The last few installments in my early math and language series have focused on language. Today, it’s time to talk a bit more about math. As with the alphabet, many adults are in a hurry for children to learn numbers. Like the letters of the alphabet, however, written numerals are actually quite abstract and, without a thorough understanding of what they stand for, are not particularly useful to young children. Early preparation for mathematics can come from many of the activities already discussed in this series, such as matching, sorting, and grading. Beyond that, there is much to do before bothering with learning numbers and operations.
My point in discussing these ideas is not to point out still more that we as parents need to worry about, but instead to highlight the complexity of the preparatory skills young children develop before they can have a meaningful understanding of numbers and other mathematical concepts. For most children, everyday life will provide plenty of opportunities to develop these preparatory skills, but it’s important that we honor the child’s process and allow them plenty of time to learn and absorb these pre-math concepts before we stress about teaching them math in a more formal way. For those interested in providing tools and activities to assist with early math learning, the following Montessori based ideas may be helpful. If you have ideas of your own, please share them!
In the Montessori classroom, the foundation a strong foundation for math is built through the Sensorial curriculum, and it’s an incredibly solid one. The Sensorial apparatus provide rich, concrete, multi-sensory experiences with concepts such as length, width, height, and weight, as well as with various geometric forms, both three-dimensional and plane. A few ideas for offering experiences with these same concepts at home:
Offer a wide variety of building materials
In Montessori, the Knobbed Cylinders, Pink Tower, Broad Stair, Long Rods, and the Knobless Cylinders all give children experiences in which they can compare and experience concepts such as height, length, weight, and breadth. To look closely at one specific material: The Long Rods, also called the Red Rods, isolate length. The ten rods are identical in every way except for one, made of a single type of wood, painted in a single color, and equal in every dimension except for their length. When a child works with this material, they not only visually see the difference in length between the various rods, but they feel that the longer rods are heavier than the shorter ones. They are shown to carry the rods by their ends, and so must open their arms wider and wider to carry each rod as they increase in length. They may note that the shortest rod, when placed in line with the second, is exactly equal in length to the third rod.
While these Montessori materials are brilliantly designed and are unique in the way that they carefully isolate a single attribute, as the red rods do with length, ordinary block play has similar benefits. Holding different blocks in their hands, carrying them, stacking them, and observing and experiencing how the weight of one affects the others are all incredibly valuable experiences. A lightweight block on top of a tower may balance easily while a heavier one sends it toppling, for example. A large prism can’t be placed atop a small, cylindrical block, but the opposite works just fine. Children are like scientists, continually experimenting, and the more tools we can provide them with, the better. So much can be discovered through block play and building.
Use mathematical language
The sensorial materials are also used in the classroom to teach mathematical terminology by way of three period lessons (see my post on teaching the letter sounds for more on three period lessons). The Long Rods can be used to teach long and short; long, longer, and longest or short, shorter, and shortest, for example. Once these terms have been learned, children can gain repeated concrete experiences with them through further use of the materials.
At home, we can of course use items we have on hand to give three period lessons, but we can also simply use mathematical language as we talk about the world around us. This is something most of us do without even thinking about it, and yet I know that I catch myself using terms that are imprecise when my daughter might benefit from more accurate language. When bringing in groceries together for example, instead of telling her a bag will be hard to carry and offering a different one, I can say, “That bag looks very heavy. Would you like to trade me for this lighter one?” Instead of telling her that a pair of pants no longer fits, I can specify that it’s “too short” and offer a longer pair. Daily life is ripe with opportunities to use mathematical and comparative language in context and children will extend their knowledge through daily life with or without deliberate efforts on our part.
Be attentive to shapes
To provide experiences with three dimensional figures in the Montessori classroom, we use the Geometric Solids, but at home we can find the same figures around the house. Any ball is a sphere, many of the blocks in our house are prisms and others are cylinders – the same is likely true in your house. Just as it’s easy to find opportunities to use mathematical language, geometry is all around us if we keep our eyes open for it. Using accurate terminology for the shapes we encounter will make it easier to identify and compare them when interest appears. One fun activity is to find an example of a figure, such as a small ball/sphere, and then go on a hunt to collect as many objects that are also spheres as possible.
For experience with plane figures, we use the Geometric Demonstration Tray and the Geometric Cabinet, as well as the Constructive Triangles. With the first two pieces of material, children can lift the various figures out, trace them with their finger, match them to cards, learn their names, compare them to one another, or even compare them to other objects in the environment. Stencils, drawings, puzzles, and handmade matching cards are a great way to introduce and provide experience with these same shapes at home. The Constructive Triangle boxes include various plane figures which can be combined to make still others, demonstrating the concept that shapes are made up of other shapes and allowing children to combine, add, and subtract from the plane figures they create to see the result. At home, pattern blocks can be a wonderful tool for experimentation with plane figures and there are some great ones available at pretty low prices, or you can make your own by cutting shapes out of foam core board or sheets of balsa wood. For older children, I love this set or this magnetic one for on the go. At her age, Annabelle loves this simple set (none of these are affiliate links, just things I’ve used at home and school).
Next week, my plan is to talk about early math activities in the classroom and at home that help develop number sense and prepare children for basic mathematical operations. Stay tuned!
This post is linked up with Montessori Monday on Living Montessori Now.