We have been using the A Beka Arithmetic program since 1994.  It's definitely a good fit for us.  There are so many good programs to choose from!  We tried quite a number of programs before we found one we liked.  Here's our story--maybe it will help you as you look for the math/arithmetic program that fits your students.  I'm sure that some of the programs mentioned below have changed since I've looked at them around 5 or 6 years ago, so please keep that in mind as you read.

When we started homeschooling, I had already read books such as Teach Your Own, How Children Fail, How Children Learn, Home School Burnout, Home Grown Kids, Home-Spun Schools.  These books are all great books.  They all seemed to imply that basically you don't need textbooks, that basically textbooks, workbooks, and memorization will squelch a child's love of learning.  So we did other things instead for math.  I had found some old math workbooks at a garage sale, but I kept them put away.

I had this niggling feeling that kept tickling my psyche, though.  I was bothered.  All the books said, memorization is bad.  However, I rather wanted my children to memorize the math tables.  It has always helped me out to have my multiplication tables memorized.  How would it hurt my child to have them memorized?  Even though I'd read all the arguments warning me of dire consequences, I still wasn't totally convinced.  So, I decided that if my son wanted to do some of the workbook pages in those garage-sale workbooks, that he could.  And he loved doing workbook pages!  I didn't require him to do them; he just liked doing them and asked for them.  But soon he had basically done all that he could in those workbooks since they were just teacher's resource books that contained extra work with no teaching.  And by now, we had basically exhausted all the great ideas in An Easy Start in Arithmetic by Ruth Beechick.

So the search for a new workbook, or basically a math program, began.  I'd heard only great things about Miquon!  So I ordered the 6 workbooks, the Lab Sheet Annotations, and some Cuisenaire rods.  My son started with great excitement, but the excitement soon fizzled.  He did not understand the problems, and he didn't like having to make up his own problems nor did he like having to use the rods!  So we skipped everything that he didn't understand or didn't like.  We got about 30-35 pages into the book before I was ready to give up.  My son had already given up.  Okay, so what was the problem with Miquon?  What was wrong with my son?  What happened?  Just the usual (though at the time I didn't know it).  It was just a case of my son's way of learning and enjoying math not meshing with the way that Miquon was presenting it.  It's a fairly common occurrence; it's not easy trying to match a curriculum with a child's learning style.  But at the time I was so disillusioned because I had heard that Miquon was so great.

It seems, and, of course, this is just my opinion, that Miquon is what was termed "new math" in the late 60s.  It reminded me a little of some of the math that I did in first grade which was called new math.  I looked up "new math" in our new (at the time) CD encyclopedia and read it.  (See Grolier's Academic American Encyclopedia from 1998 through 1993, the article entitled "Mathematics, New.") After reading that, I decided that for sure we would head toward a more balanced arithmetic program.  But which one?

Next I heard about Developmental Math by George Saad; it was termed as a good solid program.  But it was another "no go" for us.  I can't remember why we ended up not using this program.  I remember receiving some workbooks with pages that weren't fully cut apart, which, of course, is a small thing.  We used it for a few weeks, then we tried Ray's Arithmetic (prior to their publishing a workbook series).  This consisted of a little book that was written around 1900, but had been reprinted.  There were plenty of word problems, but it was too difficult for me to use with my son.  He wanted to write in a workbook, and at the time, Ray's was only a little (about 4" x 6") hardback arithmetic book.

Okay, I was getting pretty tired of searching for an arithmetic program at this point.  I was looking for a traditional program that focused more on computation than some programs do.  I had read somewhere of test results (which I can't find, so if you know about these, please let me know!) that indicated that homeschoolers were above average in *understanding how to get the answer* (concepts), but were only average in being able to *get the right answer* (computation).  And after reading the Grolier's encyclopedia article, I was looking for something that didn't bring up "set theory."  I wanted a program that supported my view concerning memorization of addition and multiplication tables.  At this point I was still trying to stay away from big textbook publishers because of all the warnings I had gotten from those homeschooling/educational books I had read.

When talking to an acquaintance in our local support group during one of our roller skating sessions, she mentioned Making Math Meaningful.  She had just bought it for her son, but loaned it to me for a couple of days since they weren't planning on starting it right away.  At that time, I thought that Making Math Meaningful was a little too light on the side of computation with what I perceived to be a new math flavor thrown in.  It appeared to be very good at teaching students *how to understand* math, though, with plenty of hands-on work with beans, macaroni, etc., for manipulatives.

Finally, for some reason (probably desperation), I looked into A Beka Arithmetic.  I went to one of their motel meetings and looked over their math curriculum.  I went ahead and ordered a second grade math workbook for my son.  And he seemed to really like it.  And we were happy with it for the time being.  Granted, I wished that Saxon had a primary grades program, but I could wait and put him in Saxon in a few years.

