Pauline Vos

Assessment of Applied Mathematics and Modelling: Using a Laboratory-Like Environment

In the Netherlands, since 1993 the mathematics core curriculum for junior secondary schools states that students should develop skills for using and applying mathematics in practical situations. For monitoring purposes, a trend study was carried out using mathematical hands-on tasks in a laboratory-like environment. The study revealed that this kind of alternative, practical assessment can have a satisfying curricular validity, higher than written tests based on the same curriculum. However, comparability of test results (between students, schools, etc) depends on the uniformity of test circumstances.

The concept of derivative in modelling and applications

Abstract The question addressed in this paper is how to measure students transfer skills with respect to the concept of the derivative in modelling and applications. We adapted a framework developed by Zandieh (2000) for analysing students understanding of the concept of the derivative. Nine grade-11 students made a test and a task-based interview, which consisted of mathematical and application problems. The task-based interview included tasks about the application of the derivative in a physics and economics context. The analysis of interview data showed some difficulties emerging with the framework. With respect to modelling and applications, we found that sometimes students cannot apply knowledge of calculus that they have, and that translations between representations, and especially between a context set in the real world and mathematics, and backwards, cannot be represented in the framework. Our analyses gave directions for further development of a framework for understanding derivatives in relation to applications.

Trends (1995 – 2000) in the TIMSS Mathematics Performance Assessment in The Netherlands

In TIMSS-95, participating countries could administer the TIMSS Performance Assessment consisting of practical tasks, and considered to match well with the Dutch intended curriculum. But in 1995, Dutch students did not score as expected on this test, revealing a discrepancy between intended and attained curriculum. Therefore, in 2000, the test was replicated. Results show an increased teachers acceptance of the test, butu200a– u200astillu200a–u200a no significant gain in Dutch students achievements. Additionally, if reliability is well controlled, the study revealed that there are valid mathematics assessment alternatives, which can supplement paper-and-pencil tests, not only in The Netherlands.

The Mathematics Curriculum in The Netherlands: Measuring curricular alignment using TIMSS-99

After a drastic mathematics curriculum change in The Netherlands in 1993, a study on the alignment of intended, implemented, and attained curriculum was carried out using TIMSS-99. For benchmarking, identical instruments were used in a neighboring country (Flanders), and for science. Two innovative methodological features were: (1) the teachers judgments on concrete items through an item-based instrument, and (2) the use of the partial overlap of the TIMSS test and the Dutch intended mathematics curriculum. Comparing the results, the mathematics curricular alignment in The Netherlands had reached an acceptable level, 6 years after 1993.

Designing mathematics lessons in Mozambique : starting from authentic resources

Abstract This article describes research on the design of student-centred instruction in Mozambique. The starting point was the use of real-life resources, such as traditional art craft objects and authentic newspaper clippings. The research was based on an instructional design model, which attempts to align theory with practice and which is geared towards improving practice. In two parallel studies, one on geometry and one on statistics, student-centred instruction was facilitated through the use of worksheets with open-ended questions tailored for group work. In a cyclic process, the prototype materials and the associated instructional method were formatively evaluated. The evaluations showed that the designs were useful even in classrooms packed with more than sixty students.

Predecessor Items and Performance Level

In 1995, two carefully sampled groups of 14-year-old Dutch students participated in a project that included a test of their mathematics achievements. Each group received a different test, but there was an overlap of test items with the purpose of comparing the outcomes of the two tests. These items originated from the Third International Mathematics and Science Study (TIMSS) achievement test for Population 2 (Grades 7 and 8). No significant difference was expected to occur in the performances of the two student groups on the overlapping items. Yet, the differences in the performances of the two student groups were statistically significant. This could not be ascribed to differences in the two samples, which were representing the same population. In no way did they differ in socioeconomic backgrounds, in gender ratio, in age, in school tracks, nor was there a difference in the circumstances under which both tests were administered. It was suggested that the only parameter that could have influenced the differences was the sequence of the items (Kuiper, Bos, & Plomp, 1997; 2000). Further study indicated that the differences in the levels of success on an item could be correlated to the differences in the levels of success on the immediately preceding item. Thus, the research question came to be: Is the performance level on a single item in a cognitive test affected by the level of difficulty of the preceding item? The passage from a “hard” item to the next might show a disturbance in the performance on the latter. Whenever only a few students mastered a preceding item, the percentage of correct scores on the following item would be lower than the performance on the same item of the control group. This evidence is described below in the first section, “TIMSS and the National Option Test in the Netherlands”. To replicate these findings, a further study was carried out, which uses data from the TIMSS achievement test administered in 1995 (TIMSS-1995) and repeated in 1999 (TIMSS-1999). The backbone for this study is the TIMSS test design, whereby the test is assembled in eight different test booklets. Clusters of items are rotated through test booklets, resulting in eight different sequences of item clusters. The study investigates students’ performances on these different sequences. The design of this study, the statistics and results constitute the core of this paper. At the end conclusions and points for further discussion are presented.