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Monday, February 18, 2013

Using Ray's for Beginning Math

Mother teaches oral lessons
When one compares the primary Ray's Arithmetic with newer curricula, there seems to be a lot missing! The copy I am holding in my hand is only 94 pages long, which pales in comparison with modern books that cover the same material.

What is more incredible is that this tiny volume was meant to be used for two years!

So what is a modern teacher to do?

Here is a general course of action, as recommended in The Manual of Methods, which was written as a guide for the Eclectic Series (of which Ray's was a part):

  • Don't allow the children to use the book or to write at all at the beginning.
  • Use common objects, without using the number symbols.
Do not teach the figures in the first lessons, and do not allow the children to do any written work; but teach orally, illustrating every operation, at first, by means of various objects. Manual of methods, page 107
  • Practice counting common objects, then grouping them and having the children recognize them in groups without counting, such as seeing 3 blocks, 3 balls, 3 spoons, etc. Children should become able to recognize groups of up to 10 objects without counting them.
  • Show children how to group and re-group within a certain number, so that it will seem natural to think of, say, 5 as being 2 and 3, 4 and 1, etc. Also do the reverse actions, such as realizing that 5 take-away 3 leaves 2, and so on.
The instruction should be entirely oral, and should deal altogether at first with concrete numbers. The little child cannot grasp abstract ideas. It is true you can teach him to repeat, "2 and 2 are 4;" "2 from 4 leave 2:" "2 times 2 are 4;" and "4 divided by 2 equal 2." But, without the proper preliminary work, these words can not possibly convey any clear meaning to his mind. This kind of instruction in a primary class is simply machine drilling on abstract numbers and words which convey no ideas, or at best a mere jumble of ideas to the child's mind. It is one of the worst, and at the same time one of the most common, faults in the teaching of arithmetic, and it is one which is very apt to disgust pupils with the subject from the outset. On the other hand, if the proper method of teaching is pursued, which may properly be called the object method, the children are taught to think; they will be interested at the very beginning, and they will be kept interested by this method until they are successfully carried to the point where the object method is no longer necessary, and their minds are ready to grasp the abstract, through careful preliminary drill on the concrete. Manual of Methods, pages 107-108

I have created flash cards in my Ray's Helps that illustrate these principles, one set without numbers, the other one with numbers, that can be printed out and used to aid a parent in this endeavor.

  • Then, and only then, begin to introduce the actual number symbols.
Teach the concrete digital numbers in regular order, from one to ten inclusive, illustrating each number by corresponding groups of objects. Manual of Methods, page 108.
It is important to realize that there are only ten written digits, and that these ten alone make up our whole number system! If we can approach this task from this perspective, things become a little more clear to our minds, and we can encourage our children that math is not that difficult, after all!

This beginning, if done in increments of only 10-15 minutes a day, should cover a number of months!

This is not complicated, not dreary, not time-consuming. My suggestion is to take a small basket and fill it with what you will need--some counters, which could be marbles, beans, pasta shapes, etc., and some flash cards. Eventually a small chalk or wipe-off board could be added, as objects and numbers are drawn, and then the child may draw objects, circle things, and eventually begin to write the numbers. 

Remember, this method was formulated for the one-room schoolhouse. A teacher in such a setting had to manage the education of a number of students in various stages of learning. I have read over and over that the Ray's method is extremely "labor intensive," but I have found the opposite to be true. Of course, if one is expecting a child to be able to grab a workbook and study without any help whatsoever, then this will not fit the bill--but I have yet to meet a child that did not require any instruction whatsoever! But Ray's only takes 15- 20 minutes a day, especially in the beginning years. For a very busy mother, this could be carried out just before bedtime, if necessary! Think of working for 15 minutes on counting, etc., then reading a nice story, saying a prayer, and kissing your babe goodnight! That is it--no muss, no fuss! And, for the real secret, as you are teaching your eldest child, the other tiny ones can be included, meaning that you will have less work to do as you go along... 

Even the next stage should not become a burden.

After a child has become very confident in the above described knowledge, two things should then happen. First, a 100 numbers board should be introduced. This is such a great tool! You can find numerous of these to print out for free on the Internet, the most frequented being the Donna Young site. You should have on printed out and either laminated or placed in a plastic protective sheet. Then the fun begins!

