Evaluation of a mathematics curriculum: Differential effects

J. Terwel, P. Van den Eeden

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this article the overarching research question concerned the influence of class level variables e.g. class composition on the learning gains of students. The data for this study were collected at three secondary schools, with a total of 482 pupils, 12 teachers and 22 classes. A ‘realistic mathematics’ curriculum was implemented in the second year of secondary education with a majority of students between the ages of 13 and 14. A pretest was administered at the beginning of the school year in which the experiment took place and a posttest at the end of that school year. In addition, data were collected from the process of implementation. The design of the learning environment was based on Freudenthal’s ideas. To put these ideas into practice a new curriculum has been developed by the National Institute for Curriculum Development in the Netherlands (SLO). The central idea behind the curriculum is ‘mathematics for all’. The curriculum developers tried to reconcile mathematics for the majority with more advanced mathematics for the minority. The aim of the curriculum is to make mathematics meaningful and effective for all students.

In this article four hypotheses were tested. The general background of these
hypotheses is that the learning process of students is influenced by variables at the
class level. The ‘individual learning-gain hypothesis’ was confirmed. Pre-knowledge of mathematics as measured by the PRETEST at the individual level has a direct and significant effect on the learning results.

The conclusions concerning variables at the class level are as follows. The ‘composition hypothesis’ was also confirmed. The composition of a class as measured by the PRETEST mean shows the predicted effects on the learning results of the low- and medium-aptitude students. The higher the mean PRETEST score of a class, the higher the score on the POSTTEST. In addition we found a positive effect of composition for the low- and medium aptitude students. The medium-aptitude students are most sensitive to class composition. The hypothesis has not been confirmed for the high-aptitude students. These students seem to be individualistically oriented. Their learning gains are not affected by the composition of the class.

The ‘implementation hypothesis’ was not confirmed in the first analyses.
However, after removing composition from the model, which proved to be correlated
with implementation, a positive effect was found for the low and medium aptitude
students. Consequently we may conclude that the ‘implementation hypothesis’
was confirmed. The ‘off-task hypothesis’ was not confirmed.

The outcome of our investigation concerning the ‘individual learning-gain
hypothesis’ is in line with other empirical studies and can be explained by cognitive
theories. In general, pre-knowledge (concepts, strategies and procedures) in mathematics accounts for an important proportion of the variance in student achievement at the end.
The research findings concerning the ‘composition hypothesis’, especially
concerning the ‘amplified sensitivity’ of the medium-aptitude group, confirm the
findings of Dar & Resh (1986) and Fend (1982). Dar & Resh explain the sensitivity of
the medium-aptitude group by the ‘threshold hypothesis’. In order to be able to benefit from a ‘richer’ learning environment, a student needs a minimum level of personal resources. Below this threshold, enrichment of the learning environment (in our case by means of a higher mean-aptitude score of a class) does not improve learning results. Medium-aptitude students benefit relatively most from being in a class with a high aptitude level and suffer relatively most in a low-aptitude class. Fends study, although carried out at the school rather than the class level, also confirms our findings. Fend claimed that the differential benefit was the most important and consistent finding in the research into the effects of comprehensive schooling (middle school), compared with schooling in the traditional (categorical) school system in Germany. A medium-aptitude student who has been placed in the higher tracks of the traditional system benefits from the enriched learning environment compared with a student of the same aptitude who has been placed in the lowest streams. The latter suffers from being placed in a relatively poor environment. Fend’s analysis was applied to overachievers and underachievers with the same intelligence score.
Original languageEnglish
Pages (from-to)457-475
Number of pages19
JournalStudies in Educational Evaluation
Volume20
Issue number4
DOIs
Publication statusPublished - 1994

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