Methodological Choices in the Content Analysis of Textbooks for Measuring Alignment With Standards

With the recent adoption of the Common Core standards in many states, there is a need for quality information about textbook alignment to standards. While there are many existing content analysis procedures, these generally have little, if any, validity or reliability evidence. One exception is the Surveys of Enacted Curriculum (SEC), which has been widely used to analyze the alignment among standards, assessments, and teachers’ instruction. However, the SEC can be time‐consuming and expensive when used for this purpose. This study extends the SEC to the analysis of entire mathematics textbooks and investigates whether the results of SEC alignment analyses are affected if the content analysis procedure is simplified. The results indicate that analyzing only every fifth item produces nearly identical alignment results with no effect on the reliability of content analyses.     

The Quality of Content Analyses of State Student Achievement Tests and Content Standards

This article examines the reliability of content analyses of state student achievement tests and state content standards. We use data from two states in three grades in mathematics and English language arts and reading to explore differences by state, content area, grade level, and document type. Using a generalizability framework, we find that reliabilities for four coders are generally greater than .80. For the two problematic reliabilities, they are partly explained by an odd rater out. We conclude that the content analysis procedures, when used with at least five raters, provide reliable information to researchers, policymakers, and practitioners about the content of assessments and standards.     

Rethinking critical mathematics: a comparative analysis of critical, reform, and traditional geometry instructional texts

This paper presents findings from a comparative analysis of three similar secondary geometry texts, one critical unit, one standards-based reform unit, and one specialist chapter. I developed the critical unit as I took the tenets of critical mathematics (CM) and substantiated them in printed curricular materials in which to teach as part of a larger study. The reform and specialist texts were both sections from commercially available textbooks. The primary goal of the textual analysis was to examine how the incorporation of critical or political themes into the required secondary mathematics curriculum transformed this curriculum. Key findings were that the CM text exchanged political for mathematical content and sent class-based messages about students’ academic potential. I conclude by arguing that the CM agenda proposed by advocates in the USA is problematic in terms of promoting equity in mathematics education.     

Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability

The purpose of this study is to introduce a measure of standards-based mathematics teaching practices, the Mathematics Scan (M-Scan), and to examine its validity and score reliability. First, we define standards-based mathematics teaching practices based on eight dimensions that have emerged in recent conceptualizations by researchers and in the context of existing observational measures. Second, we present three sources of validity evidence: content review by experts, analysis of response processes of coders, and convergent and discriminant patterns with existing observational measures. Third, we provide evidence of inter-coder (or inter-rater) reliability through analyses of variance components and calculation of reliability coefficients, using the framework of generalizability theory. Results show the M-Scan holds promise as a useful tool in mathematics education research, measuring indicators of standards-based teaching practices unique to the subject of mathematics.     

Content analysis of inquiry-based tasks in high school biology textbooks in Mainland China

Since inquiry was first introduced to science education, a lot of inquiry-based tasks have appeared in textbooks for supporting an inquiry-based approach. These tasks have great potential to direct the implementation of an inquiry-based approach, as teachers rely heavily on the use of existing instructional materials in most K-12 classrooms. However, these tasks would not actually take effect unless they could accomplish the mission of assisting in the achievement of the educational goals of an inquiry-based approach, for which it is necessary to assess the design quality of inquiry-based tasks in textbooks. Content analysis is an effective way to evaluate the design quality of textbooks. This study adopted the instrument – the Inquiry-based Tasks Analysis Inventory (ITAI), which fits the purpose and has strong reliability and validity – to analyse the inquiry-based tasks in current high school biology textbooks in Mainland China. The results show that (1) some of the inquiry-based tasks separate the inquiry process from scientific content, (2) current textbooks do not present balanced dispositions to use inquiry process skills, and (3) inquiry-based tasks in current textbooks do not reflect a proper understanding about scientific inquiry. The findings call for revisions of inquiry-based tasks in textbooks and indicate the ambiguous understanding about inquiry that may be held by the textbook authors. What is more, the problems revealed by this study are very similar to those found in previous studies in other regions, which highlights the need for continuous attention to the evaluation of inquiry-based tasks in textbooks.     

An Analysis of Problem-Posing Tasks in Chinese and US Elementary Mathematics Textbooks

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.     

