This is the deepest cognitive level and can
also be the most fun! Student-designed
projects generally fall into this category because they require pulling together multiple
ideas and skills into an experiment, survey,
model, or investigation. To utilize the multiplication facts for 9, for example, a student
might be asked to plan a party for 9 people and present a detailed list of the costs,
using newspaper ads or websites to find
prices. (For an extra challenge, the student
could be given a spending limit.) This task
obviously draws on the facts surrounding
the number 9, but also incorporates many
other skills, both mathematical (adding)
and practical (finding the best price).
Looking at these examples, you may
be able to see how rich mathematical
learning can be. You are probably wondering, though, “What does this mean for
me as a homeschooling parent?” I’d like
to suggest three possible applications:
1. Determine the depth of learning that
is best for a particular task. Not all
mathematical learning needs to
involve complicated problems or
projects. In fact, it’s generally best to
keep the activities varied to maintain
2. Determine how well you are able to
coach your child in “going deep.” You
may have never been given the opportunity to think past the second
level yourself, and even then, you
may have struggled. Being aware of
your own abilities will help you with
the next item.
3. Choose the math program that offers
the best support. If you function well
at the deeper levels in math, you can
supplement any curriculum by plan-
ning instruction and learning activi-
ties similar to the ones presented as
examples. If you are not comfortable
thinking this way, you may want to
seek out programs that include the
types of problems and activities that
encourage deeper thinking.
As homeschooling parents, we want
to ensure that our children acquire basic
math skills and are able to apply them in
advanced study and everyday life. However, encouraging them to “go deep” in
math can increase motivation, help them
learn how to think and reason, and even
make math fun!
Jean Soyke is a certified elementary educator with specialties in math and curriculum development. She taught in both
public and private schools before homeschooling her four children, grades K- 12.
For the past several years, Jean has worked
for homeschool publishing companies and
currently serves as the managing editor for
From Philip Keller, author of The New Math SAT Game Plan
"This is the book I wish I had read even while
getting straight A's in algebra. I never saw the
connections and I never learned to speak that
mathematical language until I read this book."
Packed with clear discussions and examples,
followed by exercises with answer keys and
Examine a detailed excerpt
Post questions about the book
Learn efficient ways to handle SAT math too!
Or just explore – lots of interesting math awaits!
As homeschooling parents, we want to ensure that our children acquire basic
math skills and are able to apply them in advanced study and everyday life.