Reliability and validity of a mathematics performance assessment

This study evaluated the reliability and validity of a performance assessment designed to measure students' thinking and reasoning skills in mathematics. The QUASAR Cognitive Assessment Instrument (QCA1) was administered to over 1.700 sixth and seventh grade students of various ethnic backgrounds in six schools that are participating in the QUASAR project. The consistency of students' responses across tasks and the validity for inferences drawn from the scores on the assessment to the more broadly-defined construct domain were examined. The intertask consistency and the dimensionality of the assessment was assessed through the use of polychoric correlations and confirmatory factor analysis, and the generalizability of the derived scores was examined through the use of generalizability theory. The results from the confirmatory factor analysis indicate that a one-factor model fits the data for each of the four QCAI forms. The major findings from the generalizability studies (person x task and person x rater x task) indicate that, for each of the four forms, the person x task variance component accounts for the largest percentage of the total variability and the percentage of variance accounted for by the variance components that include the rater effect is negligible. The variance components that-include the rater effect were negligible. The generalizability and dependability coefficients for the person x task decision studies (n_t, = 9) range from .71-.84. These results indicate that the use of nine tasks may not be adequate for generalizing to the larger domain of mathematics for individual student level scores. The QUASAR project, however, is interested in assessing mathematics achievement at the program level not the student level; therefore, these coefficients are not alarmingly low.     

dMath: a European project for the restatement of mathematics teaching

In this article the main characteristics of the dMath project are introduced. With the mathematical modules developed within this project a new tool is made available to the different users as a support of the teaching and learning of mathematics in the context of EHEA and of the Bologna declaration.     

The indigenous mathematics project: An overview

A multi-disciplinary team research project is described. The project is being undertaken in Papua New Guinea under the auspices of the Ministry of Education and UNESCO. The major goal is to document the relationship between environmental and cultural features, which vary widely in the country, and cognitive development. A second goal is the documentation of mathematics learning and instruction. The paper describes the various components of the project and some of the preliminary findings.     

Early mathematics assessment: validation of the short form of a prekindergarten and kindergarten mathematics measure

In recent years, there has been increased interest in improving early mathematics curricula and instruction. Subsequently, there has also been a rise in demand for better early mathematics assessments, as most current measures are limited in their content and/or their sensitivity to detect differences in early mathematics development among young children. In this article, using data from two large samples of diverse populations of prekindergarten and kindergarten children, we provide evidence regarding the psychometric validity of a new theory-based early mathematics assessment. The new measure is the short form of a longer, validated measure. Our results suggest the short form assessment is valid for assessing prekindergarten and kindergarten children’s numeracy and geometry skills and is sensitive to differences in early mathematics development among young children.     

The CXC mathematics examination: A caribbean innovation in assessment

In the last decade a new examination system (CXC) has been developed in the Caribbean. This includes mathematics examinations which incorporate three major innovatory features. These are as follows: Increased information on candidates' performance. A high degree of consultation and social concern in the development and implementation of the syllabuses. The syllabus conceived in a broader sense as a curriculum.     

Teacher change: ideas emerging from a project for the teaching of university mathematics

This paper reports the changes that occurred in the didactic approaches of three professors who participated in a project intended to develop new ways of teaching mathematics to second year university students. An enactivist perspective is used to address the process of change that emerged as a result from interactions during project meetings. We describe changes in the participants' actions by looking at data obtained from the meetings and the classrooms. Teachers were able to ‘see more’ and modify their teaching practices incorporating a more open and flexible approach in accordance to their structural state which depended on their previous history. Therefore, the results varied. It was possible to observe, however, similar changes in all members of the group which included the use of vocabulary from learning theories and the inclusion of in-depth reflections on teaching and learning.     

Integrated assessment on mathematics 12–16

In this paper we give an account of an integrated package of assessment, describing its conceptual posing as well as its formats, functions, use and effects. The package introduces a diversity of materials searching for connecting and integrating different contributions in a multidimensional scheme.     

Some difficulties in informal assessment in mathematics

In this theoretical paper the informal assessment practices of two experienced teachers are used as cases for generating questions about future developments in formative assessment practice. Both teachers maintain a consistent formative assessment focus on the development of their students as enquirers, and one of them supplements this with explicit self‐assessment activities. However, there are subject‐specific gaps in the ways in which they assess and describe their students and these are not addressed in widely promulgated advice about formative assessment. Questions are raised about how teachers might be supported to develop their assessment of subject‐specific behaviour.     

