Homefires - The Journal of Homeschooling OnlineHomefires - The Journal of Homeschooling Online

Teaching Mathematics: Where do I begin? Will it ever end?

Teaching Mathematics: Where do I begin?
Will it ever end?

Linda C. Burks, Ed. D.,

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 anxieties.

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, prefers unschooling, or selects a set curriculum in those areas, that same approach will probably suit your family in mathematics. Once you identify your teaching style, you have a place to begin your study of mathematics.

Curriculum approach

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 Singapore Math. 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 of manipulatives, such as base ten blocks, money, or 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 multiplication tables. 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 multiplication tables 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 Content Standards.

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", "Elementary Algebra," 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, worksheets, 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.

Outside help

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 math-mom.com.

Additional Math Articles