As noted in the title of this book, the sequence of lessons is wide-ranging in order to define the extremes of readiness and ability in a typical kindergarten classroom. In actuality, the skill levels range from pre-school to second grade. From experience, we all know that any single math text does not meet nor challenge the breadth of this formative group of learners. What is intended is an appeal to classroom and resource teachers to follow a system which is so divergent and advanced when compared to anything published so far. The term "advanced" is perhaps a misnomer in that one might infer a more complicated and radical methodology; this is not true.

It is only possible to challenge each child if he/she is taught individually, which is why the program was designed originally for parents. However, after experimenting with students in a classroom setting for the past six years, teachers have provided a jump-start of incredible proportions, not only for math but for reading as well, because success begets success in all forms.

The focus of nearly every game is a partial deck of Bicycle® cards. The suites are referred to as shapes, and by touching and counting they become visual and tactile reinforcers. Most children are acquiring a numeration sense for beyond the limited expectation imposed by parents at home and teachers at school. How do we then help them to have fun and at the same time master such number procedures as counting and the basic facts? Once chidren can distinguish numerals to 10 and differentiate which one is larger or smaller, the first big step is to combine counting and comparing in order to count on. From this beginning it is critical to master a series of developmental strategies and prompts which never are formed in kindergarten math texts.

The level of a child's background information plays a critical role as he/she struggles to reconcile new information with old. If the mental structures are not performed to support strategies for thinking, there will be no connection and consequently less opportunity for transfer as learning progresses. In their formative stage, children with interest and a curiosity are in a good position to develop other positive dispositions, such as motivation and industry, which have life-long affects. Of course, interest is very much related to what children already know. They tend to input best something that varies yet relates to what they already understand. Even though most experienced teachers are aware of age appropriate activities, it is more difficult for them to determine what makes something individually appropriate.

For teachers, the challenge is always managing a class of 20-25 students. Large numbers could but should not be cause for abandoning the prospect of a highly personalized math system. Because time on task is the most important variable, a differential time schedule for ability groups of no more than five students can be complemented with brief whole group and one-on-one instruction. The math textbook can provide for busy work while you are teaching direct instruction to small groups.

Such is the incredible challenge awaiting those teachers willing to follow the Ellerby approach to mathematics.