数学教学评价的内容和方法

数学教学评价的问题是关系到数学教学改革的成败问题,因此,必须正确认识数学改革中的数学教学评价,深刻理解它的意义和功能,建立科学有效的评价手段和方法。     

Differential Performance of Items in Mathematics Assessment Materials For 7-Year-Old Pupils in English-Medium and Welsh-Medium Versions

This paper draws on data from the development of annual national mathematics assessment materials for 7-year-old pupils in Wales for use during the period 2000–2002. The materials were developed in both English and Welsh and were designed to be matched. The paper reports on item analyses which sought items that exhibited differential performance in relation to whether the materials were English medium or Welsh medium. The items that exhibited consistent differential item functioning in relation to language during pre-testing are reviewed in order to discuss the linguistic factors that could affect such behaviour.     

Gender Differences in Performance on Mathematics Achievement Items

Gender differences in performance on three types of mathematics test items were investigated using data from students with three different course backgrounds. Eight randomly equivalent samples of high school seniors were each given a unique form of the ACT Assessment Mathematics Usage Test. Only students with three specific profiles of high school mathematics coursework were considered in the analysis. The three background conditions ranged from little mathematics (Algebra I only) to a modest background (two Algebra courses and Geometry) to a full mathematics program including Introductory Calculus. For each background condition, examinee performance was analyzed in a 2 (Gender) x 3 (Item Category) x 8 (Test Form) split-plot factorial design. The results indicated, that, at each of the studied background levels, females performed less well than males on geometry (strategic, geometric) and reasoning (strategic, nongeometric) items. On the other hand, females performed as well as males on algorithmic, operationsoriented items.     

Gender-Based Differential Item Performance in Mathematics Achievement Items

A procedure for the detection of differential item performance (DIP) is used to investigate the relationships between characteristics of mathematics achievement items and gender differences in performance. Eight randomly equivalent samples of high school seniors were each given a unique form of the ACT Assessment Mathematics Usage Test (ACTM). Students without requisite mathematics courses were deleted from the samples to reduce the confounding effects of differences in instruction at the high school level. Signed measures of DIP were obtained for each item in the eight ACTM forms. These DIP estimates were then analyzed in a 6 × 8 (item category by form) experimental design. A significant item category effect was found indicating a relationship between item characteristics and gender-based DIP. Predictions, based on previous research about the categories of items that would contribute to gender-based DIP, were supported: Geometry and mathematics reasoning items were relatively more difficult for female examinees and the more algorithmic, computation-oriented items were relatively easier.     

Evaluating Content Alignment in Computerized Adaptive Testing

The alignment between a test and the content domain it measures represents key evidence for the validation of test score inferences. Although procedures have been developed for evaluating the content alignment of linear tests, these procedures are not readily applicable to computerized adaptive tests (CATs), which require large item pools and do not use fixed test forms. This article describes the decisions made in the development of CATs that influence and might threaten content alignment. It outlines a process for evaluating alignment that is sensitive to these threats and gives an empirical example of the process.     

数学教学的有效性与开放性

有效的教学是数学教育领域中一个新的热点问题。这一论题的提出是对于近年来在教学方法改革中所出现的形式主义倾向的一个直接反对,从而就具有很大的合理性;但我们同时又应注意对其内涵的正确理解并防止可能的片面性,即应当坚持数学教育的三维目标,并很好地把握教学的有效性与开放性的辩证关系。     

教育质量监测试题的评价与反思

教育质量监测试题的质量关系到基础教育质量监测的科学性与权威性。评价认为,教育质量监测试题在思想与立意、目的与功能、结构与形式、指标与属性等方面具有一定优势,但也存在一致性难以兼顾、科学性论证缺位、利害性不易权衡的不足。针对其不足,提出拓展一致性分析、加强科学性论证和寻求利害性平衡的建议与策略,为我国的考试改革和教育质量监测提供重要借鉴。     

基于高考评价体系的数学科考试内容改革实施路径

高考评价体系是新时代高考内容改革的理论支撑和实践指南。以高考评价体系为指导,在明确高考数学科功能定位的基础上,确定考查理性思维、数学应用、数学探索、数学文化4类学科素养,考查逻辑思维能力、运算求解能力、空间想象能力、数学建模能力、创新能力5种关键能力,提出具有学科特点的基础性、综合性、应用性、创新性的考查要求,通过设置课程学习情境、探索创新情境、生活实践情境3类试题情境落实考查内容和考查要求。高考评价体系对指导高考数学内容改革具有重要意义。     

