**Don’t let math intimidate you! Homeschooling has the clear advantage, trust me. This post outlines the down-and-dirty, nitty-gritty truth about math instruction; what it was, what it is, what it should be!**

# First, what math instruction *was*….

**Before the 20th century people didn’t care much about mathematics.**

Beyond basic figuring most folks never gave it much thought.

Math instruction was very different back then. Most school masters couldn’t “cipher” for themselves. Students did nothing more than copy and memorize rules. No logical, gradual introduction, no practice problems. Some students learned how to figure for the merchant trade, but few pursued higher math.

**Then some rare men changed all of that. **One of them was Dr. Joseph Ray, a schoolmaster who not only loved math, but loved teaching math to children. He not only presented rules and theories to be memorized, but offered practice problems and examples of application. The books he wrote in the 1830’s made learning math logical and interesting. These texts were popular for almost a hundred years, selling 250,000 copies between the years 1903 and 1913 alone!

Regular folk still failed to see the use of math except for common trading, but times were changing. The years during which Ray’s arithmetics were sold were years of amazing invention and innovation. As technology increased, so did demand for those who could do higher math. Eventually books were published for teaching scientists and engineers.

**Then two movements changed the way we look at arithmetic.**

**The first was the Progressive Education Movement.**

Folks like John Dewey were in charge of this one. Western society was becoming more secular, even humanistic. Instead of relying on the strength of individuality, social engineers looked at children in groups and manipulated them like commodities on the stock market. Education was about manufacturing, not about learning.

Common sense approaches such as Ray’s Arithmetic were forced out, and in their place were books that were “modern” and treated children as mere calculating machines (one of Dr. Ray’s fears).

**The second movement was the Space Race.**

This began when the Russians leaped ahead by launching Sputnik in 1957. It wasn’t just about space, it was about the threat of communism. Folks believed our destiny was tied to our ability to compete in a technological age. The entire American education system was overhauled. The new curriculum put math center-stage and anyone who couldn’t measure up was left in the shadows.

# Next, what math instruction *is*…

### The pace has only picked up since the 1950’s, but it seems as though we are falling farther and farther behind.

It is almost as if we have gone back to the time in our history when arithmetic was considered irrelevant. Our children are drilled and tested more than ever, but they know *less* than previous generations.

Survey of 23 industrialized countries ranks United States at 21 for numeracy, just in front of Italy and Spain…The main problem identified by the data…was with younger American workers, who lagged in nearly every category.

(According to The Daily Mail. You can also read this article for an American take on the subject.)

Graduates these days lack basic arithmetic skills, or what is referred to in the quote above as “numeracy.”

A numerate individual has the confidence and awareness to know when and how to apply quantitative and spatial understandings at home, at school, at work or in the community.

### We’re turning out rocket scientists who can’t tie their own shoes.

# Finally, what math instruction* should be*…

### It should be logical.

There should be a gradual progression that makes sense and is easy to follow without a lot of jargon attached. None of this fuzziness, forget the complicated explanations that make children feel lost.

### It should stimulate the imagination.

Math is not just a subject in school. Our days are precisely 24 hours, each one divided by 60 minutes which are divided by 60 seconds. Even our heart beats point to rhythmic order. Some have said that we exist in a hologram built out of numerical order.

(If you have a few moments, watch this video and be amazed!)

### It should have personal value.

“Story problems” are not enough. Children need to be immersed in the huge laboratory called life so they can find out how delicious fractions are when they bake a cake or how exhilarating algebra is when they are flying around on a roller coaster.

### It should be short and sweet and leave time for natural exploration.

An hour a day of actual operational math is more than enough, and even less at younger ages. My ten-year-old does about 20 minutes, my seven-year-old less than that.

### It should start later rather than earlier.

Numbers are not concrete, they are abstract. Small children have not run around in this world long enough to have a grasp of what that means. They need time playing with cups in the bathtub, watching the arc as they swing back and forth, building with legos, estimating the exact time to mash the brakes on their bicycle, engaging in language and reasoning.

