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1.
This article explores the nature of education as a vital part of human knowledge. The argument that is presented addresses the critique of education as having epistemological weaknesses as an academic discipline. The argument is framed by scholarship that has categorised the discipline of education as derived from three main traditions of knowledge. In order to explore the coherence of education as a discipline, contrasts are made with other disciplines such as mathematics and sciences. The article also reviews scholarship in relation to the concept of education research that is close-to-practice, and the relevance of this to understanding education as an academic discipline. The article concludes by suggesting a new model that shows the relationships between practical knowledge and academic knowledge that are an intrinsic part of education. A more confident portrayal of education as an academic discipline is also advocated.  相似文献   

2.
We identify a recent trend in school mathematics as well as in some of the research literature in mathematics education: an emphasis on the practical uses of mathematics and an increased emphasis on verbalizations as opposed to numerical and computational skills. With tools provided by John Dewey, an early advocate of contextual and practical knowledge, we analyse the common research framework for discussing mathematical knowledge in terms of the procedural and the conceptual. We argue that procedural and conceptual knowledge should not be seen as opposites, and that the tendency to treat them as such might be avoided by emphasising the notion of operational skill. We argue that this is important in order for the students to gain both the contextual knowledge and the computational skill entailed in mathematical knowledge.  相似文献   

3.
Abstract educational practices are to be based on proven scientific knowledge, not least because the function science has to perform in human culture consists of unifying practical skills and general beliefs, the episteme and the techne (Amsterdamski, 1975, pp. 43–44). Now, modern societies first of all presuppose regular and standardized ways of organizing both our concepts and our institutions. The explanatory schemata resulting from this standardization tend to destroy individualism and enchantment. But mathematics education is in fact the only place in which to treat the human subject’s relationship with mathematics. And that is what mathematics education is all about: make the human subject grow intellectually and as a person by means of mathematics. At first sight, mathematics, in its formal guise, seems the opposite of philosophy, because philosophy constructs concepts (meanings), whereas mathematics deals with extensions of concepts (sets). We shall, however, turn this problem into an instrument, using the complementarity of intensions and extensions of theoretical terms as our main device for discussing the relationship between philosophy and mathematics education. The complementarity of the “how” and the “what” of our representations outlines, in fact, the terrain on which epistemology and education are to meet.  相似文献   

4.
《师资教育杂志》2012,38(4):375-387
This paper describes a study conducted with a random sample of 80 student primary teachers drawn from all four years of the Bachelor of Education (BEd) programme at a teacher education institution in Scotland, with a view to determining why there were such differing levels of engagement with an online maths assessment. The assessment was created in an attempt to address deficiencies in subject knowledge in order to reduce the amount of time spent on mathematics remediation, and to raise awareness of the levels of mathematics competence required in the primary classroom. Study of the reasons behind the differing patterns of engagement with the assessment revealed that two thirds of the group were able to reach a competence threshold and often to improve upon it by some way; a worrying third of the students, however, made little attempt to use the tool to improve their subject knowledge. A further finding indicated that students who engaged with the online assessment reported improving levels of confidence in mathematics.  相似文献   

5.
This study aimed to examine the longitudinal relations of mathematics anxiety to quantitative reasoning and number knowledge in Chinese children. Three hundred and sixteen 6-year-old Chinese children in Hong Kong participated in two waves of assessments, eight months apart. Cross-lagged panel analyses showed that prior quantitative reasoning and number knowledge predicted lower mathematics anxiety, even after the effects of gender, mothers’ educational levels, and general anxiety were taken into account. However, earlier mathematics anxiety did not predict later quantitative reasoning and number knowledge. Our findings were consistent with the Deficit Theory, which postulates that mathematics anxiety comes from poor mathematical competence but not vice versa. We also found a reciprocal association between quantitative reasoning and number knowledge, in which initial quantitative reasoning had a stronger prediction on later number knowledge. Taken together with previous research, this result highlights the importance of quantitative reasoning in children’s mathematics learning and its role in mathematics education.  相似文献   

6.
In this article we analyze the relations between academic mathematical knowledge and the mathematical knowledge associated with issues mathematics school teachers face in practice, according to the specialized literature, and restricted to the theme “number systems”. We present examples that illustrate some areas of conflict between those forms of knowledge. We point out some implications of our study for teacher education, such as: 1) the importance of making conflicts explicit and of discussing them with prospective teachers in order to develop a professionally relevant perception of academic mathematics; 2) the relevance of further research in order to better understand the extent of those conflicts and their effects on the process of integrating, in a body of professional knowledge, the different kinds of mathematical knowledge presented to prospective teachers.
Plinio C. MoreiraEmail: Email:
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7.
This study is grounded in the theoretical position that solving problems in different ways creates mathematical connections when learning and teaching mathematics. It acknowledges the central role teachers play in providing students with learning opportunities, and it is based on the empirical finding that mathematics teachers are reluctant to solve problems in different ways in the classroom. In this paper we address the contradiction between theory-based recommendations and school mathematics practice. Based on analysis of individual interviews and two group meetings with 12 Israeli secondary school mathematics teachers, we demonstrate that in the context of multiple-solution connecting tasks this discrepancy is caused by the situated nature of the teachers’ knowledge. We also reveal the complex relationship between different types of teacher knowledge and argue the significance of developing a common language between members of the mathematics education community, including teacher educators and researchers. The names of the teachers have been changed to protect their privacy.  相似文献   

