This post continues with our Wisdom’s 7 Pillars resource recommendations, today on the topic of L.E.D. Math.
UPDATE at the end.
LED MATH
Of all the things we teach our children, math is probably the hardest
for parents to implement in a “lifestyle” way, especially beyond the
very young childhood years. In keeping with LED principles, we desire
to keep math instruction as informal as possible for those early years,
and not resort to formal “school book” type programs until the formal
education years (the youth/teen years). We have implemented several
things that have worked well for us. We are working at getting those
things into a “presentable” format for others/you to use. We have also
found & recommend several resources that help us stay true to L.E.D.,
while providing instructional guidance.
INFORMAL
As a part of Lifestyle Education through Discipleship principles, we
believe most academic instruction, including math, should be fairly
informal, up to about the age of 12 or 13. The math concepts can
mostly be taught orally and informally through household objects and
dialog, with a little paperwork instruction included as needed. Our
children’s absolute favorite, and highly effective, math instruction
for the early years, we called “Money Math”. Very simply teaching them
to add and subtract through the use of money. They were “paid” for
doing things, and they “paid” for receiving things; beginning with
pennies, and progressing through nickels, dimes, quarters, half
dollars, and bills. They had to keep a running total, adding what they
were to receive, and subtracting what they were to pay. Money is
definitely the easiest and most logical way to teach our base ten
system, decimal placement, and negative numbers. We offer a booklet
called Freedom & Simplicity in Math (for the Childhood years), that
includes our “Money Math” ideas, as well as some charts and tools for
those early years. Calendars, clocks, and measuring devices round out
the *needs* of the early years.
We also love to incorporate Cusineaire rods (and counting bears) in our
hands-on, build it, see it math instruction. Yes, you can do the same
thing with popsicle sticks and dried beans, but the rods (and bears)
are so colorful, sturdy, uniform and fun. They aren’t just a “school”
tool; they are a fun “toy”, for building houses, complete with a family
to live in them. Our toddlers love the Jumbo rods and bears, too.
Our favorite resource by others, for these early years, which covers
all the topics typically taught in K through third grades, is “An Easy
Start in Arithmetic”, part of the 3 R’s series by Ruth Beechick. (We
recommend the whole series.) Mrs. Beechick includes ideas for teaching
each topic informally as you go through your day in managing your
household with your child alongside. Some written work is also
incorporated, as you design it (very simple, no daily worksheets to
write or such). A few simple chart ideas are also included. To
continue on with these ideas and foundation, Mrs. Beechick has also
written “How to Teach Your Child Successfully”. In it she gives ideas
& guidelines for older children (4-8 grade), in all foundational
subjects. We believe that “An Easy Start in Arithmetic” is all you
would *need* to teach your child math in those early years. Add on the
“Freedom & Simplicity Math”, Cuisenaire rods, and counting bears for
some practical, hands-on application ideas. “How to Teach …” will
guide you through the concepts needed to continue the rest of the later
childhood years, but many will probably want to add a little more from
other resources at this stage.
CONCEPTUAL
For those that desire to add a little more to the subject including
more written “paperwork”, we still recommend keeping the instruction
conceptual, concrete and informal, enjoyable, and “un-school bookish”
as possible. (We don’t feel these resources are necessary, but some of you may.)
The “Miquon” math series of “workbooks” utilizing Cuisenaire rods, by
Key Curriculum Press, provides this type of resource. It translates “real life” math,
that we’ve been doing concretely (with real objects through “An Easy
Start ,”) to paper. If you choose to utilize the “Miquon” books, we
still recommend using “An Easy Start in Arithmetic” as your foundation,
and adding the “paperwork” as an occasional exercise, as enjoyed by the
child, not an “everyday have-to”. There is no reason to begin this
“paperwork” at the same time you start your informal instruction with
“An Easy Start”. It can be begun even a few years later.
DRILL
Along the way, as your child learns the “math facts”, for
addition/subtraction, and in later years for multiplication/division,
you may want to work on these facts becoming “automatic” for him to
remember. This can be done by several methods. The most notorious is
by plain old fashioned flashcards, but many other ways are much more
fun and just as effect, if not more so for various types of learners.
“Math-It” turns the drill into a game, for both sets of facts using
“Add It” and “Timz It”. (Also available are “Pre Math-It”, covering
learning the addition facts through dominos, and “Advanced Math-It”,
covering percents/ decimals/ fractions.) We have devised our own type
of drill similar to “Math-It”, included in our “Freedom & Simplicity
Math”. Our children also all enjoyed learning sing-song jingles of the
facts from audio tapes, such as “Skip Counting”. The hands-on drill
tools called “Wrap-ups” are great for your kinesthetic kids, but we
found that some kids memorized where the string went more than the
actual facts. An alternative to the “Math-It” games, (I mention
because they are extremely popular with home ed parents) are the
“Calculadders” drill sheets. These are timed worksheets, and by far
the least fun and “informal” of the resources mentioned here.
