Montessori Math Concept Development to the Decimal System

“Children display a universal love of mathematics, which is par excellence the science of precision, order, and intelligence.”
 
Maria Montessori

 

Our preschooler just turned 3 and this is our first post on math so I thought we’d share what we’ve been working on up until now, and then where we’re headed from here.  
 
Let me just start off by pointing out how absolutely lovely Montessori math materials are.  Number rods and spindle boxes and golden beads.  Oh my!  I always enjoyed math growing up and was very successful at it as a result.  I received an excellent traditional education and I can only imagine how much more I would’ve loved this subject had I been working with these materials as a child.  I’m so thankful our children are/will be able to enjoy their time spent learning math concepts using these manipulatives in a Montessori environment.
 

Montessori Math Concept Development

 
The first thing we did to really introduce the concept of math was to routinely work with Montessori sensorial materials.  The pink tower, brown stairs, knobless cylinders, and geometric solids are well-loved by our preschooler and 1.5-year-old, and the repetitive and cumulative work has really set the stage for conceptual understanding and beginning math skills.  Please check out our post on the pink tower for an example of this sensorial work.  

We also keep accessible an assortment of blocks for open-ended play.  These materials reinforce concepts related to size, leverage, balance, weight, and geometry, and promote problem solving, creativity, and imagination.  Below is an example using the Grimm’s flower my husband recently gifted our children for some spring-inspired open-ended play, along with some knobless cylinders.
 
Real-life experiences have been very beneficial to our preschooler exploring early math ideas in the form of practical life and outdoor play.  Time spent in the kitchen preparing and cleaning up after meals/snacks has provided countless opportunities to incorporate math and is just one example of how math plays a role in our everyday life.  Another good one for us is grocery shopping.  There’s also no shortage of things to count in nature.  Around this time is when our daughter began rote counting, first 1-10, then 1-20.  It was observable at times the separation between the skills of memorization of number order and association to number quantity that exists during early math concept development.

Early Math Shelf Work

After building a solid foundation in sensorial and practical life work, we introduced and reinforced math concepts through what our preschooler calls games,or early math shelf work.  These activities include:  quantity comparisons of more, less, or the same, ordering/sorting by size, shape, and color, counting, fetching objects, and memory work.  These types of activities encourage an understanding of number recognition, number quantity, and one-to-one correspondence.  They have really helped provide our preschooler with a knowledge of abstract math concepts using concrete examples.  This was also around the time her rote counting expanded to 1-30.

The early math shelf work is derived from child-led interests and relevant topics and usually includes items we pull from around our home or online printables.  This is such a great time to be a Montessori homeschooler or a homeschooler in general for several reasons, with one of them being the number of highly trained and experienced members of the community who share resources for free or for a small fee to inspire and support the success of the community as a whole.  It’s a very open, intelligent, and supportive group of educators and I’ve really enjoyed hearing/reading about others’ experiences as well as sharing ours.

Other opportunities to discover math that go hand-in-hand in our home are songs and books.  We try to include books that pair well with our current shelf work.  Check out our bookshop lists for some examples of books that incorporate counting with music and/or art.

After some time spent repeating activities and reinforcing skills at this level, our preschooler graduated to her Montessori math materials, while continuing to show interest in her work with the materials previously discussed.  Red and blue rods, sandpaper numerals, a spindle box, and a number recognition and quantity puzzle were introduced one at a time.  After some time spent working with each, the sandpaper numerals especially have been incorporated into several other math activities.  They have had a tremendous impact on our daughter’s number recognition and number tracing skills.  The spindle box was very useful for teaching the concept of zero as nothing.  Below is an example of an extension of the sandpaper numerals that explores number recognition, tracing, number quantity, and one-to-one correspondence.  It, like the number puzzle and other Montessori math materials, has a built-in control of error, meaning our daughter can self-correct if needed without the aid of a guide.  It also uses worm pictures as manipulatives for the activity and our daughter is currently all about digging up worms during outdoor play so it’s very enticing work.

 

From here we will wrap up with odd and even quantities and the colored bead stair before moving on to introducing the beautiful golden beads and the decimal system.  It’s been a fun journey getting to this point and seeing our daughter’s mastery of these skills blossom with each new day.  She always looks very satisfied when she’s able to complete a new work.  The other day she grabbed a new spring-themed math tray off the shelf, laid it out on her mat, and paused to tell me she was happy before getting started.  It meant a lot to me that she felt that way and wanted to express it.  I hope she continues to feel like learning makes her happy.  We hope you and your preschooler are enjoying some exciting new math activities as well.


 
*apple printable courtesy of Jady A.

 

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