Montessori Math: Part 3
Today we conclude our look at Montessori Math.
By the time a student has transversed fundamental math concepts, and is entering FMS middle school (7th & 8th grade); they are amply prepared for experiencing pre-algebra, algebra and pre-geometry. Not only do the students perceive the “why” behind the concept presented, there is a context in their minds for the fundamental ideas being addressed.
When they are asked to perform a computation from more of an abstract level, they have a visual and tactile memory of using the Montessori materials concretely. They are the owners of their math skills, instead of simply being a retainer of math facts.
Our FMS graduates are so well prepared for high school math, that the majority of our students successfully test into honors geometry as freshman. They know how and why math concepts are employed to solve equations. They are also steeped in the joy of being able to use their knowledge as a language into solving real life problems, such as creating a matrix that analyzes the costs of doing a school dance, or for solving other real life math questions.
Math is demystified and made accessible to all students using the Montessori method, because the steps are presented with concrete materials, and the explanations for using the materials are methodically explained. The consistency of using the same materials from primary lessons through their elementary lessons (such as using the bead stair) forms a strong foundation of understanding math concepts from a concrete perspective. When more abstract math is introduced, FMS graduates have a true conceptual understanding of the math principles used.
Montessori Math: Part 2
In Lower Elementary (6-9 years old), students explore operations using the checkerboard (multiplication), racks and tubes (division), and also using the bead frames to bring home the concepts of place value and manipulating numbers to solve 4 and 5 digit equations.
Multiplication boards are employed for learning math facts, first in a tangible way and then as a tool for memorizing math facts so there is rapid recall; thus preparing them for the next big leap in doing Math in Upper Elementary (9-12 years old). Students at this level become very familiar with practical life skills of using a ruler, telling time and working with money.
It is during the Upper Elementary years that we see a significant jump in standardized test scores, where the underlying concrete understanding of fundamental math concepts and functions help the students to outperform their peers from more traditional backgrounds. It is at this time, that students spend time working with Montessori materials to understand fractions, decimals, percentages, positive and negative place value in the decimal system, and operations with whole numbers (addition and subtraction).
Some of the critical foundations of doing higher math in high school are laid in the Upper Elementary grades.
Students become very familiar with counting, adding and subtracting fractions, percents, and converting percents to decimals. Using negative numbers and delving into pre-algebra by creating and solving algebraic equations is routine for students in these grades. Finally, substantial effort is made to make square roots an easily understood concept.
*Join us next Tuesday as we continue to look at Montessori Math
Montessori Math: Part One
Today we begin a blog series on Montessori Math. For our first addition we will be discussing Montessori Math in the Primary years.
The Montessori Math program at FMS is a pathway to a deep, concrete and useful relationship with the power and recognition of numbers and their corresponding values. One of the early math works for our primary aged students are found in using the sandpaper numbers. The student feels the rough impression of the number on their finger tips, while the teacher is saying the name of the number.
As the primary-aged student begins to understand the correspondence between the number and the quantity, they have elevated their understanding to a new level of mastery.
Within the primary aged classroom, the Montessori math materials create an array of tools that solidify the child’s grasp of recognizing 1-10, the concept of 0, recognizing and creating teens and tens, and then being able to put the whole picture together by doing the 100 board.
Seeing the child connect the concept of counting 10 on a ten bar and then adding 1 single red bed to now create 11, is a milestone in their development.
Number chains afford the student the opportunity to count the beads and see the patterns emerge, such as the “2 chain” which is made up of two sets of two beads. Number chains are eventually used to demonstrate skip counting (i.e. counting by twos). Each number 1-10 has its own unique chain.
As the primary aged student learns about the golden beads, they are able to do the decimal layout and tangibly work with place value of units, tens, hundreds, and thousands.
This is truly a stepping point for the students because once this is mastered, they are now ready for performing the operation of addition (4 digits), followed by multiplication, subtraction and division.
Eventually, golden beads are replaced with the stamp game. The stamp game is made of color coded wooden tiles representing units, tens, hundreds and thousands. The work is used to do the operations of addition, multiplication, subtraction and division; affording the student the same advantage of using golden bead materials to solve the problems (and reallysee place value), but in a more contained manner.
Join us on Thursday we discuss Montessori Math in the Lower and Upper Elementary Years.