共查询到20条相似文献，搜索用时 15 毫秒
1.
The importance of students’ problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students’ mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students’ mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students’ mathematical content knowledge and their problem-posing abilities in mathematics. 相似文献
2.
“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
3.
Blatto-Vallee G Kelly RR Gaustad MG Porter J Fonzi J 《Journal of deaf studies and deaf education》2007,12(4):432-448
This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers. 相似文献
4.
Field dependence/independence cognitive style was found to relate to general academic achievement and specific areas of mathematics; in the majority of studies, field-independent students were found to be superior to field-dependent students. The present study investigated the relationship between field dependence/independence cognitive style and problem-posing ability among sixth grade students. The 94 students’ sample was clustered into three groups, according to the cognitive-style field dependence/independence (field dependents, field mixed and field independents). The results suggest that field-independent participants outperformed field-mixed and field-dependent ones in both problem-posing ability and the complexity of the problems posed. It was also found that the content of the task influenced the differences between the three groups of students as regards the ability in problem posing and the complexity of the problems posed; while in the first (informal context), second and fourth task differences were found between the groups, in the third task (formal context), no differences were evident. The results are interpreted in consideration to the relevant literature findings. Some educational implications are discussed and directions for future research are drawn. 相似文献
5.
Derek W. Haylock 《Educational Studies in Mathematics》1987,18(1):59-74
In spite of the neglect of the study of creativity specifically within the subject of school mathematics, the notion of creativity is apparently considered by many mathematical educators to be relevant and important in terms of children doing mathematics. Some of the research and literature associated with creativity in school mathematics, mainly from English speaking countries, is reviewed. Particular attention is given to attempts to assess creative ability in school mathematics. Two key aspects emerge: the ability to overcome fixations in mathematical problem-solving, and the ability for divergent production within mathematical situations. It is proposed that these might form the basis for a framework for fostering and rewarding mathematical creativity in schoolchildren. 相似文献
6.
Nerida F. Ellerton 《Educational Studies in Mathematics》2013,83(1):87-101
Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs are a good place to start the process of redesigning mathematics curricula so that school mathematics will pay more than lip service to problem posing. Data are presented and analyzed showing that teacher education students can recognize the need for problem posing both in their own programs and in school mathematics curricula. Examples of problems posed by teacher education students are presented and discussed. An active learning framework for interpreting the role of problem posing in mathematics classrooms is presented. 相似文献
7.
Responding to mathematical problems is a core activity in classrooms. The problems that teachers select determine the mathematical content, processes and nature of mathematical inquiry occurring in classrooms and thereby contribute to the development of mathematical skills and dispositions. Selecting, designing or reformulating mathematical problems is a critical skill, then, for prospective and practising teachers. This study explores the influence of a mathematical letter writing initiative in developing the problem posing skills of 28 prospective primary teachers. We examine the characteristics of mathematical problems designed by prospective teachers, and their understandings of what constitutes a good mathematical problem, prior to and following completion of a 12-week letter writing initiative with 10–11-year-old children. Analysis of the data reveals the benefits of engaging in the initiative as evidenced in improvements in several problem characteristics. There was an increase in the number of multiple approach and multiple solution problems and in the level of cognitive demand of problems posed. The challenge of posing non-traditional problems, alongside the competing demands of building in opportunities for success, may have diminished participants’ ability to evaluate and attend to the cognitive demand of problems.
相似文献8.
The reflective ability in mathematics is a highly individual mental process, which is engaged in the course of certain types
of mathematics activity. This article describes the basic meaning, characteristics, and developmental features of reflectivity
in mathematics. It is suggested that reflective ability in mathematics and its relations with other mathematical abilities
helps improve students’ long term mathematical and creative capacities. The authors develop a trial reflective component to
high school mathematics education in order to determine the degree of short-term mathematics improvement measured by examination
success, as well as long-term benefits to the student, thus promoting mathematics curriculum reform. 相似文献
9.
