Teaching Math: Subject by Subject, Part 17

(I am so pleased to welcome a guest writer who excels at presenting an insightful summary of math the Charlotte Mason way. Richele Baburina has extensively researched Charlotte Mason’s approach to math and compiled her findings in her excellent book, Mathematics: An Instrument for Living Teaching, and helpful DVD series, Charlotte Mason’s Living Math: A Guided Journey.)

Charlotte Mason valued a generous curriculum. Though emphasis on the three R’s alone makes for a meager education, these subjects did have their rightful place of study.

Charlotte valued the study of arithmetic primarily for its use in training mental and moral habits, including accuracy, attention, careful execution, neatness, and truthfulness. Though its use in daily life was important, it was the “beauty and truth” of mathematics, that awakening of a sense of awe in God’s fixed laws of the universe, that afforded its study a rightful place in Charlotte’s curriculum.

Let’s take a brief look at how mathematics are taught in a CM education—because without living teaching, that sense of wonder might not be awakened nor the desired habit training take place.

The Early Years

The study of arithmetic falls well within Charlotte’s definition that “education is an atmosphere, a discipline, and a life.” Before the age of six, a child’s education is by means of his senses, natural environment, and unstudied games. Direct preparation for mathematics in these years is considered not only undesirable but detrimental.

Elementary Arithmetic

The formal study of arithmetic begins at about six years of age and is characterized by thorough, careful work in which the children make discoveries for themselves. Its study follows Charlotte’s basic principles of short lessons with concentrated attention.

Manipulatives

Though the term math manipulative did not exist in Charlotte’s time, the use of concrete objects as aids in conveying ideas is significant in her method of teaching arithmetic.
Some important points to remember:

• All the manipulatives you need can be found in your own home—beads, buttons, and craft sticks to name just a few. A variety of simple objects should be used rather than a single specially-designed manipulative so the child doesn’t form a hard-and-fast connection between the math facts and the manipulative.
• Manipulatives are only a tool to the presentation or investigation of an idea. If a manipulative’s use requires too much teaching, it becomes more important than the idea it is to represent.
• Arithmetic tables should not be memorized until the child proves the facts first through the use of manipulatives.
• Allow your child enough time to work with the manipulatives but then progress to working with imaginary objects. Once the child can mentally picture the number, or has grasped the abstract, put away the manipulative until the introduction of a new concept.

“A bag of beans, counters, or buttons should be used in all the early arithmetic lessons, and the child should be able to work with these freely, and even to add, subtract, multiply, and divide mentally, without the aid of buttons or beans, before he is set to ‘do sums’ on his slate” (Vol. 1, p. 256).

Mental Arithmetic and Oral Work

In Charlotte’s methods of teaching mathematics, written work is used sparingly. Mental arithmetic and oral work help reinforce math facts and vocabulary, plus they are instrumental in the training of good habits.

“Give him short sums, in words rather than in figures, and excite in him the enthusiasm which produces concentrated attention and rapid work. Let his arithmetic lesson be to the child a daily exercise in clear thinking and rapid, careful execution, and his mental growth will be as obvious as the sprouting of seedlings in the spring” (Vol. 1, p. 261).

While children advance in their understanding, the oral questions should always remain within their ability.

“Engage the child upon little problems within his comprehension from the first, rather than upon set sums” (Vol. 1, p. 254).
“Now he is ready for more ambitious problems: thus, ‘A boy had twice ten apples; how many heaps of 4 could he make?’ ” (Vol. 1, p. 257).

Some points to consider:

• The oral questions we give our children should be engaging. For example, “How old will you be when your sister is four” will be more apt to fix your child’s attention than the same question given as, “Add 4 + 5.”
• Require your child to give fully worded answers in complete sentences for the most benefit.
• Along with oral work throughout the math lesson, consider following Charlotte’s schedule of five minutes of rapid drill at the end of the lesson or ten minutes for older children at another time in the daily schedule.

Careful Teaching vs. Careless Teaching

Charlotte felt that careless teaching—which includes offering crutches and failing to pronounce sums wrong—fosters habits of carelessness in children. In contrast, carefully graduated lessons, along with Charlotte’s methods already mentioned, foster the training of good habits.

“Arithmetic is valuable as a means of training children in habits of strict accuracy, but the ingenuity which makes this exact science tend to foster slipshod habits of mind, a disregard of truth and common honesty, is worthy of admiration! The copying, prompting, telling, helping over difficulties, working with an eye to the answer which he knows, that are allowed in the arithmetic lesson, under an inferior teacher, are enough to vitiate any child; and quite as bad as these is the habit of allowing that a sum is nearly right, two figures wrong, and so on, and letting the child work it over again. Pronounce a sum wrong, or right—it cannot be something between the two.” (Vol. 1, p. 260).
“Therefore his progress must be carefully graduated; but there is no subject in which the teacher has a more delightful consciousness of drawing out from day to day new power in the child. Do not offer him a crutch; it is in his own power he must go” (Vol. 1, p. 261).

Living Math Books

Charlotte believed mathematics fell outside her rule of literary presentations. She stated:

“…mathematics, like music, is a speech in itself, a speech irrefragibly logical, of exquisite clarity, meeting the requirements of mind” (Vol. 6, pp. 333, 334).

Charlotte did not employ the modern notion of “living math books” to teach mathematical concepts. She advocated acquainting the children with the “captain” ideas of math by introducing the different branches or their great thinkers through an interesting or exciting history.

Advanced Mathematics

The methods we’ve discussed today are not just for the teaching of elementary arithmetic; they also apply to more advanced arithmetic: geometry, algebra, and beyond. Whether you are comfortable teaching the higher levels of mathematics or rely more heavily on textbooks, a curriculum, or a tutor, be sure to ensure a living treatment of math for your older child as well.

• Guide your older child in discovery, allowing her to think for herself. Be patient and advance slowly. Allowing your older child to wonder, discover and permit ideas to germinate.
• Practical exercises should continue along deductive exercises in geometry, and the practical side of algebra should be introduced as early as possible.
• Provide a slow, steady approach with lots of practice.
• Exclude long or tedious examples for calculation.

The Mathematics: An Instrument for Living Teaching book includes all the details and practical step-by-step instructions that describe how math was taught through each advancing level of Charlotte’s classrooms—from learning numbers through algebra and geometry.

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