Formative assessment in mathematics for engineering students

In this paper, we present a range of formative assessment types for engineering mathematics, including in-class exercises, homework, mock examination questions, table quizzes, presentations, critical analyses of statistical papers, peer-to-peer teaching, online assessments and electronic voting systems. We provide practical tips for the implementation of such assessments, with a particular focus on time or resource constraints and large class sizes, as well as effective methods of feedback. In addition, we consider the benefits of such formative assessments for students and staff.     

Teachers' perspectives of changes in their practice during a technology in mathematics education research project

Teachers' perception of changes to their teaching practice, with respect to digital technology use in secondary school mathematics, during their participation in a research project are reported. Two case studies are presented of teacher perspectives illustrative of the range of perceived changes teachers made to their practice and positions along the ‘path of change’ during their participation in the project. Participating in a project supportive of teacher change and resulting in perception of substantial change was necessary, but not sufficient, to meet the goal of transformative use of digital technologies to increase the level of cognitive demand experienced by students.     

A second-grade teacher's adaptive teaching during an integrated science-literacy unit

This case study explored the nature of one elementary school teacher's adaptive teaching during an integrated science and literacy unit. Data were collected during four consecutive weeks of instruction, weekly interactive planning sessions, 20 classroom observations, and 20 post-lesson interviews. Our analysis suggests that adaptations may be established during planning or emerge while teaching. This study also indicated that an adaptive teacher uses ongoing formative assessment to scaffold students' learning. A coding system that typifies how and why a teacher adapts instruction across disciplines can be used to examine adaptive teaching. Implications for teacher educators and researchers are discussed.     

When mathematics and statistics collide in assessment tasks

Because the disciplines of mathematics and statistics are naturally intertwined, designing assessment questions that disentangle mathematical and statistical reasoning can be challenging. We explore the writing statistics assessment tasks that take into consideration potential mathematical reasoning they may inadvertently activate.     

Better judgement: Rethinking assessment in mathematics education

This article reviews three important recent collections of papers on assessment in mathematics education. It first examines the wider social framework of assessment and the influence of public assessment within the school system, both in inhibiting and promoting change. From a survey of the current state of assessment and common criticisms of it, three key trends are identified as forming a current agenda for reform in assessment: increasing the authenticity and realism of assessment tasks; increasing the interpretive quality of assessment information; and increasing the integration of processes of teaching, learning and assessment. These trends are explored in more detail, and critically appraised.     

探析中职数学教学中项目教学法的应用

我国向来重视教育事业的发展。中职教育也是我国教育事业的重要一环。近些年来,中职学校的招生规模不断扩大。而对于中职学生来说,如何学好数学一直都是一个难题。面对这种情况,作为中职院校的老师,应当努力采取各种教学措施提高数学的教学质量。研究表明,在中职数学教育中,项目教学法是一种较为高效的教学方法,能够有效调动学生学习的自主性和积极性,同时还能够提高学生学以致用的能力。     

An assessment model for proof comprehension in undergraduate mathematics

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in undergraduate mathematics. Building on Yang and Lin’s (Educational Studies in Mathematics 67:59–76, 2008) model of reading comprehension of proofs in high school geometry, we contend that in undergraduate mathematics a proof is not only understood in terms of the meaning, logical status, and logical chaining of its statements but also in terms of the proof’s high-level ideas, its main components or modules, the methods it employs, and how it relates to specific examples. We illustrate how each of these types of understanding can be assessed in the context of a proof in number theory.     

Developing classroom formative assessment in dutch primary mathematics education

In the last two decades Dutch primary school students scored below expectation in international mathematics tests. An explanation for this may be that teachers fail to adequately assess their students’ understanding of learning goals and provide timely feedback. To improve the teachers’ formative assessment practice, researchers, curriculum experts and teachers worked together to develop a model for classroom formative assessment (CFA). In three pilot studies, six teachers from three different schools implemented the CFA-model and evaluated its feasibility together with the researchers by means of checklists. The CFA-model was primarily changed with regard to the assessment techniques. Teachers indicated that classroom management and preparation time were preconditions for an optimal implementation. Analysis of covariance was used to explore students’ learning outcomes. The results showed that a correct implementation of the CFA-model might result in the enhancement of students’ mathematical performance. The implications of the three pilots for the implementation of the CFA-model on a larger scale are discussed.