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Homeschool Math Curriculum Reviews
Programs reviewed:
Drill Curricula Flashcards FlashMaster Jacobs' Elementary AlgebraJacobs' GeometryAlgebra II recommendations (Lial or Foerster)Precalculus recommendations (Lial or Foerster)Teaching Textbooks
DISCLOSURE: A few of the companies listed
below have provided me with a free sample of their curriculum in order
to evaluate it for a review. I also receive some advertising income from
Worship Guitar Class and IXL Math. However, all reviews are written
completely at my discretion and I try to be honest and unbiased about what I feel
are the strengths and weaknesses of each program. I do not give
positive reviews or advertising to curricula which I do not feel are
worth recommending to a friend.
Overview of Drill Curricula
Even when using the best math curricula, homeschoolers will occasionally find their children in need of some additional drill work. For our kids, this always seems to happen when they first learn their multiplication facts. The textbook just isn't enough. Although we want our math programs to be mind-stretching and conceptual, basic mastery of facts is important, too. Fortunately, there are lots of great options out there for drill work. Which you choose depends on how comfortable you are having your children online, how much time you have available to invest personally, and how many bells and whistles are necessary to engage your child's attention. Flashcards
The low-tech drill solution is flashcards. You can buy basic sets of math facts or make your own out of index cards. In our house, the kids always enjoy playing "Cross the River:" our kitchen floor becomes a raging river, the tiles islands, and I, halfway across the room, the mainland. Answering a card correctly, they can move a tile forward; errors take them a step back. A two-minute limit on the kitchen timer makes the expedition a little more exciting. While this game might sound dull, for some reason, each of my younger children has loved it. Frankly, I think they just like the extra time with mom. Flashcard games are effective and cheap. On the other hand, they offer little variety, and they do take a daily commitment of time on my part as well as the child's, so it is easy for me to let math drill work fall by the wayside when I am busy with something else.
FlashMaster
Measuring just 7" x 4" x 1", the handheld FlashMaster turns math drill into a portable computer game. With both timed and untimed modes, this little gizmo lets kids practice their addition, subtraction, multiplication, and division facts at varied levels of difficulty, with scores displayed at the end. Harried moms will appreciate the simplicity of assigning drills, and the flexibility of taking the assignment anywhere: in the car, waiting for piano lessons, in the line at the bank. The price is only $49.95+$5.00 shipping and handling. Since the FlashMaster comes with a 90-day money-back guarantee, you can try it out risk-free and see how it works with your family.
Other reviews:
"Perfect in every way. …. This is the first math product that I've ever found that I've honestly felt like it was a 'must have'. … It is, without a doubt, the best math resource I've ever come across." -The Old Schoolhouse Magazine "The academic area homeschool kids are worst at, according to the results of national standardized tests: timed arithmetic drill. ... Unlike other electronic drill gizmos we've seen, the FlashMaster is a serious educational tool. ... Obviously a lot of love and a lot of engineering went into this product!" -Mary Pride, Practical Homeschooling
IXL IXL "Mom, can I do math now? Please??" Ah! Music to a mother's ears! And that's what we've been hearing in our house since we started using IXL Math. If you have students who are motivated by goals, rewards, and computer time, IXL is a great drill option to consider. This online math practice site offers extensive content, ease of use, and regular professional reports for record-keeping. One of the greatest strengths of IXL Math is the breadth of problems available for drill. For example, the third grade level not only includes standard addition, subtraction, multiplication, and division, but also has practice areas in money, graphs, logical reasoning, geometry, fractions, and statistics, to name a few. Each of these categories includes three to sixteen subskills: everything from word problems to reading Venn diagrams or putting fractions in order. Skill categories are correlated with state standards. Currently the IXL website covers pre-K through algebra. (Geometry and trig are on the way.) Looking over your current math curriculum, pinpoint some areas where your child needs review, and you will find well-matched drill problems on IXL. Not only is IXL thorough, it is also appealing. After selecting a category to study, students watch their score increase (or drop, if they miss a problem). At certain achievement levels they earn medals and uncover images of virtual prizes on a game board. The bright colors and creative design just make math fun. For example, in the first grade telling-time drill, each of the clock faces has a unique, pretty design on it, which fascinates my six-year-old. My ten-year-old's reaction to his assignments is the same: "This is fun! I like it!" Fun for the child, but useful for the parent, IXL keeps instructors on top of their children's progress by e-mailing individualized lesson reports each week to summarize skills studied, scores, and total time worked. Special e-mails also arrive when students reach milestones, such as their first 100 problems completed. The reports are attractive, professional, and easy to follow. Parents in states with stringent record-keeping requirements will appreciate the paper trail. Although IXL could be used as a stand-alone math curriculum, it functions most naturally for supplementary drill. The site includes a plethora of practice problems, but not initial instruction in math concepts; the parent or another curriculum must provide this training. As well, IXL does not include diagnostic testing to indicate the areas where a student needs extra practice. Ideally, a parent will already know from her child's regular math curriculum where he is struggling; using that information, she can choose appropriate categories in IXL for drill reinforcement. Families can use IXL at no charge for up to twenty problems a day. However, to have the program save a child's data, send reports, and let him use the game board for awards (highly motivating), the family will need to subscribe to a monthly or annual plan. Prices run $9.95 per month for one student plus $2 per month for each additional child. Annual rates start at $79 per year, and $199 per year for a classroom. Teachers and families looking for a motivating, fun drill program to supplement their students' regular math curriculum should give IXL Math a try.
