How do students in Montessori classrooms learn differently than students in traditional classrooms
Understanding how your child learns.
By Sarah Yoho 2 Traditional MathLearning Abstract Conceptswith Abstract Symbols 3 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.
4 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. Dont forget your placeholders!
5 Lets think about multiplicationfrom a childs perspective.
Numbers theyre symbols that represent how much of something I have.
Numbers theyre like the alphabet only they mean how much instead of representing a sound.
Multiplication... it means Im working with groups instead of individual numbers.
Long Multiplication I need to work from right to left Thats not how I was taught to read! Why do I need a placeholder!
6 Using Materials Leads toDeeper Understanding 7 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.
8 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. 9 Montessori Math Materials
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 childs understanding grows
10 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
11 Lets see how multiplication is learned in Montessori classrooms. 12 Learning Multiplication Facts(in E1 Classrooms) There are many ways to practice multiplication facts in early elementary classrooms! Practicing the times table. 2x48 or Two taken four times equals eight. 13 There are also many ways to practice more difficult multiplication problems. The flat bead frame and large bead frame are similar to an abacus. 14 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.
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 3x412 and exchanges by putting a two bead-bar in the ones place and carrying a one bead to the tens place.
16 Steps to Solving a Bigger Problem7583x4 or 7583 taken 4 times Exchanging four 3-beads for a 2-bead. Carrying the one. Exchanging beads in the tens place. Setting out the beads. 7583 X 4 30332 Exchanging beads in the hundreds place. Exchanging beads in the thousands place. 17 As students master their multiplication facts they will no longer need to set out groups of bead-bars. A more advanced students 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. 18 Now lets take a look at division. 19 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 20 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 1243. 21 Golden Beads First divide the thousands. Exchange the extra thousand cube for 10 hundred squares. 5274 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 2637. 22 Stamp Game Students using the stamp game already understand equal exchanges such as 1 ten equals 10 ones. 5274 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 so 5274 12 439 R6.) 23 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 24 Students record their answer one step at a time and clear the beads after each step. Bigger problems such as 5342 are broken down into steps. Its sort of like taking a 100 bill to the bank and exchanging it for 10 10.00 bills. If there are beads left after weve given each skittle an equal amount we exchange whats left over for 10 beads of the next place value. 25
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.
26 Learning and the Human Brain
Frontal lobe reasoning
Parietal lobe controlled
movement spatial orientation
Occipital lobe visual processing
Temporal lobe memory
auditory processing speech
27 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
28 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
29 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.
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