Back then, Saxon didn't have a K-3 program for homeschoolers.  But all the local homeschoolers "just knew" that Saxon was the one and only math program.  So I was just biding my time until I could put my son in Saxon 5/4.  I had been told as soon as a student is done with A Beka 2, that they could transfer over to Saxon 5/4.  So that was our goal.

Late in 1993, we got on the internet--CompuServe to be exact.  And I joined a forum about 6 months later and found how easy it was to try out shareware by downloading it.  I downloaded some little math programs and a few geography programs.  I went ahead and bought some of the shareware math programs once I realized how much easier it was to use a computer for math drill (no, not drill and kill--just maybe two or three times a week for about 15 minutes).  Those little flash cards can become rather dull, so finding these computer math drill programs was a great find.  We're still using some of these programs.  They're named Beat the Bomb, Explorer Math (by the same authors as Beat the Bomb), Math in a Flash, and Treasure Hunt Math.  Beat the Bomb is still free for the downloading.  The others I've looked for and haven't seen, and they are old DOS programs anyway.  One math drill program we use that can still be easily bought is Math Munchers Deluxe.

So, we're happy with A Beka Arithmetic 2, but when it was time to move on to A Beka Arithmetic 3, Saxon had just come out with their primary grades program.  So I went ahead and bought the Saxon 3 since I knew that eventually I wanted him to be in Saxon (after all, everyone says it's the best, what all homeschoolers use--at least back then).  He might as well get adjusted to the way Saxon does things and having him use Saxon 3 will prepare him for Saxon 5/4.  But Saxon was a little, maybe a lot, behind A Beka when comparing/contrasting different areas of the two mathematics curricula.  I was surprised!  I could see that he would forget what he'd learned while using A Beka if I only used Saxon 3 although he would learn a very few things that weren't yet being covered by A Beka.  So I ordered A Beka Arithmetic 3 and used it in conjunction with Saxon.  Saxon 3 was great, I thought.  It was completely scripted for the parent/teacher.  It started with quite a bit of class time where the parent/teacher and the student spent time together working on such things as the calendar, sequencing, thermometer, counting change, story problems, skip counting--this was daily.  The topic of the day was also discussed and flash cards were used fairly often; timed tests (speed drills) were also available a few days a week.  Once the lesson with the parent/teacher was finished the student then did the front of the lesson page.  The back side of the lesson page was to be done in the evening as homework.  We skipped the evening homework almost every time since my son seemed to be able to grasp everything from the lesson with me.  Saxon 3 used plenty of manipulatives, but not so many that you got worn out using them.  I felt that Saxon 3 did a good job as far as explaining concepts goes, and daily review also is a great feature.  Learning how to write number sentences was another feature that I thought was a good way to teach mathematical thinking.  For each lesson, the student had to write three sentences that included the Lesson number.  For example:  for lesson 15 the sentences could be 5+10=15, 19-4=15, and 14+1=15.  Saxon 3 requires a student to think, and I liked it.  However, my son preferred A Beka.  So since he liked A Beka better and because I didn't particularly know how to keep him from losing the ground he'd gained using A Beka if we used Saxon 3, we dropped Saxon 3 after about 55 Lessons.  And I saved Saxon 3 for my daughter.

So my son continued through A Beka 3 and as he neared the end, I decided to try Saxon again since the primary grades (K-3) follow a different format than do the upper level books (Saxon 5/4 and up).  At that time, he was now 8 and nearing age 9.  The Saxon placement test was online, so I had him take it, and it indicated that he should be in Saxon 6/5.  So I waited a month or so for the 2nd edition to come out and bought it.  My son started it with gusto and joy!  But soon he absolutely dreaded it.  For some inexplicable reason, Saxon just doesn't mesh with my son's way of thinking or doing.  He said that it was boring.  I'm not sure what he meant by that.  I know that A Beka is more colorful, but I'm not sure that's what he meant.  And 6/5 wasn't too difficult for him.  I've often though that he just wasn't ready at age 8.5 to do that much writing.  A Beka is a workbook format while Saxon requires notebook paper.  Saxon seems like a solid program; I thought the mental math section was tops!  I thought that maybe he just needed to get used to Saxon 6/5, that once he got used to it he'd like it.  But it didn't work that way for us.  So after about 35-38 lessons in Saxon 6/5, he went back to A Beka 4th grade.

At this point I was troubled.  I had imagined my son doing Saxon Algebra from early on in our homeschooling adventure.  I was under the impression that Saxon was the it program.  I searched for more information on A Beka.  I wanted to know if it was a good program in the upper grades (Algebra, etc.).  So I called A Beka and asked what was covered in the upper level books.  And the lady I spoke to told me and also offered to send me the test results of students using A Beka Math once she understood my concerns.  Those test scores, and also comments from one teacher that had used Saxon in a public school and comments from other parents that had used A Beka through high school, calmed my fears.  They said that Saxon is not necessarily the best and that A Beka is a fine choice.  I also found that there are other options, such as Jacob's Algebra and Scott Foresman's UCSMP.

