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In this Newsletter:

Featured Album: Bead Bars Multiplication
Featured Article: Montessori Preschool Math Education - Here's Why it Works So Well
Teaching Resources: Super Teacher Worksheets
Parent Resouces: Book Adventure

Featured Album

Bead Bars Multiplication

Age

6-9

Materials

Box containing colored bead bars 1-10, 55 of each
Chart I (for control)

Presentation

1. We are going to represent the table of a certain number with bead bars.

2. The child is invited to choose a number, e.g., 8.

3. We start with 8 taken one time. One 8 bar is laid horizontally 8 x 1 = ?

4. The product is also represented by one 8 bar (laid vertically below the first) The child writes 8 x 1 = 8.

5. Now take 8 two times. The two 8 bars are laid horizontally 8 x 2 = ?

6. A ten bar and a six bar to represent the product are laid vertically, thus making a double row.

7. The child writes the equation in his notebook. 8 x 2 = 16

8. This continues until 8 x 10 = 80.

9. Observe the geometric figures which have been formed with the 8 bars:

8x1 is a line:

8x2 is a rectangle

and so on...

8x8 represents a square, etc.

Points Of Interest

Notice the rectangles that come before the square have a base longer than the height.

The rectangles that come after the square have a base which is shorter than the height.

8x8 produced a square, which is when the number was multiplied by itself.

Purpose

Direct Aim:

To help the child with the memorization of the multiplication tables.
To bring the child to awareness of the functions of the multiplier and the multiplicand.

Indirect Aim:

To understand that a number when multiplied by ten results in the same number of tens and zero units.
To realize that a number multiplied by itself results in a square to give the concept of forming surfaces, starting with a line, progressing to rectangles.

See complete album for Constructive Triangles: First Box

Featured Article

Montessori Preschool Math Education

Here's Why it Works So Well

By Etan Savir

After 15 years as a math educator, and parent of five children, I actually saw something new (to me) in math education this past year, which really impressed me.

My (then four-year-old) son attended a Montessori preschool class and learned math concepts in a way that I had never learned myself in the classroom, nor had any of my three older children learned before.

The Montessori Approach to Math
The Montessori math education concept is based on going from concrete to more abstract lessons, referred to in Montessori lingo as "works," which are really just manipulatives.

These well-designed, highly specialized manipulatives for each "math work" make the abstract ideas much more accessible to a child.

Each new work is introduced to the student only via a one-on-one lesson with the teacher. Thanks to this individualized instruction, the teacher can wait until each student is ready for the next level of abstraction before introducing it.

Step-by-Step Progress
Some children in my son's (mixed age) preschool class were still learning to count to twenty, while others were learning place value and addition and subtraction. But, even those younger children doing the early math works understood that they needed to master counting and one-to-one relationships in order to do the place value and addition and subtraction works.

This is an extremely important concept for children to remember. There can be no "skipping" lessons in the Montessori preschool math curriculum, (and there shouldn't be "skipping" in any math curriculum, in my humble opinion.) My son's classmates understand that mastering each lesson is a means to an end in competency in math. It is a wonderful approach to preschool math education!

Math Lessons Are Fun!
From my son's perspective, the "works" he used to learn math were almost like toys. He got to play with them in the way the teacher showed him and then he came away with mastery of a math concept. In reality, those works are just really well-designed math education manipulatives that teach one highly focused math concept.

There are works that teach key math education skills such as; measurement, counting, number order, number formation, one-to-one relationships, addition and subtraction, and even higher math concepts. Every time the teacher introduced a new math "work" the kids who were ready for that next math concept were excited and energized to learn a new math skill. They watch and help each other complete the tasks of the work and learn from their peers in that way. This is a great way to have group math work!

Montessori Works as Toys
Some of these math manipulatives would make wonderful toys and "kitchen table" lessons for parents to do with their children when introducing math concepts at home. I was very pleased with my son's progress in math using the Montessori preschool-math education method, of course he had an exceptionally talented teacher, but I think many children could benefit from using the Montessori math manipulatives at home, too.

Etan Savir is a 15-year math teacher and currently the math department chairman at Garrison Forrest School, a k-12 college prep school in Owings Mills, Maryland.

He is also the editor of http://www.sensible-math-education.com, a web site devoted to helping parents understand the fundamental math skills their children should master in each grade and math course. "So many parents just don't know what their children should learn in math. Once they have that figured out, helping their child achieve math education success is much easier.

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