Do we really need six or more years to teach children basic arithmetic?
Absolutely not!
A child who is at mathematical maturity can learn basic arithmetic in one year or less.
I know you don’t believe me, because you have been fed the same lies I was fed. You were made to feel as though school math was some hazy, hocus-pocus thing that no one can ever fully grasp.
But it is so much more clear than that!
After I am through with this podcast you are going to feel as though you can grasp basic arithmetic, and you are going to feel confident enough to help your child grasp it, too.
Instead of seeing arithmetic as a set of books that need to be plodded through, you are going to think of it as a set of concepts that can be mastered.
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In case you are new here, I’m Sherry Hayes, the “interesting” mom of 15, and I want to share some things with you today that will ADD to your life, not waste your time.
Whether you started homeschooling yesterday or years ago, if you’re serious about your child’s education, MomDelights.com has something to offer you.
I don’t follow fads or trends, I only share deep, but practical, truths that I’ve gained as I’ve homeschooled our 15 children over 37 years.
Lately, we have been talking about the Four Pillars of excellent education, which are:
- Gaining favor with God and Man
- The tools and skills for learning
- Content
- Application
Today, we are beginning our focus on the second pillar, gaining the tools and skills needed for all other learning. Specifically we are going to be covering that dreaded subject, math!
I’m going to show you how you can wrestle math down with some vintage curriculum and add in some of the best of contemporary methods so your child will be ready for whatever math studies are in their future.
There is a playlist on YouTube which includes all of the videos in this series, in case you want to watch them in sequence.
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I could go on for hours on the history of teaching math and all of its in’s and out’s, but you don’t need that today! You need to gain a grasp on the subject so you can teach it effectively to your children.
So, here it is, all boiled down so it fits neatly into this short blog post!
I have prepared a list of 15 things (since I am the mother of 15) I think you need to know, but first I’d like to clear up some confusion between what we mean when we say “math,” and what we mean when we say, “arithmetic.”
From Wikipedia:
Mathematics is a field of study that discovers and organizes methods, theories, and theorems that are developed and proved either in response to the needs of empirical sciences or the needs of mathematics itself. There are many areas of mathematics, including number theory (the study of integers and arithmetic functions), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of approximating continuous changes), and set theory (presently used as a foundation for all mathematics).
As you can see, it’s a pretty broad subject, but this podcast will deal mostly with the area of math called arithmetic:
(Also from Wikipedia):
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
In other words, we are going to be talking about the type of math that is typically taught in the elementary grades and deals with what is referred to as the operations of integers.
I like to think of it as the foundations we lay so our children are able to function well in their real lives, and also so they can take higher math if they so choose.
And, with that, let’s dig into the list of 15:
- A mentally and emotionally mature person can learn basic computation skills, from counting to exponents, in a year or less.
That’s right! It’s been proven over and over again. The trick is to be able to wait until a person is mature enough—as we all know there are officials, and nosy relatives and neighbors, who will do their best to interfere with this.
- Teaching math seems unsurmountable until you look at it as a simple list. Here is the list so you can see it isn’t all that horrible:
- Addition
- Subtraction
- Multiplication
- Division
- Fractions (decimals)
- Percentages
- Exponents
And some also might add in these helpful elements:
- Measuring
- Money
- Practical application (word problems)
- Graphs and Charts
- Basic linear equations with letters for unknowns
And there you have it—a complete arithmetical education in a short list.
- Start with the concrete, then move to the abstract. Don’t begin by introducing numbers. Begin by counting objects, such as forks while setting the dinner table. Use this same rule of thumb when introducing any new concept. Make bundles of popsicle sticks, draw pictures, use number lines, use the 100 chart, and so forth. Then you can show the concept taught as an expression of symbols and it will make more sense.
- You can teach addition, subtraction, multiplication, and division from the very beginning. You can use objects to show how to break numbers up into all sorts of configurations, and show how this relates to the three computation types.
- You don’t have to spend a lot for manipulatives.
I have an ice cream bucked filled with common objects such as dice (a lot of them), dominoes, and regular playing cards. I also like to use popsicle sticks bound in tens with a rubber band for explaining place value. I use a 100’s chart I printed out and laminated for counting to one hundred, number recognition, skip counting, etc.
- Vintage books teach the basics without the burden of grade levels. Back in the 1800’s, children did not go by grade levels but learned at their own pace. The vintage books of the past, such as Ray’s Arithmetics (which are still in print from Mott Media). They rely on content progression, not grade levels.
