Chalkdust Math
Levels: Basic math through Calculus 1 and College Algebra
DVD presentation by Dana Mosely and regular public school type textbooks, solution guides.

Strengths:

DVD lectures with a friendly teacher. The instructor is available via email for any questions. The sequence closely follows that taught in public schools (good for test takers).

Most of the explanations are pretty good and easy to understand. There are LOTS of practice problems available. (That is our son Bear's opinion about the Calculus level.)

Weaknesses:

According to our son Bear's opinion for the Calculus level:
Sometimes the video teacher doesn't go into enough depth for certain problems. Bear thought that the teacher sometimes would show you how to do something but not show the "why" of it.

Strengths:

Unique! Funny!
These texts offer a living, story approach to math. They are inexpensive. Life of Fred texts are totally self-teaching. There are home companion guides for some of the levels for moms who want "more". They are funny - oh did I already say that? The customer service is reported to be excellent.

Weaknesses:

So far the only weakness Bear has reported to me is a lack of extra practice problems (for the calculus level). He says the explanations are very good but that he needs more problems to get the concepts he's learning.

We will be trying out the fractions level with Otter in about a year. I will report more then.

Mammoth Math (MM)
Levels: Addition through Algebra I
Worktexts you can download, purchase hardcopies or get on CD.

Strengths:

The Blue Series workbooks are designed to be self teaching, so they are explained "to" the student. The texts are designed so a student has mastery of the material before moving on. The focus is on understanding mathmatical concepts instead of rote memorization. They are inexpensive. E-books can be reprinted for more than 1 child without additional cost.

Weaknesses:

Some children will need more explanation. The pages may seem boring visually to some children. We have a packet of Mammoth Math that we are going to try out. We'll report back more later.

Strengths:

It's free. It has detailed lesson plans, fully illustrated and interesting student worksheets, etc. It seems like a very solid math program that uses a variety of interesting approaches to problems and teaches solid thinking skills.

Weaknesses:

It's British so you will have to deal with some minor differences in wording and also differences in measurement and money. It's designed for a school environment so you may have to adjust a few lessons for a homeschool environment.
It can be teacher intensive.

Strengths:

The manipulatives help a child better see and understand the underlying concepts in math. The videos are helpful with the emphasis is on understanding the math vs. just memorizing algorithms. You aren't supposed to move on until you KNOW the material backwards and forwards (so you are really building a good foundation). Steve Demme (the creator of Math-U-See) can be humorous and fun in the videos. Moms are taught how to teach.

Weaknesses:

The books have no color or illustrations. My kids found them to be boring, but for others no distractions are good. The higher levels -in my opinion- are not rigorous enough. You aren't supposed to move on until you KNOW the material backwards and forwards which means some kids will stall in a certain area like multiplication facts. It covers topics in a slightly different sequence than "public school". It can be on the expensive side.

*Miquon
Levels: 1st grade - approx. 3rd grade
Workbooks, Cuisenaire rods, teacher's guide

Strengths:

It teaches kids to think through problems rather than just memorize an algorithm. It uses Cuisenaire rods to illustrate concepts. It encourages children to discover the solutions to problems, rather than just "giving" it to them. It introduces concepts like multiplication very early on but in a way that most kids can get. The workbooks are "fun" and get kids "thinking" and even creating their own problems. They really have to understand what they are doing to do that! It's inexpensive. The operations are shown as being related to each other with makes math a "big" picture instead of unrelated operations. You don't have to follow the workbook sequence, but can do it by topic. Miquon is a good program for gifted children.

Weaknesses:

It can be hard for some parents to teach as there is nothing scripted. The teacher's book doesn't usually have the answers (although they are easy to figure out). Some kids will just freeze up with a discovery based program. The workbooks are not "colorful" and snazzy, although they do have pictures - they are in line drawing format. There isn't much in the way of word problems. You may need to supplement with drill. Math-phobic moms or first time homeschoolers may not feel comfortable with it. Levels only go to approximately 3rd grade.

