Addition – Carrying Confusion!!

Addition is such simple and profound concept that it seems unnecessary to write again about addition. However observation of many kids doing addition proves otherwise – at least 20% of kids do not understand the concept of “CARRYING” – the art of taking the excess (beyond 9) during addition, to the next column when adding right to left.

Take another look, when a kid is asked to add two numbers – very gracefully and with enthusiasm quickly adds the numbers. Trouble starts for them when asked ” Verify and show that your answers is correct”.  Some students brave to subtract one of the addenda from the answer to see if the other addenda results. More so interesting is when the subtraction does not verify their answers. Now they do not know, if their addition was incorrect or the subtraction.

Most of the text books in the act of simplification, have separated the chapters on addition as (a) Simple addition and (b) Addition with Carrying. What has been lost in this seemingly innocous exercise is the REAL connection with the Place Value. 

 Lilavati of Bhaskaracharya, provided an elegant definition for addition - who can provide more elegant definition than Bhaskaracharya!! -

“Addition or Subtraction should be done Place-wise from right to left or vice-versa.”

This definition paves way for addition in any meaningful and self devised short cut (or speed) methods

PlaceValue – Sthana Bala!!

Fundamental to counting and numbers is the place value – digit by itself does not have value, however its value is determined by its position – figuratively Sthana Bala

Place Value is the fundamental GROUPING in numerical skills, and many students find mathematics difficult for lack of understanding of Place Value. A side effect to this lack of understanding by kids, is the burgeoning market for so called Speed Mathematics, Mental Mathematics and usage of tools like Abacus. All these tricks are useful and important, however lack of understanding of the underlying principle by its students  is the concern. All these techniques creatively use the PLACE VALUE.

My belief is that kid who learn place value will devise his OWN speed tricks for different computations.

A creative way to teach place value with hands-on activity is available on the internet at the following link (not mine)

http://ejad.best.vwh.net/java/b10blocks/counting.html

In the following blogs, will write about different uses of place value grouping and regrouping.

What good is Maths?

A fifth grade student posed a not so interesting, however an important comment – “if there was nothing called mathematics, life would have been easier”. This comment is not so interesting because it hurts to say maths is not important. And this comment is important because fifth grade is not understanding the basics of maths, and is fatigued.

Since this comment is important, searched for a story that explains the importance :

A bird was happily roaming around in the forest. Four hunter enters into the forest. The bird notices that a group of hunters and hides. Hunters go back disappointed. The bird notices the group going away from the forest and again starts flying freely.

The hunters come back again into the forest, this time with a clear plan to shoot the bird. The bird again notices a group of four hunters approaching the forest and hides. The hunters too hide behind a tree. After a while three of the hunters go away from the forest. The bird notices the group of hunters leaving the forest and the bird comes to fly. The lone hunter behind the tree shoots the bird. The hunters plan worked, because they realised that the birds cannot count beyond three and everything above three is “Many” or “Group”

(this story is a classic, said to have been written centuries back connecting consciousness and numbers – am trying to get the appropriate reference, however the story is worth the concept.)

Grouping and Regrouping have been fundamental to mathematics even before counting and mathematics – It is no surprise that every kid first learns grouping and regrouping, however it is sad that they loose connection to it as they advance to counting, addition and further.