Teaching Mathematics: Where do I begin? Will it ever end?
Teaching Mathematics: Where do I begin?
Will it ever end?
When homeschooling parents express concern about teaching a particular
subject, often that subject is mathematics.
Parents wonder where to begin. They are anxious about how to proceed.
Parents worry if they'll be able to advance with their kids. But there's
lots of hope! Here is some information to help you relieve these
Where do I begin?
Whatever philosophy you use to teach history, literature, or science, you can also
use it to teach mathematics! If your
family enjoys unit studies,
or selects a set curriculum
in those areas, that same approach will probably suit your family in
you identify your teaching style,
you have a place to begin your study of
If you prefer following an established curriculum, there are plenty available.
Avoid workbooks with pages of arithmetic problem after arithmetic problem. This
is not mathematics.
This is monotony! To make a wise curriculum choice, narrow your decision to three
or four possibilities. Working through a similar section, such as fraction
multiplication, will help you to taste the unique flavor of each one. Compare
your final choices by considering the following questions.
- Are new ideas presented through examples or through developing understanding?
- Do students construct ideas through investigations or through direct instruction?
- Are manipulatives used to illustrate ideas?
- Are interesting problems presented?
- Throughout the course, are problems given which review past topics?
For elementary grades, my top curriculum pick is
It has plenty of interesting problems to solve, does a nice job developing
concepts, and also incorporates review. Beware though, Singapore answers are
often "neat" numbers. In real life and in other texts and tests,
this will not always be the case!
Problem solving approach
As you grow confident in your abilities as a teacher, you might move beyond
a set curriculum. I teach mathematics
through problem solving.
Dale Seymour publishes a great series of problem decks called
"Techniques of Problem Solving."
With this terrific selection of problems, a wide range of topics is covered.
Kids love to pull out a stiff 5×8 card from the deck and solve the problem
on it. Moving the card to the back of the deck is a tangible sign of progress.
Kids are eager to try the next one! The cards are expensive, but worth the price.
As soon as a child can think through simple problems, you can begin the first
TOPS deck. This could be as young as four or five years of age. Using a variety
such as base ten blocks,
fraction strips, a
child can make sure she fully understands the problem. She can then use those
materials to find a solution. Finally, she checks her answer.
Children are highly motivated to learn arithmetic facts when they can practice
them in the context of interesting problems. I never taught my kids to memorize
If they needed multiplication to solve a problem, but hadn't memorized the facts
yet, they would do the problem with repeated addition. My fourth child laboriously
filled lots of notebook pages with repeated addition. Eventually even he decided it
would be easier to memorize the multiplication tables!
Avoiding that situation, my fifth child quickly chose to memorize the
when she was 5 years old.
Unit study or unschooling approaches
Should you be unschooling or using a unit study approach, you will come upon
plenty of math problems related to your studies. You, too, can
learn math concepts
as you need them to solve these problems. One advantage to this approach is that
students grow confident in posing their own problems and gathering knowledge to
reach a solution. A disadvantage is that the exact topics, given in that grade's
scope and sequence, may not be covered. If you are unschooling, you're probably
already comfortable making an individualized course of study. If you would rather
be sure to meet state requirements, keep systematic records of topics covered.
Then look for other problems to cover required topics you might have missed. The
state of California has a comprehensive online list of
On to high school
You can continue to learn high school level math
through unschooling or unit studies; however, if your child is
preparing for college,
you and your student will have to be significantly more creative in finding related
problems. Even with studies in art, architecture, quilting, and pattern design, it
would be difficult to cover all the ideas in a high school geometry course. It might
be helpful to supplement this type of study with a structured problem solving approach.
If you follow the problem solving approach through high school, there are several
great sources of materials. Phillips Exeter Academy has all their course materials
available for free public use at the
Phillips Exeter Math Department Web Site.
