Wednesday, June 6, 2012

Practice on Mathematics Problems

Montessori builds repetition into the materials without requiring tedium.

When a child plays a 3-period-lesson game; or language games with the sensorial materials, with the language materials, with the interconnectedness of every area of the classroom and life. From laying out a Far Eastern place setting to the continent folders of that region - in primary; from all the timelines of elementary to all the peoples and events throughout history - OUR history.

Everyone seems to accept these sorts of connections and repetitions and reinforcements with ease and peace.

Addition - when a child is adding 2957 + 3495 - he is really doing 4 addition problems. More when you consider the carrying.
Subtraction? Same deal. 4824 - 3604 - the child has 4 subtraction problems in ONE.
Multiplication? We start with numbers such as 1242 taken twice. And quickly move into 4958 taken 4 times. LOTS of carrying.
Division? Same idea.

These are 4 year olds.

As they work with the materials, they get the patterns because they're not just writing it out, they're DOING it. Then they have the stamp game, bead frames, racks and tubes for short division and other tools to continue working with BIG numbers; and the memorization boards to start memorizing the basic math facts in each operation.

Let's consider a short division problem: 5,496,284 divided by 2. There are SEVEN division problems in that one problem alone.

And that is primary level.

By elementary, they are getting into long division, intense fractions work, decimal fractions, squaring and cubing - and again, we are working with real numbers with real materials so that the child, even by manipulating the material, gains an understanding of what is going on.

If a child starts in the middle of the elementary with no Montessori background, he still gains from the experience, because he is still working with the material, surrounded by children who already "get it" and who are joyful to help him just where he is, without doing the work for him. Bank game, long division, and fractions are fantastic materials for new-to-Montessori elementary children.

Repetition is built in. Use the materials; use language and other games to get the materials out and put them away; provide real math problems; invite the children to think of their own (they always want to work with something harder than we provide anyway - LET them!). And they have joy in their work.