Length measurement, which is a fundamental domain for measurement learning, plays a prominent role in measurement education in most countries. Although there seems to be a great consistency about the aspects of those concepts, there may be differences in the curricula and teaching practice of length measurement. The preliminary findings of our research project on length estimation showed differences between German and Taiwanese children which may be attributed to different learning opportunities on length and on estimation.
The purpose of this study was to examine similarities and differences in Taiwanese and German elementary written textbooks concerning the treatment of length understanding, measurement, and estimation.
Our analysis showed that in both countries, nearly the same time of teaching length is intended with. The comparison between both countries suggests that length learning in Germany seems to be more concentrated than in Taiwan: starting in second grade and offering only one unit per grade. As in other countries, procedural affordances predominate the conceptual learning situations in the both countries, a tendency which was stronger for the German than the Taiwanese textbook series. Although units can be converted, reasoning and justification and benchmark learning were the most common conceptual elements in both countries, their importance differed. The Taiwanese textbooks mainly stressed the idea of conversion, whereas the German textbooks focused more on benchmark learning. Additionally, the textbook series in both countries contained some problems involving visual estimation, which is related to length estimation, though the amounts of the problems were less than those of reasoning and justification.
The comparison of procedural elements showed that both countries very often focused on unit conversion, measuring with a ruler, and addition and subtraction of length. In the Taiwanese textbooks more tasks asked for direct comparison and measurement with nonstandard units, whereas the German textbooks stressed visual estimation. Overall, the Taiwanese textbooks concentrated much more on concrete actions, whereas the German textbooks focused on more abstract and mental procedures.