Math is frequently a "problem subject" for home school families. There aren't too many professions that require its constant use, and it's one of those things you either use or lose—chances are, if you haven't studied algebra since high school it'll be pretty difficult to teach it to your kids when they're in high school. It's not that we don't care, it's just that the information we need to remember pushes out the less essential data.
Fortunately, a number of home school math curricula take this into account. Those that aren't altogether studentdirected at least provide parents everything they need to present lessons and guide students' work. Many of the programs we offer were originally intended for use in a classroom situation, but great attention has been devoted to adapting them for home schools, usually to excellent effect.
Why is math in particular so difficult to teach, and why is it so difficult to retain? Both questions can be answered the same way: to be good at mathematics, you need to learn to think mathematically. In school, most of us learned no more than how to complete problems, unaware there were actual reasons behind the seemingly senseless steps.
Many courses have been designed with the goal of teaching kids to think mathematically specifically in mind. The old "learn and regurgitate" books are still out there, but they're gradually giving way to the new stronger methodology that realizes simply giving students lists of facts and procedures to memorize is a perfect recipe for instructional failure.
Three basic ways of teaching math have emerged: the spiral method (in which kids learn little bits of concepts over a long period of time) and the linear (or mastery) approach (in which kids learn all about a single topic before moving on to the next). The third method is less clearly defined, but could be called the tactile method or the experiential method; this approach guides students toward learning discovery using manipulatives, games, flashcards and the abacus, and many other objects intended to foster mathematical development.
Our four top sellers at Exodus Books are Saxon Math, Singapore Math, Horizons Math, and Life of Fred. Saxon and Horizons are both incremental, moving slowly through concepts with constant review and expansion. Singapore Math integrates elements of the incremental approach, the mastery approach (topics are comprehensively presented), and the experiential method (manipulatives are integral). Life of Fred is in a class by itself, using a fictional storyline and realworld application to teach everything from arithmetic to calculus and statistics.
Math curricula we offer, arranged by type of curriculum:
Spiral & Incremental programs

A Beka Arithmetic & Mathematics Grades K12
This can be either studentdirected or teacherled, depending on your home school approach and your kids' needs. A Beka Arithmetic & Mathematics is a straightforward textbook program, mastery based, with lots of drill to cement important concepts in place. Some users complain about the lack of information in the student books, but there's plenty of teacher support in the teacher editions. There isn't a lot of emphasis on thinking mathematically, though practical applications and realworld examples are emphasized.


Harold Jacobs with Dr. Callahan DVDs Grades 812
In our increasingly mediasavvy culture, textbooks with DVD supplements are gaining popularity; Harold Jacobs Mathematics is one of the best of these. With books on algebra, geometry, and college math for older students, these texts form an engaging incremental approach to more advanced math. The Ask Dr. Callahan DVD lectures thoroughly explain each of these texts through Dr. Callahan's inclass lessons.


Horizons Math Grades K8
One of the best sellers at Exodus Books, Horizons Math has a deservedly high reputation among home educators. While the course follows the spiral method, it does so more flexibly than many similar programs, teaching concepts little by little but with a more logical progression and taking more time for difficult ones. The curriculum covers grades K8, with two 160lesson consumable workbooks per grade, as well as a teacher's guide (which, after grade 3, is indispensable). The only downside is that the course doesn't cover through high school, but there are plenty of good options to move to after 8th grade, particularly Saxon Math.


Saxon Math Grades K12
DIVE & Teaching CDROMs available
This has long been the standard home school math curriculum. It's incremental in approach, introducing part of a concept, moving to other territory, and only later returning to the original concept to expand on it. This isn't to say kids have nothing to do with the concept in the interim: a feature of Saxon is its constant and thorough review. Each lesson includes 2530 exercise problems designed for drill. There are three basic segments: the K3 books, the 5/48/7 books for elementary grades, and the Algebra 1/2Calculus books for secondary students. Each text is genuinely studentdirected, with the exception of the K3 books, which are teacherintensive.

Linear (Mastery)

ACSI Purposeful Design Math Grades K6
ACSI Purposeful Design Math is masterybased, with a strong emphasis on thinking mathematically. Students learn each concept first in its concrete/practical context, then as a mathematical abstraction. This is an excellent course for grades K8, introducing material usually reserved for much later and always retaining a biblical emphasis, but it is very teacher intensive. The teacher guides are expensive and fairly overwhelming, making this a difficult program to implement for most parents (especially those with lots of kids of different ages), but if you can get through these Purposeful Design is one of the best and most rewarding courses we've seen.


AOP Lifepacs: Math Grades K12
Each grade from 112 is covered in ten consumable workbooks (K is covered in two larger workbooks) for students to complete on their own. The kindergarten and first grade levels are teacherintensive; the rest are studentdirected. The kindergarten level includes two student workbooks, and the first grade level includes two teacher guides; other than that, the format is the same throughout all the grades.