*RightStart (Right Start or RS)
Levels: Preschool/Kindergarten - Intermediate math (geometry) for 5th (?) grade
Lesson book (teacher's manual), workbook, card games book, lots of manipulatives including an abacus

Strengths:

Right Start uses a lot of manipulatives in creative ways. It teaches a lot of mental strategies and makes great use of the abacus for visualizing quantities. It is fully scripted for parents (great for those who are "unsure" about teaching math). It doesn't put a lot of emphasis on filling out workbook pages. It has lots of games to play that reinforce learning in a "painless" way. It uses a multisensory approach.

Weaknesses:

It could become time consuming if teaching multiple grades. Some kids hate manipulatives and love workbooks. The workbook pages are "boring" - in that there is no color and graphics to dress up the pages. It's expensive at the outlay. Parents may not want to play the card games with their child or children and the kids themselves may find them dull. It doesn't follow a public school sequence.

Strengths:

It really drills kids so that they are good and efficient at completing their math problems, it's fully scripted in the lower grades for parents. It makes use of a variety of manipulatives through about 3rd grade. Kids usually test well with it. There is continual review.

Weaknesses:

It's emphasis is on rote memorization and algorithms. There is less parent support for the higher grades unless you buy like the DIVE Cd's to teach the lessons. Some kids bog down and get sick of the spiral review approach. Kids may be less sure on how to solve problems they are not familar with. Some parents call Saxon the "drill and kill" program. The workbooks are not colorful or engaging.

Strengths:

It is colorful with plenty of excellent story problems. It teaches good problem solving and approaching problems in different ways (thinking mathmatically as opposed to "rote" memorization). It has good homeschool teacher's manuals for the younger grades (this wasn't always the case). It helps develop mental math skills and provides an excellent foundation for higher math. It's inexpensive. Students in Singapore using this program have some of the highest math scores in the world. The supplemental word problems are awesome. It uses pictures to explain things concretely before moving onto the abstract.

Weaknesses:

Sometimes it pushes too fast. There is not much review of some materials (though you can purchase additional workbooks for practice) It covers materials earlier or different than a usual American sequence (some kids might not be ready for abstract thinking yet). You may need to supplement with some drill or the additional practice books in the series. No hands-on manipulatives are generally associated with it, although you can certainly use them to illustrate the problems. The higher math programs (7th grade +) will be difficult to use if a teacher is not strong in that level of math.

Strengths:

There is a fully explained, narrated and animated solution for every single problem of the entire series. Teaching textbooks is designed to be self taught via the excellent, multimedia presentations on the computer CD's. Problems in the higher levels are designed to get students familar with items that will be on the SAT test. The program is very user-friendly. Little or no involvement is needed from a parent. My "math-hating" daughter likes it a lot. Nuff said.

Weaknesses:

There may not be enough practice problems for students who need more work on a concept. Some kids may not want to do lessons via the computer and may not enjoy reading them out of the textbook instead. It is expensive. Some concepts that are normally presented in many Algebra II programs are not presented until their pre-calculus program.

*Thinkwell
Levels: Prealgebra-Calculus
Videos, online work and solutions

Strengths:

This program doesn't use a traditional textbook. Instead it uses a series of video lectures.
Our son bear opines that the explanations are some of the best of any homeschool math program he's ever used. The instructor is entertaining and very thourough. There is a good balance of video time and interactive exercises. Exercises are graded instantly and each problem has a detailed solution.
Compared to some other homeschool programs, it is less expensive if you use the independent subscription..

Weaknesses:

There is no textbook and the program is set up to be used online. Although you can get a CD with the videos on it, you must do the exercises online.
You are limited to a 1 year contract, so in order to use this program again, you'll have to pay for it again.

Strengths:

The instruction is based on truly understanding the material. Explanations don't take any shortcuts and are explained via multimedia. Understanding the "why" behind things makes it so your student doesn't have to overload on practice problems. Video Text is totally self-teaching. There is a toll-free number for support where an instructor can walk a student through problems. It is endorsed by the author of the Apologia science series as one of the only math programs that will properly prepare a student for higher level science courses.

Weaknesses:

The program is expensive and doesn't follow a traditional schedule of topics. I don't like how there are quite a few different soft-bound texts in each level. It gets tiresome going between the books. The individuals who teach on the DVD's can be sort of "dry" and there is no humor or anything to spice the lessons up. Some students may find it boring.