The mere mention of math, for some people, causes a guttural sense of dread. All thanks to endless tests and worksheets from traditional math education. In Montessori however, children LOVE math. In fact, some concepts are learned by playing “games.”
Concrete to Abstract
Montessori math, at it’s core, comes down to helping the child learn on a continuum starting with concrete to more abstract concepts. Many sensorial materials that Montessori children are presented with at a young age, help prepare a foundation for abstract math that they will learn later on. They start by learning the most concrete concepts such as shape, dimension, relationships, and amounts. Then they learn the numerical symbols that represent the amounts. Later when they are ready, they learn how to record/write the amounts.
Materials
Montessori math materials allow them to conceptually learn numbers instead of just memorizing. For example, a Montessori child is able to feel and hold a 10 red and blue number rod, and see how much bigger and heavier it is compared to the 1 number rod. Once they understand quantity in this way, then they can learn the symbols and names for the quantity (1, 2, 3). They can point to the number rod and say, “this is 10.” Then they can point to the number card and say, “this says 10.”
Terminology
Terminology used in Montessori also starts as concrete. For example, the child learns how to “take away” amounts when subtracting. Once they have a good foundation in the concept of subtraction, they learn the mathematical vocabulary (and symbol), “subtract” or “minus” etc.
Consistency
Colors used in Montessori materials have purpose and is not simply just for aesthetics. In Montessori math, each place value is assigned a specific color. Each bead chain represents a specific quantity which has it’s own assigned color. The colors are consistent throughout all the Montessori math works to help the child visually learn and map out the concepts in their minds. As they develop a mastery of the math materials, they are able to progress toward abstract thinking.
Self Teaching/Correcting Materials
Montessori materials have a “control of error,” which means that the materials are self correcting. The child can figure out on their own if they are making an error while using the material and can then correct his or herself. This helps build confidence and independence in their learning. The self correcting materials are stimulating and inviting. For example, using sandpaper number cards makes tracing more interesting and effective. The materials are appealing to the child who then wants to explore it again and again. The repetition helps with order, sequencing, and precision; as well as memorizing math facts.
Learn more from these sites!
Montessori math fundamentals, materials and curriculum from TrilliumMontessori.org
Montessori math overview and guidance on materials from CarrotsAreOrange.com
Video tutorials of math materials My Works Montessori
Video tutorials of math materials by Elizabeth Park
Spreadsheet of Montessori math lessons from MontessoriCompass.com
Examples of Montessori Math Works
Pre-Math/Sensorial
- Pattern Making Activities
- Pink Tower (ideally with ten)
- Brown Stairs (ideally with ten)
- Red Rods (ideally with ten)
- Knobbed Cylinders (ideally with ten)
- Knobless Cylinders (ideally with ten)
- Metal Insets
- Geometric Solids
- Constructive Triangles
- Fractions
- Binomial Cube
- Trinomial Cube
Learning numbers 1-10
- Red and Blue Number rods
- Sandpaper Numerals
- Spindle Box
- Mystery/Memory Game
- Cards and Counters
- Odd and Even
- Short Bead Stair
Place Value aka Decimal System
- Introduction to Golden Beads Quantity
- Introduction to Golden Beads Numerals
- Golden Beads Quantities and Numerals Combined
- Nine Tray/Layout
- Exchange Game
Linear Counting
- Teen Bead Bars
- Teen Board
- Teen Board and Bead Bars
- Tens Bead Bars
- Tens Board
- Tens Board and Bead Bars
- Hundreds Board
- Hundred Chain
- Thousand Chain
Math Facts for Addition and Subtraction
- Addition With Small Number Rods
- Addition With Short Bead Stair
- Addition Strip Board
- Addition Strip Board Making Tens
- Addition Snake Game
- Addition Finger Chart
- Subtraction With Small Number Rods
- Subtraction With Short Bead Stair
- Subtraction Strip Board
- Subtraction Strip Board Making Tens
- Subtraction Snake Game
- Subtraction Finger Chart
Other Extensions
- Measurement
- Money
Lower Elementary
Math Facts for Multiplication and Division
- Multiplication Bead Box
- Multiplication Bead Board
- Multiplication Finger Chart
- Division Bead Board
- Division Finger Chart
Large Number Operations (Static and Dynamic)
- Golden Beads
- Stamp Game
- Small Bead Frame
- Checkerboard and Multiplication Bead Box
- Racks and Tubes
- Large Bead Frame
- Dot Game
- Decimal Board