Other reviews of IXL Math: "The breadth of skills covered is indeed quite impressive ... an excellent math practice website." -HomeschoolMath.net
"A welcome alternative to dreary worksheets, presenting math quizzes ... in a visual way." -School Library Journal
Singapore Primary MathematicsEvery four years, a prestigious international research study ranks countries' success in math education, and every four years, the little nation of Singapore comes out on top. One of the reasons? The Singapore Primary Mathematics curriculum. This outstanding first through sixth grade program has worked for children in Singapore, and now works for thousands of homeschoolers worldwide as well. For the last seven years, our family has used Singapore Primary Math with our four children, and we love it. As an engineering graduate myself, I am impressed by the way Singapore Math teaches mathematical concepts. The student understands the why before he is drilled on the how. When introducing a new idea, the curriculum presents it from several different directions, so if one way of learning doesn't make sense to a child, another may. For example, addition is taught by sets of apples joined together, and by a cartoon character walking along a number line, and by matching numbers that add up to ten. As one would expect with a conceptual emphasis, the curriculum has a strong affinity for word problems, in order to test and cement comprehensive understanding. Singapore has a strong reputation for providing a solid foundation in mathematics. After using Saxon and Developmental Math for years, a friend of ours finally switched to Singapore for her younger children. Impressed, she raves about how much better prepared her Singapore-trained students are in understanding math, not to mention their improved standardized test scores. In our own family, our eldest progressed smoothly from Singapore Primary Mathematics grade six without any problem directly into Jacob's Algebra. Watching her whizzing through the first several chapters of algebra - all review to her - reinforced our conviction that Singapore Math provides a thorough foundation. Once a young child can count and has a basic idea of addition, he can start directly in Singapore level 1A. Beginning with a preparatory kindergarten curriculum is not necessary. If moving a child to Singapore Primary Math after using a different curriculum, be aware that Singapore is a half year or more ahead of typical American programs. Looking online, parents can find placement tests to indicate the appropriate level for a child to begin.
When implementing the program, a typical day involves briefly discussing the textbook material with the child, then letting him do the workbook exercise on his own. Many days there is nothing new to go over in the textbook, and other days it is minimal, so parental teaching time is minor: perhaps fifteen minutes twice a week, per child. By the end of fourth grade our children were usually able to read the textbook on their own, further reducing daily parental time requirements.
Singapore Math is a pleasant and affordable program to use. Young children appreciate the cartoons and bright colors. Parents appreciate the price. For each year, a family will need two non-consumable textbooks ($8.70 each) and the two accompanying consumable workbooks ($7.70 to $8.70 each). If you live in the States, look for the U.S. edition; the old Third Edition is just as good, but uses Singapore currency. For the higher grades, the Singapore Primary Mathematics Answer Key Grades 4-6 is helpful ($7.50). Workbooks are easy enough to correct at a glance in the younger grades, but an answer key will be appreciated when the problems get longer in fourth grade. Thus, by spending under $40.00 a year, a family can have a topnotch, appealing math curriculum, half of which is reusable for subsequent children.