The Impact of Sustained, Standards-Based Professional Learning on Second and Third Grade Teachers’ Content and Pedagogical Knowledge in Integrated Mathematics

This 3 year longitudinal study reports the feasibility of an Improving Teacher Quality: No Child Left Behind project for impacting teachers’ content and pedagogical knowledge in mathematics in nine Title I elementary schools in the southeastern United States. Data were collected for 3 years to determine the impact of standards and research-based teacher training on these aspects of teacher quality. Content knowledge for the scope of this research study refers to the knowledge that teachers have about subject matter. Teacher quality is directly related to teachers’ “highly qualified” status, as defined by the No Child Left Behind mandate. According to this mandate, every classroom should have a teacher qualified to teach in his subject area and be able to “raise the percentage of students who are proficient in reading and math, and in narrowing the test-score gap between advantaged and disadvantaged students.” Participants were six second grade and seven third grade teachers of mathematics from nine schools within one failing school district. The implementation of standards-based methods in the nine Title I Schools increased teacher quality in elementary school mathematics. In fact, qualitative and quantitative data revealed significant gains in teachers’ mathematics content and pedagogical knowledge at both grade levels.     

中、澳、芬数学课程标准中内容分布的比较研究

以中国、澳大利亚维多利亚州、芬兰官方数学课程标准为研究对象,通过对三国数学课程标准的内容数量、结构框架、详略程度、要求程度、内容分布、内容变化方面进行比较发现:中国数学课程标准内容条目最多、最详细,其次是澳大利亚维州数量居中,芬兰最少、概括性强;三个国家数学课程标准中数与运算、几何内容都较其他内容所占比重更大、强调更多;中国数学课程标准在不同学段上所侧重的内容不同,呈动态变化趋势,而澳大利亚维州各学段各部分内容比重相当,随学段增长,不同内容所占比重无明显变化,芬兰不同学段内容设置不固定,内容所占比重也不固定,不受统一模式限制。     

Standards-based external exams and students’ science-related career expectations: an international perspective

Students’ science-related career expectations are important for predicting their future science, technology, engineering, and mathematics (STEM)-related educational and occupational attainments. This study examines the degree to which standards-based external examinations are associated with a student’s propensity for pursuing science-related professional occupations. The science-related fields included in the analysis are mathematics, physical and life science, and engineering/computing. Three-level hierarchical generalized linear models are employed to analyse international survey and student achievement data from the Programme for International Student Assessment (PISA). The analyses show that students in national education systems that require standards-based external examinations have lower expectations for science-related professional careers than students in the systems that do not use such examinations. This negative association remained constant by gender as well as across levels of science performance. From an educational policy point of view, the results suggest the negative consequence of standards-based external exams in fostering students’ interests in pursuing science-related careers.     

俄罗斯国家数学教育标准(小学部分)简介

俄罗斯最新(2004年)颁布的小学数学教育标准包括:小学数学的教学目的;教学大纲规定必学的最少内容;对培养毕业生水平的要求。为保持俄罗斯小学数学教育的统一性,并为教科书的编写和教师的教学提供宽广的创造性空间,教育部还提供了一个示范性小学数学教学大纲。     

小学数学教材内容和结构改革六十年

建国60年来,小学数学教材的内容和结构发生了巨大变化。前30年由于受政治运动影响,教材改革几经曲折,起伏较大;后30年改革开放,实施义务教育,教材改革着眼于学生整体发展,稳中求变。60年来的改革历程表明:教材改革要在广泛实验的基础上慎重进行,宜有适度频率,宜于渐进发展,并通过评价促进教材不断优化。     

内容分布与认知要求双重视角下数学课程标准比较研究--基于“中国”“美国”“新加坡”小学初中学段之比较

选取在国际上有代表性的美国及亚洲的新加坡与中国的小学及初中数学课程标准为研究对象,从内容分布与认知要求两个维度进行编码比较研究。主要研究结果显示三国数学课程标准分别呈现如下特征：中国在内容维度上,几何内容拥有的认知要求最多,在认知要求维度上最重视数学推理,并且数学推理主要是以几何内容为主要载体的;美国和新加坡在内容维度上,数与代数拥有最多而丰富的各类认知要求,在认知要求维度上两国均十分重视“问题解决”,美国还重视“关联”类认知要求。     

