Mathematical Journeys

Math is Everyday Life!

by Susan Baccellieri

Contributions from Holly Fleming, Madeline Lee, Michelle Lee, Lynette Oshiro and Kalsom Wali Pre‐elementary Teachers

When young three‐year‐old students enter their new Pre‐elementary classrooms, they are immediately presented with their first mathematical experience. They open their lockers and behold, there are two hooks, one on each side. One hook for their coats and one hook for their backpacks! This is their first experience with a “real‐life” one to one mapping activity. It is just the beginning of their journey as students move between formal math lessons and informal, experiential math activities. The many pouring exercises in Practical Life offer tangible experiences in the concept of more than/less than, stringing beads is a colorful introduction into the pattern of number, and even the three‐year‐olds know when there is not enough snack! Math matters, even for the three‐year‐old students.

The young students discover the universal math concepts of biggest/smallest, longest/shortest, thickest/thinnest through their interactions with the Montessori Sensorial materials. Higher levels of thinking are introduced through their activities of ordering, comparing and contrasting these materials. In addition, these materials match the young child’s need for movement, love of carrying large things and eagerness to move through the sequenced curriculum.

Presenting concrete concepts before abstraction is critical in all areas of math. Ask the youngest students how old they are and the answer most often received is three little fingers proudly held up. Quantities matter to them! The numerical symbol is just that, a symbol. Quantities are always presented first so that when the symbol is presented it has meaning. As the students work with concrete materials, the stage is set for the gradual discarding of matter, until only the abstract idea is left. Observing a four‐year old discover the meaning of the symbol zero is observing scientific thinking! As more activities are presented that strengthen the quantity/symbol correspondence between zero and ten, the pattern of number is strengthened and the initial foundation of the decimal system is laid.

Students love counting and the young ones can often be heard chanting, “Ten, eleven, twelve, fifteen, sixteen, twelve, twenty‐teen…” as they practice. There are many materials in the math curriculum area that provide concrete experiences that help refine these linear counting skills. Joining a Ten Bar with a colored bead bar from the Short Bead Stair provides meaningful lessons about the Formation of the Teens. Using the Ten Board helps define the transition from twenty‐nine to thirty, and soon, twenty‐teen becomes a lost number.

Once there is a strong understanding of units up to ten, then why hold the young student back from understanding tens, hundreds and thousands? It is rather like learning to swim. Once a person can swim, she need not stay in shallow water; she is ready for all water! The Montessori Golden Beads ease this transition into “big” quantities because they concretely illustrate the decimal system. There is no such thing as ten units, but there is something at “The Bank” that is an equal amount; one ten of course! When the four‐year old is doing four‐digit addition and adds six hundreds with seven hundreds, he will sound the alarm when he counts to ten hundreds. There is no such thing as ten hundreds, so the child will go exchange his ten hundreds at The Bank for one thousand, and then count the remaining three hundreds for his sum. This is operational math that is vigorous! It stimulates the child’s curiosity of number far beyond that of rote memorization. As the foundation strengthens, the materials used become smaller, more concise, and the students become adept at using more abstract representations of these base ten concepts.

As students progress, math lessons become layered while they work on multiple concepts. They continue to strengthen their understanding of the decimal system through the four‐digit operations of addition, multiplication, subtraction and division. The Square and Cube chains allow them to practice linear counting up to a thousand while introducing them to multiplication concepts. Practicing math facts reinforces students’ understanding of the pattern of numbers. When they were younger, the students discovered the odd and even pattern while using the exercise, Cards and Counters. When they are older, this initial number pattern is explored, reinforced and internalized further through working with Addition and Subtraction Strip Boards, the Multiplication Bead Bar layout, Snake Game exercises (subtraction) and the Division Bead Board. Together, these math activities provides concrete explanations of how numbers are constructed so that the students can rely on cognitive reasoning to make conclusions instead of rote memorization.

Math activities are not limited to the school hours of nine to three, either. Fun, everyday math experiences can be done at home to strengthen the child’s problem‐solving skills and build a love for the process of mathematical functions. Concrete experiences such as slicing a pie into four parts can then lead into dividing the clock into four sections which can then lead into noting that four quarters make one dollar. Have a measuring wall or chart at home to keep track of each growing child. Keep a tooth chart to graph the loss of baby teeth. Check out storybooks from the library about math concepts, numbers, or patterns.

The language of math surrounds the lives of Eton's Pre-elementary students.

“I am taller than you!” boasts the four‐year standing atop a playground rock.

“Is Library Day tomorrow?”“What time is lunch?”“The Thousand Cube is heavy!”“How many slices will this apple make?”

Math units including measurement, telling time, fractions and money further expose children to the language and world of math. Through all the hands‐on, concrete activities, students find meaning in their learning. The world of math surrounds them, and at school, it all starts with a three‐year old opening a locker. •