Among this curriculum's greatest strengths are its simplicity and flexibility. The program does not drown the student in superfluous exercises, forcing the parent to pick through assignments and choose which problems to skip. "There isn't excessive repetition," one mom explains. With enough daily exercises to master material, and periodic review quizzes throughout, the balance is great. But, all kids are different. Since some may need more practice than others, Singapore offers excellent supplemental materials for those who need them. Well-designed and effective, extra practice books come in single-volume and two-volume sets for each grade level. There is also a CD-ROM available for review in computer game format. Also optional, the Home Instructor Guide ($21.00 per grade level) may be helpful to parents who are less math-oriented themselves, or who appreciate additional teaching explanations and suggestions. Walking step-by-step through the thought processes of new concepts, the guides also include mental math exercises, ideas for implementing manipulatives, an answer key, and a schedule for integrating text, workbook, and CD-ROM. Not all extras are necessary, though. In fact, a family might consider delaying the purchase of supplemental materials until they have tried out the program, to see whether they will need extra helps or not. Our household has only used two extra practice books in fourteen years worth of child instruction. Many homeschooling families appreciate the simplicity of having just a textbook and workbook to cover each day, not to mention the cost savings.
Internationally acclaimed for its proven track record, Singapore Primary Mathematics is a truly outstanding curriculum. The bright, cheerful books are as appealing as they are affordable. Simple and effective in its basic format, the program is easily expandable for families needing extra practice or help. Most importantly, Singapore Math provides a strong conceptual understanding of mathematics, laying a solid foundation for higher-level studies. As homeschoolers, we are grateful for the availability of this powerful and well-designed curriculum.
Other reviews of Singapore Math: "This series is recommended for those who want a challenging math series with a proven international track record that will carry them part way into advanced math." -HomeschoolMath.net "Children who learn well with Singapore math will come away really understanding math on a level that many of us missed out on as children." ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Jacobs' Elementary Algebra When our family was looking for an algebra curriculum, we wanted something which communicated clearly, which our children could use independently, and which led to mastery of the material. Concerned about minimizing our kids' screen time, and interested in cost savings, we decided to select a textbook-based course rather than a computer or DVD curriculum. We have been resoundingly pleased with our choice, the popular Elementary Algebra by Harold Jacobs.
I'll admit it; I love algebra. There's a beauty and order to it which satisfies me like a well-organized bookshelf. But some of the textbooks I previewed for my kids were so dry, so obtuse, and so off-putting, they made even an algebra aficionado like me start to hate the subject.
Jacobs' Algebra is different. With a conversational style, the text is readable and entertaining. You might call it a living books approach to mathematics. For example, each lesson starts with either a cartoon (such as Peanuts or B.C.) or a photo and story illustrating the point of the day. The opening illustrations are so funny that we had to make a rule in our house that the kids couldn't read ahead until they finished the previous lesson. Even the layout and font of Jacobs Algebra are easy on the eyes. Unlike other texts I examined, Jacob's Elementary Algebra manages to be appealing and engaging while still effectively communicating algebraic concepts.
The format is straightforward: each lesson includes four problem sets, the first being a brief review of previous material. The second and third sets are equivalent to each other, both covering concepts from the new lesson. More than mere drills, these sets include an inductive learning element, leading the student through new material to a point of mastery. The fourth and final problem set of each lesson is a puzzle question, the sort which can be used for extra credit or just for a challenge. Like riddles, the challenge problems motivate because they are intriguing, but their solutions always depend in one way or another on the new concept learned in that day's lesson. At the end of each chapter is a summary and review section; midterm and final review sections round out the reinforcement.
Not all of the problem sets need to be used, which is nice for homeschool moms having to adjust a curriculum for different children. One of our kids learned algebra well by doing only one problem set per lesson, sometimes every other problem. A later child in our family required more practice and so did two or three sets per lesson. The curriculum is easily adjustable to meet the level of review needed by your child.
Algebra programs aren't cheap, but they don't need to break the bank, either. Elementary Algebra's sturdy, non-consumable hardback text retails for $100.50, but can be found for significantly less from distributors. (You can see current used prices at Amazon in the link to the left.) In theory, a family could get away with using the textbook alone, because the back of the book includes answers to one of the new-material problem sets for each lesson. Since each chapter ends with a summary and review section, the problem set for that section could be used as a chapter test. The midterm and final could be taken in the same way. A textbook-only approach minimizes expenses.