They also contain some genius ways for doing math operations that are not taught in modern textbooks. They present basic operations without all the frill and fluff that make math take up so much time. Practical Arithmetics is also a series which does the same things, but these were published later, in 1934, so they are slightly more modern, but still without a lot of the confusion of later teaching methods.
An additional way to go about this is to nab an older sixth grade textbook published before 1957. Why sixth grade? Because a sixth-grade textbook includes review of all of arithmetic at the beginning of the book, then teaches the rest of basic arithmetic learned in sixth grade.
- Think mastery, not pace. This is one of the most genius things about homeschooling. You don’t have to push your child to move on through the curriculum before he is able to completely grasp a concept. If you come across something he struggles with, you can take a pause and go over and over that concept until he can grasp it before moving on. We all know that conventional schools never do this! I know I’ve felt totally lost many times because of this, and I know you have, too.
One way to gain better understanding of a subject is to utilize free worksheets online. I like to use Math-drills.com, but there are a number of others.
- Watch WhyU.com videos. We discovered these a number of years ago, and they really helped our children with number sense and explaining things such as prime numbers, etc. (there is a little bit of caveman reference here, but only as part of a story for understanding, which is easily dismissed).
- Use a chalkboard or white board. There is just something about being able to write out a problem on a board that helps clear up confusion. I’ve used this simple technique multiple times while teaching basic arithmetic, and found it also helps with higher math.
- You don’t have to be good at math in order to teach it. As you follow along with the curriculum, you will find you remember more than you realize about your own education. As you teach your child, your own understanding will increase, and you will find yourself learning right along-side him. (It is a proven fact that we learn better ourselves when we teach others, whether it be in reading, writing, math, or any other area of study.)
- There are two pathways towards memorizing multiplication facts:
- By drill and practice of the facts
- By doing many complex multiplication and division problems with a cumbersome multiplication chart.
I have had not a few children who did not at all enjoy being drilled in the basic facts, so I would give them pages of three and four digit multiplication and division problems, and it wasn’t long before they had the basic facts memorized because it saved them time!
- Teach your child about money by allowing him to earn and spend some. Amazing how effective this is!
- Allow your child years of exploring the world around him and building his language and communication skills before attempting formal arithmetic instruction.
For this I refer to an experiment done by a man named L.P. Benezet back in 1929….You can find out about the experiment for yourself by going to the Psychology Today website and reading the article.
- Remember, math is more than numbers, it is understanding our physical existence with numbers and other symbols as a language to express this understanding.
- It all begins with God, who is a god of order. Math is only a reflection of His personality; it is not the order or the Person Himself. It is the expression of the amount of that order we have discovered so far, but there are still layers we have not even imagined, nor can we fully understand until we are translated into the life to come.
And here are some concrete suggestions:
- Start with games. Dice, card games, board games that involve counting.
- Explore outside, observe, do some experimenting.
- Bake cakes and cookies together and hand your children a bag of m&m’s and have them portion them out among each other.
- Pay them for some extra chores and then take them to the store to buy something special.
- Move to no more than ten to fifteen minutes a day with basic number sense.
- When they are able to express themselves well, can read at a sixth grade level and can write short papers of a paragraph or two, then begin to introduce the operations of math.
- Don’t go through a series of graded textbooks, go through some vintage textbooks, with some modern ideas presented along the way.
- Gradually increase the length of the lessons and the amount of work required.
- If your child grasps a concept easily, don’t belabor it, but move forward to keep him from the frustration of boredom.
- If your child has trouble with a concept, slow down and give him extra time, even a short break from math, and then, don’t punish him with more work each day on the subject, just more days with the same amount of work in the area of his difficulty. Try and find new approaches to learning the concept. Be patient and kind and try and keep your own ego out of it.
Sounds too easy, right?
And here’s something to consider:
Almost all children are able to learn basic arithmetic, but it may take extra patience for some, even though they are bright and capable in many other areas. It has even been suggested that not all of us are capable of learning abstract mathematical concepts at young ages, and that some of us don’t “catch on” until we are into our late teens, or even early 20’s.
I know for many of you this whole idea seems impossible because you live in a state that requires testing and proof you are following along with the typical curriculum. My advice is to pray for wisdom, and then look for ways around things. I believe the unschooling community deals with this continually, so I would look there for support.
I hope this has encouraged you and given you a new way of looking at this often intimidating subject!
In our next few podcasts, I hope to go into the third pillar of learning, which is content—it should be a lot of fun!
Here are links to this as a podcast on these streaming services:
iTunes: Mastering Math Without Fear
Spotify: Mastering Math Without Fear