I cannot do this idea the justice Denise Gaskins has in her delayed arithmetic series.

Here is an excerpt:

It’s counter-intuitive, but true: Our children will do better in math if we

delay teaching them formal arithmetic skills. In the early years, we need tofocus on conversation and reasoning— talking to them about numbers, bugs, patterns, cooking, shapes, dinosaurs, logic, science, gardening, knights, princesses, and whatever else they are interested in.

Gaskin refers to a math teacher who tested his theory of delayed math instruction by the name of L. P. Benezet. You can read an article about his findings here.

I have found this to be so very true with my own children. **Delaying formal math has not hurt them, it has helped them.** The ones who started later moved forward faster and stayed interested longer than those who began early and learned to hate the whole process.

Today the ones who struggled early-on are handling businesses, coding websites for colleges, and keeping out of debt via careful budgeting.

Professor Ray had it right. **Children who find math logical, interesting, and life-enhancing have no trouble learning it.** When done right, homeschooling does not put children behind, it gives them a head start.

I love this post!

I studied math education in college and have long felt the number one reason people don’t like math is because of how they were taught. It has always saddened me, which was part of why I went into math in the first place. Fancy methods and fads aren’t needed. Just solid, methodical instruction. And, while I don’t use math now, much except in teaching and occasionally cooking, the logical building blocks in it have prepared me to be a more capable peer to my philosopher/theologian husband.

Amen! Math is more than some worksheets and testing angst! I try and get my children enthused with the logic (as in the order of God and as His fingerprint in the universe) of mathematics as it is expressed in even the fractals of clouds and the leaves on trees. It even reaches to the logic of the Word, as you have so deftly said.

Do you have any opinion about the math books by George Albert Wentworth, David Eugene Smith? They were described as very Upton Strayer-like. https://diyhomeschooler.com/2016/11/15/school-arithmetics-free-ebooks/

Looks good! Upton Strayer is one of the best, so any book like that has to be quality 🙂

We are using Life of Fred series by enjoying but not rushing. Learning Math through reading and writing at the same time. Every kid is born uniquely by the image of our Savior. Thank you for the post, this is such a great encouragement.

That is so true! I’ve heard good things about Life of Fred.

I have used both Ray’s and Wenworth’s math books for years and I love them! I have found that they make math meaningful and logical just as Sherry says. They are challenging and fun. They teach children to use math in practical, everyday ways. Math becomes more than memorizing formulas and techniques; it really comes to life and makes sense.

I have been homeschooling for over 2o years. With my older kids (now graduated), I used most of the popular math curriculums. After using these books with my younger kids (ages 5-12), the results were surprising. My younger kids have enjoyed math more and their skills and understanding are better than my older kids’ were at their age. In short, I find that these books have given my children a superior education. The lessons fit a Charlotte Mason education in the fact that they are short and focus on quality over quantity.

Personally, I prefer Wentworth’s School Arithmetics because the problems seem just a little more interesting, but the difference is only slight.

Thanks again, Sherry, for a very informative and helpful post. I think Math can be one of the most frustrating and difficult subjects to teach when, as you have said, that doesn’t have to be the case at all.

Thank you for your valuable input, Jill! I just looked up Wentworth–seems terrific. I know what you mean about the difference between the older methods and the new. My children moved seemlessly from Ray’s to Saxon algebra with little to no stress.

Can you provide a source to Wentworth’s math books?

Yes, thank you for sharing your experience, Jill. It is always wonderful when a veteran gives a nod to what you are considering.

Can you provide a source to purchase Ray’s or Wentworth’s math books?

Actually, you don’t have to purchase these–they are free online. Here is the link to the Wentworth’s Primary Arithmetic on Google Books:

https://books.google.com/books?id=klc_Z2yNtGwC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

I love your articles! I have wanted to use ray’s but get so confused by the texts because they move so fast! How do you actually use them? I’ve read and reread but I can’t wrap my mind around them.

Also I am still loving Longs Language and wish there were something like them for older kids and even highschoolers. Have you ever run across something for 7th-12 that is easy to use and similar to Longs language?

