Better@Math - Better@Thinking
Rote Memorization - According to Merriam
Webster Online, “Rote” is
defined as:
1. the use of memory usually with little
intelligence
2. mechanical or unthinking routine or
repetition
Intelligent Repetition - Mastery through skill
acquisition, incentives, and
a practice-based traditional
learning method, which
leads to the freeing of
“mental real estate”.
Thinking Skills -
Rote Memorization
vs. Intelligent Repetition
The Process of Addition
How do we actually perform addition? There are 3 techniques which must be mastered in order to add any series of numbers (Simple, Best Friend, and Second Friend).
Technique 1 - Simple Addition
The Problem: How do we solve 2 + 2?
Using the 1’s beads, move 2 beads up toward the white bar. 
Now we want to add 2 more.
Since there are 2 free 1’s beads, we can just push them up. 
As we can see, the answer is 4.
Technique 2 - Friends to 10
The Problem: How do we solve 2 + 9?
Start by placing 2 on the Soroban. 
Now we want to add 9 more.
Looking at the unused beads on the Soroban, there is one 5-bead, and two 1-beads, for a total of 7. Since we do NOT have 9 more to add, we challenge our kids to ask “What else can I do?”
We teach our students to use the TENS column.
Tens Ones
So, instead of adding 9 (which is impossible), we add 10 instead.
But, 10 is 1 more than 9, so we have to take 1 away.
As we can see, the answer is 11.
Technique 3 - Friends to 5
The Problem: How do we solve 2 + 4?
Start by placing 2 on the Soroban. 
Now we want to add 4 more.
Looking at the unused beads on the Soroban, there is one 5-bead, and two 1-beads, for a total of 7. Since we cannot make a 4 out of the available beads, we challenge our kids to ask “What else can I do?”
The first inclination is to use the previous technique, Friends to 10.
The student adds 10, and because 10 is 6 more than 4, we attempt to take 6 away from the Ones place. But we encounter another problem, we only have 2, so how can we take away 6??????
Once again, our students are challenged to ask themselves “What else can I do?”
So, instead of adding 4 (which is impossible), and instead of adding 10 (which we reasoned was a dead end), we add 5 instead.
But 5 is 1 more than 4, so we have to take 1 away.
As we can see, the answer is 6.
Let’s review what went into solving the addition problems above.
Instead of simple memorization, our kids are challenged to analyze the number on the Soroban. They reason whether they can simply move beads up or down to add the number onto the Soroban. They theorize a potential solution. Visualize whether that solution would work. And finally, they develop alternative solutions until they can solve the problem.
Is this method difficult? When compared with rote memorization, this technique requires much more thinking and processing. But, therein lies a major benefit.
Our children are constantly growing and learning. We want to stimulate their young minds to become powerful thinking machines. If we wanted them to be simple minded, we would sit them in front of an electronic babysitter (television or video games) all day.
Here you have the opportunity to choose between practicing Rote Memorization or develop Thinking Skills. It is a fact that all children must learn arithmetic. The question is whether to choose the avenue of memory recall, or the path that challenges your child to perform analysis, reasoning, theorizing, and problem solving.
Rote vs Thinking
(Analyzing, Reasoning, Theorizing, Problem Solving)
