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Like most children, my son was curious, had a thirst for knowledge, and reveled in exploration and discovery. He was also a bundle of kinetic energy. If you have a child like this you’ll understand when I say that it wasn’t that he wouldn’t sit still, it almost seemed he couldn’t.
Charlotte Mason tells us that, “Children are born persons” and reminds us that we are not to “despise, offend, or hinder” these little ones. So, I knew that I would need to meet my child where he was—which often meant on the floor for a 5-minute math lesson.
Slowly, his five minutes of focused attention turned to 10, then to 15, and then to 20. One day, in about junior high, my son was tasked with drawing a series of angles without the use of a protractor, then he was to measure the angles and note the difference for each. He grabbed his straight edge and set to work, wondering aloud about the assignment and how close he could actually get. His wonder turned to happy surprise when, upon measuring, he found he’d drawn the angles with such precision they weren’t even a degree off.
Now, my child is not alone in his experience. Charlotte tells us
The chief value of arithmetic, like that of the higher mathematics, lies in the training it affords to the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders.Home Education, p. 254
Her emphasis on nurturing good habits during the math lessons means that, over time, fixed attention and careful execution becomes second nature to our children, along with a slew of other good habits, and these habits shape our child’s character.
In this post, we want to focus on the discipline of habit—the second of three educational tools in the motto, Education is an atmosphere, a discipline, and a life. If you missed the first part of this series, when we talked about the atmosphere of the math lesson, you can follow the link and take a look at that post. Today, let’s take a look at some simple ways to cultivate good habits during the math lesson.
From beginning operations in arithmetic through higher mathematics, tremendous mental effort is expended by your student and, just as a runner doesn’t sustain a sprint for an extended period of time, the child’s brain shouldn’t be intensely exercised for a prolonged length. With short, concentrated lessons—up to 20 minutes in the earlier grades, then never extending beyond 30 minutes, even in high school—a child is able to maintain alertness rather than plodding through long ineffectual lessons. To further help her avoid mental fatigue, be sure to alternate the math lesson with subjects that use different parts of the brain or body, such as singing, dancing, picture study, or even a walk to the mailbox or a bit of playtime.
Interesting and Interactive Lessons
Lessons don’t need to be dull when there are so many exciting things to be done with numbers. Charlotte tells us that giving “short sums, in words rather than in figures,” serves to excite “the enthusiasm which produces concentrated attention and rapid work” (Home Education, p. 261). A variety of interesting questions given in a lively way can spark a child’s imagination and promote habits of readiness, insight, and attention. For example, “How many legs have two lambs? If they’re joined by another lamb, now how many legs?” and, “Lillian has 7 candles on her birthday cake. She blows out 6, how many lit candles remain?” These types of questions are more apt to fix a young child’s attention than the same sums given as: 2 x 4, 8 + 4, and 7 – 6.
When reading, handwriting (and even sitting) can be difficult for a child, questions of an interesting nature allow him to focus on the ideas presented. As a child advances in understanding or is exceptionally alert during a lesson, these engaging questions can give way to more challenging work with numbers, and can involve more than one operation, fractions, weights and measures, and beyond.
In the same way, the ideas and concepts found in more advanced math become more interesting whey they’re given alongside their captain ideas or linked with reality. For example, the study of Prime Numbers becomes fascinating when we explore where they occur in nature and realize their involvement in our daily life. Equilateral triangles spark interest and excitement when we investigate how Michelangelo used their dimensions in his plan for Saint Peter’s Cathedral.
Do you see how interactive lessons, where the child isn’t merely memorizing an algorithm, will engage a child’s mind? Charlotte tells us that a “habit is set up by following out an initial idea with a long sequence of corresponding acts” (Parents and Children, p. 125). Captain ideas and interesting examples set these ideas in motion, serving to fix a student’s attention, ignite the imagination, and awaken her reasoning powers—cultivating what Charlotte calls good intellectual habits.
Now let’s talk about the review component of our math lessons. If I were to ask you right now what 4 + 5 is, you would probably answer immediately, without having to write the problem down, count on your fingers, or even give it much thought. This is because the addition facts became part of you in childhood through a fair amount of review.
While a student may have mastered a concept and is able to work comfortably with it, review is still an important part of the weekly lessons and should not be skipped. Periodic review of concepts and facts helps to further solidify them so that they become internalized—that is, they become habits of thought.