What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems 总被引：1，自引：0，他引：1
School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical
problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics
education reform vision that seeks to promote mathematics as an worthy intellectual activity. In this study, the authors explored
the problem-posing behavior of elementary prospective teachers, which entailed analyzing the kinds of problems they posed
as a result of two interventions. The interventions were designed to probe the effects of (a) exploration of a mathematical
situation as a precursor to mathematical problem posing, and (b) development of aesthetic criteria to judge the mathematical
quality of the problems posed. Results show that both interventions led to improved problem posing and mathematically richer
understandings of what makes a problem ‘good.’ 相似文献
10.
《Learning and Instruction》2006,16(1):12-25
This paper focuses on the role of evaluation in mathematics in 749 elementary school children. The macroevaluative skills and calibration scores of high versus low mathematical problem solvers were contrasted as measures of metacognition. No relevant calibration differences were found for gender. In addition, the performances of children with mathematics learning disabilities could not be explained according to the maturational lag hypothesis. Finally, although macrometacognitive evaluation and calibration seem attractive alternatives for time-consuming on-line metacognitive assessment techniques, our data show that a global and retrospective assessment of the macroevaluation is not always enough to get the picture of mathematical problem solving in young children. 相似文献
11.
12.
Jinfa Cai Chunlian Jiang 《International Journal of Science and Mathematics Education》2017,15(8):1521-1540
This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People’s Education Press in China over 3 decades. Study 2 compared the PP tasks in Chinese and US elementary mathematics textbooks. This allows for the examination of PP tasks from an international comparative perspective, which provides one point of view about the kinds of learning opportunities that are available to students in China and the USA. We found evidence that the inclusion of PP tasks in the Chinese textbook series reflected, to some degree, changes in the curricular frameworks in China. However, the distribution of PP tasks across grade levels and content areas, as well as the variety of types of PP tasks included, suggest a need for greater intentionality in the design and placement of PP tasks in both the Chinese and US textbook series. Findings from the 2 studies reported in this paper not only contribute to our understanding about the inclusion of PP tasks in curriculum both historically and internationally, but also suggest a great need to systematically integrate PP activities into curriculum and instruction. The fact that both Chinese and US curriculum standards have heavily emphasized PP in school mathematics, despite there being only a small proportion of PP activities in both Chinese and US elementary mathematics curricula, suggests the existence of challenges that are delaying the implementation of reform ideas such as problem posing in school mathematics. 相似文献
13.
This study considers the potential for advanced mathematical studies to impact pre-service teachers' beliefs about mathematics. Results show that, after completing a degree which includes advanced mathematical studies, many prospective teachers' beliefs still reflect limited interpretations of key terminology and do not value the theoretical and conceptual network underpinning the rules and procedures of secondary mathematics. Many of their beliefs about the nature of mathematics also fail to recognise its capacity to stimulate analytical thought and creativity. In cases where pre-service teachers showed evidence of well-developed beliefs, the study explores the role of their advanced mathematical studies in this development. 相似文献
14.
It is well established that early general language during preschool is critical for children's mathematical abilities. In an attempt to further characterize this association between language and mathematics, an increasing number of studies show that one specific type of language, namely mathematical language or the key linguistic concepts that are required for performing mathematical activities, is even more critical to children's mathematical abilities. The purpose of this systematic review is to summarize the evidence on mathematical language and mathematical abilities. We focus on preschool children as nearly all of the existing work has been done at this age. We first explain how mathematical language has been defined across studies, and report how it has been evaluated in studies in preschool. Next, we present the results of our systematic review. Following the PRISMA guidelines and after a critical appraisal, we ended with a set of 18 papers that were all of sufficient methodological quality. In these studies, mathematical language was defined as terms that are about numbers and operations on numbers (e.g., nine), but also included linguistic terms that do not directly refer to numbers, yet are important to understand mathematical concepts (i.e., quantitative and spatial terms such as fewest and middle, respectively). Some of these studies evaluated children's performance on mathematical language tasks, while others evaluated the mathematical language input provided to the child by their (educational) environment (teachers/parents/interventionists). Mathematical language correlated positively with children's mathematical abilities, concurrently and longitudinally. It also directly affected children's mathematical abilities, as was shown by intervention studies. We discuss potential directions for future research and highlight implications for education, arguing for more support for teachers and parents to improve the use of mathematical language in the classroom and in home settings. 相似文献
15.
