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Your June 2014
ShillerLearning Tidbit
Does ShillerLearning skip around?
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 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 sprial 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.
So which is better?
At ShillerLearning 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.
ShillerLearning 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 (which occurs with mastery): The student must also have closure (which occurs with spiral). 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.
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 lesson is incomplete. That's why with ShillerLearning 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 ShillerLearning 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 ShillerLearning 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. Lessons are periodically revisited if necessary until competency and closure are achieved. The ShillerLearning 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 ShillerLearning 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 ShillerLearning it's not mastery vs. spiral: It's 2C!
A poet, a priest, and a mathematician, all male, are discussing whether it's better to have a wife or a mistress.
The poet argues that it's better to have a mistress because love should be free and spontaneous.
The priest argues that it's better to have a wife because love should be sanctified by God.
The mathematician says, "I think it's better to have both. That way, when each of them thinks you're with the other, you can do some mathematics."
June 2014 Puzzler [Grades 8-12]
Jane wants to study for 45 minutes. But she's on a camping trip with no electronic devices. She does have two unevenly burning twigs, each of which burns in total for 1 hour, and a match to light them. Can she time exactly 45 minutes?
Provide the correct answer by June 25, 2014 to be this month's puzzler winner.
I hope you enjoyed this short math break.
Sincerely,
Larry Shiller
Publisher
June Tidbit special: Free shipping on any kit. Use promo code FREEJANE. Expires June 30, 2014. Only at shillerlearning.com.
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