The Privilege of Homeschooling the Charlotte Mason Way

As a homeschool educator I have the privilege to witness things that most parents miss with their children at school and I am very grateful for the opportunity.  This week was our first week back after summer break and I would like to share some observations from our week.

When we listened to Igor Stravinsky’s ballet, Firebird, and he listened to the story, I saw my son’s imagination take flight as he played out parts of the story and then he created a new story.

Dull textbooks, busy work, or worksheets have no part in my child’s education.  Instead he is presented with a wide variety of living books with vital ideas written by authors who are passionate about their subjects. His science book is Fabre’s Storybook of Science. This week’s readings sparked an intense interest in pearls and the ocean.  He was fascinated by mollusks, the slimy creature in its shell that would form a protective crystalline coating, nacre, around an irritant and the pearl divers that risked their lives in the days of old, to get them.  We watched a video I found on YouTube about the unique and rare Sea of Cortez pearls and were mesmerized by the beautiful array of colors in pink, blue, purple, green, silver and black.  I pulled out my big bag of shells and we looked at the different shades of mother of pearl and sorted them by their attributes.  It created a desire in him to see the ocean and feel the sand under his feet as he searches out shells.  Yes, there will be a trip to the shore in the near future.

Then nature study happened quite by surprise, while walking home from the neighbor’s house, he found a toad and captured it.   What a joy to observe his desire to care for the toad properly so that he may observe it.  He got out his book, Pets in a Jar, by Seymour Simon to learn about what it ate and how to care for it.  We found his toad on the internet and learned his Latin and common name.  Each day he searched out morsels for his toad, Robert, to eat such as worms and even a baby gecko.  I did cringe a bit at the gecko, but Robert ate it.  Everything was meticulously recorded in his nature notebook, first by carefully painting a picture, working to match the color properly with watercolor paints.  Then, he recorded everything that happened, being sure to include the Latin name, Bufo speciousus, and common name, Texas Toad as well.  I was there to watch his pleasure and satisfaction in a job well done.

While reading in his history books, This Country of Ours by H.E. Marshall, George Washington’s World by Genevieve Foster, and Abigail Adams: Witness to a Revolution by Natalie Bober, I witnessed his growing understanding of the cost of war in lives, property, and civilization.  He is learning that our freedom was bought with a high price and what happens on our shores or in foreign lands, has a global impact.  He is coming to know that what happened in the past affects the present.

Through his citizenship book, Plutarch’s Lives, he can see that the character of a man can have an impact on others for good and evil. Through our grand conversations I see how he is taking in these ideas and it is growing his character.  We have the opportunity live out our faith by applying what we are reading in the Bible to our lives all day, every day.

We study artists, geography, Latin, grammar, foreign language; we read poetry from the best poets, literature with rich vocabulary and has stood the test of time, Shakespeare, and sing songs.    Every day I see him drink from the feast of knowledge that I present to him and it has created an even greater hunger to know.  I am a witness to how the ideas presented by the best artists, authors, creation, and Creator are shaping his character and equipping him to think for himself, to take in what he needs or what is right and reject the rest.  It is truly a privilege and an honor that I wish every parent could have.

How to Choose a Curriculum Part 2

How to Analyze the Curricula

If you have not read my last two articles in this series, I encourage you to take the time to do so before reading this article.  This article only makes sense in light of those.

There are two main approaches to presenting mathematics concepts in textbooks.  One type is a spiral curriculum in which the assumption is that children understand mathematics through repetition.  Mastery of a concept is not expected until it has been reintroduced several times, sometimes over years.  New concepts continue to be presented and then the previous concepts will be reviewed with each progressive lesson.  A spiral curriculum touches on a wide number of concepts in a year in less depth with less time devoted to each new concept.  Saxon Math is an example of this type of curriculum.

The other type of curriculum is content mastery.  The assumption is that learning is sequential and concepts build upon each other.  Foundational to this approach is the idea that children learn mathematics through understanding and mastering concepts.  A concept or skill is presented in many different ways and is mastered before moving on to the next.  Fewer concepts are covered than in a spiral approach and more time is given for each concept because it is taught in more depth.   Mastery of a concept is required before moving on to a new one.  Making Math Meaning by Cornerstone Curriculum is an example of this type of curriculum.