8.
In comparing content knowledge (CK) and pedagogical content knowledge (PCK) of Taiwanese and German inservice mathematics teachers, the present study examines whether the two-dimensional structure of teachers' subject matter knowledge is cross-culturally invariant and whether differences in teacher education and in teacher selection are reflected in teachers' subject matter knowledge. The results confirm that CK and PCK represent two distinct, but correlated dimensions, even in teachers from completely different backgrounds. Taiwanese inservice teachers showed considerably higher CK and also higher PCK scores than German teachers. Teacher education and teacher selection should be considered important levers for reform in mathematics education.  相似文献   

9.
Why are some teachers more effective than others? The importance of understanding the interplay between teacher preparation, pedagogy and student achievement has motivated a new line of research focusing on teacher knowledge. This study analyses the effects of teacher mathematics knowledge on student achievement using longitudinal data from rural Guatemalan primary schools. After presenting a conceptual framework for linking the work of the teacher with student learning in mathematics together with an overview of the different forms of teacher knowledge, the paper introduces the Guatemalan context and the analytical framework including the sample, data and methods. Overall, the results provide some empirical support for a widely held, if infrequently tested, belief in mathematics education: effective teachers have different kinds of mathematical knowledge. The results also suggest specific mechanisms by which effective teachers can make substantial impacts on student learning, even in extremely poor contexts.  相似文献   

10.
Abstract

The aim of this study was to analyse the relationship between sociometric types, behavioural categories and academic achievement in a sample of 1,349 compulsory secondary education students (51.7% boys), ranging in age from 12 to 16 years. The students’ sociometric identification was performed by using the Programa Socio and academic performance was measured by school marks provided by teachers in the subjects of Spanish language, mathematics and average academic performance. The results show that sociometric types were significant predictors of academic achievement, as students who were rated positively by their peers (popular, leaders, collaborators and good students) were more likely to have high academic achievement (in mathematics, Spanish language and average academic achievement) than students rated negatively by peers (rejected-aggressive, rejected-shy, neglected and bullies).  相似文献   

11.
This theoretical paper examines the concept of pedagogical content knowledge (PCK) and explores how it might contribute to conversations around quality teaching and learning in outdoor education. This paper begins by summarizing the historical and contemporary literature, including issues of definitions, curriculum, content, and pedagogy in outdoor education. We then review the concept of PCK, its history, and contributions to other subject areas, including mathematics. We present a framework for PCK from the field of mathematics education and propose a 'modified' PCK framework for outdoor education. We postulate that this framework might help articulate knowledge areas needed by a teacher of outdoor education, and how these differ from and are similar to those required in other subject areas. We conclude by exploring how the idea of PCK and the modified framework might add to existing understandings of what it means to provide high quality outdoor education teaching and learning experiences.  相似文献   

12.
Powerful knowledge and geographical education   总被引：1，自引：0，他引：1  
Michael Young has argued that pupils should be given access to ‘powerful knowledge’. This article examines the extent to which his concept of powerful knowledge is applicable to geographical education, in particular to the study of urban geography. It explores the distinction Young makes between everyday and school knowledge, how this relates to geographical education and to the academic subject of geography. It then considers the extent to which geographical disciplinary knowledge has the characteristics of powerful knowledge. Finally, it raises issues related to curriculum and pedagogy.  相似文献   

13.
In broad terms, this study describes preservice elementary teachers' beliefs, conceptions, and practices during the mathematics methods course and teaching practica of a teacher education program. In particular, the study employs qualitative data to investigate preservice teachers' views of mathematical and pedagogical content knowledge. The study reveals symbiotic relationships between their views of content knowledge and their instructional actions which remain problematic. With unwavering beliefs and practices, and without reconceptualizing their roles as future elementary teachers, at the end of the semester the preservice teachers emerge as poor duplicators of mathematics methods instead of initiators of learning.  相似文献   

14.
This paper describes a research project whose major aim was to evaluate first-year teacher education students' understanding of subject matter knowledge in the domain of area measurement. In contrast to many previous approaches to evaluating teacher education students' subject matter knowledge, the approach adopted in this study not only focused on the student teachers' substantive knowledge but also on their knowledge about the nature and discourse of mathematics, their knowledge about mathematics in society and their dispositions towards mathematics. To this end, each student was clinically interviewed whilst engaged on a set of eight tasks that were developed for the study. The development of the tasks was a major component of the study and this is described in detail. The results of the tasks are given and the paper concludes with a discussion of the findings. This discussion focuses primarily on the implications that these results have for preservice mathematics education courses.  相似文献   

