ShillerLearning Math is quite different from other math programs familiar to homeschoolers. Yes, it's a manipulatives-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 ShillerLearning Math kits: Math Kit I, Math Kit II, and the Fractions Kit, each take approximately four to five years to complete. Math Kit I covers pre-kindergarten through third-grade concepts, Math Kit II covers fourth grade through the completion of pre-algebra, and the Fractions Kit goes from a basic introduction to fractions through the advanced fractions used in pre-algebra. The numbers in the titles of the books in the kits show the sequence of completion rather than grade levels.
One feature of the ShillerLearning Math program that I greatly appreciate is that lesson presentation from a single book makes the program very efficient to use—no sorting through both teacher manuals and student books. In addition, the scripted lessons require little or no lesson preparation, and the time spent on math 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 ShillerLearning Math's 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 small-motor and large-motor activities. Auditory learners hear their parents presenting concepts and they can also listen to the songs on the CDs that come with each kit. The songs 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 first 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 as well as to those who simply hate to write out their answers. There is some traditional math work on activity book pages, and there are also 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. ShillerLearning Math suggests that parents encourage children to repeat or drill such activities. If it's not obvious how to drill, suggestions are provided.
I particularly like the way ShillerLearning Math develops mathematical thinking skills rather than simple arithmetic computation skills. Computation skills are taught in ShillerLearning Math, 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 a student lacks basic computation skills, the mental math will be very difficult.
In addition to conceptual emphasis, ShillerLearning Math 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 at a time, the lesson sequence can be modified by using the Concept Index (described below) to identify all of the lessons that teach a particular concept.
Math Kit I
Now, let's start with Math Kit I. The first thing that hits you when you open the large box containing ShillerLearing Math 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 (numbered 1, 2, and 3) and the parent guide, plus a high-quality finish on the cutouts 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 Math Kit I are a plastic balance; plastic cubes, rods, and flats—similar to Base Ten blocks, but color-coded for place value; a large plush mat to be used as the student's 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 and brief information on the methodology. This is important information that one might be tempted to overlook. ShillerLearning 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 the 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.
Math Kit II
Math Kit II is similar to Math Kit I. It has three sequential lesson books (numbered 4, 5, and 6), each with a separate, printed answer key. The manipulatives in the second kit are decimal chips, assemble-yourself 3-D shapes, 14 Multi-colored 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 Math Kit II, you will no longer have the full 100 included in Math Kit I. MathKit II also includes an audio CD with 25 additional math songs that integrate with the three Math Kit II books.
The lessons in Math 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 or something similar.
The Fractions Kit takes students from a basic introduction through the advanced fractions they will use in pre-algebra. While the Fractions Kit can be used simultaneously with or subsequent to any of the ShillerLearning Math books, it is most commonly introduced alongside Lesson Book 2 in Math 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 (Math Kit II) since the student will need those skills to progress further. The Fractions Kit includes the lesson book, answer guide, parent guide, tracking sheets, two fractions songs downloads, and two sets of fraction circles.
Basic Kit and Digital Kits
A Basic version of Math Kit I that does not include many of the hands-on resources might work for those who already have most of the hands-on resources available to them. All three kits are also available in "digitall" kits. 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.
For the Parent
In ShillerLearning Math, 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.
All of the lesson books have separate answer keys, and record-keeping sheets are also included. The record-keeping sheets and the 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 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 them at a later date.
Scope and Sequence
The scope and sequence is unusual—so much so that you cannot easily move from ShillerLearning Math to a different program without a little juggling of topics. However, the folks at ShillerLearning Math tell me that their customer experience has shown that children who use ShillerLearning Math have transitioned into traditional curricula with no problems.
Coming into ShillerLearning Math from other programs is easy. You just administer the appropriate test pages from one of the three ShillerLearning Diagnostic Testing PDF Packs to identify concepts that students have not mastered. Fill the 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 will be if you are starting with children in fourth grade and above. Depending on the student, you might need Kit I to be able to teach all of the "missing" concepts before children are ready to move into Kit II. (You need to purchase the diagnostic tests, but the cost is credited toward the purchase of a kit.)
The Montessori approach is very mindful about introducing concepts that are developmentally appropriate for the child. ShillerLearning Math introduces everything in a concrete fashion first, then gently moves the child to abstract thinking and applications. Because of this, some concepts are included earlier than in other programs. For example, place value into the 1000’s and 4-digit addition are introduced in Lesson Book 1 in ways that are understandable for a young child. Some abstract concepts are introduced later. For example, time and calendar are not introduced until Lesson Book 3.
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 Math Kit I. Amazingly, it begins by having the child multiply 2,963 by 3. Even though it is unusual to start with a four-digit multiplicand, it works because it is done with manipulatives and children have learned other concepts that make it understandable, including learning about multiples, skip counting, and square numbers in Lesson Book 2. 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.
ShillerLearning Math has added Concept and Manipulative Indexes to their books to add ease and flexibility to the use of the curriculum. For instance, If your child is becoming aware of time-telling before it is introduced, just look up the concept in the Concept 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.
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. ShillerLearning's explanation is that even though these concepts are not normally introduced in other curricula at this level, they are included because 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 Math Kit II regarding the broad range of topics as well as methodology. For example, Lesson Book 4 introduces topics such as negative numbers, inequalities, absolute value, "combinatorics," map directions, set theory and symbols, and exponential notation.
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 unlimited 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. You can also call the publisher for a personal consultation with a trained representative who has used the program with their own children.
Many homeschooling parents have been interested in using Montessori methods for teaching math, but most of them have found that trying to put together a Montessori program on their own is overwhelming. ShillerLearning has done all of the work for us of creating the specialized resources and scripting a program that makes it practical for homeschooling parents, even if they have no experience with Montessori methods.