Montessori Education

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Montessori Education

• How do students in Montessori classrooms learn
  differently than students in traditional
  classrooms?
• Understanding how your child learns.

By Sarah Yoho
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Traditional MathLearning Abstract Conceptswith
Abstract Symbols
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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.

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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!

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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?!

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Using Materials Leads toDeeper Understanding
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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.

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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.
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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 childs
  understanding grows

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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

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Lets see how multiplication is learned in
Montessori classrooms.
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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.
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There are also many ways to practice more
difficult multiplication problems.
The flat bead frame and large bead frame are
similar to an abacus.
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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.

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• 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 3x412 and exchanges by
  putting a two bead-bar in the ones place and
  carrying a one bead to the tens place.

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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.
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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.
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Now lets take a look at division.
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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
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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.
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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.
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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 so 5,274 12 439 R6.)
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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
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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.
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• 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.

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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

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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

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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.

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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.