In light of the way in which we know how children learn math naturally as explained in part one of this series, one of these two methods seem counter to that.  Can you identify which one?  If you said the spiral approach you are correct.  What this approach does is to take teaching the new mathematics concepts out of their proper real world context.  If you take a concept out of its context you are taking away the one thing that gives the idea real meaning.    Do you think your child would understand an abstract concept if you use another abstract concept to teach it?  No, the natural learning occurs when you use something your child already understands to explain something abstract.  Each lesson presents a new concept before your child has had the opportunity to grasp the one presented the day before.  When your child is struggling to understand a concept, she experiences the physical effects of anxiety.  If you ask any child how their tummy feels while they are in a state of confusion with a new concept or skill, they will tell you that they feel a knot or butterflies.  When there is mastery of that difficult concept or skill, the anxiety is gone and there is a rush of relief and joy.  Their perseverance is rewarded and their confidence is elevated.  I have observed this over and over again in teaching children mathematics.  With the spiral approach to mathematics, day after day the child is exposed to new concepts with no mastery of that concept.  The amount of anxiety and frustration they are feeling is rarely relieved.  After years of learning with this type of curriculum the student can lose heart and give up.  They believe that they can’t learn math.  It does not have to be this way.

Do you remember what Mason revealed as the practical value of a mathematics education?  Those were the training in reasoning and the habits of understanding, a willingness to work, accuracy, and being intellectually truthful.  Do you think this lofty goal can be achieved through the spiral approach?

So how do you know what a spiral curriculum looks like?  You have to look at how the curriculum is set up.  Look at the scope and sequence from kindergarten through 12th grade if it goes that high.  Look for concepts that are taught, year after year.  Look at a specific grade level text book.  You can look at any grade level textbook table of contents at the Saxon Math website to see an example of how a spiral approach textbook is set up.  Determine how often new concepts are presented and if mastery of that new concept is achieved after it is taught.  Look at the assignments to see if they are loaded with computation problems with little or no word problems? A quick search on the internet for spiral math programs will also be a big help to you in identification of this type of curriculum.

Not all mastery programs are created the same.  They all start with the correct foundation that children learn through mastering concepts sequentially taught, but the way the concepts are taught may be artificial and frustrate a student.  When looking at mastery curricula, keep in mind the foundation of teaching mathematics that it starts with a problem that requires understanding before moving to the abstract symbolic representation of that problem.  This is the way you help the child connect an abstract concept to something real that they already understand.  Be aware, that there are many mastery programs that teach in the traditional method of starting with the symbolic representation of a problem then using objects to make the symbolic real.  Remember that the objects themselves are a representation and can be abstract to the child.  The proper context for mathematics is the real world math problem that needs to be solved first, with objects if needed, and then using the symbolic representation to show what they already know from solving the problem.

Before deciding on a curriculum, read the scope and sequence.  Make sure that there is mastery of concepts before presenting a new concept.  Fewer concepts will be taught with more time given to teach each one.  Read sample lessons to see if you are comfortable with the teaching format.  Look for a focus on word problems first, rather than the symbolic representation of the math concept. There may be some lessons with mostly computation problems, but this should be the case only after the concept has been presented in the real world context with word problems.  At the website for Making Math Meaningful by Cornerstone Curriculum you can find a good example of what a mastery approach mathematics curriculum looks.  It also adheres to the teaching of mathematics that corresponds with how children learn naturally.    You can see the concepts and skills taught for each grade level as well as sample lessons to see how they are laid out.  There are more curricula available like this one, so you have options and can chose one that best suits you.

The curriculum should not require a lot of expensive manipulatives.  Dried beans or centimeter cubes work well as counters, Unifix Cubes work well for making groups and fractions, and some type of place value blocks are sufficient for teaching addition, subtraction, multiplication and division.  They can be found cheaply online, used, or in local stores so they don’t blow your budget.

