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 lesson books, but these are used as teaching texts more than as workbooks. The three ShillerMath kits: Kit I, the Fractions Kit, and Kit II each take approximately four to five years to complete. Kit I covers pre-kindergarten through third-grade concepts, Kit II covers fourth grade through the completion of pre-algebra, and the Fractions Kit goes from a basic introduction to fractions through advanced fractions used in pre-algebra. The book numbers do not 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. However, ShillerMath tells me that customer experience has shown that children who use ShillerMath have transitioned into traditional curricula with no problems.
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 and 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 Kit I Virtual 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! The next thing you're likely to notice is the quality of the printed materials—full color throughout the three lesson books, three answer guides, the parent guide, plus a 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 plastic balance; plastic cubes, rods, and flats— similar to Base Ten blocks; a large off-white plush mat to be used as workspace; a wooden tray for working with number cards and place value; an audio CD with 25 original songs relating to math topics; a set of wooden dominoes; plastic coins; a geared clock; and colorful wooden shapes.
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 is 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. It has three sequential lesson books, numbered 4, 5, and 6, each with a separate answer key. The manipulatives in the second kit are decimal chips, assemble-yourself 3-D shapes, 12 see-through blue plastic shapes with removable filler caps for volume and mass measurement, a geared clock, a ruler, and 100 unit cubes—chances are that by the time you get to Kit II, you will no longer have the full 100 included in Kit I. Kit II also includes an audio CD with 25 additional math songs that integrate with the three Kit II books.
Lessons in Kit II also call for some common household items that are not included in the kit—ruler, compass, protractor, pen, pencil, markers, crayons, kitchen scale, measuring cups and spoons, and Post-it labels.
The Fractions Kit takes students from a basic introduction through advanced fractions they will use in pre-algebra. While the Fractions Kit can be used simultaneously with or subsequent to any of the ShillerMath books, it is most commonly introduced alongside Book 2 in Kit I. You will come to a point later in the fractions book where it tells you to stop until you reach a certain lesson in Lesson Book 6 (Kit II) since the student will need those skills to progress further. The Fractions Kit also employs the multi-sensory, Montessori-based approach of Kits I and II. It includes the lesson book, answer guide, parent guide, tracking sheets, two fractions songs downloads, and two sets of fraction circles.
Not sure which kit to choose? Shiller has put downloadable copies of their diagnostic review testing on their website and makes these available to everyone at no charge. Each review test contains test items on topics covered within the foregoing section of that book. The answer key for each test shows the list of lessons that teach the concept for each question so you can go directly to just those lessons to review or reteach concepts missed on the test.
In ShillerMath, parents teach directly from the lesson books. These books are scripted, telling parents exactly what to say and do through each lesson. However, parents have the option to have the children work independently, once they are competent readers.
A previous edition of Kit I included answers in the activity books. However, all three kits now have separate answer keys. Record keeping sheets are included. These plus student activity pages from preprinted pads (you can print extras from your free downloads) 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 lesson 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.
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 only about 15 minutes per day for four-year-olds, 20 minutes for five-year olds, and five 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.
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 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 in the earlier lesson books 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 or drill such activities. If it's not obvious how to drill, suggestions are provided.
The scope and sequence is unusual. The Montessori approach is very mindful of introducing concepts as they are developmentally appropriate for the child. ShillerMath introduces everything in the concrete first then gently moves the child to abstract thinking and applications. Because of this, some concepts are included earlier than a traditional curriculum. For example, place value into the 1000’s and 4-digit addition are introduced in Book 1 with ease for a young child. Some abstract concepts are introduced later. For example, time and calendar are not introduced until Lesson Book 3. ShillerMath has added Concept and Manipulative indexes to their books to add ease and flexibly to the use of the curriculum. If your child is becoming aware of time before it is introduced, just look up the concept in the index and go through the lessons that teach that concept. Also, if your child wants to work with a particular manipulative one day, you can look that up in the Manipulative index to see all of the activities in which that material is used.
Here's another 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 parents might think that there is an overabundance of topics for young children. For four- and five-year-olds these might include rotations; the concepts of "solo," "duet," and "trio;" Roman numerals; and probability—all appearing in the first lesson 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.
On a more positive note, I particularly like the way ShillerMath develops mathematical thinking skills rather than simple arithmetic computation skills. 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 Sayers 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. (http://groups.yahoo.com/group/shillermath/message/79, posted Tuesday, July 6, 2004. Note that this Yahoo group is no longer active. Interaction has moved to other ShillerMath social media sites.)
This emphasis on conceptual understanding prior to fact mastery reflects an educational philosophy quite different from that of the Sayers 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 appeals to children who like variety. If a child prefers to concentrate on one topic, lesson sequence can be modified by using the Concept Index to identify all of the lessons that teach a particular concept.
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 and download free diagnostic testing at the publisher's website before buying. You can also call the publisher for a personal consultation with a trained representative.
Note: ShillerMath 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. You can also use the PDF files on a tablet device with a PDF annotator app (such as Notability), virtually eliminating the need for printing.