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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.
AbstractThe aim of this study is to establish to what extent teachers’ knowledge, in association with school socioeconomic level, students’ previous knowledge and level of mathematical knowledge achieved in school contribute to the knowledge that fourth-grade students reach in conceptualizing fractions. Information was obtained from 328 fourth-grade students of nine schools and their respective mathematics teachers. The results show that the 77% of variability observed in the conceptualization of fractions could be attributed to student-level variables, while the remaining 23% would be attributable to school-level variables. On the other hand, 38% of the intra-school variance could be explained by students’ previous knowledge, and virtually all the between-schools variance would be explained by the academic level of the school or, in 32% of cases, by the socioeconomic status of the school. Teacher knowledge, alone or in combination with other factors, accounts for about 10%, with a significance of 10%. 相似文献
3.
This research analyses preservice teachers’ knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students’ knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students’ understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers’ knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning. 相似文献
4.
Talking about mathematics 总被引：1，自引：0，他引：1
Gilah C. Leder 《The Australian Educational Researcher》1990,17(2):17-27
Students in a grade 3 class in a primary school in an outer suburb of Melbourne were encouraged to talk about, and ultimately reflect on, the work they had learnt in mathematics. Four lessons, each of approximately 50 minutes duration, were videotaped. Key excerpts were subsequently replayed to the children in a one-to-one setting. The data presented focussed on a lesson aimed to extend the children’s knowledge of fractions beyond a half and a quarter. By tracing the responses of four students in particular, two low and two average achievers, substantial individual differences in the ways children constructed meaning out of shared mathematical experiences were identified. The investigation confirmed that listening to students talk about their own mathematical experiences provides a rich data base for investigating students’ learning, error analysis, and subsequent teaching. 相似文献
5.
徐彦辉 《宁波大学学报(教育科学版)》2022,(5):66-072
数学理解包括三种基本形态,即:记忆性理解、解释性理解和探究性理解,这三种数学理解分别对应着“记得、晓得和明得”三种不同的状态。三种数学理解对数学学习都是有价值的,但仅有记忆性和解释性理解是不够的,探究性理解才是数学教学的最终目标。实践中,不少水平不高的教师常常只能让学生达到记忆性理解,有一定水平的教师能让学生达到解释性理解,真正让学生达到探究性理解的教师并不是很多。教师要不失时机地促进学生数学理解层级的迭代升级,促使学生最终达到探究性理解,吴文俊院士数学学习的经验对把握数学理解的三种基本形态有借鉴和启迪意义。在课堂教学中引导学生从事生动活泼的数学探索性活动常常是一个相当艰难的过程,对教师的数学探究素质提出了较高的要求,教师应努力引导学生去探求数学知识的意义和发现的过程,促使学生数学探究性理解方式的养成。 相似文献
6.
《The Journal of educational research》2012,105(6):663-675
AbstractThe purpose of this study is to examine how fifth grade students were impacted by the infusion of multiple writing tasks in mathematics. In this study, writing tasks provided opportunities for students to communicate prior knowledge, share ideas to construct and justify arguments, for reflection, and assessment. In this deductive qualitative study, students’ work samples were analyzed. Findings indicated that students grew in their understanding of mathematics and ability to self-reflect and self-evaluate through multiple opportunities to write for a variety of purposes. The opportunities for constructing mathematical understanding with activities that included writing and discourse also fostered learning between peers. The findings suggest a variety of opportunities to write and engage in mathematics discourse encouraged reflection, evaluation, and learning. Implications for future research include the need to examine the impact of these activities on students’ mathematics understanding as measured by assessments or an analysis of student work samples. 相似文献
7.
Understanding and using symbolic fractions in mathematics is critical for access to advanced STEM concepts. However, children and adults consistently struggle with fractions. Here, we take a novel perspective on symbolic fractions, considering them within the framework of relational structures in cognitive psychology, such as those studied in analogy research. We tested the hypothesis that relational reasoning ability is important for reasoning about fractions by examining the relation between scores on a domain-general test of relational reasoning (TORR Jr.) and a test of fraction knowledge consisting of various types of fraction problems in 194 s grade and 145 fifth grade students. We found that relational reasoning was a significant predictor of fractions knowledge, even when controlling for non-verbal IQ and fractions magnitude processing for both grades. The effects of relational reasoning also remained significant when controlling for overall mathematics knowledge and skill for second graders but was attenuated for fifth graders. These findings suggest that this important subdomain of mathematical cognition is integrally tied to relational reasoning and opens the possibility that instruction targeting relational reasoning may prove to be a viable avenue for improving children’s fractions skills. 相似文献
8.
