Commentary on papers to investigate the international assessment of mathematical knowledge for teaching

The guest editors and contributors to this issue of ZDM onthe topic of mathematical knowledge for teaching (MKT)are to be congratulated for the quality of their research, fortheir contributions to the effective teaching of mathematicsand success of students, and for the interest and furtherresearch these ﬁve papers will undoubtedly generate. Thereare many aspects of the papers to like and one of them isthat the papers describe teacher education work movingforward in ﬁve countries—Ghana, Iceland, Indonesia, Ire-land and Korea. My prediction is that we will see both anexpansion of this type of research in other countries, andwe will see teacher education researchers in science,reading, social studies, and other subjects developingvariations of the MKT instrument for their own use. Ibelieve this collection of papers and the research alreadypublished by Deborah Ball, Sean Delaney, and their col-leagues, is going to have an immense impact on teachereducation research.What made the papers especially interesting to me isthat all of the papers addressed the important methodo-logical problem of translating and adapting instrumentsfrom one language and culture to another. The papers areabout relevant methodologies and their ﬁndings. Becauseof the inﬂuence of these papers not only on the substantiveissues of teaching mathematics, but on the methodology ofadapting instruments, I wish the papers had acknowledgedor referenced the International Test Commission (ITC)Guidelines for Test Adaptation (http://www.itctestcom.org).These validated guidelines have been used in manycountries and were developed by seven internationalorganizations of psychologists. They are frequently cited inthe international testing literature, and because of theirpopularity, a second edition has been prepared and is aboutto be released. These ITC Guidelines would have provideda framework for each of the research teams (and researchteams to come) and I think the methodologies used by theresearch teams would have been even better and moreuseful. Instruments like the MKT are increasingly beingadapted to support an expansion of research and often tocarry out cross-cultural research. As useful as I think theITC Guidelines are, I think the work by Delaney (cf. 2008and this issue) is an outstanding example too of testadaptation methodology. That the researchers in this issuetook their inspiration from the Delaney et al. study is veryimportant too.Overall, I think the papers used excellent methodolo-gies, and the adapted instruments are going to be valuableto researchers in these ﬁve counties as well as the UnitedStates for many years to come. At the same time, somemethodological changes would have improved the use oftranslators and judgmental designs in this work. Translatorsneed to know the languages and the cultures involved in theadaptation. It is surprising to note that these characteristicsare not always respected, and the educational and psy-chological journals are littered with papers that did notfollow these guidelines. Ype Poortinga, a well-knowncross-cultural psychologist and past editor of the Journal ofCross Cultural Psychology, once noted that 80 % of thecross-cultural research prior to 1990 should not have beenpublished because of the poor quality of the translationsand adaptations (see Hambleton, Merenda, & Spielberger,2005). It is desirable too that translators know somethingabout the construct being investigated and instrumentdevelopment. Without these skills they are not wellequipped to carry out an effective translation and