## Current case Studies in the Child Friendly Math Education Framework:

Objective: To demonstrate the effectiveness of the CFMEF.

This study is an ongoing private algebra class at countonme.us's Learning Center in Saint Paul, MN.

Students selection: Random.

Setting: Study room with a whiteboard.

Delivery method: Concept demonstration and direct engagement.

Use of technology: No (Plan for future).

Class: 2 sessions per week with each session spanning 1 hour.

Learning condition: After a regular school day.

Duration: At least 6 months to observe results.

Homework: No, only practice multiplication tables.

Observation and success rate:

Since our initial start in Colorado, we have been continuing the evaluation and improvement of our approach.

Although the data is numerically insignificant, we are able to observe and confirm that the outcome

continues to validate our approach. We are now in the process of conducting a large scale research and

development of the Child-Friendly Math Education Framework. The following videos are the testimonies of

students from various backgrounds solving algebra equations beyond their grade level.

# Part1

The 5th-grade student commands the computation of positive and negative numbers in all aspects and possesses the algebraic knowledge and skills to solve an equation without relying on formula or memorization. She is ready for algebra I.

The 3rd-grade student is making progress in learning the principles of algebra.

All our students follow the same successful path of learning algebra without experiencing math anxiety.

The 4th-grade student just followed his brothers to our learning center. He started algebra in 2nd grade. Now, he is capable of manipulating a more complex equation. He will be successful in completing algebra I on time or ahead of schedule.

The 5th-grade student came to us from Kumon. His mom told us: "Each trip to Kumon is a constant struggle, and we fight all the time. He is burned out from a ton of worksheets."

He joined our program with no algebraic knowledge. He learns algebra with zero homework. After 8 months, he advances at a fast pace. He possesses already a solid command on algebraic manipulation, and ready for algebra I. He doesn't need any formula. We are certain that he will be successful and complete algebra I by 7th grade.

# Part2

The 3rd-grade student starts learning the principle of algebra. He understands the principles of fairness (or equality). Our approach to teaching the computation of positive and negative numbers allows him to master them in just a few weeks. He would still make mistakes, but the good news is that he is fully aware of the mistakes. This example shows that he can solve equations in many combinations. Our approach builds confidence from the first lesson.

More videos are coming soon!

## Previous case Studies in the Child Friendly Math Education Framework:

Objective: To demonstrate that young and at-risk students are able to learn the fundamentals of algebra.

This study was an ongoing class at Castle Rock Library in Colorado from February 2014 to February 2015.

Student selection: Random.

Setting: Study room with a white board.

Delivery method: Concept demonstration and direct engagement.

Use of technology: No (Plan for future).

Future delivery method: 1. Online engagement 2. Direct engagement & practices in class.

Class: 2 sessions per week with each session spanning 1 hour.

Learning condition: After a regular school day.

Duration: At least 6 months to observe results.

Homework: No, only practice multiplication tables.

The success rate after 12 months of training: 100%

###### Student: Brice, 7th Grade

Brice is a 7th-grade student. He is a happy student who shows interest in learning. He commands arithmetic, multiplication tables and possesses basic algebra knowledge. After 9 months of learning, he is capable of solving systems of equations, linear equations, and basic quadratic equations.

###### Student: Alllan, 9th Grade

Allan is a smart 9th-grade student, but he had difficulty in learning Algebra with existing methods. He struggles with math, but after 9 months of training, he is making progress. He learns to solve linear equations, system equations, and quadratic equations.

###### Student: Ella, 4th Grade

Ella is a 4th-grade student. She had no knowledge of algebra and only learns when she is in the mood. She needs special attention and the instructor must engage her. She also learns the principles of algebra. She is capable of solving 9X+ 3 -8X = -7-2 or 3(X-4) = -6 demonstrating the understanding of various concepts of algebra. She advances according to her pace and shows no shortfalls in her intellectual and reasoning ability.

###### Student: Rolland, 5th Grade

Rolland commands arithmetic and multiplication tables but had no algebra knowledge. He is an attentive student and a quick learner. He started learning algebra in 4th grade. After 6 months of training, he is capable of solving rational equations, a system of equations and basic quadratic equations. He is transitioning to more advanced algebra.

###### Student: Laura, 1st year College

Like countless college students, Laura needed to take her algebra remedial class, She repeated the same ineffective classes that didn't work out. She didn't do well in high school and is still unable to solve basic equations. After 1 month of training, she has overcome her weakness and fear in learning algebra. She finally enjoys algebra class for the first time.

###### Student: Bertrand, 3rd Grade

Bertrand is a curious 3rd-grade student and eager to discover new concepts. Like other young students, he grasps the principles of algebra right from the beginning and advances steadily. After 6 months of training he solves:

9X-3 -5X = -7-2X ; 2(-X +2) = (X -3)(-5) and

3/(-X+3) = 2/7 without relying on formulas. He is on his way to excel in algebra.

###### Student: Ben, 2nd Grade

Ben started learning algebra in 2nd grade. He had no knowledge of algebra. He is a quiet and attentive student. After 4 short months he successfully learns the fundamentals of algebra and solves -8X+2 -4X = -16X-12;

3(X -2) = (X+5)4 and 5/(X-1) = 4/3

###### Student: Alice, 3rd Grade

Alice started learning algebra in 3rd grade. She had no knowledge of algebra. She is a dynamic student. After 4 short months, she successfully learns the fundamentals of algebra and solves -8X+2 -4X = -16X-12

2(-X +2) = (X-7)3 and 3/4 = 9/(X+2)

###### Student: Dean, 2nd Grade

Dean started learning algebra in 2nd grade. He had no knowledge of algebra. He is a quick learner. After 4 short months, he successfully learns the fundamentals of algebra and solves -8X+2 -4X = -16X-12

2(-X +3) = (X-7)2 and 6/5 = (X-1)/3