Introduction to Living Math



What does calculating the cost of a grocery item per pound, measuring the dimensions of a garden, anticipating the number of days left before a family celebration, and following a recipe have in common? They are all examples of using math in daily life.  In the home education world, we call this “living math.

To teach or learn by using “living math” means to learn, understand, and apply a mathematical concept in a situation which the child encounters in daily life.

Beginning with counting and developing calendars to mark time – scientists, mathematicians, and scholars have been investigating and discovering math for centuries through experimentation, then passing this knowledge on to students.

A philosophy or teaching method of using “living books” and teaching the living concepts of math was utilized and written by a teacher, Charlotte Mason, in the 1800’s in England. From these ideas, “living math” strategies are used to teach math alongside a math textbook or, in most homeschool cases, replacing the textbook.  There are many curriculum writers now publishing living math books and you can get a lot of living math curriculum and videos online, some for free.

Teaching math the “living math” way, homeschoolers read books that include the history of math and its development, and mathematicians. They study math in a chronological manner, exploring and understanding the concepts in the order in which they were discovered and developed. For example, reading Archimedes and the Door of Science which includes an extensive chapter on the development of the concept of Pi is a great way to prepare for celebrating “Pi Day.”

Some homeschoolers read books that tell a story in which the characters in the book need to use a mathematical concept in order to solve a problem. While others enjoy books that present problem solving puzzles and games in order to understand how to use various mathematical procedures.

Presenting a new math concept involves using concrete manipulatives (or objects the child can manipulate) to represent the quantities being calculated in the equation. As the child “sees” the concrete representation of each part of the equation, he can better understand the concept. Once the concept is understood, the child can then move to visualizing the quantities and mentally calculating the solution on his own.

Math manipulatives can vary from beans to attribute blocks to base 10 rods. These manipulatives can demonstrate everything from the concept of counting or sorting to calculating complex equations. There are even 3-dimensional geometrical shapes which can be filled with rice to compare volume or algebraic tiles and scales to complete algebra equations and to understand negative numbers.  However, the math experts which we have consulted with at HECOA advise not trying to run before your child can walk.  In other words, teaching algebra before understanding fractions is not a good idea.  Teaching fractions before understanding multiplication and division can be really confusing.  So be sure that whatever source you are using to teach living math is teaching in the correct order.

HECOA members have access to a complete list of math concepts in the order they should be taught, all the way through Calculus.  It’s found under the member Toolbox.

As previously mentioned, there are a number of authors and math “living book” series which can help homeschoolers begin to implement a living math program in their homes. All of these books can present math in an auditory (when read aloud), visual, and fun way to understand the abstract concepts and motivate interest and learning. Adding tactile manipulatives to the use of “living books” brings another concrete dimension to the learning experience. A number of these books have additional activity suggestions in the back to extend the learning experience.

Learning math does not have to be a dry and abstract experience. Using the “living math” methodology makes the math experience more understandable, enjoyable, and a more concrete living experience for the child.

What are some of your ideas for teaching “living math”?

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