The Beauty of Simplicity- The Concept of Isolation

The norm in math education seems to be “more”- more graphics, more music, more colors, more sounds. With the prevalence of iPads in the classroom, math is often taught through flashy apps with avatars and silly games. Pick up any math workbook at the store and you’ll see what I mean- the pages are crowded with bright colors and silly drawings that have very little to do with the calculations. Even manipulatives, the tools we use to help children discover math, are brightly colored and often shaped like toys (take the teddy bear counters most kindergarten students use, for example). When your materials look like toys, its only natural for children to play with them.

While I know it can be very difficult to engage children in math (trust me, I’ve been there), many of these strategies distract from the math concepts being taught and fail to develop true critical thinking skills. Montessori math has a solution and it’s called “isolation of the quality“.

In Montessori math, isolation of the quality means changing only one thing in a material. When you can only change one aspect of your manipulative, you need to be very intentional- both in making your material and in understanding what you want the child to discover. That is where the Montessori math program excels. All of the Montessori math materials feature isolation of quality, but let’s look at fraction models as an example.

Montessori vs. traditional fraction models

At face value, traditional fraction circles and Montessori-style fraction circles look very similar. They both feature circles cut into a different number of pieces to represent different fraction values. However, you may notice that the traditional fraction circles are much more colorful (every fraction family has a different color) and each piece is labeled with a unit fraction (for example, 1/4). The manufacture’s goal here is to make the material as versatile and visually attractive as possible- you can build fraction families, compare them easily, learn the fraction notation, and do operations all with one material, what’s not to like! But when we consider a child who is just beginning their fraction learning journey, we can see the confusion all of this extra can cause.

Let’s look at the model for the fifths family. When we use this model to try and teach the child what 1/5 is, there is a lot of room for confusion. What does “one fifth” mean? Is it a red circle? Is it a circle cut into five pieces? Is it a piece with “1/5” on it? There are too many differences between the fifths model and the rest of the model- the child has to work hard (maybe too hard) to figure out which differences matter and which don’t. And the difficulties continue even after the child has learned to label the fractions. Many students rely on the color coding to tell the fractions apart. So, they don’t fully internalize that fifths has five pieces and halves have two pieces and instead rely on the fact that fifths are red and halves are yellow (I’ve had middle school students as my, “what color is that one?” when working with fraction addition and subtraction).

Compare the traditional model to the Montessori fraction circles. At face value, the Montessori model seems very boring- all of the fraction families are the same color, red. There are no labels or extra decorations. The only difference between each family is the number of segments the circle is cut into (and, as a result, the size of each piece). This is isolation of quality– by changing only one thing (the number of segments) a child quickly realizes that the name “fifths” refers to a circle cut into five equal pieces, which is the definition of a fifths fraction. The Montessori material also “forces” the child to learn to associate the number of pieces with the fraction name because there are no “short-cuts” (aka, they can’t rely on an easily identifiable difference like color).

Using the concept of isolation to help your math learner

Whether you choose to use Montessori math instructional practices or not, you can still help your child by trying to use the concept of “isolation of quality” whenever possible. Here are some ideas:

• Look for support materials that are as simple as possible. These items don’t need to be store bought. For example, using large Lima beans as counters for working on addition and subtraction (instead of those brightly colored counting cubes) keeps the focus on the mathematical processes
• Avoid manipulatives that are also toys. Google “math aids” and you’ll find a slew of toy-like items (dinosaur count and color sort, fun!). These items are fine as toys, but kids can’t resist playing with them… instead of keeping their attention on the math.
• Try to use worksheets that limit extra images and text. By seeing only the math problem, your child will have an easier time focusing.
• Isolate one problem at a time. If your child does come home with a “busy” worksheet from school, you can help them stay present with their math by blocking everything but a single math problem. A blank piece of paper with a rectangle cut in it works great for highlighting a single problem (and canceling out all the noise)

Ready to learn more about Montessori Math?

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