Okay, so this isn't really a curriculum. But it fills a gap that a lot of courses ignore, and does a pretty good job of it. The Mathematical Reasoning books emphasize critical thinking, problem solving, and logic skills in their approach to math instruction, assuming that computation skills are useless without an understanding of why they work. This series can be used either as a supplement or as a remedial tool for students behind in math. Many parents also use these books to ensure their kids do well on standardized tests.
This series only covers the lower grades (PreK-4), but it helps kids to think mathematically and logically (and to see the logic of math) in a way that many full-blown curricula do not. The first four books are very colorful with a wide variety of fun activities to engage young learners; the last two books are more straightforward with no pictures and simple black and white text, but with plenty of work to keep kids busy. These are not just throw-away busy work pages; though the series is designed for younger kids, the activities are ones that will make them think creatively to find answers. They will need to learn their math basics (addition, subtraction, multiplication, etc.) elsewhere, since a grasp of those skills is necessary in order to work through these texts, none of which address any of those issues directly.
The first four books in the series are stand-alone student worktexts; the first three books are basic enough they don't have answer keys, the fourth (Level C) includes answers to questions at the back of the book. The fifth and sixth books (Books 1 and 2) include student worktexts and separate teacher's manuals with notes for instruction of key ideas as well as solutions to problems. Because each activity has simple and clear instructions, children who can read will probably be able to work on their own. Each activity is logic-based, designed to develop critical thinking in students by leading them through ideas step-by-step.
Books 1 and 2 may seem more advanced than fourth or fifth grade at first glance. They deal with geometry, number sequence, classification, graphing, etc., though in such an unmystical and straightforward way that kids should be able to grasp the material. Again, this is not about computation facts; this is about the reasons computation facts do what they do, and about giving kids an understanding of those reasons so they can apply the principles they learn in a variety of contexts.
This is not a series of drill books. There are no pages full of endless addition or subtraction sets, no identical pages of identical problems. If your child needs help or reinforcement in a specific area, there are much better resources (the Key To series, for instance). If your child has trouble thinking mathematically, however, and if you don't want to switch to another curriculum altogether, this is a reliable choice. Again, don't try to use this as an independent curriculum in itself, but as far as supplements go this is unique and effective.
Not only is this series very educational, it is very fun and engaging. Kids who don't want to do math because they just don't get it may actually change their minds once they understand what's going on "behind the scenes" of each problem they solve. Many educators say kids retain information much better if they're required to "figure it out" for themselves, and this appears to be the approach of the authors of the Mathematical Reasoning series.
Many curricula claim to train kids to think mathematically, but all too often their approach causes them to fall short of this goal. By focusing on critical thinking and problem solving (and by avoiding the temptation to write a full curriculum), the writers of this series have risen to meet the need. If your kids are able to grasp math on a conceptual basis at an early age, and not just on a fact-and-rule basis, they will be far more likely to succeed at math later when the more abstract ideas start popping up.