基于AHP的教材出版质量综合评价

出版教材质量的综合评价是一个比较复杂的问题,它牵涉到六大指标体系和22个具体评价指标.利用层次分析法(Analytic Hierarchy Process,简称AHP)对教材出版质量进行综合评价,可以准确、全面地反映教材出版流程中各方面的质量要求,为评价教材出版质量建立科学、合理的方法.     

模糊层次评价在高职学生职业能力评价中的应用

职业能力可根据系统组成原理划分成职业特定技能、行业通用技能和核心技能三个层次.运用层次分析法建立层次结构模型,构建比较矩阵,计算出因素权重并做一致性检验.运用模糊评价方法确定影响因素的模糊判断矩阵,就可逆向确定各层次组成因素的得分,为高职学生职业能力层次和影响因素的判断提供了依据.对职业能力按层次进行模糊评价分析,为高职学生职业能力评价提供了新的方法.     

矩阵分块方法的应用

矩阵的分块方法是矩阵论的一种重要方法,选择合适的分块方法可使一些证明变得简单明了.利用矩阵的分块方法给出关于矩阵的秩、特征多项式、行列式的若干等式、不等式及相关命题的简洁证明,有利于初学者理解和掌握.     

基于层次分析法的选股决策

应用层次分析法 ,通过建立递阶层次结构和判断矩阵 ,并结合定性评价和定量评价 ,对投资股票项目中的股票进行评价和排序 ,进而做出合理的选择决策 .通过实证表明 :层次分析法在股票选择中是一种实用、有效的方法 ,有较好的应用价值 .     

基于顾客满意度的电子商务网站评价

基于文献分析,提出从顾客满意度的视角对电子商务网站进行评价,构建了以顾客满意为基础的评价指标体系,采用层次分析法与灰色评价相结合的评价方法进行网站评价.这一方法避免了层次分析法在生成各项评价指标权重时主观性的特点,从而使评价矩阵更接近现实.最后,通过实证分析验证了方法的科学性,并对发展我国电子商务提出了策略建议.     

高校数学公共课教材质量定量比较评价模型

首先建立了评价高校数学公共课教材质量的指标体系 ,依据该指标体系 ,运用层次分析法 ,构建了对高校数学公共课教材质量进行定量比较评价的模型 .最后给出了应用实例 ,介绍了具体的评价分析方法 .     

用层次分析法对学生进行综合评价

学生的综合评价工作是学校的重要工作内容.如何从思想、学习、生活等各个方面对其进行综合考察,并使之科学化、合理化,是各个院校学生工作一直探索的问题.采用能给定量描述的决策问题带来极大方便的层次分析法(Analytic Hierarchy Process),把学生评价体系归结为5个准则27个指标,通过计算各级判断矩阵,得到了各个指标的权重,并把最终的计算结果应用到学生评优评三好等多项实际工作中.     

多元相关的聚类分析法在企业效绩评价中的运用

运用多元函数相关分析中的聚类分析法 ,根据由指标数据形成的矩阵 ,计算确定各项指标的权数 ,建立效绩评价的测定方程 ,对各企业效绩进行测定和评价 .     

教育信息化基础建设的综合评价模型

以广西区域教育信息化现状调查为基础,选择合适的评价指标并利用双基点法计算各指标权系数,从软、硬件方面对学校信息化基础建设状况做出综合评价.     

基于改进风险矩阵法的医院建筑火灾风险评价

在对国内外广泛采用的风险矩阵法进行全面系统的分析和总结的基础上,针对风险矩阵方法的不足,结合医院建筑火灾风险评价的的客观实际和需要,对风险矩阵法进行了改进,并将风险矩阵法引入医院建筑的火灾风险评价,提出一种融合改进风险矩阵法与层次分析法的医院建筑火灾风险评价模型,并实例验证该模型的有效性和可行性.     

Opportunity to learn problem solving in Dutch primary school mathematics textbooks

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide ‘gray-area’ tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.     

Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples

Mathematics textbooks play a very important role in mathematics education and textbook tasks are used by students for practice to a large extent. Since the nature of the tasks may influence the way students think it is important that the textbooks provide a balance of a variety of tasks. The analyses of the requirements in textbook tasks contain the usual dimensions of content, cognitive demands, question type and contextual features. The aim of this study is to embed a new fifth dimension into the framework: mathematical activities. This addresses the question of what a student should do in a particular textbook task: to represent, to compute, to interpret or to use argumentation. The analysis encompassed more than 22,000 tasks from the most commonly used Croatian mathematics textbooks in the 6th, 7th and 8th grade. The results show that the textbooks do not provide a full range of task types. There is an emphasis on computation, while argumentation and interpretation activities, reflective thinking and open answer tasks are underrepresented. The study revealed that incorporating mathematical activities into the multidimensional framework of textbook tasks may help to better understand the opportunities to learn which are afforded students by using mathematics textbooks.     

The State of Proof in Finnish and Swedish Mathematics Textbooks—Capturing Differences in Approaches to Upper-Secondary Integral Calculus

Students’ difficulties with proof, scholars’ calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related reasoning in integral calculus, a key subject in transitioning from secondary to tertiary education. We analyze expository sections and nearly 2000 students’ exercises in the four most frequently used Finnish and Swedish textbook series. Results indicate that Finnish textbooks offer more opportunities for learning proof than do Swedish textbooks. Proofs are also more visible in Finnish textbooks than in Swedish materials, but the tasks in the latter reflect a higher variation in nature of proof-related reasoning. Our results are compared with methodologically similar U.S. studies. Consequences for learning and transition to university mathematics, as well as directions for future research, are discussed.     

