Unlocking Fractions: A Montessori Math Learning Progression

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Recently, I stumbled across a 2017 post from Scientific American about fraction learning among American students. It’s an interesting read, but one statistic stood out to me- middle school students answered basic fraction problems (like 1/6 +4/6 and 3/5+2/3) correctly only 50% of the time. This statistic became even more stark when I considered my own Montessori students- my five year olds can confidently perform these calculations with very few errors.

What could account for this difference? Were my five years olds smarter than middle school students? Absolutely not. My children had simple had different experiences- they learned fractions using the Montessori method.

So, how are fractions taught in Montessori? Let’s explore!

The Montessori Philosophy for Teaching Fractions:

Montessori does a great job of making fractions approachable to even the youngest children. Here’s how:

• Activities move from concrete to abstract- all lessons are build around the fraction insets, a physical model they can hold and touch. All lessons carefully build on a child’s understanding and experiences to introduce more complex ideas.
• Materials use “isolation of quality“- only one thing changes (the number of pieces and therefore the size of each piece), which makes telling fractions apart easy.
• Explicitly teaching vocabulary- the names of a fraction (“one fourth”) are no different than the name of any other item (like “whale” or “spoon”). We take the time to teach the name and naming convention, giving plenty of time for the child to associate the name with the model.
• Child-led exploration: the hallmark of Montessori education, we don’t “teach” the child fraction math through examples (writing out the process for solving 1/5 + 2/5). Instead, we use a carefully designed sequence of lessons to help them make the discovers for themselves. This leads to a greater understanding of fractions and a strong sense of accomplishment.

The Montessori Fraction Progression:

What specific lessons will a child experience while learning about fractions? Here’s the general learning outline:

• Fractions as puzzles– Children as young as three and a half start using fraction insets as puzzles, learning to manipulate and combine pieces to understand the concept of fractions. This hands-on activity helps them develop a visual understanding of each fraction and how the pieces change as they progress through different combinations.

• Equivalency puzzles– Around age three and a half, children are introduced to the concept of equivalency through hands-on activities. They learn to select a fraction, remove a piece, and identify which other fractions complete the whole.

• Naming Fractions: Children are introduced to fraction names around the age of five because naming fractions is more complicated than naming whole numbers. First, children learn the fraction “family name” (e.g., fifths), then they building and naming fractions based on their “first name” (e.g., two fifths for two fifth-pieces).

• Writing fractions– After naming fractions comes writing. Children learn fraction notation (1/6), then practice building and writing different fractions until they are confident.

• Operations with fractions– We use the metal insets to model a problem (for example, dividing the physical fraction 4/6 into two equal groups to represent 4/6 divided by 2) and give the child plenty of opportunities to practice.

• Word problems– Throughout the fraction progression, we tell stories and make connections to real world fractions. Children get to experience word problems through their learning journey, so reading a story and writing an equation is not something new. This is actually the highlight for many of our children… because their adults find it so impressive.

But does it work for children without Montessori experience?

In this article I’ve talked a lot about “Montessori-trained children” and you may be wondering… can a child without that experience also benefit from the Montessori method of teaching fractions? The answer, in short, is absolutely! Even older children (up to forth or fifth grade) can benefit from having a hands on model for fractions and a clear, linear learning path.

If you’re interested in exploring the Montessori method of teaching fractions with your child, I recommend finding a fraction inset set and beginning with fraction puzzles (try to find a set that is a single color and has no writing, like this one). You can also check back in September 2024 for our self-paced fraction program and student workbook.