# Mastery vs. Spiral: The Debate Continues

If you like lively discussions, conduct an internet search of the topic mastery vs spiral. The intensity of the interest in this topic runs at the same level as discussions related to reading methods (phonics? literature-based?) and which philosophy to follow (classical? unschooling?). While it is always interesting to read the opinions of others (particularly those who are veterans), thoughtful homeschooling parents take the time to research the options, consider their individual children, and make the decision that is best for their own families.

Basically, the terms mastery and spiral describe the most commonly-used approaches to teaching math. Proponents of math mastery believe that math is learned best when learned incrementally, with one skill building on the next. In a mastery math program, a student develops a thorough comprehension of one topic before moving on. For example, in the Gamma level of Math-U-See, students become competent with multiplication, learning all the facts and how to regroup with multiple digits, before moving into division (Delta level). The spiral approach, however, presents a given set of topics that repeat from level to level. Each time the material is revisited, more depth is added, linking new concepts to the learning that has already taken place. A program designed according to the spiral approach, for example, might have a student learn multiplication facts in one level, multiply two-digit numbers in the next level, and multiply three-digit numbers in the following level. At the end of both programs, the same concepts have been covered, but the order and the manner in which the students learn them differ significantly.

The spiral approach is probably familiar to you, as it has been characteristic of American education since 1960. However, a shift began in the early 1990s, when the United States began participating in international testing. International Mathematics and Science Studies conducted since 1995 show American students performing in the lower half of all the countries represented. This caused U. S. educators to start looking at how math was being taught in some of the highest-performing countries in the world (Finland, Singapore, Japan, etc.). It was soon discovered that these countries preferred a mastery approach over spiral instruction, and when these methods were adopted in Western classrooms, significant differences in student achievement were the result. Today, most textbook publishers and educators support a mastery model in math instruction.

While the educational community today believes that mastery learning is the best practice, there are still some criticisms of this approach. One concern is that students never have the opportunity to go back and review previously learned material. Math-U-See, which follows a mastery approach, addresses this by incorporating Systematic Review pages, where students are not only able to review past concepts but are also able to practice with the new one in the context of other problems– a necessary skill for being successful on a standardized test. Second, critics of the mastery approach suggest that students are all pushed along the same path, with no opportunity to pursue topics in more depth. Math-U-See’s Application and Enrichment pages are designed to meet the needs of the students who want to know more, offering engaging and interesting activities that build on the concepts presented in the lessons. Finally, the mastery approach has been accused of focusing on individual concepts one at a time, never showing how they all fit into the glorious whole. Math-U-See addresses this issue by tying each new concept learned back to the same group of manipulatives, giving students the underlying, cohesive foundation they need to be successful in math.

As research on the brain and learning continues to inform effective math instruction, the conclusions drawn only further support the fundamental design of the Math-U-See program—a mastery approach based on a set of manipulatives that help students truly see and understand math.