However, for about $34 the paperback Teacher's Guide to Elementary Algebra is a real plus. With an answer key to all textbook problems, this instructor's manual opens up the full benefit of the textbook review exercises and challenge questions, as well as the additional problem set on new lesson material. The 258-page Teacher's Guide does have additional explanations, games, and instructional suggestions for each lesson, some quite interesting, but we only used it for the answer key. If a family wants even more practice problems, they can spend another $34 to buy the Test Masters. However, most students should find that the textbook with teacher's guide answer key provide adequate exercises for review and testing on each chapter, as well as midterm and final, without buying the Test Masters.
Jacob's Algebra is not for everyone. Since the Teacher's Guide provides an answer key without fully-worked solutions, a student may occasionally need outside help to understand why his answer is wrong. Parents whose own grasp of algebra is tenuous may be uncomfortable providing troubleshooting help. While many students won't have issues learning the material on their own from the textbook, some may prefer a more interactive environment, based on their learning style. However, for plenty of families looking for a well-written, user-friendly curriculum, Jacobs' Elementary Algebra is an excellent choice as an affordable and understandable program providing students with a solid foundation, and even offering a little fun along the way. Other reviews of Jacobs Algebra: "Jacobs often brings in problems...that are historical, showing students a bit of the intrigue of math history along with a problem solving challenge. He has problems from Roman times, puzzles from turn of the century recreational math books, and even one from the English poet Samuel Taylor Coleridge...I hope you'll decide to take a look at these books, especially if you want to turn (your kids) away from a fear or dislike of mathematics." "This is an atypical algebra text...it invites students to explore algebra in a friendlier environment than other texts." - Cathy Duffy (one of her 100 Top Picks) "Author Harold Jacobs is an exceptional math teacher with a great sense of humor... Much easier to present and use than Saxon Algebra." Tina Rice, Senior Research, The Old Schoolhouse
Jacobs' Geometry
I'm hoping to post a full review of this soon, but until I do, I just wanted to mention the name here for reference. We have been just as pleased with Jacobs' Geometry as we are with Jacobs' Algebra- both are excellent courses. If you are looking for his Geometry, keep an eye out for a copy of the second edition rather than the current third edition. The second edition teaches kids full geometry proofs, which I prefer; the logic skills developed by proofs are one of the main benefits of learning geometry.
More comments coming later...
"If you decide on Jacobs for Geometry I heavily suggest using the 2nd
edition... as the 3rd edition is a 'discovery method' and does not have
the rigor--a typical problem in the 3rd edition will say 'draw___ and
tell me what you think.' It is lacking in direction, very little
'teaching' is in the text--only a handfuls of examples that really do
not relate to the homework... and there are VERY FEW practical problems
for the student to work out. The second edition is quite the opposite!
The downside is the lack of a worked-out solutions manual for the 2nd
edition." -Jann in TX, Math guru on The Well Trained Mind forums
Algebra II: we like Lial's or Foerster's
Both of these are excellent. If you choose Lial's, make sure you get the paperback Intermediate Algebra (Developmental Math series), not the hardcover - the hardcover is a different curriculum. Older editions are fine; we used the Lial 8th edition, ISBN 0321279204, and got it for pennies on Amazon. So long as you don't need a fully worked out solutions manual, you will be fine with just the student textbook. There are a lot of examples in the student textbook, worked out in full detail. The student text has answers to every other problem in the back, and answers to all the chapter tests. The Lial text has TONS of homework problems so you won't be lacking. The Teachers Manual is just the student text with the answers filled in... not needed.
Foerster is also an excellent Algebra II text (recommended by Harold Jacobs). Lial is designed as a community college textbook to review high school algebra II, so it is written for a student to use as a self-teaching guide. Because of this, it is a bit wordier than Foerster, which makes it more approachable or more annoying, depending on your perspective. Lial's Algebra II does not include
trig; you get that in his precalc. Foerster's Algebra II includes trig
but so does his precalc. Foerster himself recommends you do the trig in
his precalc book, not the trig in his algebra II book, because of how the latter teaches graphing calculators.
Here is how we broke down Lial to use over a year:
If you use Lial after Jacobs Algebra, note that 16 of the 60 lessons in Lial you will have already completed in Jacobs. This totals 44 blocks.
