Spiral vs. Mastery Instruction in Mathematics Education

We all have memories of our experiences in math class. A text book, a chalkboard/whiteboard, a teacher who would model procedures for solving problems, and homework assignments. Maybe sometimes if we were lucky, the teacher would assign the odd numbered problems so you could check your answers in the back of the book. This type of mathematics education is embedded in American society.

In a world that is becoming increasingly intertwined it has become apparent that the U.S. education system is not preparing our students to compete and lead in this global environment. The Pew Research Center and the Brookings Institute both report that U.S. scores on international tests like the PISA and the TIMMS consistently show the U.S. ranking well behind other countries, especially in the area of mathematics. It has become clear to everyone that something needs to be changed in order to prepare our citizens to be global leaders.

Approaches in mathematics education have changed somewhat from the scene I described earlier, but effectiveness and consistency have yet to be proven or achieved. A debate rages on among educators and those involved in education policy about which approach to teaching mathematics is best: spiral curriculum or mastery based curriculum.

In a mastery based model it is believed 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. This is widely considered to be the best approach for teaching mathematics currently as the goal is to insure that students "master" something before moving on to a new concept. It is also worth noting that Singapore, which has consistently ranked number on in mathematics as measures by international tests, uses a mastery based approach. Critics of a mastery based curriculm bring up the ideas of:

• student fatigue - getting tired of a topic before they are able to demonstrate mastery
• student frustration - it is common to many students to be successful in one area of mathematics such as algebraic thinking while struggling with geometry, in a true mastery approach a student may be "stuck" in a topic that is naturally a struggle for them.
• students do not have a chance to go back and practice skills that they have previously shown mastery in. 

A spiral model 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. The spiral approach is what has been widely used in the U.S. since the 1960's. The spiral curricular approach also receives criticism with the most powerful being, that if this is what we have been doing for the last 50 years, it does not appear to be working. Spiral math curriculum also does not allow for serious intervention when a student does not understand a topic. It is moved on from, and when presented the next year, with added complexity, students are missing the foundational pieces they need to be successful at higher levels.

What do you think? Is spiral the best approach? It certainly is what is familiar to most of us. Is mastery the best approach? Just because other high performing countries are doing it should we too?