With the growing popularity of homeschooling, there are new mathematics curricula entering the market every year.  Your choices are vast, but don’t be intimidated.  You do not have to be an expert mathematician in order to teach mathematics.  All you need is determination and the knowledge of how children naturally learn mathematics.  You have the knowledge you need to choose an effective math curriculum.  I wish you well on your search and wisdom for your decision making.  

The Mathematics Curriculum: Should it Stay or Should it Go?

“I don’t like the math curriculum we are using.  Which curriculum would you recommend?”

Having taught mathematics in the public schools, I get this question every year.  I am sharing my thoughts on this topic to give you a perspective you may not have considered in the past.  When you hear a fellow homeschooling friend rave about the math program she is using in her homeschool, a lot of us can’t help having order envy.  Maybe we would be a lot happier doing math with that curriculum instead.  As a result many end up tossing over their current curriculum only to find that the grass was no green on this side of the fence.  This cycle may continue to perpetuate itself because you are looking for something that does not exist.

Every mathematics program has a scope and sequence or an outline of skills and information to be taught, organized by grade level.  If you switch the curriculum from year to year the unavoidable consequence is that your children will have gaps, concepts they did not master but should have, in their mathematics education.  The more often you switch the curriculum, the bigger and vaster the gaps.  As a result of these gaps, it is a lot harder for them to understand the more difficult concepts in the later years because they have not mastered the necessary foundational concepts needed.

My recommendation would be to stick with what you have.  I cannot stress enough persevering with a curriculum so that your children are taught all of the concepts they need, when they need them.  The bottom line is that there is no mathematics curriculum available that makes you want to cheer with excitement.  Yes, there are different types of mathematics programs, but ultimately math is math; the concepts to be taught are absolute.  2+2 will always equal 4 regardless of the curriculum.  Mathematics is not thrilling to most people no matter how the curriculum company presents it, but it can be enjoyable to master new concepts that were difficult.  There is satisfaction in that.

“My child is struggling with the concepts presented in the curriculum I am currently using.  Isn’t that a good reason to switch to a different curriculum?”  

First, the beauty of homeschooling is that you are not on anyone else’s timeline.  If you need to spend much longer on a difficult concept, then you have the freedom to do that.  If you want to skip pages in a section that has been quickly mastered, then you are free to do that.

Second, the struggle to grasp new concepts is not an indication that the curriculum is not working for you. It is also not a sign of academic weakness in your child or an indication that your child is not mathematically minded.  Struggle is the means in which your child learns hard things.  A weight lifter cannot start with the heaviest weight.  He must work his way up to it by regular practice with light and then gradually heavier weights in order to build and strengthen his muscles.  It is like this with mathematics as well.  It requires frequent practice of solving math problems with gradually increasing difficulty.  As a result, your child will develop the habits of accuracy, observation, and perseverance. Each struggle strengthens the child.  There is nothing more exciting for the child who has persevered with a difficult concept to finally understand it.  There is such an overwhelming sense of relief and joy in seeing the problem through to its successful end. In the midst of your child’s struggle, if you see him begin to lose heart, remind him of that last moment of success as a means of encouragement.

“Mathematics depends upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken imagination.” 

Charlotte Mason Vol. 6 p. 233

Finally, it falls upon the teacher to present the concept to the child in a way that he can understand.  The curriculum is only a guide.  If your child does not understand the concept after you have presented it as suggested by the curriculum, then you as the mathematics teacher must find a different way to present that concept.  Mathematics was one of the subjects that Mason agreed relied heavily on the teacher and she was correct.  This may seem daunting to some, but do not let this idea stop you from being a good math teacher.  There are so many resources online, that I have full confidence that you will be able to find the help you need.  If you are part of a homeschooling network, then there are many people within who could help you as well.

I would like to encourage you to persevere with your curriculum choice.  Make it work for you.  You have chosen the hardest thing already by choosing to homeschool, you can do this too.



Look for my next post on how to choose a mathematics curriculum.