You may wonder why I was worried about algebra when my son was only 9.  The reason is because I wanted to use one program that took my son up and out of high school math.  Switching back and forth from A Beka to Saxon really caused us some upheaval and loss of momentum.  I didn't want to have to switch later and then try to fill in any gaps that had been missed. 

So back to our story, my son then went on to the 5th grade A Beka book, finishing it without any troubles and asked to skip the 6th grade book.  So after averaging 90% or above accuracy on the last 30 or so lessons in the 5th grade book, I let him skip the 6th grade book.  He's now in the 7th grade book called Basic Mathematics I.  I had him do some of the Key To ... booklets because I thought he needed a little more practice and explanation than the A Beka book was providing.  So he did the percent booklets for a few months and is back in the 7th grade A Beka book working on learning how interest is figured.

Overall, I think that the strengths that A Beka possesses are
(1) They use the same kind of "spiraling" technique that Saxon and other programs use; they constantly review old material while introducing new material so that the student doesn't forget long division just because they're focusing on fractions or statistics.
(2) The topic of the lesson is introduced, usually about a third of the lesson is on that, then the rest of the lesson is review.
(3) I like the fact that they usually have a few of story problems every day.  Story problems are the type of math that we all encounter in everyday life.
(4) The books are workbooks so the kids don't have to rewrite the problems onto notebook paper which is difficult for some students that aren't used to a lot of writing, and it can also lead to extra errors if the problems are copied incorrectly.
(5) The books are colorful (particularly in the lower grades) with a few puzzles and cartoons.
(6) A Beka provides a firm math foundation.

A Beka is weak in manipulatives, in my opinion.  Possibly they are suggested in the Teacher Curriculum books.  I don't buy the Teacher Curriculum books because they seem to be filled with activities that are for a whole class.  Yes, I could be missing something worthwhile in the Curriculum books, but I didn't find much useful info in the 1st or 2nd grade Curriculum books when I bought them--plus they cost an arm and a leg ($40 at the time), so we just buy the student workbook, a teacher's key for correcting, and a solutions manual starting with Pre-Algebra.  But back to the manipulatives (which is what the topic sentence indicates that this paragraph is supposed to be about!)  We really like Cuisenaire rods.  Base ten blocks would also be good.  I think we like Cuisenaire rods because we started out with them with Miquon.  Plus, the ideas in Ruth Beechick's book, An Easy Start in Arithmetic, are also very good--like the popsicle sticks.  Right now my daughter is in the 3rd grade A Beka Math book and is learning multiplication and division.  We use the Cuisenaire rods all the time.  She understands the concepts much more easily using manipulatives; my son, on the other hand, was only frustrated by using manipulatives--so we skipped them for the most part with him.  Not every child needs manipulatives.  So, buy or make manipulatives if you find your child needs them.

I think this review is getting too long, but I don't want to neglect Math It.  Math It is a nice little program that helps students to memorize their addition and multiplication tables.  The set I have came with a cassette tape, an instruction booklet, some tiny little cards with math problems on them, and some large cards for placing the little cards on.  It sounds confusing, and it is until you read the instruction booklet.  There's a little more to it than that, but we've only used it for memorization of addition and multiplication tables.  I'd say for it's for kids around the ages of 7-10.  I thought that it was a little pricey new, so we bought one used.  I just found out that it is retail priced at $49.95 these days.  I cannot recommend it at that price.  Wow, maybe they've added a bunch more features to it; let's hope so for that price.  (I'm beginning to wonder if my surprise at the prices these days is a sign of my increasing age.)

Some supplementary mathematics books might be nice to throw in every now and then for a breather.  Here's a couple of ones we use are Math for Smarty Pants, Math Wizardry for Kids, and The I Hate Mathematics! Book.  A couple of other books along these lines that are on my wish list are Arithmetricks, Cool Math, and The Book of Think.

So, to finally wrap this thing up--what math curriculum would be best for your student?  I wish I could tell you.  I'm not a lot of help here.  Our tortuous journey proves that it's not so easy to find the best math program.  And one student's best math program might be another's worst.  Developmental Mathematics, Miquon, Making Math Meaningful, Saxon, and Ray's may not have worked for us, but they are working for a lot of homeschoolers--please don't overlook these programs just because they didn't work for us.  To find the right program for your student, you've just got to find out about the program and then figure out if it will fit with your student--a bit of trial and error.  Even when you think you've got it figured out, be prepared and willing to switch gears if your student is having troubles.  There are a lot of good programs out there; matching a good program to your child's way of learning is the key to a good learning experience.