Dit project betreft het onderzoek naar de implementatie en effecten van een nieuw programma voor wiskundeonderwijs voor leerlingen van 12-16 jaar: ‘Wiskunde voor iedereen’. Kenmerkend voor dit nieuwe wiskundeonderwijs is dat leerlingen - onder begeleiding van de leraar- in heterogene klassen en in heterogene subgroepen samenwerken aan de oplossing van wiskundige problemen. Het didactisch concept is gebaseerd op de theorie van Freudenthal en de uitwerking in concreet curriculummateriaal is gerealiseerd door de projectgroep voor de leerplanontwikkeling ‘Wiskunde 12-16’ van de Stichting voor de Leerplanontwikkeling (SLO). Het onderzoek is uitgevoerd in 3 projectscholen en 2 vergelijkingsscholen. In totaal deden 33 klassen en 763 leerlingen mee aan het onderzoek.
Eindrapport en artikelen (titels en abstracts) van het Project“Interne Differentiatie Wiskunde 12-16” (ID 12-16/SVO-project 0647)De links naar de artikelen waarvan u hieronder een samenvatting ziet, vindt u in het veld 'Relation' hierboven. / You'll find links to the articles mentioned hereafter in the field 'Relation' of this dataset.Terwel, J., Herfs, P.G.P., Dekker, R., Akkermans,W. (1988). Implementatie en Effecten van Interne Differentiatie. Een empirisch, vergelijkend onderzoek naar de realisering en effecten van interne differentiatie in heterogene groepen in de eerste fase voortgezet onderwijs bij wiskunde. ‘s Gravenhage: Stichting voor Onderzoek van het Onderwijs (SVO), Utrecht: Rijks Universiteit Utrecht, Vakgroep Onderwijskunde.(SVO-project 0647, ISBN 90-6472-122-X). http://hdl.handle.net/1871/52070.Dit is het eindrapport van het project Interne Differentiatie 12-16, het verslag van een onderzoek naar de implementatie en effecten van een nieuw programma voor wiskundeonderwijs voor leerlingen van 12-16 jaar: ‘Wiskunde voor iedereen’. Kenmerkend voor dit nieuwe wiskundeonderwijs is dat leerlingen - onder begeleiding van de leraar- in heterogene klassen en in heterogene subgroepen samenwerken aan de oplossing van wiskundige problemen. Het didactisch concept is gebaseerd op de theorie van Freudenthal en de uitwerking in concreet curriculummateriaal is gerealiseerd door de projectgroep voor de leerplanontwikkeling ‘Wiskunde 12-16’ van de Stichting voor de Leerplanontwikkeling (SLO). Het onderzoek is uitgevoerd in 3 projectscholen en 2 vergelijkingsscholen. In totaal deden 33 klassen en 763 leerlingen mee aan het onderzoek. Uit het onderzoek blijkt dat leraren verschillend omgaan met het nieuwe programma. Een lage of hoge score op de voortoets blijkt in hoge mate bepalend te zijn voor de score op de natoets. Over het geheel genomen zijn de leereffecten van het experimentele programma beter in vergelijking met een traditioneel programma. Projectleerlingen behalen meer leerwinst dan de vergelijkingsleerlingen. De effect size is .22. Conditie verklaart 2 procent van de variantie op de natoets bovenop de variantie die de voortoets verklaart. Er is dus een klein positief effect van het experimentele programma. Projectleerlingen met middelmatige en hogere score op de voortoets profiteren meer van het vernieuwde onderwijs dan leerlingen met een lagere score. Hoewel het model Freudenthal, zoals uitgewerkt door de SLO, in vergelijking met een traditionele aanpak goed blijkt te werken, blijven er wensen over, in het bijzonder voor de zwakkere leerlingen. Daarom is een nieuw model ontwikkeld: het model Adaptief GroepsOnderwijs. Dit AGO-model zal in een vervolgonderzoek op uitvoerbaarheid en effectiviteit worden onderzocht.Terwel, J. (1988). Effecten van differentiatie en heterogeniteit in de eerste fase voortgezet onderwijs. Pedagogisch Tijdschrift, 13, nr. 5, 326-340. http://hdl.handle.net/1871/36778Het Instituut voor de Leerplanontwikkeling (SLO) maakte op basis van de theorie van Freudenthal een programma onder de titel ‘Wiskunde voor iedereen’. Dit programma is in een empirisch-vergelijkend onderzoek op uitvoerbaarheid en effectiviteit onderzocht. Het onderzoek vond plaats in het tweede leerjaar op vijf scholengemeenschappen (800 leerlingen). Het programma heeft een positief effect op de leerresultaten in vergelijking met een traditionele aanpak.Van den Eeden, P. & Terwel, J. (1994). Evaluation of a mathematics curriculum: Differential effects. Studies In Educational Evaluation, Volume 20, Issue 4, 1994, Pages 457-475ISSN 0191-491X/94. http://hdl.handle.net/1871/10982.