Our study investigates perspectives of mathematics teacher educators related to the usage of their mathematical knowledge
in teaching “Methods of Teaching Elementary Mathematics” courses. Five mathematics teacher educators, all with experience
in teaching methods courses for prospective elementary school teachers, participated in this study. In a clinical interview
setting, the participants described where and how, in their teaching of elementary methods courses, they had an opportunity
to use their advanced mathematical knowledge and provided examples of such opportunities or situations. We outline five apparently
different viewpoints and then turn to the similar concerns that were expressed by the participants. In conclusion, we connect
the individual perspectives by situating them in the context of unifying themes, both theoretical and practical. 相似文献
16.
数学教学中数学建模思想渗透 总被引：4，自引：0，他引：4
通过叙述数学建模概念与数学建模思想,结合实例,提出了在中学数学教学中渗透数学建模思想,培养学生数学建模能力的步骤和途径,以培养学生的学习兴趣,提高学生的创新意识和实践能力. 相似文献
17.
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
18.
Shuk-kwan S. Leung 《Educational Studies in Mathematics》2013,83(1):103-116
This paper reports a study about how a teacher educator shared knowledge with teachers when they worked together to implement mathematical problem posing (MPP) in the classroom. It includes feasible methods for getting practitioners to use research-based tasks aligned to the curriculum in order to encourage children to pose mathematical problems. Techniques, challenges, and strategies of implementing an MPP focus were also reported. 相似文献
19.
Gender differences in achievement in mathematics, a traditionally male-stereotyped subject, have long been a concern for many educators around the world. Gender differences in mathematical achievement have decreased in recent decades, especially in Western countries, and become small or insignificant in large-scale tests, such as the Programme for International Student Assessment (PISA). The situation in China has not yet been studied. The recent PISA report lists China B-S-J-G (representing Beijing–Shanghai–Jiangsu–Guangdong) as an educational system with no significant gender difference in mathematical achievement. Based on a secondary analysis of PISA 2015 mathematics data from China B-S-J-G, this study more deeply scrutinized gender differences in Chinese students’ mathematical performance, emphasizing societal factors, namely students’ socioeconomic status, school level, school type, school location, and socioeconomic status at school level. This analysis revealed important differences within the overall picture. Most importantly, significantly more boys than girls scored in the top tier of mathematics achievement. At the lower- and upper-secondary school levels, boys performed significantly better than girls, with the achievement difference increasing at the upper-secondary level. Furthermore, this study found that, on average, Chinese (B-S-J-G) girls achieved significantly lower average scores on the PISA 2015 mathematics test than boys in the same school. Overall, students’ individual characteristics and school characteristics need to be separated and both taken into account to examine the role of gender in mathematical achievement, which has not been thoroughly investigated in the past. 相似文献
20.
This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011–2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. Particular attention is given to the epistemological positioning of the researchers as this influenced both the curriculum design process and also the theoretical framing of the research study which are both described. The project was set up within a design research framework, which aimed to promote classroom-based action research on the part of participants through the course and also research by the university researchers into the process of curriculum development. The research questions focused on the teachers’ confidence, competence, attitudes and beliefs in relation to mathematics and their expectations and experiences of the impact on pupil learning arising from this course. Empirical data were drawn from pre- and post-course surveys, interviews and observations of the discussion forums in the online environment. Findings from this study highlight the way the course had a transformational and emancipatory impact on these teachers. They also highlight ways in which the ‘framing’ of particular aspects of the curriculum had an oppressive impact on learners in the ways that suppressed creativity and limited the exercise of learner autonomy. Furthermore, they highlight the ways in which a number of these teachers had experienced mathematics as a school subject in very negative ways, involving high levels of ‘symbolic violence’ and of being ‘labelled’. 相似文献