Lial has 10 summaries and 10 reviews; we counted these as a total of 10 blocks.
There are 10 tests, which we counted as 10 blocks.
There are 10 cumulative reviews. We did 2 of these: one as a midterm and one as a final. We counted each as 2 lessons (total 4 blocks).
44 regular lesson blocks
+ 10 summary/reviews
+ 10 tests
+ 2x2 cumulative reviews
= 68 blocks
Broken over 34 weeks this is 2 blocks per week. Therefore, to finish in a year, the student should take 2-3 days per lesson.
Precalculus Again, both Lial's and Foerster's are good. Lial's Algebra II does not include trig; you get that in his precalc. Foerster's Algebra II includes trig but so does his precalc. Foerster himself recommends you do the trig in his precalc book, not the trig in his algebra II book, because of how the latter teaches graphing calculators.
I have been told that Lial offers several precalc formats, and that you should look for the one which has more emphasis on graphing calculators. (Don't know which one this is!) I've also been told that the paperback College Algebra and Trigonometry is the same text as the hardbound Pre-Calc - they share the same solutions manual. The third edition (2005) ISBNs are:
Student text: 032122762x
student solutions manual (suggested) 0321227700
Graphing calculator manual (suggested) 0321227719
For Foerster, I have read that we will need:
hardback student text 978-1-55953-788-9
paperback instructor's manual 978-1-55953-790-2 (has CD_ROM w/all tests and solutions)
paperback solutions manual 978-1-55953-792-6
You don't need the Assessment Resources for Foerster, because the same material is included in the CD-ROM that comes with the instructor's manual.
The Foerster links above are for the 2nd edition, c.2006; I don't know if the first edition is just as good or not. Updates in the second edition compared to the first are here. There is also a third edition available: 978-1-60440-044-1 student text, 978-1-60440-045-8 Teacher's Edition, 978-1-60440-058-8 Solutions Manual. Updates in the third edition are listed here.
Teaching Textbooks and other upper level programs
Teaching Textbooks is a popular math curriculum using multimedia instruction to teach math at a wide variety of grade levels. Many homeschooling families swear by how much they enjoy it based on how easy it is to understand. It has received good reviews from Cathy Duffy, Sonlight, and Timberdoodle.
However, friends of ours who have used it and several online reviewers express concern about whether the curriculum teaches math with enough thoroughness and at an appropriate grade level (eg. whether the Algebra II curriculum actually covers concepts which most curricula cover in Algebra I). For example, when Jay Wile (author of Apologia Science) is asked which math course he likes, he brings up Teaching Textbooks as a curriculum he doesn't recommend: "Although it presents the math in a very easy-to-understand way, it is simply not rigorous enough to prepare students for our science courses."
Then again, I recently read comments from Diane Allen, a respected homeschool reviewer, that Teaching Textbooks has come out with newer versions of the curriculum which are more rigorous than the first edition. "It appears to me that all of these concerns are laid to rest in the newest editions," she states.
Conclusion: Not having used Teaching Textbooks in our own family, I don't feel I can give firm recommendations one way or the other. It may be a good choice for non-math-oriented students, or those who want an accessible introduction to the material and intend to follow up with more in-depth curriculum afterwards. However, those heading into math and science related fields after high school might want to do some careful research before committing to Teaching Textbooks as their sole curriculum.
If you are really wanting a video course in math, take a look at Chalk Dust as well. It is a little pricey but it gets high reviews.
I have also heard some good things about Math-U-See compared to Teaching Textbooks. Math-U-See is also a video-based program. Glancing at its table of contents, most of its Algebra 2 contents is covered in the Algebra 1 text we use (Jacobs Algebra): Exponents, Rational Expressions, Scientific Notation, Combining Like Terms, Radicals, Factoring Polynomials, Fractional Exponents, and Solving Equations with Rational Expressions. However, I have read some stronger recommendations for Math-U-See in terms how how solidly it prepares students for higher level math, compared to Teaching Textbooks.
DISCLOSURE: A few of the companies listed
above have provided me with a free sample of their curriculum in order
to evaluate it for a review. I also receive some advertising income from
Worship Guitar Class and IXL Math. However, all reviews are written
completely at my discretion and I try to be honest and unbiased about what I feel
are the strengths and weaknesses of each program. I do not give
positive reviews or advertising to curricula which I do not feel are
worth recommending to a friend.
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