Mathematics at NewGate Montessori School

Mathematics and Geometry Ages 3 to 12

Often, students learn math by memorizing facts and solutions, with little true understanding or ability to use mathematics in everyday life. Math is a series of abstract concepts for most children, and learning tends to come much more easily when they have hands on experience with concrete educational materials that show what is taking place in a given mathematical process.

Montessori’s famous hands-on learning math materials make abstract concepts clear and concrete. Students can literally see and explore what is going on in math. Our approach offers a clear and logical strategy for helping students understand and develop a sound foundation in math and geometry.

As an example, consider the very basis of mathematics: the decimal system ­– units, tens, hundreds, and thousands. Since quantities larger than twenty rarely have any meaning to a young child, Dr. Montessori reasoned that we should present this abstract concept graphically. Children cannot normally conceive of the size of a hundred, thousand, or million, much less the idea that a thousand is equal to ten hundreds or one hundred tens.

Dr. Montessori overcame this obstacle by developing a concrete representation of the decimal system. Units are represented by single one-centimeter beads; a unit of ten is made up of a bar of ten beads strung together; hundreds are squares made up of ten ten-bars; and thousands are cubes made up of ten hundred-squares. Together, they form a visually and intellectually impressive tool for learning. Great numbers can be formed by very young children: “Please bring me three thousands, five hundreds, six tens and one unit.”

From this foundation, all of the operations in mathematics, such as the addition of quantities into the thousands, become clear and concrete, allowing the child to internalize a clear image of how the process works. We follow the same principle in introducing plane and solid geometry to very young students, using geometric insets and three-dimensional models which they learn to identify and define. Five-year-olds can commonly name geometric forms that most adults wouldn’t recognize. The study of volume, area and precise measurement in everyday applications around the school is introduced in the early years and continually reinforced and expanded.

Montessori mathematics climbs in sophistication through the higher levels. It includes a careful study of the practical application of mathematics in everyday life, such as measurement, handling finances, making economic comparisons, or in gathering data and making a statistical analysis.

Elementary students continue to apply math in a wide range of projects and challenges. They prepare scale drawings, calculate area and volume, and build scale models of historical devices and structures.

Precise measurement and comparison is a crucial application of mathematics, and our students engage in all sorts of calculations: determining the amount of gas used by the family car, the electricity burned when our lights are left on overnight, and the perimeter of the buildings.

Our students are typically introduced to numbers at age 3:

learning the numbers and number symbols one to ten: the red and blue rods, sand-paper numerals, association of number rods and numerals, spindle boxes, cards and counters, counting, sight recognition, concept of odd and even.

Introduction to the decimal system typically begins at age 3 or 4. Units, tens, hundreds, thousands are represented by specially prepared concrete learning materials that show the decimal hierarchy in three dimensional form: units = single beads, tens = a bar of 10 units, hundreds = 10 ten bars fastened together into a square, thousands = a cube ten units long ten units wide and ten units high. The children learn to first recognize the quantities, then to form numbers with the bead or cube materials through 9,999 and to read them back, to read and write numerals up to 9,999, and to exchange equivalent quantities of units for tens, tens for hundreds, etc.

Mathematics & Geometry Ages 3 to 12

Missing Sign Problems

In a given situation, should you add, divide, multiply or subtract ?
Introduction to problems involving tens of thousands, hundreds of thousands, and millions (Normally by age 7).

Study of Decimal Fractions

All four mathematical operations. (Normally begins by age 8-9, and continues for about two years until the child totally grasps the ideas and processes.)

Practical application problems, which are used to some extent from the beginning, become far more important around age 7-8 and afterward. Solving word problems, and determining arithmetic procedures in real situations becomes a major focus.

Computing the Squares and Cubes of Numbers

Cubes and squares of binomials and trinomials (Normally by age 10).

Calculating Square and Cube Roots

From concrete to abstract (Normally by age 10 or 11).

The history of mathematics and its application in science, engineering, technology & economics.

Reinforcing application of all mathematical skills to practical problems around the school and in everyday life.

Basic data gathering, graph reading and preparation, and statistical analysis.