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1.
The present study aims to explore the use of assessment in mathematics content courses for future elementary school teachers.
Analysis of self assessment data on mathematical understanding and peer assessment data on oral mathematical presentation
showed that pre-service teachers had a balanced understanding of procedural knowledge and problem solving. Conceptual understanding
was not in the structure of pre-service teachers’ mathematical knowledge. Understandings of conceptual knowledge, procedural
knowledge, and problem solving had no meaningful effects on gains in mathematics performance. Aspects of oral mathematical
presentation were associated with improved understanding of procedural knowledge and in particular conceptual knowledge. The
result of the study calls for a conceptual approach to mathematical knowledge and sufficient mathematical problem solving
in college-level mathematics content courses and in particular the infusion of assessment into college-level mathematics education
for pre-service teachers. 相似文献
2.
ABSTRACT— This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based approaches to understanding the ways in which children become proficient in mathematics. Task analysis indicates that executive cognitive functions likely operate in concert with procedural and conceptual knowledge and in some instances might act as a unique influence on mathematics problem-solving ability. It is concluded that consideration of the executive cognitive demand of mathematics can contribute to research on best practices in mathematics education. 相似文献
3.
Andrew Munns 《European Journal of Engineering Education》2017,42(6):1062-1075
Professional bodies expect engineers to show competence in both mathematics and engineering topics such as mechanics, using their abilities in both of these to solve problems. Yet within engineering programmes there is a phenomenon known as ‘The Mathematics Problem’, with students not demonstrating understanding of the subject. This paper will suggest that students are constructing different concept images in engineering and mathematics, based on their perception of either the use or exchange-value for the topics. Using a mixed methods approach, the paper compares 10 different types of concept image constructed by students, which suggests that familiar procedural images are preferred in mathematics. In contrast strategic and conceptual images develop for mechanics throughout the years of the programme, implying that different forms of competence are being constructed by students between the two subjects. The paper argues that this difference is attributed to the perceived use-value of mechanics in the career of the engineer, compared to the exchange-value associated with mathematics. Questions are raised about the relevance of current definitions of competence given that some routine mathematical operations previously performed by engineers are now being replaced by technology, in the new world of work. 相似文献
4.
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
5.
M. Stewart Townend 《Teaching in Higher Education》2013,18(2):203-215
Case studies have long been used to support the mathematics education of undergraduate engineers. Changes in the mathematical ability of entrants to engineering programmes and, indeed, the changing nature of many of the programmes themselves indicate the need to make the students' mathematical experiences more 'user friendly'. We describe here an approach which uses case studies, not as illustrations of applications of mathematics after a mathematical topic has been discussed, but in a fully integrated central role as vehicles for whole group discussion from which the students 'discover' the necessary mathematics which is taught subsequently. Not only is the 'carrot' of the application then central to their learning, but the need for the mathematics being taught is also clearly demonstrated. This approach has been tried with a group of 50 first year engineers. The effects on student motivation, ability and knowledge retention are discussed together with an indication of the Integrated Case Studies which were used. 相似文献
6.
The aim of this mixed methods study was to investigate the difficulties prospective elementary mathematics teachers have in solving the Programme for International Student Assessment (PISA) 2012 released items. A mathematics test consisting of 26 PISA items was administered, followed by interviews. Multiple data were utilized to provide rich insights into the types of mathematical knowledge that a particular item requires and prospective teachers’ difficulties in using these knowledge types. A sample of 52 prospective teachers worked the mathematics test, and 12 of them were interviewed afterwards. The data-sets were complementary: the quantitative data showed that PISA items could be categorized under contextual, conceptual, and procedural knowledge and indicated the most frequent difficulties in the combined contextual, conceptual, and procedural knowledge items. The qualitative data revealed that few prospective teachers could give mathematical explanations for conceptual knowledge items, and that their contextual knowledge was fragmented. Educational implications were discussed. 相似文献
7.
数学教师的数学观和数学教育观 总被引：18，自引：2，他引：18
作为数学教师素质结构的先导性成分,数学观由数学知识观、数学本质观和数学价值观构成.数学教育观包括数学教育目的观、数学教育过程观和数学教育价值观3个主要部分.数学教师的数学观对其数学教育观有重要影响.数学教育文化观、数学教育哲学观和数学教育价值观之间有着复杂的互动关系. 相似文献
8.