"数学实验"是一种为了获得某种数学结论,检验某种数学猜想,解决某类数学问题,而引导学生在创设的特定物质条件下,在多种思维活动的共同参与下,最后领悟概念和解决问题的教学手段。而"支架式教学法"则以"最近发展区"为指导,只在超出学生当前水平时,教师才给予"支架"协助,直至学生能自己承担任务或掌握知识。因此两者的结合,需要教师在将实验的精神赋予学生的同时,构建恰当的教学支架,使学生的学习能力得到提升。 相似文献
9.
Eunice Mthethwa-Kunene Rian de Villiers 《International Journal of Science Education》2013,35(7):1140-1165
This study explored the pedagogical content knowledge (PCK) and its development of four experienced biology teachers in the context of teaching school genetics. PCK was defined in terms of teacher content knowledge, pedagogical knowledge and knowledge of students’ preconceptions and learning difficulties. Data sources of teacher knowledge base included teacher-constructed concept maps, pre- and post-lesson teacher interviews, video-recorded genetics lessons, post-lesson teacher questionnaire and document analysis of teacher's reflective journals and students’ work samples. The results showed that the teachers’ individual PCK profiles consisted predominantly of declarative and procedural content knowledge in teaching basic genetics concepts. Conditional knowledge, which is a type of meta-knowledge for blending together declarative and procedural knowledge, was also demonstrated by some teachers. Furthermore, the teachers used topic-specific instructional strategies such as context-based teaching, illustrations, peer teaching, and analogies in diverse forms but failed to use physical models and individual or group student experimental activities to assist students’ internalization of the concepts. The finding that all four teachers lacked knowledge of students’ genetics-related preconceptions was equally significant. Formal university education, school context, journal reflection and professional development programmes were considered as contributing to the teachers’ continuing PCK development. Implications of the findings for biology teacher education are briefly discussed. 相似文献
10.
文章依据开展数学建模活动的实践经验,阐述了数学建模对高职院校学生应用与创新能力培养的重要意义,探讨了如何通过数学建模活动培养高职学生的应用与创新能力,并对高职院校开展数学建模提出了几点思考。 相似文献
11.
Soo Jin Lee Jaehong Shin 《International Journal of Science and Mathematics Education》2015,13(2):329-355
In the present study, we describe a participating student’s (Carol’s) distributive partitioning scheme and operations along with Steffe’s and his colleagues’ studies about children’s constructions of fraction knowledge as a particular model of mathematical learning. Analysis of Carol’s mathematical behaviors indicates that an operationally common mathematical behavior (distributive partitioning operation) was revealed in various mathematical problem situations such as fraction multiplication, fraction division, and multiplicative transformation between fractional quantities. It both provides a rationale for why becoming versed in one mathematical subject could facilitate working with another mathematical subject and also implies the necessity of describing and defining students’ mathematical behaviors from an operational view of knowledge, which might lead to building foundations of a substantial cognitive map for students’ mathematical development. 相似文献
12.
Lee Soo Jin Shin Jaehong 《International Journal of Science and Mathematics Education》2013,13(2):329-355
In the present study, we describe a participating student’s (Carol’s) distributive partitioning scheme and operations along with Steffe’s and his colleagues’ studies about children’s constructions of fraction knowledge as a particular model of mathematical learning. Analysis of Carol’s mathematical behaviors indicates that an operationally common mathematical behavior (distributive partitioning operation) was revealed in various mathematical problem situations such as fraction multiplication, fraction division, and multiplicative transformation between fractional quantities. It both provides a rationale for why becoming versed in one mathematical subject could facilitate working with another mathematical subject and also implies the necessity of describing and defining students’ mathematical behaviors from an operational view of knowledge, which might lead to building foundations of a substantial cognitive map for students’ mathematical development.
相似文献13.
数学知识、数学能力和数学情意是影响数学免费师范生数学专业素质的主要因素.数学免费师范生的数学情意素质具备程度较高,数学能力素质具备程度较低;数学专业素质在性别和年级之间存在差异;数学专业素质与数学知识、数学能力和数学情意均存在显著的正相关;数学知识、数学能力和数学情意对数学免费师范生的数学专业素质的形成和发展有不同程度的影响。 相似文献
14.
