This viewpoint paper presents the writer's opinion that while the use of problem solving as the core method for learning mathematics is valid and reasonable in secondary schools (where students generally possess the necessary prior skills and strategies) there are many obstacles to applying the same method in primary schools, particularly in the early years. In addition to acquiring a conceptual understanding of number, young learners--and older students with learning difficulties--need to develop automaticity in recalling basic number facts and in applying computational procedures. To do this they require both active experience with number relationships and direct teaching with guided and independent practice. There is no hard evidence that most students achieve adequate mastery of basic numeracy skills simply by engaging in exploratory problem solving. Drawing on the relevant literature the writer identifies and analyses the potential difficulties associated with using such an approach as a main method for teaching primary mathematics.