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Julie Brennan, June 2008:

I don't feel a personal need anymore for much of a guide for primary level math teaching. It seems that over the years these concepts get taught through real life exposure and short lessons during our sit down math times with living math literature. BUT, most people do not have the ability or confidence to do this, and so my initial purpose in checking out Ray's was to look at it as a resource for families that want to use a living math approach to learning, but who want a guidebook to all the concepts that are typically taught through the grades, and guidelines as to when and how they are taught.

I have only used the Primary and Intellectual Arithmetic books with my daughters so far, which go through about 4th grade. I can see using the next book up, Practical Arithmetic. I didn't care for the Higher Arithmetic book, which would have been the one my 7th grader would have gone into, because I felt there were better resources. I do feel that book has some uses, and I'll share those.

What I found was that the format of the little books were so friendly to use, I kept them out on our coffee table as a strewing resource, and since then we've used the books on a weekly basis during our math times to work on basic skills. They appeal to us, and this is big! In particular, my younger daughter has owned her book, referring to it for her math facts if she wants to look things up or review them on her own. The banks of word problems are quaint, fun and effective. Rather than needing workbooks, teacher's manuals and a lot of complex curriculum components, all the basics are on a few pages presented simply and in an unintimidating way. So we still spend the majority of our math time doing living math in a natural way, but the books have provided a little more structure than we had before, and as my kids enjoy it, it is not unwelcome.

On the Living Math Forum we've talked many times about how to use living math while making sure "everything is covered." Ray's seems to be a very easy, inexpensive and effective way to do this. A child can in fact teach herself much mathematics using the books herself, mine do. There is no waste, as in years of using workbooks, inevitably large portions are either never completed or are completed but didn't need to be. There isn't a lot of cost, so you don't feel compelled to use things even if they aren't optimal because you have so much invested in them it feels a waste to skip or drop things.

We do lessons either orally or using their composition notebooks they write their math work into. We tuck the books in my purse if we have time at a piano or violin lesson to work on ideas. We have been going in order, but skip things that become easy, and stay working on things that might need more time. When we've introduced an idea, my girls use their notebooks to do exploratory activities with the concepts. The Parent Guide encourages you to use manipulatives, games and any other activities you might have on hand to be able to spend as much time on an idea as you need. So, for example, fractions are a big conceptual meadow that I spend a lot of time on. When we look over a Ray's lesson and do the word problems, we also play games, draw pictures, use fraction manipulatives, read living math books on fractions, etc. Ray's introduces the initial concept, but exploration, discovery, reinforcement and practice happens through living math activities.

We've adopted the books as part of our living math lifestyle, because they fit it. We like resources that don't require much prep and aren't difficult to figure out how to use, and I love the compact, non-consumable format. I don't need the books to teach from, but my girls like them, so they are a recurring feature of our math times. I'll be talking about an idea in the book, and my daughter will remember a math book that covers the same concept, and the next thing you know we're off reading the book (my youngest is my resident librarian, almost infallibly having a knowledge of where all the math books are :o) and a 15 minute "lesson" has become a 45 minute math exploration.

About the older books. I did post a fair bit on the Ray's list because I didn't see how I could use the Higher Arithmetic (HA). Beginning with the Practical Arithmetic (PA), the fact that the applications are based on outdated or obsolete situations shifts from being quaint to being historically interesting, but irrelevant to our children's lives in a modern, technological society. What I do like about PA is the fact that it DOES cover ideas like taxes, simple interest, bankruptcy, insurance, exchange rates, etc. With my finance background, I have naturally covered all these subjects with my children as they got to an age to understand it, pulling out pencil and paper and showing them how these things work. Ed Zaccaro's books provide quite a few chapters on finance related ideas such as payday loans and bank mortgages that give us real life exposure to these important topics. But I've rarely seen these in an elementary *curriculum*. And I think that many people would not know how to teach these topics or even think of them at these ages.

The PA book after covering decimals, percents etc. goes into these applications and as such provides a "living" approach to learning how to use basic arithmetic skills. Of course, the examples in these areas are dated, but a parent can use current examples - for example, teaching about taxes, go over your own property tax bill with your child, or a tax return, or research current bankruptcy law. We've done all of these things in our family. It is on these kinds of applications, however, I feel the Ed Zaccaro books are a better resource, being based on modern situations and technology. The 25 Real Life Math Investigations book is current and as such seems to be relevant to my son as we work through each chapter, motivating him to "do the math" and find out the economics behind the questions posed in the book.

HA seems to pick up where PA left off, but with much more elaborate (and dated) applications, and this is where I asked the Ray's list, who has actually done these? There is chapter after chapter of applications that I just can't see my child finding remotely relevant unless something catastrophic happened that eliminated all our technology and sent us back to the turn of the 20th century. And even then, many applications would still be totally dated, a comment one person made on the list is that agrarian skills would be relevant, but knowing how to manually compute life insurance premiums? I don't think so. The emphasis is very heavy on personal finance, but who would do all these manual computations? No one does today. We only have a limited time to spend learning concepts, and I just felt that that time was much better spent focusing on current applications and developing skills in the area of probability and statistics, geometry, preparation for algebra, etc. I did find a chapter on longitude and time very interesting. In fact, this would be a fun book to use for historical mathematics, and I was going to try out some of the material when we went through some of our math history next year, I plan on revisiting navigational mathematics. But I wouldn't make it the *basis* of my child's math education at 7th / 8th grade - there are so many applications out there that are far more relevant if my child is to go on in higher level mathematics.