Bob Jones University Math Grades K12
BJU Math is one of the few monolithic math programs available, covering all grade levels and every major discipline. It's very teacherintensive (parents must guide students through lessons), with a mastery approach that uses thorough presentations and drill to internalize concepts and get kids thinking about the why as well as the how of math. This is one of the better programs, though it is designed for classroom use, and home school families with kids across the age spectrum may find it difficult to implement.


CLP Liberty Mathematics Grades K2
So far just three workbooks covering K2, the plan is for a 6volume set of worktexts covering most of elementary math. There's lots of review, some limited color and illustrations, and not much teacher support. While these aren't bad books, the fact that they only cover the first few years makes them difficult to implement for those committed to longterm homeschooling. Still, the Bible focus is good, and at this age you don't necessarily need anything fancy to introduce your kids to the math they need.


"KeyTo" Math Grades 49
The Keyto Math series is a collection of workbooks on a variety of topics (from algebra to metric measurement to percents) for older elementary to early high school students that can be used remedially, supplementally, or as a core course to base further study around. Each workbook is slim and easytouse with clear instructions and lots of white space. Most topics have 34 books with answer keys and test books. Algebra has 10 workbooks with 3 answer keys; Geometry has 8 workbooks with 4 answer keys.


MathUSee Grades K12
The authors of MathUSee understand that math instruction shouldn't simply be an academic pursuit; rather, it needs to help students toward essential practical applications. This is a teacherintensive course, with parents watching the lessons on DVD and reiterating the content to their kids later in a lesson format, who use proprietary manipulative blocks as they learn. If your kids are having trouble, you can have them watch the lesson with you before moving on to complete the problems sets, which are all oriented to a realworld understanding of mathematical concepts.


MCP Math Grades K6
For the authors of MCP Math, review is key. Concepts are drilled over and over and over before new ones are introduced, with the goal of student mastery each step of the way. The course covers grades K6, and kids simply work through consumable pages sparsely illustrated by happy animal drawings. The teacher editions are some of the best we've seen for a reasonable price: student lessons are presented in a twopage layout, with extra information, answers, and more. Many parents will be able to teach this course just fine without the guides, but they do make life a lot easier and math time less stressful.


Rod & Staff Math Grades 110
This is very much a teacherintensive course; fortunately, the teacher guides are thorough and each lesson is fully scripted for parents. There isn't a lot of text for students to read (which many kids will love), but this does mean you'll need to spend time with them on their math every day. Rod & Staff Math focuses on the rote learning of the basics, but covers them so thoroughly that once kids get to the hard stuff like algebra they should be able to transition fairly easily. It's probably a good idea to move to a different program after the elementary years, though for testing purposes this isn't necessary.


Teaching Textbooks Math Grades 312
The brothers Sabouri have developed a computerbased math curriculum that is the direct answer to many parents' distressed prayers. Parents need know nothing about math, since kids interact directly with CDROM lectures and problems, doing their work onscreen and having it evaluated as soon as they complete a problem or problem set. Many typical kids like it as it has a quirky feel and moves at a leisurely pace, but it's not a good option if you wish to challenge them.
We aren't able to sell Teaching Textbooks new at this time, though we do take any used sets that come in and sell them for a competitive price.

Other

Art of Problem Solving Grades 612
This challenging series aims to teach math as creative problem solving rather than a series of formulas to memorize. Recommended for "advanced" students, the problems are extremely hard but also extremely rewarding. Meant to follow Beast Academy.


Beast Academy Grades 27
In a world of blackandwhite, drillandkill textbooks, a former math Olympian has created a strangely bright and innovative curriculum. Beast Academy is a series of (challenging) math graphic novels for 2nd5th grade. It features a group of colorful monsters who attend the eponymous Beast Academy, where they learn math alongside life lessons. Not recommended as a core curriculum, but makes a great supplement for kids who want more fun or more challenge in their math.


Life of Fred Grades K12
Perhaps the most unique approach is that found in Stan Schmidt's Life of Fred series. The books cover elementary math all the way to calculus and statistics, using an organic approach that couches problems in practical terms. Students follow the silly adventures of a genius little kid named Fred in stories that impart all the basics of math, its more advanced disciplines, and all kinds of things in between. These are super fun, super popular, and highly recommended, if not as your core program, then as supplements.


Math Lessons for a Living Education Grades 16
Drawing on Charlotte Mason philosophy, this series uses stories of a pair of twins to connect math with real life as it focuses on the "why" of math before the "how". Eschewing normal drill focus, and incorporating learning techniques like narration, MLFLE encourages the student to turn their brain on, keep it on, and keep connected to what is going on in their own learning journey. The author doesn't worry too much about normal grade requirements, and these run a little easier than many other programs, so you may be able to start Level 1 in Kindergarten if desired.


Math Mammoth Grades 17
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Math in Focus Grades K5
For those who want both the Singapore Math approach and the incremental method, Math in Focus is pretty much the only choice. Published by the same company that produces Saxon Math, this is an American version of the Singaporebased programs for grades K6, complete with more colorful student books, more elaborate teacher manuals, and computerbased manipulatives.


