Translating and Adapting the Mathematical Knowledge for Teaching (MKT) Measures: The Cases of Indonesia and Norway

Abstract

AbstractThis paper examines issues of translating and adapting an instrument that aims at measuring mathematical knowledge for teaching in Indonesia and Norway. The instrument was created for use in the U.S., and we discuss problematic and challenging issues of translation and adaptation. Two items from the released items pool were translated using a common framework modified from a previous study to exemplify critical issues that need to be resolved prior to using such instrument in another country. Themes identified in this study include a) minor challenges due to cultural differences; b) the use of technical language in schools; c) incommensurable contexts across countries; and d) the use of mathematical models.Keywords: cross-national comparison, instrument translation, instrument adaptation, mathematical knowledge for teachingIntroductionThere is a growing interest and need to develop valid and reliable instruments to measure teachers' knowledge of mathematics due to a climate of increased accountability. Few scholars will dispute that teachers' knowledge of mathematics is one of the most important influences on teaching practices and eventually on what students learn (Ball, 1990; Ball, Lubienski, & Mewborn, 2001; Hill, Ball, & Schilling, 2008; Hill, Blunk, Charalambous, Lewis, Phelps, Sleep, & Ball, 2008). Thus, the availability of measures to reliably assess what teachers know holds promises for further understanding factors contributing to this knowledge and thus inform teacher education programs. Moreover, with the increased attention to comparative studies in mathematics education in the past decades, examining the quality of teachers' mathematical knowledge in different countries may provide insights on improving students' achievement (An, Kulm, & Wu, 2004; Cai, 2005; Ma, 1999). However, the scope of cross-national studies on teachers' mathematical knowledge has been limited to a few countries, and these selective countries perform well when compared to the United States on international comparison (e.g., An et al., 2004; Cai, 2005; Ma, 1999; Stigler & Hiebert, 1999; Zhou, Peverly, & Xin, 2006). Widening the range of these studies to incorporate more countries, including developing countries, may be useful to reach a greater understanding of the teaching and learning of mathematics. This article reports an initial stage of such endeavor by examining issues of translation and adaptation of a U.S. based instrument for measuring teachers' mathematical knowledge in Indonesia and Norway, where the focus is on the challenges faced and problems encountered when using this instrument in different cultural settings. To illustrate the underlying complexity of the translation process of such instrument, a case study was conducted in which two items were translated and adapted for use in the two countries, and are discussed in this article.Bradburn and Gilford (1990) suggest that using existing test instruments for international comparative studies is beneficial in that there is linkage to other ongoing studies. However, Emenogu and Childs (2005) remark that even when rigorous processes of translation, verification, and field-testing are followed, translation may introduce measurement non-equivalence. Differences may occur, not only due to language differences, but also variability in teaching practices. For instance, curriculum differences such as the sequence of mathematics courses, the time spent on topics, availability of textbooks and other materials may cause differences in the relative item difficulty of measures (Emenogu & Childs, 2005). Understanding the context of the intended country where the measures are to be used is therefore deemed necessary.One set of measures for teachers' mathematical knowledge that has been widely studied and shown to be successful in the United States is the Mathematical Knowledge for Teaching (MKT) measures (Learning Mathematics for Teaching Project, 2006)1. …