Many studies have shown the difficulties of learning and teaching the decimal
number system for whole numbers. In the case of numbers bigger than one hundred,
complexity is partly due to the multitude of possible relationships between units. This
study was aimed to develop conditions of a resource which can help teachers to enhance
their teaching of this concept, and learners to overcome some of its difficulties. ‘‘Didactical
engineering for development’’ is a methodology that consists in cycles of conception of a
resource and experiment with teachers, with a comparison of the a priori and a posteriori
analysis. Overall choices for the design of the resource are described and the two main
tasks designed with the support of a fundamental situation too. The type of collaboration
between teachers and researchers evolves during the cycles of experiments in order to
reach the conditions outside the research context. The analysis serve both to study how
ordinary teachers appropriate the proposals made in the resource and to identify what is
essential to disseminate to teachers. The results show how the situations can potentially
help students to learn place value concepts, but they also indicate some resistance from the
teachers when dealing with the decimal (base ten) principle of the numeration system. This
is related to the influence of manipulative in teaching place value and to some charac￾teristics of regular teaching practices. These results indicate the limitations of a resource in
changing teachers’ practices, and they show that further teacher training about the decimal
principle of the number system is needed.

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• New perspectives for didactical engineering: an example for the development of a resource for teaching decimal number system

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