15.
促进中小学生数学学力发展是数学教育的重要任务。本文选用了日本"全国学力调查"小学六年级数学试卷,对中国五省部分六年级学生的数学基本知识的掌握情况和灵活应用的能力进行测试,并与日本同龄小学生进行比较,分析两国小学生数学学力的异同,对我国数学课程与教学改革进行一些思考。  相似文献   

16.
This article focuses on the cognitive factors that impact on students in the middle school years experiencing learning difficulties in basic mathematics. It begins with a review of selected literature providing information about the learning difficulties in mathematics. Focus then shifts to an implementation of the QuickSmart intervention. QuickSmart is a basic academic skills intervention designed for persistently low-achieving middle-years' students. In this small-scale study, 12 middle school students experiencing learning difficulties participated in the QuickSmart mathematics program. Comparisons are made between the mathematics progress of the intervention group and eight average-achieving peers. The results indicate that on measures of response speed and accuracy QuickSmart participant students were able to narrow the gap between their performance and that of their average-achieving peers. Further, on standardized tests of more general mathematical knowledge, participant students improved significantly from pre-test to post-test. Implications are drawn regarding the importance of interventions that emphasize automaticity in basic mathematics for middle years students with learning difficulties.  相似文献   

17.

Maturity and citizenship in a democracy require that laypersons are able to critically evaluate experts’ use of mathematics. Learning to critically reflect on the use of mathematics, including the acquisition of the mathematical knowledge and skills required to that end, has been repeatedly postulated as an indispensable goal of compulsory education in mathematics. However, it remained unclear in how far such reflection is possible, even for the well-educated layperson in mathematics. We use different discussions in German mass media on the pandemic policy in the SARS-CoV-2 crisis in 2020 as examples with far-reaching individual and social consequences. The selected discussions build heavily on mathematical concepts such as mortality rates, casualty numbers, reproduction numbers, and exponential growth. We identify the concepts and discuss how far they can be understood by laypersons. On the one hand, we found that some mathematical models are inappropriate, which can also be determined by laypersons. On the other hand, we found uses of mathematics where ideal concepts are intermingled with complex statistical concepts. While only the ideal concepts can be understood by laypersons, only the statistical concepts lead to actual data. The identification of both types of concepts leads to a situation where the use of mathematics evades social control and opens spaces for misconceptions and manipulation. We conclude that the evaluation of experts’ use of mathematics by laypersons is not possible in all relevant cases, and we discuss possible implications of this result.

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18.
In contrast to subjects such as mathematics and the sciences, it has been argued that technology education lacks a clear definition and a clearly defined knowledge base. This discursive article seeks to inform the debate by highlighting the matter of subject definition and in addition to examine the key issue of the knowledge which underpins technology education. The nature of the knowledge involved in technology education is explored by focusing on the types of knowledge (declarative/conceptual, procedural and conditional/strategic) that are required to secure full engagement with this subject. Drawing on extant literature on knowledge, the article takes technology as its focus and highlights the challenges this presents for teachers. A conceptual framework based on the presented evidence is included to show the relationships between knowledge and the skills, the problem‐solving and the values that are integral to technology education. This article concludes that to be effective, technology teaching must be based upon an appropriate subject definition indicating what it is endeavouring to achieve. In addition the existence of such a specialist subject knowledge base must be fully acknowledged, and at the same time there must be full recognition of the need to draw upon relevant knowledge from other subject areas in an appropriate manner in order to inform classroom teaching of the subject.  相似文献   

19.
Research in mathematics education usually attempts to look into students’ learning and other mental processes. It could therefore be expected to build on knowledge acquired within the academic discipline of cognitive psychology. Our aim in this paper is to show how some recent developments in cognitive psychology can help interpret empirical results from mathematics education. In particular, we will be looking into the heuristics-and-biases research by Kahneman and Tversky, the alternative views by Gigerenzer et al., and the more recent dual-process theory that has come to play a central role in interpreting this research. We first introduce the relevant background from cognitive psychology and survey its connections to previous work in mathematics education; then we apply this theoretical framework for re-interpreting previously-published empirical data from mathematics education research. We conclude with a discussion of potential theoretical and practical benefits of such synthesis.  相似文献   

20.
Teachers of mathematics orchestrate opportunities for interactions between learners and subject matter. Therefore, mathematics teachers need rich, multidimensional content knowledge for teaching mathematics, which incorporates knowledge of the subject matter, students, and teaching. Studying this mathematical knowledge for teaching (MKT) necessitates more than a unidirectional assessment. In this study, the mathematical knowledge for teaching reasoning and proving of two secondary mathematics teachers was investigated through classroom observations and clinical assessments. Results indicate that using MKT as a frame for examining classroom practice, in addition to assessing the MKT a teacher possesses in a clinical setting, provides an in-depth and innovative method for investigating MKT. The comparison of the two cases also identifies student positioning as a key mediating factor between MKT and opportunities to learn. Implications for using MKT as a lens for examining practice in teacher education are discussed.  相似文献   

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