Cathy Duffy Reviews home > Math > ShillerMath


Publisher: Shiller & Company, Inc.
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ShillerMath is quite different from other math programs familiar to homeschoolers. Yes, it's a manipulative-based program, but it uses manipulatives with a Montessori approach. It has workbooks, but these are used as teaching texts more than as workbooks. Kits I and II cover approximately five years and three years of math respectively, but the books do not necessarily represent grade levels.

The scope and sequence is not typical of other homeschool programs — so much so that you cannot easily move from ShillerMath to a different program without a little juggling of topics. If you begin with ShillerMath, it would be best to stick with it through the sixth grade at which point it will be easier to shift into other programs. (At the time of this review, ShillerMath said it is working on the junior and senior high school kits).

Coming into ShillerMath from other programs is much easier. You just administer the Shiller diagnostic tests to identify concepts that students have not mastered. Fill these gaps by using only the lessons/activities prescribed for the missed questions. Then once you've reached a level at which your child is largely unfamiliar with the topics, you can start to work through lessons sequentially. The only catch would be if you are starting with children fourth grade and above. Depending on the student, you might need the entire Kit I with the manipulatives to be able to teach all of the "missing" concepts before children are ready to move into Kit II.

Now, let's start with Kit I. The first thing that hits you when you open the large box containing ShillerMath Kit I is that there's everything here but the kitchen sink! Next thing you're likely to notice is the quality of the printed materials — full color throughout the three workbooks and on the number cards, glossy cover on the parent guide, and high quality finish on the cut outs for construct-them-yourself thousand cubes.

You're also likely to be attracted by the colorful and interesting looking manipulatives and wooden boxes. Space doesn't permit me to list all of them, but among the manipulatives and equipment in Kit I are a large plastic balance; plastic cubes, rods, hundreds flats, and one thousand cube — similar to Base Ten blocks but in different colors; a large white felt mat to be used as workspace; wooden tray for working with number cards and place value; CD with original songs relating to math topics; set of dominoes; plastic coins; geared clock; and colorful wooden shape cutouts.

A small Parent Guide provides some background on why the program was created, then brief information on the methodology. This is important information that one might be tempted to overlook. ShillerMath borrows some key ideas from Montessori education, and these are explained in this booklet. Among those ideas are a respectful attitude toward the child, exhibited by use of language such as "You may put ten cubes on the mat" rather than "You need to put ten cubes on the mat." Praise and encouragement are essential. If a child is frustrated, you put away the activity until another time. Children learn to treat learning materials with respect — returning items to the resource bank immediately after each usage and always putting things away neatly.

Kit II is similar to Kit I but it has three sequential activity books, numbered 4, 5, and 6, plus a Fractions book, each with a separate answer key. The Fractions book may be used simultaneously with or subsequent to Book 4. The manipulatives in the second kit are fraction circles and trays, decimal chips, assemble-yourself 3-D shapes, and 12 see-through blue plastic shapes with removable filler caps for volume and mass measurement. Kit II also includes an audio CD with 25 math songs that integrate with the four Kit II books.

Lessons in Kit II also call for some common household items that are not included in the basic kit — ruler, compass, protractor, compass, pen, pencil, markers, crayons, kitchen scale, measuring cups and spoons, unit cubes, and post-it labels.

For both kits, there are no separate teacher manuals beyond the Parent Guide. Parents teach directly from the activity books. These books are scripted, telling parents exactly what to say and do through each lesson. However, with Kit II parents have the option to have the children work independently.

Some Kit I activities will be performed with manipulatives on the mat. Some will ask the student to work in the activity books. One potential problem with this in the three books in Kit I is that the scripting and answers are often visible below each activity. As children become capable readers, they might easily spot the answers. Kit II has separate answer keys, so this is only a problem in the first kit. ShillerMath has already addressed this issue by creating an alternate version of the kit that contains activity books with no answers. Not sure which one to choose? Shiller has put downloadable copies of both versions on their website and makes these available to those who have purchased Kit I at no extra charge. Review tests (four per activity book) in all the activity books already have answer keys printed elsewhere in the books.

The aforementioned review tests also serve as diagnostic tests. Each test contains test items on topics covered within the foregoing section of that book. The answer key for each test shows the lesson in which the concept was taught so you can go directly to those lessons to review or reteach concepts missed in the test.

One feature I really like about ShillerMath is that lesson presentation from a single book makes the program very efficient to use — no sorting through both teacher manuals and student books. Also, the lessons are scripted, telling the teacher exactly what to say and do as they direct the various learning activities. This means that there is really no lesson preparation. On top of that, lessons should take about 15 minutes per day for four-year olds, 20 minutes for five-year olds, and 5 minutes more per day for each year of age.

Another plus for parents with weak math backgrounds is that the conceptual approach helps them understand math better than when they learned it in school.

Record keeping sheets are included. These plus student activity pages from preprinted pads are three-hole punched so you can collect them with other pages representative of student work in the binder that comes with each kit. Students will likely do as much or more written work on these pages as in the activity books. You can record activities that have been completed and mastered on the record keeping sheets. However, you may also use the record keeping sheets to track topics that students didn't get the first time around so you can come back to those topics at a later date.