Occasionally these can be used with older children for brush up, but we
don’t use them with our younger “informal stage” children. Freedom &
Simplicity Math (or “Math-It/Advanced Math-It”) and the “Skip Counting”
tapes are our recommendations.
TOPICAL
Shortly before your child advances to formal math instruction you will
want to make sure they have not only the basic facts “drilled”, but
also all their basic arithmetic down pat. This “transitional” stage is
usually between the ages of 10 and 12. During this time they will
begin doing regular “workpage” “math problems”, covering all concepts
of addition, subtraction, multiplication, division, fractions, decimals
(money), and percents, as well as measurements, time, place value,
negative numbers, and Roman Numerals concepts. Much of this will be
review, but also solidifying and pulling it all together. The “Key to
” series by Key Curriculum Press has booklets covering Fractions,
Decimals, Percents, and Measurements. Also, you could begin utilizing
the program recommended below, by covering each concept (not workpage)
in the beginning levels and using some of the word problems and/or
tests from the “extra practice” booklets/pages as indicators that the
child has good comprehension.
INCREMENTAL
Formal instruction, including formal math instruction, begins for our
children around 12 or 13 years of age. We believe the best math
program, that includes all elementary and high school math concepts,
taught in a line upon line, incremental, conceptual (understanding of
the principles, not just rote memorization) and concrete way (with
manipulatives) is “Math U See”, by Steve Demme. So, if this program is
complete, conceptual, and concrete why do we bother recommending the
other resources and not just start with “Math U See” and use it all the
way through? We feel “Math U See” is an excellent program, & love the
way it integrates conceptual teaching & concrete manipulatives for
applying math to “real life”. However, and for us and Lifestyle
Education this is a big however, we do not feel such a formal
structured program should be implemented for young children. We do
feel it is the best program for our older students, in those formal
instruction years.
All the resources recommended here have their own strengths for their
own stages of learning. We have picked the best in each category (as
we see it, from the wide variety we have used and thoroughly reviewed,)
for working within the principles of Lifestyle Education through
Discipleship. In review, those are: “Freedom & Simplicity in Math” and
“An Easy Start in Arithmetic” for early Childhood stage (and
optionally, “Miquon” math w/ Cuisenaire rods); for the later Chilhood
stage, “You Can Teach Your Child Successfully”, “Freedom & Simplicity
Math” (or”Math-It”), “Skip Count” tapes, “Key to …” series, (and
optionally, “Wrap-ups”); and for the Youth/teen stage, the
complete series of “Math U See” (which goes up through Trigonometry, if
you so desire).
One key component of Lifestyle Education is through “Notebooking”. Our
“Freedom & Simplicity in Math” includes guidelines for Notebooking
Math. As with all the other topics/subjects we Notebook, the goal is
to produce the child’s own Book of what they’ve learned and now know,
their own “teaching” guideline, – their own “text”, if you must. This
provides the “written work” the child does and provides him his own
personal reference book for looking up concepts and procedures for
figuring out problems. As far as we know this is the only resource of
this kind. It will, Lord willing, be available for purchase later this
Spring. Please pray for its timely completion as we put the finishing
touches on this “published version” of our L.E.D. Math methods for
Freedom & Simplicity™ in YOUR homeschool.
UPDATE: We have not changed our opinions on the above mentioned resources. We still like them and all the “pros” of them still stand. However, there is one more addition to our list, and also another preferred resource.
I would add Making Math Meaningful by David Quine of Cornerstone Curriculum, as another option alongside of Math U See. It too teaches math in a real life setting, using manipulatives, and teaches reasoning. There are some lesson “perspectives” I prefer in it, but some presentations, (like Steve’s video examples, and the uniformity of manipulatives) that I like better in MUS.
My preferred resource now though is Ray’s Arithmetic. It is a completely non-consumable program (a big plus for big families), and teaches completely through the principles of math, real life application, and reasoning skills. It is a series from the 1800’s, and therefore a bit more advanced than today’s teaching, but the books are not “grade-leveled” so that doesn’t really matter. It does not come with manipulatives, but it is expected that you will use real objects to present the lessons. It explains how you reason through to the solution of the problems. It also expects early lessons to be done orally and mentally with manipulatives, not paper and pencil, so it can be used with our informal early teaching.