The other problem I had with HA is that the small book format, which is an asset in the early books, became more of a liability in this book. There is so much information cramped in a small space. The book has to be four times thicker than the Primary Arithmetic book my youngest has. It feels crowded. I find that a texts like Harold Jacobs and Ed Zaccaro much easier to use for these ideas.

I have not seen the algebra or geometry books to comment. After recently revisiting trig and calculus classes at a local community college myself, I'm finding I have more of a bias toward a modern approach to the study of functions. I have been leaning toward a belief that while classical approaches to algebra and geometry have value in terms of mathematical thinking, a good modern algebra course will be preparing a student with the end of calculus in mind, the way calculus is used today.

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Comments by Lisa:

People seem to use Ray's in different ways, and our approach (at the moment) may be different to the norm, so that's something to keep in mind. We don't use it in a fixed way, according to any schedule. We're working on multiplication at the moment so I mainly use it as a source of word problems that we can work on. After researching it, I decided to buy the Basic CD. This CD goes through Grade 8, and consists of four books (Primary, Intellectual, Practical, and Higher). The CD also comes with the answer key for the three latter books, though solutions are given for only the more difficult problems. The CD with all these books was $29.

Here's the contents of the 4 books that I have:

Primary (Grade 1&2): Numbers and Figures, Oral Exercises (adding and subtracting using manipulatives), simple Addition, simple Subtraction, Multiplication (single digit), Division (single digit), Signs (introduces - x /), US Money, English Money, Weights and Measures

Intellectual (Grade 3&4): Numeration; Addition, Subtraction, Multiplication, Division (all single-digit); Fractions, Weights and Measures, Ratio, Percentage

Practical (Grade 5&6): Arabic Notation, Roman Notation; Addition, Subtraction, Multiplication, Division (multi-digit); Compound Numbers, Factoring, Fractions, Decimal Fractions, Metric System

Higher (Grade 7&8): Numeration and Notation, Addition, Subtraction, Multiplication, Division, Properties of Numbers, Common Fractions, Decimal Fractions, Circulating Decimals, Compound Denominate Numbers, Ratio, Proportion, Percentage, Percentage - Applications (without time), Percentage - Applications (with time), Partnership, Alligation, Involution, Evolution, Series, Mensuration

The workbooks must have been added on because parents wanted them. After canvassing opinions on the Ray's list, I eventually decided against them. This was based on some users' comments that they bought the workbooks and found them unnecessary, that the problems in the books were sufficient. So, if someone wants to use it like a workbook curriculum, then they do have that option, but it works fine without them.

Re teacher's manual, there is only one manual that covers all of Grade 1-8. Its the "parent-teacher guide" written by Ruth Beechick, and costs $11. Here's the description from www.mottmedia.com. "Guides your scheduling and planning through the books above. Shows where you can adapt to the needs of slower or advanced students, making selective use of basic portions that are important for all students and high-level portions that challenge the best students. Provides a test for each unit. Describes games and activities which add variety to your teaching." While we haven't used it up to now, looking at it now has sparked my interest again. It has weekly "plans", like Monday you introduce the textbook lesson orally; Tues you practice the content with manipulatives/flashcards/games; Wed do the lesson again; Thurs repeat practice as on Tues; Fri review the texbook lesson. It has the following chapters:

Introduction (What are Ray's Arithmetics, Scope and Sequence, Tips for Teaching)

Grade 1 (Teaching First Grade, A Typical Day, A Typical Week's Schedule, Plannning Guide, Progress Record, Testing First Graders, Test Schedule, Unit Tests, Answer Key for Unit Tests) Grade 2 (same format as above) Grade 3 " Grade 4 " Grade 5 " Grade 6 " Grade 7 " Grade 8 " Projects and Games

LAYOUT OF RAY'S:

Here's a link to a book called "First Lessons in Numbers" that looks very similar to Ray's.

http://digital.library.pitt.edu/cgi-bin/t/text/text-idx?c=nietz&view=toc&idno=00ACZ7992m

Another called "First Lessons in Arithmetic" also seems quite similar. http://www.donpotter.net/math.htm The owner of the site felt that this is better than Ray's, but couldn't remember why he'd said that when I asked him.

Instead of using either of these, I decided to get Ray's because it continued into the higher years. There is also another series that we have called "Practical Arithmetic" by Strayer-Upton. Its the program used by Benezet in his math "experiment". There are 3 hardcover books, for Grade 3-4, 5-6, and 7-8.

http://www.keepersofthefaith.com/Catalog/Math_Books_73.asp

http://www.keepersofthefaith.com/Catalog/Curriculum/Curriculum_Mathematics.asp