This is truly a multi-sensory program. Hands-on learners get plenty of work with manipulatives as well as other large motor activities. Auditory learners hear parent's presenting concepts and they can also listen to the 25 original songs on the CDs that come with each kit — these are very professionally recorded with catchy tunes that actually teach math concepts. Conceptual learners are able to see how math algorithms actually work through manipulative demonstrations translated into arithmetical symbols. Relational learners get lots of interaction with a parent, and possibly siblings, as they work through math lessons.

An important feature to note is that students respond orally more than with written answers. This should be very appealing to the child with poor small motor coordination or those who simply hate to write out their answers. There is some traditional math work on activity book pages, and there are also the aforementioned pads of specialized worksheets that students use both for lessons and for practice. However, some children might need more practice with written work than is provided. ShillerMath suggests that parents encourage children to repeat/drill such activities. If it's not obvious how to drill, suggestions are provided.

The scope and sequence is unusual and I found it a bit difficult to get an overview of the scope and sequence to see the details of what is being covered throughout the kits. There are no tables of contents and no indexes in the books. However, ShillerMath has addressed this by publishing tables of contents for each activity book on their website.

Now, here's an example of the unique scope and sequence. The first lesson I found that teaches what looks like traditional multiplication was at the beginning of the third book in Kit I. Amazingly, it begins by having the child multiply 2,963 by 3. This actually makes sense because it is done with manipulatives and because children have learned other concepts that make this understandable even though it is unusual to start with a four-digit multiplicand. Two such lessons are followed by one on recognizing operations signs. Then division is introduced with two lessons using four-digit dividends and single digit divisors, again using manipulatives to introduce the concept.

Some may say that there is an overabundance of topics. For four- and five-year olds these would include rotations, the concepts of "solo," "duet," and "trio," Roman numerals, and probability — all appearing in the first activity book. ShillerMath's explanation is that those topics are included because, although they are not normally introduced in other curricula at this age, children are developmentally ready for them. Of course, parents are free to skip activities until a later time if they so choose.

I have similar concerns about Kit II regarding the broad range of topics as well as methodology. For example, Book 4 introduces topics such as negative numbers, inequalities, absolute value, "combinatorics," map directions, set theory and symbols, and exponential notation (e.g., "4372 = (4 x 10 3) + (3 x 10 2) + (7 x 10 1) + (2 x 10 0)" (activity 4-123). Those who remember "new math" will recognize some of this as familiar elements of that approach.

On a more positive note, I particularly like the way ShillerMath develops mathematical thinking skills rather than simple arithmetic computation skills. For example, ShillerMath does not expect children to master their times tables until the beginning of Kit II. Computation skills are taught in ShillerMath, but you might need to spend more time than is specified in the books, repeating or expanding activities. I think you will be able to tell if your child needs more practice with computation skills when he or she tackles the frequent mental math problems. If they lack basic computation skills, the mental math will be very difficult.

Whether ShillerMath is the right program for you is a question of educational philosophy. The Dorothy Sayer camp of the classical education movement, for example, believes that children in the early elementary grades are at their zenith in their ability to memorize. They emphasize lots of memorization in the early elementary grades. In contrast, Larry Shiller, author of ShillerMath, in a reply to a concerned parent in the Yahoo loop regarding this very question, writes:

One of the many issues with public schooling is the disconnect between what is taught and what is developmentally appropriate for children of age 4-8.

Your email points out this disconnect quite well. Children first learn concretely and then gradually abstract what they know through their senses. For children to learn math facts before understanding their real life application and use is counterproductive and results in math learning disabilities as they progress through school.

Please rest assured that in a year or two, your child will have absolutely no difficulty with his math facts, because at age 8-9 - with the proper learning environment - a child will have reached the developmentally appropriate age for him to have them memorized. (, posted Tuesday, July 6, 2004)

This emphasis on conceptual understanding prior to fact mastery reflects an educational philosophy quite different from that of the Sayer camp. While homeschooling parents might lean toward one or another educational philosophy, I think the bottom line for most parents is figuring out what really works best with each of their children rather than adherence to a particular philosophy.

In addition to conceptual emphasis, ShillerMath uses a spiral methodology for presenting concepts, which means it introduces a topic and then revisits it periodically at slightly higher levels of difficulty. As in Saxon Math, lessons jump from topic to topic. This might appeal to children who like variety, but it can be frustrating to children to prefer to concentrate on only one topic until they develop a certain level of understanding.

The complete kits include everything you need (aside from the household items for the second kit described above). In addition, the publisher offers free downloads of consumable student pages and activity sheets that make the program totally reusable. You don't even need to purchase new student books! On top of that you get five hours of free phone support — although I think you're unlikely to need the support since the program is so self-explanatory. You can view free sample pages at the publisher's website before buying.

Note: Shiller Math is now also available in "virtual" versions of each kit for $99.95 each. While you will still need to supply a few manipulatives or other resources, everything else can be printed from the downloadable files.


Kit I for ages 4 – 8 $349.95
Kit II for ages 9 – 11 $249.95
virtual kits - $99.95 each

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    • Audience: grades PreK-6
      Need for parent/teacher instruction:
      Prep time needed:
      Need for Teacher's Manual: essential
      Educational Philosophy: Montessori
      Religious perspective: secular but "Christian friendly"

    Publisher's Info

    • Shiller & Company, Inc.

      258 Thunder Lake Road
      Wilton, CT 06897
      888-556-6285 FAX