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 theclass 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 cognitivetheories. 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.Terwel, J. & Van den Eeden, P. (1992). Curriculum evaluation and multilevel analysis: Effects of cooperative learning in mathematics. Studies In Educational Evaluation, Volume 18, Issue 2, 1992, Pages 133-148. ISSN 0191-491X/92. http://hdl.handle.net/1871/10981In this article an instructional model of cooperative learning in secondary mathematics education was put to the test. Students worked in cooperative groups of four on real life mathematical problems based on Freudenthal’s adagium 'Mathematics for All' and his theory of ‘Realistic Mathematics Education’ (RME). The data were collected at three secondary schools, with a total of 482 pupils, 12 teachers and 22 classes. The curriculum was implemented in the second year of secondary education with a majority of pupils in the ages of 13 and 14 years. The research design was pretest-posttest. Differences in implementation were found, in particular, in the extent to which the Freudenthal model had been implemented with regard to schools, teachers and pupils. We investigate the effects of the curriculum by relating these differences in implementation to differences between students' learning results. Given the basic idea behind 'Mathematics for All', the research question about the differential effects of this curriculum is important. Which pupils benefit most from the implementation of the new curriculum and how can we explain the differences in learning results?As the analysis has shown, the effectiveness of the 'Freudenthal model' differs for the three different aptitude groups and the learning results within each of these levels are dependent on different variables. Especially, the learning results for the medium aptitude group are remarkable. The pupils of this group seem to profit most from innovation. Their learning results are totally determined by the teaching-learning situation. The extent to which the new curriculum has been implemented affects learning results, with class composition (mean class level) and increase in standard deviation (from pretest to posttest) playing a facilitating role. The learning results of the medium aptitude group are relatively independent of prior knowledge. Within this group the hypothesis has been confirmed: the greater the degree of curriculum implementation, the better the results.Although this hypothesis does not hold for the lows, there is a significant effect of class composition (mean class level). This is in accordance with other research findings in which the low aptitude groups proved to be more sensitive to class composition than the higher levels (Dar & Resh, 1986; Beckerman & Good, 1981; Good & Marshall, 1984). It was concluded in another study that the gains of this aptitude group are relatively low (Terwel, 1988b). Judging by our multilevel analysis this conclusion can be confirmed. The 'Freudenthal model', with an emphasis on comprehension of mathematical problems in stories of real life situations, problem solving and discovery learning, probably assumes a repertoire of concepts and strategies that these pupils do not possess. In addition, the model does not provide remedial help for pupils who fall behind.The results of our multilevel analysis can be explained by introducing a kind of 'threshold hypothesis': in order to profit from this type of innovation students need a certain level of prior knowledge. Without a minimum of prerequisite skills the gains will be low. Although we were not able to test the validity of this hypothesis, our interpretation is in accordance with the findings of recent studies by Van Streun (1989, in press). The pupils in the high aptitude group are relatively less affected by their learning environment. These pupils do not respond to differences in the extent to which the curriculum has been implemented. High-level pupils seem to rely more on their own abilities than medium- and low level pupils. Contrary to our expectations this group proved not to be affected by the increase in thestandard deviation. The only effect we find for this group is related to time off-task in the class.Het team bestond uit Jan Terwel (projectleider), Paul Herfs, Rijkje Dekker en Wies Akkermans, allen werkzaam binnen de vakgroep Onderwijskunde van de Universiteit Utrecht.
