Door-2-Math Blog

Let’s say little Jane learned the rules of addition and eager to try it out. Her mom gave her the following instructions “keep the 5 in your head and count from 6 because 6 comes after 5″. So Jane obediently stuck out her fingers and started to bend 1 down to keep track of how many she’s added to “5″. Further, let’s suppose Jane is very patient, organized, and focused, so after bending all the fingers down, she counted to “10″. “Keep going Jane,” mom encouraged her. “You’re almost there. Just count 2 more fingers and then you’re there.” So our little girl counted 2 more fingers down on her other hand since all five fingers on the other hand were counted already. Finally, she arrived at the correct answer of “12″. “Excellent!” Both mom and daughter were thrilled. Success on the first try.!

As effective in arriving at the correct answer at the first try, what this mom didn’t know is that Jane just equated counting fingers to addition. And how many fingers do we have? And what to do when we have to add a number lager than 10? What about when one day Jane all of a sudden realizes that she’s the only one in class who is adding by counting on her fingers?

Let’s say Jane is resilient and didn’t want to give up math altogether. So she hides her fingers under the table. Counting on her fingers after all is all she knows how to do when adding. Remember when she got the correct answer on the first try way back? So she continues to count on her fingers, under the table. Then one day, Jane realized that she’s the last one to get the right answer. Somehow, other kids just know.

So what went wrong? Addition went wrong. It went wrong because the mom adapted the “effective” way over the efficient way in introducing addition to her daughter. With the effective way, we are only concerned with one thing and one thing only – get the result. Counting on fingers gets the result and for most students it’s the most natural way too. But here’s where it failed Jane. She equated learning new concepts to getting the right answer not getting to know what this new concept is really about.

A small deviation at the beginning really does set up a child’s lifelong learning pathway. And different pathways do lead to different destinations – sometimes so different that the destination is almost unrecognizable.

So what could Jane’s mom done differently? Two things. One is to handle the situation differently when Jane’s math started to show signs of trouble. The other is to introduce new material with the goal of “getting the gist” instead of “getting the result”. Results will follow if the essence of the new concept is introduced and actively sought after.

Mastery of addition is of utter  for success in K-12 mathematics. Addition is the first mathematical operation that we encounter. Mathematical operations is where we “do something” to the numbers that we learned to count. A collection of operations makes up the “bones” of the K-12 math material, whereas numbers and expressions (introduced in pre-algebra) are the “muscles”. Other bones after addition are s9ubtraction, multiplication, division (K-3), exponentials (4th grade), logarithms (9th grade), trigonometry (11th grade), and differentiation and integration (calculus 1 and Calculus 2).

Mathematical operations are made up of rules whereas mathematical building blocks such as “numbers” and “expressions” are made up by common agreement. We (or the collective body of us humans) agree to let a symbol “5″ to represent the number that comes after “4″. It could have easily been some other symbol, say an ampresand sign “&”.

The rules of addition are the simplest yet most powerful. Simply stated, it asks us to “continue counting forward”. Take, for example, 5 + 7, where it’s agreed that the “+” sign is short hand for “keep counting 7 more beyond 5″.

As simple as it sounds, this is where math struggle starts for the vast majority of students. It’s not that they can’t count forward or keep track of how many they counted forward. It’s because they stop at the literal wording of the rules. And what’s wrong with that? Everything!

Most children will show you how they want to learn. Your job is to observe first and follow their lead. This is the most efficient way to impart knowledge to your child.

One day, I was scooping up rice into my hands to make some rice balls for my son at the dinner table. As I was putting the rice ball into his plate, one by one, out of nowhere he started to repeat after me. “one”, he said “two” I said. “Two” he said. “Three”, I said. “Three” he said. As you guessed it, I went out an started counting everything after that.

Our daughter was more of a self-learner. From very early on, I noticed that she waited to examine the toys I played with after I was done with the. To facilitate her learning, I played with this green toy frog that sang “one-little, two-little, three-little Indians”.  It paused and then waited for me to push the next number – a button with 4 on it, then the frog continued counting. After watching me several times, our daughter picked it up without any further instructions from me. To my amazement, one day I came home and found that she mastered the entire alphabet from the buttons on the same frogs belly!

Let your child lead, then follow…