Friday, March 7, 2014

Literal Mathematics - Montessori

If my children had attended school, it would have been Montessori.  I love the way education is approached in the Montessori tradition, especially mathematics.  Children are literal and Montessori appeals to that part of a child.  One morning after grumbling about not wanting to sit down to do his Singapore Math, I decided we would instead do an inventory of our Gold Bead Materials. This is an expensive investment in Montessori and I wanted to see if I could piece it together through other Montessori math materials I already had on hand.  In the process, I thought I would sneak in a lesson.

First I asked LionHeart to stack up all of the 1,000 cubes.  Sure, he knew that one thousand is a big number, but now he can see a visual representation of just how large that number really is in comparison to 100.  He figured this out after a few karate chops.  I had to explain that Montessori materials are not toys and should be treated respectfully.

Next we counted out our 10-unit bars.  You need about 45 of them to do the Golden Bead Material work.  Check! After we counted them all out, I asked LionHeart which number was larger 52 or 75? He said 75, but when I asked how did he know, he could not answer.  He certainly didn't tell me because 75 has two more 10s than 52.  So I decided to show him why it was larger.  This led to us doing comparisons of several other numbers.

Next we discussed how many 1,000s go into a 10,000 chain.  He held one end and I held the other.  I walked from the living room all the way back to my bedroom.  He was absolutely amazed! We discovered this after I untangled him.  These numbers now have so much more literal meaning for him.

What does 170 really mean? Using Montessori materials, LionHeart is able to figure it out.  Expanded notation takes on a whole new life.  The 100 square is 10 squared and it's actually a square.  Nothing is accidental in Montessori.

In Montessori there is a game called Go Get It. He loved this game.  Give me more, he pleaded.  LionHeart never, ever does that with our book work.

After our inventory was complete, I discovered that all I really need are more of the wooden squares.  I'll use my decimal symbol cards from Shiller Math.  In the meantime, we'll keep working with what we have.  Taking inventory has never been this much fun.

Using Montessori to teach math helps LionHeart understand all of the things I had to memorize as a child without any real meaning or true understanding of what I was doing.  This blog post explains it best: Everyone Should Learn Math the Montessori Way.

Later in the week LionHeart was much more receptive to learning about place value.

This lesson even survived a wardrobe change.  LionHeart will literally be able to see why 7,000 is larger than 700.

Interchanging 3 math programs can become exhausting.  But it comes in handy when there is a stall in understanding or when seat work just won't cut it for the day.  I deliver these programs the Singapore Math Way: Concrete, Pictorial and finally Abstract! Traditional Montessori is my concrete lesson.  Shiller is my pictorial lesson.  Finally, Singapore Math is my concrete lesson.  It takes a little longer, but what's the rush.  True understanding is all that matters.


  1. Actually....concrete, pictorial and finally abstract is completely the Montessori way! ;>) Maybe if you immerse yourself with some additional Montessori materials, you won't need to interchange three math programs....I can point you to some good resources if you would like. Email me at info at DowninTheSouthland dot org

  2. With every article, I read on homeschooling, my confidence rises, and I know we can do it successfully for our kindergarten and pre-schooler.