Math-U-See is a fairly new Math program, designed especially for homeschoolers, which runs from Kindergarten all the way through high school. The author is a former high school Math teacher who has attempted to balance a solid conceptual understanding of math with enough practice to let it "sink in." The program consists of a student text (workbook format), a teacher's manual, and optional practice sheets, special Math-U-See blocks and a teacher training DVD. I am very impressed with this program. The author does a fine job of allowing the students to become well aquainted with using numbers. I found math concepts very easy to explain to my daughter with the use of the very clever manipulatives (which might be thought of as a cross between "Base-ten Blocks" and Cuisinaire Rods). I was particularly impressed with how clearly place value is taught and how thoughtfully the child is prepared for future lessons (e.g. early on in addition, the child starts doing simple "solve for the unknown" problems in preparation for subtraction). Other skills learned include telling time, measurement and a heavy emphasis on skip counting (in preparation for future multiplication and factoring). My only complaint is that some of the material is contained only in the teacher's manual (I can imagine that this might have been done intentionally to force the parent to follow along in the teacher's manual rather than letting the child work entirely on their own. The author demonstrates how each concept works on the DVD so that the parent may more confidently teach the concept to the child.

Over the years we haven't always used Math-U-See as our primary Math text, but we have always found the DVDs and blocks useful no matter what we were using.

Miquon Math is a series of 6 math workbooks designed to be used in 1st through 3rd grade. They are named by color and not by grade level, so that an older child can use them without feeling they are "remedial". The workbooks are designed to be used with Cuisenaire Rods. I have had the books for a couple of years but have only started using them this year as a supplement for my 3rd and 4th graders. I hesitated using them before because they have an unusual format -- the pages don't necessarily have to be done in order, and are grouped by topic rather than in sequential chapters. Multiplication is introduced along with addition in first grade, and advanced concepts such as squared numbers and pre-algebra are introduced through use of concrete manipulatives. However, my 3rd grader now says she "loves this kind of math" and both the children have shown a better grasp of what numbers mean since they have started using the books. We've discovered that when the manipulatives come out and are used to illustrate concepts, the "littlies" want to join in. My 5yo was watching carefully as my 8yo tried to figure out the square of 4, and suddenly announced "It's 16!" He was so proud of himself!
I have ordered the Orange Book (the first one in the series) to start with my almost 6 year old. After completing the Miquon Series, a child can go straight into Saxon Math 54 or 65.

Saxon 2 covers the arithmetic topics of addition and subtraction of one and two digit numbers and simple multiplication and division as well as the related topics of patterns, graphing, time, measurement, money, geometry and estimating. Although it uses manipulatives it is not a "manipulatives-based" program.

Each day's lesson begins with oral exercises called "The Meeting" during which use of a calendar, counting, time, money, and patterns are practiced. The actual lessons follow and are completely scripted in the teachers edition. They are designed for four days of new material and one day of review. Math facts are practiced every day as well, using flash cards provided with the kit and fact sheet drills in the workbook.

The beauty of Saxon is repetition. Concepts are introduced and then reinforced over and over again. In Saxon 2 there are games, art projects and physical activites as part of the lessons which provide a break from strict pencil and paper work. My children had been doing a strictly manipulative based math program previously so I thought they wouldn't like Saxon, but they love it. I believe it is because of the variety of activities.

One drawback to Saxon is the price which is close to $100.00 for the homestudy kit. The kit includes a teacher's manual, workbook, meeting book and cardboard manipulatives and flash cards. It can be found in discount catalogs or used from fellow homeschoolers. It requires a set of manipulatives which can be purchased separately at teacher supply stores or as a kit from the source given by Saxon and various homeschool catalogs.

Singapore students are scoring the highest in the world in math and science. The web page for these texts in the US is http://www.singaporemath.com

Singapore Math seems to solve the "conceptual/drill...Saxon jumping around problem". Here's an example from a problem in the first half of fifth grade book

<< Mr Li paid $36 for 3 singlets and 2 T-shirts. A T-shirt cost 3 times as much as a singlet. How much did Mr Li pay for the 2 T-shirts?>>

Apparently the children are taught to "think mathematically" and are able to solve these types of problems in 5th grade without using algebra....these types of problems lead up to a better understanding of algebra.

Multiplication asian style The children learn facts families in sets ....for example they chant as follows

2 2 4 2 3 6 2 4 8 2 5 10

They don't say "times" or "equal" although that is explained to them. They are taught the reciprical nature of multiplication and division after they can chant this from memory they write out the sets as-

2x2=4 2x3=6 and so on
4/2=2 3x2=6......
6/2=3
6/3=2

and finally provide answers for equations....then they go on to memorize the next set which would be

2 6 12 2 7 14 2 8 16 2 9 18

If anyone is thinking about going with this program I would suggest making the move before going in to New Elementary Math. It would be easier to acclimate to this way of thinking while still in Primary Math I believe.

There are answers at the back the book but no other aid. To be honest I think I would have trouble teaching this material. I did "ok" in math but not great and I don't remember more then basic algebra. If you tend to think mathematically and enjoyed algebra, trig. you could probably use this without too much effort.

The Singapore texts actually do have almost as much drill as other books I've used (Miquon, Horizon) but not as much as Abeka. For example in 3rd A Singapore gives about 8-10 examples of adding 5 digit numbers then the workbook has at least that many that the child does on their own. The difference is that Horizon has the child doing a few of those problems every day for a week or two while at the same time they introduce new things. Singapore moves on after 2 lessons that cover that...but the child should have mastered that skill before they can move on to the next lesson. In Asia the kids spend a lot of time working on drills at home.

In Saxon you learn to add fractions then you repeat the same level of adding fractions for 6 or 8 lessons in the doing 3 or 4 problems in each practice section. During the intervening lessons you jump from learning short division to dividing with remainders to using metric scale etc before you finally get back to fractions again.

With Singapore you learn to add fractions and spend maybe 3 lessons learning how to do that (slight difficulty increase with each lesson) then you move on to using the skill of adding fractions with word problems (real life) for a few lessons. By this time the child has probably done more fraction addition problems overall then they would do in Saxon. The skill is learned and won't be touched again until the review chapters. If the child has trouble, the teacher/parent shouldn't move on. I did this a few times with my son and regret it. The review chapters occur often enough that the child shouldn't forget.