How much review is necessary will differ from child to child but we want to give enough to maintain fluency but not so much that he becomes bored.
A simple way I like to think of this is “New, Review, and Mental Math, too” and all three parts should make up the math lessons throughout the week. If you are just introducing a new concept that day then there might not be a time of Review (outside of that found in the 5 or 10 minutes of mental math.) Review not only helps the student maintain fluency, it will also help her make gradual gains in speed and instill the habits of accuracy and steadfast thinking, so make sure review is a consistent part of the week’s math lessons.
Mental math, sometimes called rapid oral work, is a scheduled activity where work is strictly oral and without the use of concrete objects or manipulatives.
The time of mental math should be lively and engaging. Varying between 5 and 10 minutes— depending on the level of math the student is working—it’s often given at the end of the math lesson or can be taken at a different time of the day. If you notice your child’s attention waning, changing to mental math can be a good way of livening the lesson up and regaining her concentration.
Mental math is perfect for helping students learn their math facts or maintain fluency and helps building speed and accuracy in many math processes. It’s also a fun activity as all ages can work together and pose one another questions or your child can pose questions to you. If you’re working with more than one student, they can take turns answering aloud while all write their answer on a dry erase board or piece of paper.
The questions asked should always fall within the scope of a child’s learning. Here are some examples of the types of oral questions that might be given through the years, beginning with engaging problems before moving to pure number.
- Nicholas bought 2 gumballs for 5 cents each. How much did he give for both?
- Georgiana needs 8 apples for a pie. She has picked 5 apples. How many more should she pick?
- 3 bunnies were in the garden when 3 more bunnies joined them. How many bunnies in the garden?
- And if 4 bunnies hopped away, how many bunnies remained in the garden?
- 9 + 4 – 3 =
- 11 + 3 – 2 =
- 12 + 2 – 3 + 4 =
- 7 – 5 + 8 – 6 =
Let’s do some multiplication and division table work.
- 3 cats and 2 kittens. How many legs among them?
- If 5 children are wearing shoes, how many shoes in all?
- How many 5s in 35?
- How many 2s in 12?
- 9 taken 4 times is?
- If Elizabeth picked 1/2 of 40 apples, how many did she pick?
- If Colin picked ¼ of 20 apples, how many did he pick?
- If 45 is half of a number, what is that number?
Weights & Measures
- How many ounces in a cup?
- Jésus drank 3 cups of water. How many ounces of water did he drink in all?
- Reduce to lowest terms:
How did you do? Can you see why Charlotte believed mental arithmetic is instrumental in training good habits? Some habits mentioned in her writing and those of her lecturer in Mathematics, Irene Stephens, include:
- Effort of mind
- Rapid work
- Clear thinking
- Careful execution
- Steadfast thinking
- Accurate thinking
- Independent work
- Honest work
- Exactness and
Good Physical Habits
If you’ve ever given Charlotte Mason-style handwriting lessons, you know that a few well-executed strokes written as beautifully as possible are more desirable than rows of sloppy work.
In like manner, teaching a child to write numbers in her math lesson closely resembles these early handwriting lessons and the same care given to letters is given to numbers.
We use plain easy-to-read figures and the child is encouraged to make strokes and bars as straight as is in her power. The curves in 2, 3, and 5 should always be fully open and those in 6, 8, and 9 fully closed.
A gridded math notebook also goes a long way in fostering habits of neatness and order. The size of grid chosen should be based on the child’s writing so that one number can go inside each square. The grids help keep everything in proper place value order and easy to read—which of course makes for more accurate work. As writing ability progresses, a ¾” grid or ½” grid will eventually give way to the standard ¼” grid and, when a child is in the beginning stages of any new notation—be it long division, fractions, or algebra—we start with simpler equations that involve little work in order to first secure neatness and orderly arrangement.
When working with weights and measures, we want to be sure not to rush the child, giving her the time she needs for careful work while encouraging precision and neatness with the scale and ruler. After weighing and measuring concrete quantities, her ability to judge accurately and carefully is increased by having her estimate the length, width, height, and weight of various things in the home and then having her determine her own accuracy.
Before beginning formal geometry, children can learn to handle mathematical tools—like the compass and protractor—through practical exercises in drawing and measurement. Corners should be kept square and lines drawn should be tidy. Having gained foundational ideas and familiarity with the mechanics of drawing will allow him to focus more fully on logical reasoning when formal geometry is begun.