On students' understanding of volumes of solids of revolution: An APOS analysis

We apply Action-Process-Object-Schema theory (APOS) to (1) examine the textbook used by students in the study to infer mental constructions the book proposes that students could do to understand solids of revolution, (2) use semi-structured interviews with nine students to find out which of the textbook’s proposed constructions students actually do, and what unconjectured or unexpected constructions students do, and (3) use the results of the interviews and the research literature to inform and set forth an alternative proposal for constructing volumes of revolution. Results suggest that many students have not constructed processes to visualize solids of revolution and to relate Riemann sums to the corresponding definite integrals. Implications for curriculum and instruction are discussed.     

Reasoning-and-Proving in School Mathematics Textbooks

Despite widespread agreement that the activity of reasoning-and-proving should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that teachers make about what tasks to implement in their classrooms and when and how to implement them are mediated by the textbooks they use. Yet, little is known about how reasoning-and-proving is promoted in school mathematics textbooks. In this article, I present an analytic/methodological approach for the examination of the opportunities designed in mathematics textbooks for students to engage in reasoning-and-proving. In addition, I exemplify the utility of the approach in an examination of a strategically selected American mathematics textbook series. I use the findings from this examination as a context to discuss issues of textbook design in the domain of reasoning-and-proving that pertain to any textbook series.     

A semiotic interpretation of the derivative concept in a textbook

Differential and integral calculus textbooks are widely used as the main resource for teaching. They appear in a variety of forms and adopt various approaches to present the content. In this paper, we turn our attention to one chapter of a calculus textbook and our focus is on the introduction of the derivative concept. With the purpose of examining the presentation of the derivative concept in the textbook, we give a view of Peirce’s semiotics, in particular of his classification of sign-vehicles. The analysis allows us to point out that the sign-vehicle in relation to the derivative concept may be iconic, indexical, or symbolic. These do not constitute mutually exclusive kinds of signs, but they are interrelated in such a way that we can identify iconicity in indexicality and indexicality in symbolicity. We conclude that the textbook has the potential to enable students to conceptualize the derivative. However, in some aspects, the book may constrain students’ conceptualization and it could be improved to meet the students’ needs to make meaning of the derivative concept.     

Interpretations of National Curricula: the case of geometry in textbooks from England and Japan

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.     

The Brazilian mathematics textbook assessments

This paper briefly reviews Brazilian textbook policies during the twentieth century, and pays careful attention to its latest development, PNLD—Programa Nacional do Livro Didático (National Textbook Program) and its textbook assessments, which selects textbooks that are freely distributed by the Ministry of Education (MEC) to students of public elementary, middle and high schools. We focus on the mathematics textbook assessments, describing their evolution and commenting on some of their accomplishments and problems. The first assessment was carried out for the 1997 school year and retained basically its initial formulation, with changes and improvements, til the assessment for the 2018 school year. As of now, the program is undergoing substantial changes which are briefly discussed and which worry many educators. This assessment was responsible for a definite improvement of mathematics textbooks for elementary, middle and high schools in Brazil. It constitutes a good example of a successful program, coordinated by competent persons from mathematics education, schools of education and mathematics departments of good universities, at first without political interference, and strongly backed by powerful officials in MEC. In the last few years, pressures from publishers and conservative groups have undermined the assessments, with possibly serious consequences.     

The textbook-in-use: students’ utilization schemes of mathematics textbooks related to self-regulated practicing

This paper presents a qualitative study on how students make use of their mathematics textbooks for practicing. The study was carried out in two German secondary schools with 74 students (44 in 6th and 30 in 12th grade). Students’ utilization of textbooks for practicing is analyzed using the theoretical framework of instrumental genesis. The results indicate that students’ choices of contents from the book for practicing can be categorized into three utilization schemes: position-dependent practicing, block-dependent practicing, and salience-dependent practicing. In terms of position-dependent practicing the relative position of the textbook’s contents to teacher-mediated sections guides the students’ choice. Block-dependent practicing relates to the use of contents from the book that belong to particular blocks. Finally, salience-dependent practicing is a utilization scheme of the book where students’ choice is guided by perceptual salience of the book contents. These findings both show how textbook users are influenced by the way mathematics is presented in textbooks and provide insights into students’ conceptions of practicing mathematics.     

A Comparative Analysis of the Addition and Subtraction of Fractions in Textbooks from Three Countries

In this paper, we report on a comparison of the treatment of addition and subtraction of fractions in primary mathematics textbooks used in Cyprus, Ireland, and Taiwan. To this end, we use a framework specifically developed to investigate the learning opportunities afforded by the textbooks, particularly with respect to the presentation of the content and the textbook expectations as manifested in the associated tasks. We found several similarities and differences among the textbooks regarding the topics included and their sequencing, the constructs of fractions, the worked examples, the cognitive demands of the tasks, and the types of responses required of students. The findings emphasized the need to examine textbooks in order to understand differences in instruction and achievement across countries. Indeed, we postulate that within a given country there may exist a recognizable “textbook signature.” We also draw on the results and the challenges inherent in our analysis to provide suggestions and directions for future textbook analysis studies.