The article discusses the entry of standardised measurement into the educational systems of Sweden and Germany and the processes of shape-shifting associated with this process. In the first part of the article, we investigate how standardised measurement challenged existing ways of conceiving education in Sweden and Germany during the first half of the twentieth century, leading to the introduction of a system of national tests in Sweden, but not in Germany. In the second part of the article, we explore standards-based reform in Sweden and Germany contemporaneously, including the role played by standardised measurement in this process. We analyse how psychometrics functioned as a "quick language", i.e. a shorthand means of communication in educational matters, and the role it played in processes of shape-shifting of standardised measurement, i.e. transformations in directions very different from that which early proponents of standardised measurement had envisaged.