Teaching Math

My son has issues sitting in a chair.  Math usually occurs all over the house, upside down, jumping on the bed and for rather brief moments sitting at a desk.  He grasps things quickly but hates to repeat and practice problems unless they are very easy.  The time it takes to complete his daily math lesson of 27 problems on Teaching Textbooks varies depending on how closely supervised he his and the threat/reward system in place.  It can take a long time factoring in all the distractions.

I used to teach him using the Montessori Method.  I'd give him short lessons with colorful and ingenious, game-like material abstractions of math concepts.  Then I would require him to repeat the lesson with the materials.  This he found way too boring.

You see, my son is an innovator and doesn't like to do the same thing twice.

But I have perseverance and determination.

After 3 years worth of Teaching Textbooks, we have suddenly reverted back to Montessori Math.

What changed?

A gorgeous work partner!  Making a wonderful timeline of math concepts throughout the ages, incorporating his passionate love of history and hands on ingenuity!  Extra short, yet frequent math lessons using impressive materials, cut and paste, comics and math he has never seen before....

Tristan now has a work buddy.  She is also making the timeline and doing Montessori lessons on fractions.  Tristan watches her attentively, pulling the occasionally impressive stunt as he revises fractions! all the while making half hearted attempts at his own work.  Bottom line: it is not cool to work hard in front of a beautiful girl.  He is quick to assist her in any way (getting a hammer or fetching a print out) when the need arises.

He is the quintessential knight in shining armor.

On the other hand, when not in the presence of the beautiful girl he needs to be one step ahead on his work on the timeline.

This is the timeline.  He makes matching cards with an explanation on the back.

He is quite proud of his hieroglyphic of Sirius, the brightest star in the night sky.  He learnt how to use Paintbrush on Apple to draw his hieroglyph.  Now he is making delightful pictures.

Distraction.  Distraction Distraction.

I love making timelines.  Making things to represent learned concepts is making the timeline come to life.  Today Tristan made a representation of the moon phases and the notches an early human may have carved on wood to work out how long it takes for the moon to move through its phases.

He spent a while working out how to put 29.5 notches in the space on his model.  He ended up spacing each notch 3/8 inch apart, then chiseling them out.  It was a bit messy, laborious even to carve these notches across grain but we had some interesting discussions.

We also hooked up his model of the sun rising in the East and setting in the West, that shows how people must have been reliant on shadows to work out approximate time way back when.  Here is the model...not painted yet...but the sun (lightbulb) moves across the wire.  The tree made out of Sculptey melted in the oven.  Now we have only a stick to mark shadows.

When he paints this, it will be more obvious that there are mountains on the right.

We are using a book written in 1955.  I love the illustrations and explanations.  It is outdated yet it is hard to find modern books with such clear and great illustrations.  This gem was a discard from a library in Oregon.

Tristan's job is to work out a way to make a model of this/these discoveries.

From this picture of how the ancients located the Polaris, the North Star, Tristan decided to make a light box showing the Big Dipper rotating around Polaris.

In between these little excursions into handmade models we do math on paper.

Right now we are doing a Montessori series on squaring and square root.  Montessori teaches the children to do square roots by hand into the hundred thousands.  To do this a child needs a deep knowledge of the decimal system and how it works.  The series begins with breaking the hundred square into binomials and understanding what a binomial is.  It has taken a week and 5-10 lessons for Tristan to get a firm understanding of a binomial.  I have presented the lesson in several ways, talked and played games, made up comics and constantly tried to reaffirm the basics to integrate this concept so he is prepared for the more abstract versions of this lesson to come.  I am anticipating this will take me a couple of months until he can calculate the square root of a number in the hundreds of thousands by hand.

Today he said.  "I get this math.  But, what I don't get is why I have to do it."  I am hoping he buys my explanation which is that I am developing your mind, helping you understand complicated concepts so that you increase your capacity to understand complicated things.  I said, "This will get even more complicated and you may feel your brain stretching...let me know how that feels."  So far he is staying with me.

Luckily I have the beautiful girl card, because I know that Tristan will endure anything to have this particular young lady do lessons with us!