Montessori Education How do students in Montessori classrooms learn differently than students in traditional classrooms? Understanding how your child learns. By: Sarah Yoho
How were you taught to multiply large numbers? • If you were taught the same way I was, first you memorized multiplication facts. • Then you were taught to multiply a large number times a single digit multiplier. • After much practice, you were taught to multiply a large number times a two or three digit multiplier.
Your teacher probably demonstrated: • First, you multiply the ones from the bottom number with the ones in the top number. Repeat the process, working from right to left, with the number in the tens place, the hundreds place, and so on. 2. Then you follow the same procedure, multiplying the tens from the bottom number with the digits in the top number, working from right to left. Don’t forget your placeholders!
Let’s think about multiplicationfrom a child’s perspective. Numbers… they’re symbols that represent how much of something I have. Numbers… they’re like the alphabet, only they mean how much instead of representing a sound. Multiplication... it means I’m working with groups instead of individual numbers. Long Multiplication… I need to work from right to left? That’s not how I was taught to read! Why do I need a placeholder?!
Early Math Concepts Beginning in preschool, students are taught to understand both numbers and place value, not as abstract symbols, but as objects that can be seen and touched.
Understanding Grows(These materials are found in preschool and E1 classrooms.) The Golden Beads visually and physically (by weight) represent units, tens, hundreds and thousands. An understanding of place value develops. The bead cabinet has chains of colorful beads that represent ones through tens. Students learn to rote count, then skip count, in order to understand multiples.
Montessori Math Materials • are colorful • are meant to be handled • are repetitive (For example, green represents ones, blue represents tens, red represents hundreds.) • show geometric representations of mathematics concepts • are used for a variety of lessons as the child’s understanding grows
Helping All Students Learn When learning Montessori math, students are encouraged to: • touch and manipulate the materials • record their work • practice with peers • practice on their own • share what they have mastered with other students
Learning Multiplication Facts(in E1 Classrooms) There are many ways to practice multiplication facts in early elementary classrooms! Practicing the times table. 2x4=8 or “Two taken four times equals eight.”
There are also many ways to practice more difficult multiplication problems. The flat bead frame and large bead frame are similar to an abacus.
Checkerboard Multiplication(Used in both E1 and E2 classrooms.) • The colorful checkerboard materials build upon students’ prior knowledge. When children begin with the familiar, there is no reason to panic when learning more challenging concepts. • The colors green, blue, and red representing the ones, tens, and hundreds place values are repeated from previous materials to give the child a sense of mastery. • The beads are the same colors and represent the same amounts as the bead cabinet found in Montessori preschools and early elementary classrooms.
3x4 • The multiplicand is placed on the bottom and the multiplier is placed along the side. • The student sets out three bead-bars, four times. • The student sees that 3x4=12 and exchanges by putting a two bead-bar in the ones place and carrying a one bead to the tens place.
Steps to Solving a Bigger Problem7,583x4 or 7,583 taken 4 times Exchanging four, 3-beads for a 2-bead. Carrying the one. Exchanging beads in the tens place. Setting out the beads. 7,583 X 4 30,332 Exchanging beads in the hundreds place. Exchanging beads in the thousands place.
As students master their multiplication facts, they will no longer need to set out groups of bead-bars. A more advanced student’s work may look more like this. First, multiply & set out the beads. Add beads in the units place, tens place & hundreds place by sliding them diagonally, keeping to same colored squares. Add the thousands, the ten-thousands, the hundred-thousands & the millions. • Write down the problem. • Record the partial product after each row of beads has been set out. • Record the final answer. Exchange beads to get the final answer.
As with multiplication, there are a number of materials that help students learn and practice division problems in the early elementary classroom. Golden Beads Stamp Game Division Unit Board Test Tube Division
The idea of division is simple really. Then you prepare to separate them among friends, or in this case, among four unit skittles. You take some objects, such as 12 beads. The answer is always what one unit skittle gets, so 12÷4=3.
Golden Beads First divide the thousands. Exchange the extra thousand cube for 10 hundred squares. 5,274 ÷ 2 = Next divide the hundreds, then the tens. Exchange the extra tens bar for 10 units. Finally, divide the units. Record that each of two friends received 2,637.
Stamp Game Students using the stamp game already understand equal exchanges, such as 1 ten equals 10 ones. 5,274 ÷ 12 = Set out stamps to represent the dividend and skittles to represent the divisor. Divide the stamps. Whenever the tens skittle receives a thousand stamp, the units skittles receive a hundred stamp and so on. (The answer is always what one unit skittle receives so5,274 ÷ 12 = 439 R6.)
Long division is a bit more complex. We begin with problems that are already familiar to the student. The test tube division materials are set up. Six beads go in the cup. Two skittles are placed on the board. The answer is always what one unit skittle gets. 6 beads ÷ 2 skittles = 3 each
Students record their answer one step at a time and clear the beads after each step. Bigger problems, such as 534÷2, are broken down into steps. It’s sort of like taking a $100 bill to the bank and exchanging it for 10, $10.00 bills. If there are beads left after we’ve given each skittle an equal amount, we exchange what’s left over for 10 beads of the next place value.
As students gain confidence in their abilities, they are challenged with bigger and bigger problems. • In addition to recording the answer, E2 students are taught how to record the steps. • With practice, the steps become internalized and students learn to solve problems without the materials.
Learning and the Human Brain • Frontal lobe – reasoning & problem solving • Parietal lobe – controlled movement & spatial orientation • Occipital lobe – visual processing • Temporal lobe – memory, auditory processing, speech
In Short… When students use hands-on materials to learn, in an environment where they are encouraged to move and help each other, all parts of the brain are activated. In addition, Montessori math materials connect the right and left hemispheres of the brain. Right = spatial and creative reasoning Left = abstract and logical thinking
Understanding How Your Child Learnsin a Montessori Environment • Students understand concepts on a much deeper level because all lobes of the brain are actively engaged. • Interest is high and pressure is low as students are allowed to learn at their own pace and work with their peers in a non-competitive environment.
Other Areas of Study • Colorful materials are used for other areas of study as well. • Students help each other learn and achieve a stronger understanding. • Student-chosen projects are strongly encouraged.