Spiral or Mastery: Must One Choose?Sometimes Choices Are Make BelieveBy Antoinette LaGrossa 
Broadly speaking, many people classify a math curriculum as mastery (unit study) or spiral.
First, some definitions. Mastery or unit study is a more siloed approach: The student studies one isolated topic for several days - or in the case of some curricula, months - at a time. The spiral approach covers many more topics covered more briefly. With the unit study approach students delve more deeply into each topic area. But they do not build strong connections between different aspects of math and parents complain that their children do not have good "context" and are unable to apply their knowledge. With the spiral approach students get a broad understanding of how math topics fit together. But they may not have deep knowledge of each topic and parents complain that their children don't always have enough specific knowledge. For example, a second grader might study patterns, addition, subtraction, square numbers, Roman numerals, and triangles. The $1 million question: So which is better?At ShillerMath we reframe the question. It's not a matter of mastery vs. spiral: Deep understanding of math comes from both mastering individual math topics and also from knowing how they fit with other topics. ShillerMath takes a unique approach to combine mastery and spiral: We call it the 2Cs: Competency and Closure - and both occur only when a student achieves both competency and closure on a particular lesson. It's not enough to get the right answer: The student must also have closure. And competency and closure only truly occur when lessons are multisensory. For example, when doing multiplication it's not enough to be able to multiply two 2-digit numbers by hand. Does the student understand visually what that means? Can the student spatially understand what multiplication is? By using manipulatives, visuals, and songs, students literally get a 360 view of each critical math topic - and how it relates to other, sometimes seemingly unrelated math topics. These connections are more difficult to come by with a siloed mastery approach. Sometimes a student gets mastery quickly. A parent sees that and wants the child to move on. But unless that child has closure - a complete understanding using all the senses and relationships to other math concepts - the comprehension is incomplete. That's why with ShillerMath we ask parents to let their children fully explore each lesson and get closure on their own terms before moving on. On occasion a parent tells us that ShillerMath "skips around" - but upon further investigation the only thing that happened was the child was not given the opportunity to get closure. When children are allowed to achieve closure they learn both deeply and broadly. Towards this end ShillerMath makes it easy to track mastery of the lessons with the "Lessons to Be Revisited" column on the Completed Work Sheet, which is included with each lesson book (and can be downloaded from the customer downloads). Lessons are periodically revisited if necessary until competency and closure are achieved. The ShillerMath diagnostic review tests (four per lesson book) then measure long-term retention of concepts, redirecting the student back to lessons for any skills not retained. At ShillerMath we don't pretend to know all the creative ways that children learn. Our goal is to give them - as natural learners - the environment to fully leverage their magical learning abilities. With ShillerMath it's not mastery vs. spiral: It's 2C! Learn more about integrating your math with spiral and mastery by implementing the ShillerMath 2C approach in your homeschool math in a free webinar: Thursday, December 17th.
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