This paper reports on a study that examined if it is possible to start teaching algorithmic problem solving as early as elementary school, given the condition that studying mathematics is augmented by suitable use of computer technology. Three pre-service teachers, enrolled on a course on algorithmic problem solving in mathematics and who were already teaching in elementary schools, participated in the study. By analysing the results of teaching a unit of work to 9 and 11 year-old pupils, the results show that the topic of algorithmic problem solving can be modified to suit elementary school pupils. The data show that pupils exhibited better number sense and better ability to make mathematical generalizations. Most pupils were able to write an adequate algorithm to a given problem and to "run" it on a computer using a spreadsheet. (Contains 2 tables and 4 figures.)