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers’ views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result of continuous connection making. However, in contrast to the popular view which separates understanding into conceptual and procedural, Chinese teachers prefer to view understanding in terms of concepts and procedures. They place more stress on the process of concept development, which is viewed as a source of students’ failures in transfer. To achieve mathematical understanding, the Chinese teachers emphasize strategies such as reinventing a concept, verbalizing a concept, and using examples and comparisons for analogical reasoning. These findings draw on the perspective of classroom practitioners to inform the long-debated issue of the meaning of mathematical understanding and ways to achieve mathematical understanding. 相似文献
9.
Tonya Gau Bartell Corey Webel Brian Bowen Nancy Dyson 《Journal of Mathematics Teacher Education》2013,16(1):57-79
This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered. 相似文献
10.
Ewa Lakoma 《European Journal of Engineering Education》2002,27(3):279-288
Current changes, especially the wide application of information technology, in all fields of our life, mean that mathematical knowledge becomes necessary in almost every domain. It implies new expectations for mathematical education. An urgent need of a new mathematical literacy for all—also a new mathematical literacy for engineers—is evident. It is necessary to consider a process of mathematics learning at tertiary level from the epistemological perspective and to investigate students’ ways of mathematical thinking. This epistemological knowledge is especially indispensable when students use information technology. In this article current requirements regarding mathematical education are discussed, especially those for future engineers. Analysis of examples of learning elementary statistics, using graphing calculators as supporting tools, leads to the formulation of essential aims for mathematics educators concerning mathematics teaching for future engineers. 相似文献
11.
In an experiment, we studied beliefs about the structure of students' mathematical knowledge that may affect teachers' formative assessments. Using a novel approach that simulated an assessment situation, we measured the beliefs of N = 42 preservice mathematics teachers. Teachers' responses revealed that they predominantly thought of students' conceptual and procedural knowledge as being symmetrically related but not identical, which is in line with recent findings about students' knowledge. Their assessments may, thus, not be biased by incorrect beliefs. Teachers, however, did not believe conceptual and procedural knowledge to be more interrelated as a result of students' increased expertise. 相似文献
12.
Mathematics has always played an important role in the education of engineers and production managers. At the present time, the importance of mathematics has increased significantly and it is quite natural that in universities around the world engineering students are taking courses in mathematics which constitute, as a rule, a significant portion of their programme. At the same time, however, the mathematical education of the engineer is far from ideal and its improvement deserves the closest scrutiny. The present article deals with several general aspects of this problem. 相似文献
13.
This study utilized discourse-based instruction as an alternative method of instruction that emphasizes the teaching of mathematics by actively engaging students in mathematical discourse practices. A quasi-experimental study was employed to determine the effectiveness of mathematical discourse-based instruction in enhancing eleventh-grade students’ conceptual and procedural understanding of probability and statistics. A researcher-constructed test instrument was used for data collection from the experimental and control groups. The data analysis performed using the Kruskal-Wallis test showed that the experimental group outperformed the control groups in terms of conceptual and procedural knowledge. Furthermore, the results suggest that discourse-based instruction when appropriately designed and implemented can increase students’ understanding of mathematical topics. 相似文献
14.
A series of surveys provide the basis for comments on the mathematical education of engineers in Australia. The respondents were graduates and employers. This paper summarises their views and contrasts undergraduate and postgraduate courses. The former tend to be traditional and structured. There is a need for more course work with the latter with more emphasis on mathematical modelling. Desirable professional attributes which should come from education with mathematics rather than mere training in mathematics are listed as they are seen in the milieu of the market place. 相似文献
15.
Paulo Tan 《Emotional and Behavioural Difficulties》2016,21(4):361-376
Recent shifts in focus on academic interventions for students diagnosed with emotional and behavioural disorders (EBD) create a need to evaluate existing interventional research in content areas such as mathematics. Literature reviews in the area of mathematics interventions for students with EBD have mostly focused on the outcomes and the rigour of existing studies with limited attention to the quality of the pedagogical methods used in those studies. The purpose of this conceptual review was to use a teaching-for-understanding lens to examine existing research interventions in mathematics for students with EBD. Teaching-mathematics-for-understanding requires pedagogical methods that aim to activate and capture students’ mathematical reasoning and thinking. An iterative electronic and hand search of the literature found 30 studies covering three decades (1985–2015) that met the criteria for inclusion in this review. Results of the analysis include: (1) mathematics assessments utilised ranged from very basic to comprehensive, with most studies applying basic assessments; (2) a majority of the studies focused on intervention strategies targeting procedural and rote knowledge; (3) most studies utilised quantitative inquiry methods; and (4) in more recent years, studies have increasingly examined conceptual mathematical understanding and incorporated qualitative inquiry methods. 相似文献
16.
