacher community through teachers increasing orientation to classroom-based interventions for struggling students alongside more collegial participation patterns, contributing an empirical example of teacher learning within a community of practice. 相似文献
14.
Alexander Renkl 《European Journal of Psychology of Education - EJPE》1999,14(4):477-488
Recent research has shown that learning from worked-out examples is of major importance for initial skill acquisition in well-structured domains such as mathematics. However, only those learners who actively process the presented examples profit noticeably from this learning mode. Specifically, the learning outcomes depend on how well the learners explain the solution steps presented in the examples to themselves (‘self-explanation effect”). In a series of studies on learning mathematics from examples, learners’ spontaneous self-explanations and instructional means used to encourage self-explanations were investigated. In this research, the following main findings were obtained. Most learners were rather passive with respect to their spontaneous self-explanations. Among the active and successful learners, two subgroups employing different self-explanation styles could be identified. With regard to the instructional means used to induce effective example processing, it turned out that to employ “learning by teaching” in order to stimulate explanation activities was of very limited use. Attempts to directly train for or elicit certain types of self-explanations were more successful. However, even in the latter case, self-explanations had inherent deficits (e.g., proneness to errors). Thus, we sought to design learning arrangements that try to integrate self-explanations with well-timed and well-adapted instructional explanations (e.g., from tutors) in order to enhance students’ problem-solving skills. 相似文献
15.
One hundred and thirty-three mathematics teachers of deaf students from grades 6-12 responded to a survey on mathematics word problem-solving practices. Half the respondents were teachers from center schools and the other half from mainstream programs. The latter group represented both integrated and self-contained classes. The findings clearly show that regardless of instructional setting, deaf students are not being sufficiently engaged in cognitively challenging word problem situations. Overall, teachers were found to focus more on practice exercises than on true problem-solving situations. They also emphasize problem features, possibly related to concerns about language and reading skills of their students, rather than analytical and thinking strategies. Consistent with these emphases, teachers gave more instructional attention to concrete visualizing strategies than to analytical strategies. Based on the results of this study, it appears that in two of the three types of educational settings, the majority of instructors teaching mathematics and word problem solving to deaf students lack adequate preparation and certification in mathematics to teach these skills. The responses of the certified mathematics teachers support the notion that preparation and certification in mathematics makes a difference in the kinds of word problem-solving challenges provided to deaf students. 相似文献
16.
ABSTRACT The purpose of the current study was to investigate students’ overall learning process during the implementation of educational escape-the-room games (EERGs) in classrooms. This study adopted a two-stage case-study methodology, namely single-case and multi-case designs. In the first stage, a well-designed EERG for a Chinese language class was developed on a web-based game platform. A total of 15 second-grade students from a public elementary school in Taiwan used tablet computers to engage in problem-solving tasks in the EERG. In the second stage, five schoolteachers from other elementary schools who had adopted similar EERGs in their classrooms in the previous academic year participated in the study to share their instructional experiences. The results indicated that students actively collaborated with their team members to address problem-solving tasks during the EERG activity. Positive collaborative learning experiences and learning attitudes towards the EERG were identified in the students’ self-reflection worksheets. 相似文献
17.
Qingmin SHI 《Frontiers of Education in China》2014,9(4):577-602
Teacher efficacy in a particular content area is seen as an important factor shaping teaching practice and student learning in the Western literature. However, inadequate efforts have been made to examine this assumption empirically. Drawing on the Trends of International Mathematics and Science Study (TIMSS) 2011 mathematics teachers’ data at the eighth grade level, this study examines the relationship between teacher efficacy in teaching mathematics and teachers’ mathematical instructional practices in five Asian countries/regions. Guided with Bandura’s social cognitive theory, this study finds that overall teachers in the five countries/regions reported much lower teacher efficacy in teaching mathematics and lower levels of instructional practices than the international norms. The relationship between teacher efficacy and instructional practices varied within these countries/regions. Teacher efficacies in teaching mathematics are not always statistically and positively related to their instructional practices in engaging students. Together, these findings challenge the theoretical assumption about the positive relationship between teacher efficacy and instructional practices. Possible reasons of these findings and future directions are discussed. 相似文献
18.
The authors investigated the degree to which school-level teacher characteristics and resources are related to the mathematics learning of kindergarten children using a sample drawn from a large US database. Kindergarten-level teacher characteristics were operationalised as collective teacher efficacy, teacher experience and teacher preparation; kindergarten resources were operationalised as efforts that schools make to reach out to parents, classrooms with mathematics manipulatives, and classroom technology. Kindergarten students learned more in mathematics over a year in schools where teachers’ collective efficacy was high. School resources yielded a range of significant yet mixed results in young children’s mathematics achievement. Notably, younger students and students entering kindergarten with lower levels of mathematical skills benefited greatly from classroom resources. Overall, the presence of classroom technology as a school-level resource was positively related with older kindergarten students’ learning. Based upon the findings, organisational and policy implications are discussed. 相似文献
19.
Investigating the mechanisms of learning from a constrained preparation for future learning activity 总被引：1，自引：0，他引：1
Many studies have shown benefits associated with engaging students in problem-solving activities prior to administering lessons. These problem-solving activities are assumed to activate relevant knowledge and allow students to develop some initial knowledge structures, which support understanding of the lesson. In this paper we report the results of two studies in which we investigated the underlying benefits of engaging in a preparatory activity—setting up experiments without running them or receiving feedback—prior to an interactive computerized lesson on experimental design compared to only engaging in the interactive lesson. We predicted that the seventh-grade participants who demonstrated some initial knowledge of the topic—experimental design—would benefit more from spending the whole time engaged in instructional activities. However, we expected students who did not demonstrate initial knowledge would benefit more from engaging in the preparatory activity, which would allow them to activate or develop initial knowledge that would aid their understanding of the subsequent instruction. The predicted condition by initial knowledge interaction was found in both studies. In Study 1, the benefit of only engaging in the instruction was found only for the lowest-knowledge of students who demonstrated initial knowledge. For students who did not demonstrate some initial knowledge, the benefit of completing the preparatory activity appeared to be due to the development of an understanding of the general goal of the activity rather than of specific knowledge of experimental design. Based on this finding, in Study 2, we investigated an initial goal by condition interaction. In fact, students who did not express an understanding of the task goal on the pretest benefited from engaging in the preparatory activity and students who did benefited more from the instruction. Again, this benefit appeared to be due to students’ development of an appropriate understanding of the task goal during the preparatory activity. 相似文献
20.
During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional activities were based on scaffolding instruction and included modelling problem solving, stimulating reflection, and giving feedback on the process of collaboration. These activities were gradually developed and implemented in collaboration with teachers who participated in the study. The main research question in this study was whether student collaboration while working in small groups creates a learning context where students work on open-ended problems and where instructional activities are aimed at stimulating collaborative problem solving in mathematics.To answer the research question, an experiment was undertaken in two classes in different schools. Two groups of students were videotaped while they tried to solve mathematics problems collaboratively. Observational data were analysed with a schema that was developed as part of this research. Analyses of the data showed that, in both groups, collaboration-oriented patterns increased during the school year. It is argued that the approach of gradual implementation of instructional activities that are designed in cooperation with participating teachers is effective in stimulating collaborative problem solving. 相似文献