Aligning an Early Childhood Assessment to State Kindergarten Content Standards: Application of a Nationally Recognized Alignment Framework

This article describes an alignment study conducted to evaluate the alignment between Indiana's Kindergarten content standards and items on the Indiana Standards Tool for Alternate Reporting. Alignment is the extent to which standards and assessments are in agreement, working together to guide educators' efforts to support children's learning and development. The alignment process in this study represented a modification of Webb's nationally recognized method of alignment analysis to early childhood assessments and standards. The alignment panel (N = 13) in this study consisted of early childhood educators and educational leaders from all geographic regions of the state. Panel members were asked to rate the depth of knowledge (DOK) stage of each objective in Kindergarten standards; rate the DOK stage for each item on the ISTAR rating scale; and identify the one or two objectives from the standards to which each ISTAR item corresponded. Analysis of the panel's responses suggested the ISTAR inconsistently conformed to Webb's DOK consistency and ROK correspondence criteria for alignment. A promising finding was the strong alignment of the ISTAR Level F1 and F2 scales to the Kindergarten standards. This result provided evidence of the developmental continuum of skills and knowledge that are assessed by the ISTAR items .     

Alignment of Mathematics State-Level Standards and Assessments: The Role of Reviewer Agreement

This article examines the role of reviewer agreement in judgments about alignment between tests and standards. We used case data from three state alignment studies to explore how different approaches to incorporating reviewer agreement changes alignment conclusions. The three case studies showed varying degrees of reviewer agreement about correspondences between objectives and test items. Moreover, taking into account reviewer agreement in the analyses sometimes had a marked effect on alignment conclusions. We discuss reasons for differences across case studies and alignment approaches, as well as implications for future alignment efforts.     

Resistance to Confounding Style and Content in Scoring Constructed-Response Items

An assumption that is fundamental to the scoring of student-constructed responses (e.g., essays) is the ability of raters to focus on the response characteristics of interest rather than on other features. A common example, and the focus of this study, is the ability of raters to score a response based on the content achievement it demonstrates independent of the quality with which it is expressed. Previously scored responses from a large-scale assessment in which trained scorers rated exclusively constructed-response formats were altered to enhance or degrade the quality of the writing, and scores that resulted from the altered responses were compared with the original scores. Statistically significant differences in favor of the better-writing condition were found in all six content areas. However, the effect sizes were very small in mathematics, reading, science, and social studies items. They were relatively large for items in writing and language usage (mechanics). It was concluded from the last two content areas that the manipulation was successful and from the first four that trained scorers are reasonably well able to differentiate writing quality from other achievement constructs in rating student responses.     

透视数学表现性评价

数学表现性评价创设具体情境,从“做”中评价数学知识与技能：它凸显数学化思想,分层评价发现问题、解决问题的能力;而且它更新评价理念,全方位关注学生的数学情感与态度．我们要重视数学表现性评价,进行“测验嵌入式”和“教学嵌入式”数学表现性评价的实践研究．     

数学欣赏选修课教学内容的探讨

数学欣赏教学以介绍数学的发展为契机,引导学生从数学美学、数学哲学、数学应用的角度去欣赏数学,进而激发学生探索数学的兴趣,提高他们对数学的整体认识.     

Student Assessment of Teaching Effectiveness

Abstract

Expectations for tenure-track faculty are often high. Professors must often balance schedules filled with teaching, service projects, and other duties, leaving little time for meaningful research. The author suggests ways to connect research to other professional responsibilities to increase engagement, enthusiasm, connectedness, and overall productivity.     

Reflection on the Assessment of the Assessment of Mathematics Learning

Assessment is a critical issue in the teaching andlearning of mathematics. For many students, theassessment is still one that is based on a behaviouristapproach where discrete facts and skills are tested,where grading and ranking are the primary goals.Kilpatrick argues that an alternative vision isnecessary for today's classrooms. The challenge is toproduce an assessment practice that does more thanmeasures a person's mind and then assign a mindtreatment. We need to understand how people cometo use mathematics in different social settings and     

基于课程标准的学业成就评价:韦伯模式之研究

学业成就评价必须基于课程标准,这是国家对基础教育整体质量卓越的诉求。韦伯博士是美国基于标准的评价运动的重要代表人物,他提出了学业成就评价与课程标准保持一致性的分析维度、分析程序、分析方法等一整套一致性框架,并开发了基于网络的评价与标准一致性工具。全面深入研究韦伯模式,对我国基础教育阶段学生学业成就评价改革具有重要意义。