Abstract

This dissertation contains a number of articles reporting on research on instruction for students who have difficulties learning mathematics. The focus lies on the kind of instruction that these students need to adequately master the mathematics skills required by the elementary school curriculum. Recent developments in mathematics education ask for
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guided instruction. In the study reported on here, the effectiveness of guided instruction for low-achieving students was investigated by conducting an intervention study in schools for regular and special elementary education. The effects of guided instruction were compared to the effects of directed instruction, which was found to be effective in former research. This study showed that guided instruction is almost equally effective as directed instruction. It is therefore concluded that both directed instruction and guided instruction can be effective for teaching multiplication to students with difficulties learning mathematics.
In chapter 1, it is described how students normally receive mathematics education and how instruction could be adapted to their specific needs. Chapter 2 reports on a meta-analysis on studies that described the effects of different interventions for elementary school students with math learning difficulties. Interventions that focused on the learning of basic math skills proved to be the most effective. The results also show that directed instruction and self-instruction are more effective than guided instruction.
A pilot study has been conducted to investigate the suitability of the intervention program and the testing materials. The results presented in Chapter 3, showed that both interventions were more effective than the regular math curriculum. Furthermore, it was found that guided instruction resulted in higher effects on the students multiplication ability than directed instruction and especially for the students in regular education.
The main study is described in the Chapters 4 and 5. A total of 283 students from 24 schools for either special or general education have participated. The group of students was divided into three conditions: guided instruction, directed instruction, and regular instruction (control group). The results show that the students who had received directed instruction improved more than the students who had received guided instruction, although the differences between the two conditions proved to be small. It was also found that both experimental conditions were more effective than the control condition. Furthermore, it was found that the students strategy use improved significantly during the intervention period. The experimental students showed greater improvement than their control peers. The differences between both experimental conditions were nevertheless small.
The study described in Chapter 6 was meant to investigate the relation between mathematics learning difficulties and cognition. The results showed that students with math learning difficulties perform on average lower on the PASS (Planning, Attention, Simultaneous, and Successive processes) scales than their peers without specific learning difficulties. The results also showed that students with specific math difficulties, such as difficulties with automaticity or with problem solving, have other cognitive profiles than both students without math difficulties and students with general math difficulties.
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