The philosophy of Saxon is that learning need not be difficult, but it does take time. As a result, the publisher takes an "incremental" approach, which means they introduce concepts in small pieces and then continually review that concept as they add more pieces. Topics are never dropped; instead, they are gradually increased in complexity, allowing them to become second nature.
In these levels, Saxon is designed to be completely taught by the parent or teacher. A kit always contains a teacher manual, an extremely important book which includes fully scripted lesson plans, telling you exactly what to say and do. It also includes a meeting book, used daily. In the "meeting," students learn and practice skills like reading calendars, using a thermometer, and making graphs. From grades 1 to 3, a set of two workbooks with flashcards is added to the mix. It has been our experience that some parents try to use just the workbooks, but we would discourage that plan, as we believe they are, at best, expensive drill books without the teacher's edition. Throughout all four levels, there is an emphasis on using manipulatives (not included in the kits), with which students learn about counting, patterns, geometry, and many other concepts.
Saxon generally moves fairly slowly and repetitively, but at these levels that is especially true. The kits are fairly expensive (more so when you add the manipulatives), and the lessons are time-intensive for both parent and child. Although we've met a number of people who really like these levels, they have been exceptions rather than the rule. We cannot highly recommend Saxon K-3 for most families, and generally steer our customers towards Horizons or Singapore (and sometimes Math-U-See) at these levels. If you do choose to use it, we would recommend skipping the kindergarten level entirely and starting with the first grade.