This study examines how various teacher characteristics and contextual factors are related to early primary teachers’ beliefs about mathematical teaching and learning and teachers’ attitudes toward their own learning of mathematics. A total of 396 early primary teachers across Nebraska participated in the study. Teacher characteristics and contextual factors were grouped into four sets: teacher professional background, teacher mathematical knowledge for teaching, teaching contexts, and students’ experiences. Multiple regression analyses were conducted with each set of predictors separately, as well as with all four sets together. The results showed significant relationships between teachers’ mathematical knowledge for teaching and teacher-centered beliefs, motivation in learning mathematics, and anxiety toward learning mathematics. Teacher certification level, the number of college math courses taken, and perceived support from colleagues and administrators were also related to some aspects of teachers’ mathematical beliefs and attitudes. The findings suggest the potential role of teachers’ mathematical knowledge for teaching in improving teachers’ mathematical beliefs and attitudes. 相似文献
15.
Eun-Jung Park Kyunghee Choi 《International Journal of Science and Mathematics Education》2013,11(3):683-706
In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem solving used in scientific inquiry. In this regard, several studies have attributed students’ decreasing interest in science to the presence of these mathematical representations. In order to better understand student learning difficulties caused by mathematical components, the current study investigates student understanding of a familiar science concept and its mathematical component (pH value and logarithms). Student responses to a questionnaire and a follow-up interview were examined in detail. “Measure” and “concentration” were key criteria for students’ understanding of pH values. In addition, only a few students understood logarithms on a meaningful level. According to students’ understanding of scientific phenomena and mathematical structures, five different student models and the critical features of each type were identified. Further analysis revealed the existence of three domains that characterize these five types: object, operation, and function. By suggesting the importance of understanding scientific phenomena as a “function,” the current study reveals what needs to be taught and emphasized in order to help students obtain a level of scientific meaning that is appropriate for their grade. 相似文献
16.
This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.
相似文献17.
加强实践性教学有利于教师教学知识发展,有利于提升师范生的数学教学观念.泰山学院在数学教育类课程计划的编制、课程开设、教学组织形式等方面开展了实践性教学的实践和研究,通过加强实践教学内容、开展教师技能训练、教学设计、模拟数学教学活动、感悟教学理论知识的生成过程,积累教学经验、提高数学教学技能,提升师范生的就业竞争力. 相似文献
18.
Johanna Rellensmann Stanislaw Schukajlow Claudia Leopold 《Educational Studies in Mathematics》2017,95(1):53-78
Drawing strategies are widely used as a powerful tool for promoting students’ learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling performance. Sixty-one students were asked to create a drawing of the situation described in a task (situational drawing) and a drawing of the mathematical model described in the task (mathematical drawing) before solving modelling problems. A path analysis showed that strategic knowledge about drawing was positively related to students’ modelling performance. This relation was mediated by the type and accuracy of the drawings that were generated. The accuracy of situational drawing was related only indirectly to performance. The accuracy of mathematical drawings, however, was strongly related to students’ performance. We complemented the quantitative approach with a qualitative in-depth analysis of students’ drawings in order to explain the relations found in our study. Implications for teaching practices and future research are discussed. 相似文献
19.
Lung-Sheng Lee Yunn-Horng Guu Liang-Te Chang Chih-Chien Lai 《Environmental Education Research》2013,19(5):620-638
Energy saving and carbon-emissions reduction (ESCER) are widely regarded as important issues for progress towards ensuring sustainable forms of economic development. This Taiwanese study focuses on the effects of a series of educational activities about ESCER on students’ knowledge, attitudes and behavior. Sixty fifth-grade students from two elementary school classes were assigned to an experimental group, and 59 from two others to the control. Covariance and qualitative data analysis were conducted after 14 lessons on the topic in both ‘treatments.’ The following key findings emerged. First, hands-on ‘energy-saving house’ learning activities seemed to have positive effects on students’ knowledge, attitudes, and behavior toward ESCER, even as the design of authentic learning activities was recognized as not being as closely aligned to the students’ daily lives as they could have been for achieving behavior-related outcomes. Second, students demonstrated slight gains in conceptual knowledge and procedural knowledge via the hands-on activities, but some ESCER misconceptions persisted. We conclude that students’ learning processes, prior learning and authentic contexts for ESCER-related work should not be ignored in the attempt to link knowledge to action in teaching and learning activities. 相似文献
20.
在小学数学课程教学过程中,课堂练习占据重要地位,同时也是学生学习数学知识、掌握数学技能的重要方式.高效的课堂练习具有重要意义,不但有助于集中学生在课堂学习中的注意力,让他们将所学的数学知识应用到数学习题的解答中,而且高效的课堂练习还能帮助教师了解和掌握学生的学习情况,从而针对学生对数学知识掌握薄弱的地方采取针对性的策略... 相似文献