Design and results of an investigation attempting to analyze and improve children's solution processes in elementary addition and subtraction problems are described. As background for the study, a conceptual model was developed based on previous research. One dimension of the model relates to the characteristics of the tasks (numerical versus word problems, direct versus indirect, etc.). The second dimension has to do with the problem-solving process that is conceived in terms of three stages: thinking phase, technical or executive phase, and control phase. Using error analysis and individual interviews, the action structures (appropriate as well as inappropriate) of first and second graders were analyzed. On the basis of this ascertaining study, important shortcomings of children's knowledge and solution strategies were discovered. It also seemed that these shortcomings could be overcome by instruction; therefore, a teaching experiment was undertaken wherein systematic instruction was given for two weeks to an experimental class, while in a control group the usual arithmetic program was taught. Experimental instruction related mainly to the following three topics: an exact notion of the equality sign (=), the whole-part relation, and the action of controlling the outcome of an arithmetic operation. Results of the experiment are discussed. (Author/MK)