There are so many things that can be done with such a chart that I have collected some sites that list them:

20+ Things to Do With a Hundreds Chart

The Wonders of the Number Chart

A hundred chart looks deceptively simple, but complex understandings can be developed by using one. On it children can learn to count, and to consider prime numbers, and everything in between. Use the chart often enough that children will carry its image in their minds for years--for as long as they need it, which may be a lifetime or at leas until they are so far into abstract thinking that they don't need the image anymore. Ruth Beechick, You Can Teach Your Child Successfully, Mott Media
Begin with simply counting to ten for a few days if necessary, then quizzing the student and having him find a number as you call it out. Do the same to 20, then by 10's, then to 100. After this is mastered, you are ready to introduce a number of the other fun games.

As you are exploring this avenue, then begin to work through the text. There is a bit of confusion here concerning the first lessons. It needs to be understood that formal math instruction was not begun in most schools during this time until a child was already reading--in fact, math was often delayed until the ages of 9 or 10. If you are working with a pre-reader, or a struggling reader, then you might want to skip to lesson V and VI, and proceed from there. 

Lessons VII-IX are good just as an initiation. Lessons X-XX could be done in this way; read through the math facts and the lesson, asking questions and, if necessary, using objects to illustrate the different principles. Each day afterwards, read the facts out loud and have the child repeat them. After a number of days, ask the child to recite them from memory, helping at first. When mastery is achieved, go over the questions in the text once more. Lessons XXI and XXII are good for extra practice in mental exercise and review of the previous facts learned. These review lessons could take a number of days--no need to hurry through them!

In this same way, the first 37 lessons can be covered. This is meant to be the first entire year of study!
...for more excellent results, you should faithfully follow the mental system in Ray's Arithmetics. Avoid the temptation to hurry the children into writing rows and rows of problems so you can put them to work and take a recess. many children are better off not starting formal arithmetic study quite so early as our society tends to think. So, particularly in a home school setting or small one-room school, you can use real-life situations, manipulative objects, and games to help children develop in their understanding of numbers. Relax and take things at the children's pace. Ruth Beechick, from the Parent-Teacher Guide for Ray's New Arithmetics, published by Mott Media.
Feel free to have fun with all sorts of games, flash cards, etc. You are building a foundation here that will help your child, not only to master math, but to enjoy it!

Of course, for fun and reinforcement, other things can be added. We like the Rod and Staff  books for coloring and counting fun, as well as other practice. Each workbook is only $2.95, which is very reasonable.

After Ray's Primary Arithmetic is completed, then it is best to move on to Ray's Intellectual, but that is for another post, since this one was to answer questions about beginners!

Here are the wonderful ways to obtain your own copy of this wonderful book: 

Dollar Homeschool. This is a collection of all of the Eclectic Series textbooks, including Ray's and all of its complimentary resources, such as teacher's manuals, etc. which have been scanned in and put on DVD. Having all of these delightful works together in one place was so helpful that I just had to write guides so that others could enjoy them, and these guides are now included! 

Mott Media. These folks have reproduced hard-bound copies of the original McGuffey's and the "new" Ray's, and also offer guides written by Ruth Beechick along with consumable workbooks to go along with the series (which I have never used).

There are others which offer hard-copies of the McGuffey's, usually the revised series (1880 or so). Amazon is also a great source.

Of course, there are numerous ways to obtain these books online for free, and Internet Archive is the fastest way I know of to find all sources at once.

I would also strongly suggest reading Ruth Beechick's guides on teaching at the elementary stage, as are listed on the Mott Media site.



Above is a poster page that will serve as a reminder of the ideas suggested in this post. Just click and save the image to your computer, perhaps pasting it into a word-type page and printing it out. 




3 comments :

  1. Thank you so much for this post! I just finished reading your "Homeschool Sanity" and am so very interested in learning more to use these methods. I homeschool an 11 year old and have a 4 year old that LOVES to learn and wants to do learning activities everyday. I also have two younger children. (Though the 17 month old is in heaven and Jesus is her perfect teacher!) Anyway, I have been all over the board teaching my 11 year old. And have been concerned about my approach with my 2 boys. From what I've read in your book and am learning online, I really do think the eclectic methods are my answer to my many prayers! My 4 year old is on his 2nd math workbook from the Critical Thinking Co. and he devours those. So it sounds like I better get busy and introduce Rays Math to him, so he can start thinking that way. Anyway, I didn't mean for this to be such a long comment, but I just want you to know how much I appreciate how you work to get this kind of information out there! God bless you!

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  2. Glad you posted this! I just started Ray's and I love its simple lessons that you just take your time over, but I admit to feeling a little nervous about doing it right. This is great!

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  3. I just purchased the Ray's set. I am thrilled that you wrote this with beautiful timing for me! *smile*
    btw... how did your speaking engagement turn out in Yakima? I so desparately wanted to go, but a random gall bladder crisis hit me that week. *sigh*
    Someday I hope to meet you~
    Sheri

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