Miquon Grades K3
Some programs have stayed away from modern technology, but have nevertheless adopted experimental or nontraditional methods of instruction. Of these, the oldest (and therefore most timetested) is Miquon Math which uses student exploration with manipulatives and workbooks to guide them toward math knowledge. Kids are given a number of manipulatives to "play with" in a guided environment that directs them toward formal math knowledge; workbooks and plenty of teacher resources supplement.


Principles of Mathematics Grades 68
A unique two book curriculum that connects prealgebra with Christian worldview, showing students how math demonstrates an orderly [created] universe. These seem to cover all the needed bases, but may not provide adequate review for some kids. The publisher recommends these for use after Math Lessons for a Living Education and before going on to Harold Jacobs Elementary Alegbra.


Ray's New Arithmetic Grades 18
For the oldfashioned folks, Ray's New Arithmetic are textbooks written by Joseph Ray in the first half of the 19th century, and which are becoming more popular with proponents of Charlotte Masonstyle and Classical education. Just small books that resemble the McGuffey Readers, these aren't very well supported for teachers, and they certainly aren't exciting, but they are thorough and sound.


RightStart Mathematics Grades K8
RightStart Mathematics uses flashcard games as reinforcement for abacus work and more traditional problem solving. Dr. Joan Cotter has studied Asian methods of math instruction and reproduced them in this teacherintensive course for elementary and middle school students. The games are intended for review and reinforcement, but are fun enough to be used outside of class time (and are thereby more effective, as kids will want to play the games instead of looking at them as just more schoolwork).


Singapore Math Grades PreK12
There is actually no curriculum called "Singapore," just a variety of products imported from the country of the same name. Each topic is introduced, thoroughly explained, then drilled until kids have it internalized. That's not to say there's no review later on, but it isn't as constant as in Saxon, and it generally shows up in the peripheral books (like Extra Practice or Intensive Practice, rather than the textbook or workbook). Singapore's great strength is its ability to move from concrete examples to pictorial representations to abstract concepts, teaching kids not just to know how to solve problems, but how to think mathematically. The philosophy behind Singapore Math is that kids need to know why 2+2=4, not just that it does,and the books move rapidly to maintain impetus.

Supplemental

Core Skills Grades 19
Core Skills: Math offers workbooks for supplementation and test practice. 1page consumable review/drill lessons allow students to cement skills they've already learned elsewhere. This is straightforward math review, no cute pictures or hooks to get kids involved, but they're all the more useful for their simplicity. There is no teacher support, but answers to all problems are included in the back of each book (pages are perforated if you'd prefer your kids not to have access to the answers while completing their work.


EvanMoor Math Grades 16
Designed to help students understand core concepts and prepare them for standardized testing, each of the four series from EvanMoor—Basic Math Skills, Building Math Fluency, Daily Math Practice, and Daily Word Problems—is notable for its easeofuse both for parents and kids. If your child is struggling to keep up generally, having a hard time with a particular concept, or just needs some drill and review, you need look no further than these books.


Kumon Math Skills Grades 17
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Spectrum Math Grades 18
These are mostly designed for review and test prep, though they also make excellent supplemental texts for students who need more practice. Each consumable text is colorful and straightforward, with instructions for completing problem sets as well as space to work the problems. This is by no means a complete course, and exposure to the concepts drilled is presupposed, but it is a great way to make sure your kids know what they need to know, either for testing purposes or simply to keep up in their studies.

Plenty of drill books, manipulatives, and other resources are available, which you'll find here.
It's important to remember that, at the early levels, math is necessarily a teacherintensive subject. Just as kids can't teach themselves to read, they can't teach themselves how numbers work or how to think abstractly about symbols, so you'll have to guide them. Even when they're older, unless they're complete geniuses, students will need all the help they can get, though by high school they should understand the methods behind mathematical thinking enough to guide their own studies.
Consequently, we don't think programs that require a lot of teacher involvement at the elementary level should drive anyone away. A building can't stand without a firm foundation; kids who haven't been guided at the outset can't be expected to be able to learn on their own later. The time you invest in the early years will inform your kids' attitudes toward and understanding of math as they grow, and finding the right program to help you teach them is crucial.
We've done our best to provide thorough, informative, and not overly boring reviews of all the major math curricula we offer, as well as many resources and supplements. We encourage you to take the time to understand the different methods employed, the ways each program interprets those methods, and which works best for you and your family before making a decision. And remember: our attitudes toward what we teach will greatly inform our children's attitudes—and we want them to enjoy and to understand math.

Review by C. Hollis Crossman
C. Hollis Crossman used to be a child. Now he is a husband and father, teaches adult Sunday school in his Presbyterian congregation, and likes weird stuff. He might be a mythical creature, but he's definitely not a centaur. Read more of his reviews here.

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