Thank you, Shantel! After Long’s Language I like to use Harvey’s Grammar. There are a few places you can find it for free online or you could order the physical book (an answer key is also available) from Mott Media. As for the Ray’s, the primary book does move a bit fast. You could use it as an outline and fill it in with flash cards and things you find online, or you could use the Intellectual book, which goes a bit slower. One book that fills in the blanks for you is the Wentworth series you can find via Google Books for free.

Hope this helps!

Hi Sherry,

First, let me say that your writing has been a true blessing to me in the last couple few years. Your articles are relatable, encouraging and never fail to point me back to the Lord.

This year I followed your path and have switched from Ray’s to Hamilton’s, bringing me a greater deal of math peace. However, I’m still struggling with it. Is there a teacher’s manual? Or have you sussed out the details that are still a mystery to me? (I just had my sixth baby and suddenly feel terribly outnumbered! Must I switch to a program that outsources my teaching, like Math U See?) Here’s what I need most: a finish line! Have you figured out how to seperate the chapters into grades? I know that as homeschoolers, we’re not bound by public school’s scope and sequence, but it would boost my confidence to know how far to push for each year. (My “big girls” are in fifth, fourth and first grade this year.) Thank you for any help you can offer!

Those are all excellent questions, Lindsay. By all means, if you need something that gives you more peace of mind (that aligns with the public school expectations you face with all the children you have) use it! I have a few that don’t need much help at all, and others that struggle daily. I think something like Hamilton is most useful for those who struggle because it is so gradual and logical. If you have a few that shoot off like rockets, then something modern and standard just may be the ticket. Something like Hamilton’s is perfect for our struggling ones because they already don’t line up with grade levels ;P Hope this is more clear than mud…

Hi Sherry,

Have you written a post on Hamilton’s Arithmetic? I have searched your website and can’t seem to find it.

Thanks so much,

Anna

About Ray’s New Primary Arithmetic: How much time do you spend on each lesson? Do you wait until the child has all the problems memorized, or do you just get them familiar with the concept before moving on? I suppose this could be up to personal preference. I’ve been staying on the same lesson until the child has all the facts memorized. We use counters and do the lesson about once a day until the child masters the facts. But I haven’t used Rays past the Primary Arithmetic. If the next books repeat enough, maybe the Primary isn’t meant to be used as a facts memory program? I’d like to know what others who have used Ray’s think about this. I think getting the facts down is important.

I really enjoy vintage math books. I’ve tried Hamilton’s, Stayer-Upton’s, Wentworth’s, White’s, Olnly’s, and a few others. They are all excellent, but due to indecisiveness and switching back and forth, I decided to just stick with Ray’s now! It seems to be the most basic and popular and I just needed to stick with something. We also use Life of Fred, and Ray’s seems to be the easiest supplement.

I had to chuckle at your struggles with indecisiveness! I suffer from the same malady 😛 It seems that sometimes we have to put FOMO aside and just stick with one thing, don’t we? I think Ray’s Intellectual Arithmetic may offer some solutions.

I have tried modern math curriculum, but always go back to Rod and Staff. It is straight forwards and slow and teaches math concepts that are used in day to day life.

Rod and Staff is great for the basics, and very affordable to boot! Thanks for the input

I know you talked about Hamilton Math, but I can’t find where. I was telling someone about it and referred them to your site, but I can’t seem to find where you mentioned it. I think I read it about a year or 2 ago…..

Just found the link:

Could you post this link, please?

Did it not show up? I’ll try that again…https://www.google.com/search?tbm=bks&q=hamilton%27s+arithmetics

Hi Sherry,

I’m looking to switch to Ray’s, but I’m worried about the lack of answers, even in the answer key. Am I missing something? I’d really like the children to be able to check their own work — I need to simplify my life! I really like the idea of Ray’s, but I’m not prepared to work out every answer myself to make sure they are getting it right. What do you do?

Which book of Ray’s are you using? If you are using the Mott Media version there is an answer book you can purchase separately for the higher ones. If you download these for free online the answers are all in the back of the book except for the primer.