Again, be sure your student keeps numbers, symbols, drawings, and layouts neat and orderly. Good physical habits will aid in the accuracy of her work and her ability to communicate it to others.
We discuss Charlotte Mason’s use of everyday objects in-depth in The Atmosphere of the Math Lesson. Using a variety of simple everyday objects that are easy to handle also fosters good habits by helping a child attend to the main idea of the lesson and encourage concentration and clear thinking. When work is done in the concrete, we want to establish a habit of orderliness by having the child arrange the objects in tidy rows, groupings, or in proper place value order rather than messy piles. Vary the objects with each lesson and put them away when no longer necessary so they are stepping stones on the way to abstract thinking, rather than a source of distraction or boredom and loathing.
One of the most frequently asked questions by parents regards Charlotte’s principle of “no do-overs” in the math lesson. Let’s hear it in Miss Mason’s own words though so we can understand her reasoning before pronouncing this a draconian measure:
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. That which is wrong must remain wrong: the child must not be let run away with the notion that wrong can be mended into right. The future is before him: he may get the next sum right, and the wise teacher will make it her business to see that he does, and that he starts with new hope. But the wrong sum must just be let alone.Home Education, pp. 260, 261
Charlotte understood that it’s often the teacher, (in this case, the parent) that undermines habit training by allowing sloppy work, giving excessive explanations, teaching to the test, cramming or immediately helping a child over each difficulty rather than allowing him time to investigate, think, and do the work himself. If a child gets an answer wrong due to carelessness, then a do-over only reinforces the behavior, but, if it’s because he doesn’t understand the concept, then the teacher should take the time to secure his understanding before giving a new problem. Either way, it is the teacher that has something to rectify.
Of course, honest mistakes do happen. There are times we’ll realize our child, whom we were sure understood a math concept before moving ahead, has somehow gotten off track. What should we do in this situation? The same thing you should do if you realize you’ve gotten off a mountain trail—stop, stay calm, then retrace your steps. In the mountainous land of mathematics, every step should be taken on firm ground. So, simply go back a few steps to find where our student left the path, then secure his understanding through various exercises before moving ahead on the right path.
C.S. Lewis tells us that this principle works whenever we seek truth, whether in arithmetic or otherwise.
We all want progress. But progress means getting nearer to the place where you want to be. And if you have taken a wrong turning, then to go forward does not get you any nearer. If you are on the wrong road, progress means doing an about-turn and walking back to the right road; and in that case the man who turns back soonest is the most progressive man.Mere Christianity, p. 36
Charlotte’s approach to do-overs comes from the value she placed on the habit of integrity. It also allows the student to advance on solid ground and with hope!
Let’s review some of the principles and practices in Charlotte’s approach to teaching math that help cultivate good habits:
- Short Lessons—up to 20 minutes in earlier years and never exceeding 30 minutes, even in high school.
- Interesting and Interactive Lessons—guiding ideas and engaging examples not only hold a child’s attention, they spark the imagination and cultivate her reasoning powers, too.
- Ample Review—periodic review helps math processes already mastered become second nature to a child.
- Mental Math—this lively time free from pencil, paper, and manipulatives cultivates creativity and concentration, solidifies math facts along with other math processes, and helps build speed and accuracy.
- Physical Habits—from notation of numbers and symbols to drawing lines and graphs, habits of neatness and orderliness promote accuracy and clear communication.
- Everyday Objects—Using a variety of simple objects helps keep the focus on the ideas being presented and off the manipulative. Rather than a distraction, they aid in reasoning and clear thinking. They also nurture good physical habits like neatness and orderliness.
- Honest Work—Fight the urge to help your child over every difficulty, or allow sloppy work and endless do-overs. Rather, let her put forth mental effort and cultivate intellectual truthfulness and honest work.
Remember, every math lesson comes with an amazing opportunity to draw power out of our children, excite their enthusiasm, and allow them the time they need to wonder, play, and grapple with numbers as well as more complex math.
Charlotte Mason reminds us, “sow a habit, reap a character.” One of our chief duties in the education of our children is to intentionally sow good habits. These habits not only help develop a child’s ability to think mathematically, they’ll also be a benefit to her, and others, for life.
For more guidance, be sure to take a look at our Charlotte Mason Elementary Arithmetic resources.