中美新三国初中数学教材习题综合难度的比较研究——以“三角形的有关角”为例

数学教材中的习题在数学教学中发挥着重要的作用,习题的难度在一定程度上反映了教材的难度。文章在鲍建生教授建立的"探究、背景、运算、推理和知识含量"五个因素的基础上对中国、美国、新加坡三国初中数学教材中的"三角形的有关角"的习题难度进行模型比较,以期为中国的初中数学教材编写提供参考。     

华人数学课堂之透视

同世界其它各地一样,华人地区的新数学课程改革也已经全面铺开,深入到课堂.传统的教学观念和改革取向的教学要求在课堂中产生了激烈的震荡.如何提升数学课堂教学质量,已经成为数学教育和教学工作者的迫切任务.本研究在系统分析有关华人数学课堂研究的基础上,试图刻画华人数学课堂教学的基本特点.最后,讨论如何在张扬传统优点的同时改进华人数学课堂教学.     

论教科书空无内容的内涵与类型

教科书的空无内容是教科书中应该呈现却没有呈现的内容。根据判断主体的不同,教科书的空无内容可分为官意类空无内容、民意类空无内容、专家类空无内容、教师类空无内容和学生类空无内容等五类。探讨教科书的空无内容,对于教科书的编审和使用具有十分重要的意义。     

The Impact of Reform: Challenges for Mathematics Teacher Preparation

The mathematics education community has been widely recognized as a leader in the standards-based reform movement. Despite the widespread interest and attention that reform documents such as the NCTM Standards have generated, what has yet to be fully understood is the impact of these types of reform documents on the preservice teacher preparation process. This paper examines the state of the standards-based reform effort in mathematics teacher education by presenting the results of a three-year study of six cohorts of secondary mathematics student teachers (n = 63). Examined in particular are the ways in which these student teachers' professed beliefs about and knowledge of the NCTM Standards contrast with their teaching practices. Possible explanations for the mismatch between belief and knowledge statements and teaching practices are examined, along with other implications for mathematics teacher preparation.     

The Rating and Matching Item-Objective Alignment Methods

Central to the standards-based assessment validation process is an examination of the alignment between state standards and test items. Several alignment analysis systems have emerged recently, but most rely on either traditional rating or matching techniques. Little, if any, analyses have been reported on the degree of consistency between the two methods and on the item and objective characteristics that influence judges' decisions. We randomly assigned judges to either rate item-objective links or match items to objectives while reviewing the 2004 Arizona high school mathematics standards and assessment. Across items we found moderate convergence between methods, and we detected apparent reasons for divergently scored items. We also found that judges relied on item and objective content and intellectual skill features to render decisions. Based on our evidence, we contend that a thorough alignment analysis would involve judges using both rating and matching, while focusing on both content and intellectual skill. The findings have important implications for states when examining the alignment between their standards and assessments.     

Integrating qualitative and quantitative approaches to the analysis of video data on classroom teaching

Video data provide a means of integrating quantitative and qualitative approaches to the study of classroom teaching. This chapter begins by discussing the usefulness of integrating quantitative and qualitative analyses, and then describes how large-scale video surveys can enable a cyclical process of generating and validating discoveries. The importance of sampling and technology as they bear on efforts to implement the process is noted. The advantages video data offer to researchers are described. Finally, the TIMSS Video Study, a large-scale international video survey of mathematics lessons, is used to illustrate how this cyclical process can be applied to the analysis of lesson content.     

以科学素养为视角的“正式课程”分析模型

科学素养是当代科学教育的中心概念。科学素养理念在理科课程标准和教科书的落实情况是学术界关注的热点。通过相关文献的回顾,笔者整理出当下以科学素养为视角对"正式课程"分析的两种理论模型:"课程重点"和"课程平衡"。本文对两种理论模型及相关的实证研究进行了介绍、评述与比较,希望为我国科学教育工作者研究理科课程标准和教科书提供参考与借鉴。     

A comparison of Korean and American secondary school textbooks: the case of quadratic equations

This study compares quadratic equations sections of Korean and American textbooks. The number of topics, contents and mathematics items were analyzed. The results show Korean students learn some topics relatively earlier than American students. American textbooks include more problems requiring explanations and various representations and problems requiring higher level cognitive demand. This result could indicate that textbooks might not be the reason for American and Korean students’ performances in international comparative studies. More studies analyzing other standards based textbooks and teaching practice might be needed to have further understanding of mathematics education in two countries.