With the Spirit of Math program, we break away from the spiral math curriculum traditionally used in schools today. In the “scatter-gun” approach that typifies the spiral math curriculum, students learn a little bit about, for example, operations with fractions every year.
In Spirit of Math, in grades 5 and higher, we math teach topics thoroughly once. Students are, for example, taught in the first year how to handle all situations involving fractions and how to perform the operations necessary both with a calculator and by hand before moving on to a new topic. In every math topic that follows the fractions topic, the materials assume that the students have a firm grasp of fractions and use fractions throughout. Although you never teach topics in Spirit of Math a second time, your students constantly review and refine the concepts as they cover new work.
New topics must build a foundation. This provides a firm grounding on which students build competency in arithmetic and develop an in-depth understanding of mathematical ideas. Because all those involved understand why one topic follows another, learning goals are clear and students progress with a deeper understanding of math.