Mathematical potential of special education students

Abstract

This PhD research was aimed at investigating the mathematical potential of special education (SE) students. SE students often have a severe delay in their mathematical development compared to peers in regular education. However, there are indications that SE students could attain more and that there might be unused talent in SE students. In the research project, two mathematical domains were chosen as a topic of investigation. One topic is part of the mathematics curriculum in SE and is generally recognized as rather difficult for weak performing students in mathematics, i.e., subtraction up to 100 with ‘crossing the ten’. The other topic goes beyond the standard curriculum in SE and requires mathematical problem solving, i.e., elementary combinatorics. To reveal SE students’ potential on these two topics, new assessment approaches were used that offer students opportunities to show what they are able to do. Therefore, several ICT-based assessment environments were developed and used in a series of small-scale studies in which 8- to- 12 year old SE students participated. In a first study, an ICT-based assessment environment was developed containing an optional auxiliary tool that SE students could use for solving subtraction problems with crossing the ten. Both students’ performance and solution process in the ICT environment were analyzed in relation to their tool use. Also, a secondary analysis of the data was carried out in which a cognitive load perspective was adopted. The findings showed that enriching assessment by incorporating an optional auxiliary tool in an ICT-based assessment environment can help SE students to overcome obstacles in solving subtraction problems. Furthermore, the results showed that such an ICT environment can help to examine students’ solution process in much detail. In a following study, a series of subtraction problems within an ICT environment was developed in order to asses SE students’ ability to use the adding-on procedure instead of the standard taking-away procedure. It was found that designing test items with particular item characteristics can disclose SE students’ flexible solution methods when solving subtraction problems up to 100. The next step was the development of yet another ICT assessment environment which contained a series of elementary combinatorics problems. Again, SE students’ success rate and solution process were investigated, this time when dealing with a mathematical topic that was completely new to them. It was found that presenting elementary combinatorics problems in a dynamic ICT environment can uncover SE students’ systematic strategy use. Overall, the findings of the assessment studies helped to obtain a more complete picture of the mathematical potential of SE students. Finally, in addition to the assessment studies, an inventory was made of teacher perceptions of SE students’ mathematical potential. Data were collected by means of an online questionnaire. The results showed that the majority of teachers who responded believe that there is unused mathematical potential in SE students. All together, the findings of this PhD research show that there is a good basis for working on better utilizing SE students’ mathematical potential.