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
17.
With a Meta-Analytic Structural Equation Modeling approach, we investigated the role of whole-number knowledge on fraction performance, accounting for domain-general skills, age, and mathematics-difficulty status. We conducted analyses based on 6,096 students from 39 independent samples within 29 studies. Findings suggested conceptual whole-number knowledge emerged as a significant and stable predictor of conceptual and procedural fraction knowledge. More importantly, students experiencing mathematics difficulty demonstrated a distinct pattern of performance compared to typically-achieving students, including: conceptual whole-number knowledge had lesser impacts on conceptual fraction knowledge; procedural whole-number knowledge had greater impacts on procedural fraction knowledge; and working memory and fluid intelligence made fewer contributions to fraction knowledge. 相似文献
18.
KARL A. SMITH 《European Journal of Engineering Education》1988,13(3):317-330
Engineering is the application of science and mathematics to human problems. This is a view that pervades engineering education. Recent emphasis in the United States is ‘engineering is design’. The thesis of this paper is that engineering as science as well as engineering as design are inadequate conceptions of engineering. The thesis is supported by comparing school and out-of-school knowledge. The nature of engineering is explored in terms of the activities of engineers and the goals of engineering education. Koen's definition of the engineering method, “The engineering method is the use of heuristics to cause the best change in a poorly understood situation within the available resources”, is introduced. The nature of expertise is examined. Alternatives to the ‘empty vessel’ model are presented for the development of engineering expertise. The alternatives include cognitive apprenticeship, reflective practicum, co-operative learning and problem-based instruction. 相似文献
19.
Leslie Cunliffe 《牛津教育评论》2013,39(4):547-556
This article explores and attempts to rectify current conceptual confusion found in secondary art education in the UK between procedural knowledge or ‘knowing how’ and declarative knowledge or ‘knowing that’. The paper argues that current practice confuses procedural knowledge with declarative knowledge. A corollary is that assessment evidence for ‘knowing how’, which is shown or demonstrated, is confused with assessment evidence for ‘knowing that’, which requires spoken or written forms of reporting. The confusion is replicated in the national examination, the General Certificate of Secondary Education, taken by students at the age of 16. The article traces this confusion to three dualisms: the Cartesian dualisms of mind and body, an individual mind and the distributed mind of culture, and the more recent mind‐in‐brain hemisphere dualism. The article advocates a Wittgensteinian embodied, socio‐cultural view of mind as a way of solving the current conceptual confusion that prevails in art education in the UK. 相似文献
20.
Ailish Hannigan Olivia Gill Aisling M. Leavy 《Journal of Mathematics Teacher Education》2013,16(6):427-449
The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of statistics and are willing to give more relevance to the teaching of statistics; however, many mathematics teachers do not consider themselves well prepared to teach statistics. The aims of this study were to investigate the conceptual understanding of statistics of prospective secondary mathematics teachers; the nature of their attitudes towards statistics and if there was a relationship between attitude towards statistics and conceptual understanding of statistics. Conceptual understanding was measured using a standard assessment instrument (comprehensive assessment of outcomes in a first statistics course) which allows comparison across other disciplines. Despite being very mathematically able and confident, the prospective mathematics teachers in this study do no better in the assessment than students from other (mostly non-quantitative) disciplines. This, perhaps, gives further evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking. Conceptual knowledge was poor in some fundamental areas of statistics such as being able to properly describe the distribution of a quantitative variable and data production. The attitudes of these teachers towards statistics were measured using a widely used instrument (survey of attitudes towards statistics). The results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn. No strong correlation was found between attitudes and conceptual knowledge. It is recommended that in order to improve teacher knowledge, teacher education programmes must include tailored modules in statistics and highlight the differences between mathematical and statistical thinking. 相似文献