Lessons Learned: What International Assessments Tell Us about Math Achievement

8: Examining Educational Technology and Achievement through Latent Variable Modeling

The use of computers in the teaching and learning of mathematics appears to be increasing exponentially year by year. Consequently, the amount of research on the relationship between computer use and achievement has been exponentially increasing as well. This trend is reflected by the change in how the International Association for the Evaluation of Educational Achievement (IEA) has approached the computer-achievement relationship. In 1984 when the Second International Science Study was conducted, a single question was included regarding the availability of computers in schools.1 By 1995 the student background questionnaire from the Third International Mathematics and Science Study (TIMSS) included four very broad computer-related questions . Two of the questions asked about the frequency with which the students used computers in their mathematics and science classes. The other two questions asked whether students liked using computers for mathematics and for science. In 1999 the student background questionnaire of the Third International Mathematics and Science Study–Repeat (TIMSS-R) included three times as many computer-related questions, which were much more specific compared to the TIMSS-1995 questionnaire. In the 2003 TIMSS, the number of computer-related questions did not increase, but they became even more specific, focusing on the locations in which computers are used by students, as well as on the types of activities that are being performed on the computer, with an emphasis on the use of the Internet. Examining Educational Technology and Achievement through Latent Variable Modeling elena c. papanastasiou and efi paparistodemou 8 205 206 elena c. papanastasiou and efi paparistodemou The inclusion of such questions reflects the increasing and more detailed attempts to examine how computer environments could be effectively used to improve students’ understanding of mathematics and science. However, this is not a simple task since the relationship between computer use and school-related variables such as student achievement is constantly transformed by the ever increasing presence of computers in everyday life, and by society’s increasing reliance on computer technologies. As a result, educators must constantly adapt their practices to conform to the changing educational needs of the students. The purpose of this study is to propose a model concerning the current relationship between technology use and mathematics achievement and test it with data from TIMSS 2003. This model is examined in four countries: the United States, Cyprus, the Russian Federation, and South Africa. The present study attempts to enhance the current understanding of how the technologyachievement relationship has evolved in recent years, during which the number of computers at home and in school settings has increased, and technology has become an integral part of daily life. Educational Technology and Mathematics The key feature of a computer-based environment is that it presents a formal, computable representation of mathematical objects and relationships. Papert’s early work has been very influential in the development of computer environments called microworlds.2 According to Papert, learners interact with the microworld and build their own computer-based models. These models reflect the learners’ thinking about the mathematical objects and relationships as they work on particular activities. Noss and Hoyles define a computer environment as a flexible, interactive, expressive medium for working with mathematical objects and operations.3 Computer-based environments provide access to formal mathematical knowledge through the nature of the “intermediate” screen objects with which students interact in order to construct and manipulate new objects and relationships . Moreover, these environments allow the learner to explore simultaneously the structure of the accessible objects, their relationships, and the representations that make them accessible. It can be said that the microworld “evolves” as the learner’s knowledge grows. According to Lajoie, Jacobs, and Lavigne, computer-based learning environments support the “learning by doing” philosophy.4 For example, in a computational modeling approach to statistics, a modeling language and various sets of associated tools are made available to learners, allowing them to pursue personally meaningful investigations. Learning by doing involves building up mental structures so that concepts may become linked into a mental network that allows some ideas to be assimilated readily while others become radically transformed by the assimilating structure. If a concept that is taught is well assimilated to the teacher’s internal structure, but the learners’ structures differ sufficiently from the teacher’s, then what is taught will be radically transformed, and there will not be an effective link with the student’s mental network.5 Arguing...