The texts at the online Art of Problem Solving also contain a terrific
selection of problems. These books include "Introduction to Geometry,"
"Introduction to Number Theory," and "Introduction to Counting and Probability"
There are two very good high school curricula for homeschoolers. Harold Jacob's texts,
"Mathematics: A Human Endeavor",
and "Geometry: Seeing, Doing, Understanding"
are timeless classics. The lover of mathematics will immediately be intrigued by Jacob's
detailed descriptions and interesting applications. For students who needs a little more
color and flare to motivate them, The
University of Chicago School Mathematics Project
is a good choice. UCSMP has a lot of current topics and applications. Written for students
to read a section and learn the topic themselves, it is ideal for homeschoolers. It
adequately prepares students for college entrance tests. If your child isn't planning
to attend college, Jacob's "Mathematics a Human Endeavor"
and "Transition Math,"
the first book in UCSMP series, are still a great way to gain an appreciation for
the beauty of mathematics and its applications.
Assessing level of understanding
After settling on an approach, determine your child's current level of understanding.
If you choose a curriculum, the dealer will usually help you select the appropriate
level text. For example, Sonlight Curriculum offers
Singapore Math placement tests.
If you prefer to teach by problem solving, finding the best starting place is not
straightforward. Should you buy a
TOPS problem solving deck
that's too easy, your child will have a great time, whiz through the problems, and build
her confidence; however, you might be disturbed by how much money you spent for that brief
experience. If you start with problems too difficult, you can always back up and purchase
an earlier deck.
It can be a good experience for a persistent student to struggle to solve a problem.
The time spent on the problem should be active. The child may be looking for patterns,
searching online for facts at such places as Math World or The Math Forum at Drexel,
and experimenting with different approaches. If a child is wholeheartedly engaged, he
can easily spend one day's entire math time on a single problem. If the child is
overwhelmed and has no idea how to approach a solution, it's too hard!
For unit studies, the best way to approach math is to look for problems within
your field of study. For example, suppose your family was interested in developing
some tasty smoothies and starting a smoothie business. You could ask all kinds of
math related questions.
- Suppose one large banana is on the list of the ingredients for an 18 ounce smoothie. To make nine 24 ounce smoothies to sell at your stand, how many bananas do you need?
- How can you estimate the volume of a banana 1 inch in diameter and 8 inches long?
- If four workers and four blenders are needed to make 60 smoothies per hour, how many workers and how many blenders are needed to make 100 smoothies per hour?
- Graph the amount of smoothies sold each of hour of day.
- Design a work schedule.
These questions cover many levels and interests. Younger kids solve easier problems.
Older kids solve harder ones. To broaden your math experience, view your topics from
different perspectives. Pose new questions. Be creative. Have fun!
Memorizing Math Facts
Even with all these motivational techniques, some kids need some extra help to memorize
facts. It takes work. Still, even a reluctant memorizer can catch on to the facts like a
champ! Multiplication facts
are typically the toughest to master. Be sure your child understands the underlying concepts.
Present problems which use multiplication.
Practice mental math techniques.
In our house, flash cards,
and other memorization gadgets quickly drift to the bottom of the toy chest. But they
may be just the right tool to fix facts firmly in a child's mind. My favorite is
Math Shark, an electronic drill,
which keeps a record of success. Math Shark displays the amount correct. It also shows time
used. Kids like to beat their past score and improve their time. Kids can advance to levels
of increasing difficulty. For the kinesthetic leaner, drills on
Learning Wrap-Ups may also help
them learn the multiplication facts. Tunes in the
Schoolhouse Rock CDs or videos
may be best for an auditory learner.
For parents who want help teaching math, there are options available. The
Chalk Dust Company provides instruction on DVD
or VHS tapes, textbook work, and personal help online or via telephone. For a
more personal touch, consider hiring an older student as a tutor. As a seventh
grader, my son started tutoring a boy four years younger than himself. It
continues to be a terrific experience for both boys. Don't feel limited to an
older child teaching a younger, peers can also learn a lot from each other. To
challenge those talented in math and to motivate those who might not be so
interested, organize a math club.
Will it ever end?
As a mom or dad, your math teaching really began long before you started homeschooling.
When you counted steps, played finger rhymes, or
sorted stones with your
toddler, you were doing mathematics together. Similarly, your math work does not end
when your children have completed "school." It is my hope that you will continue
the journey of learning new mathematical topics for your whole life. At least you and your
student can use the problem solving skills, which you developed in the school years, to
set goals, make plans, and tackle life's challenges.
Want to learn more?
I am working to develop all of these ideas more fully on my website,
math-mom.com. Here you will also find top
picks for each grade level. See specifics on recommended resources
to make learning math a fun, positive, and meaningful experience at
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