Before jumping into the example, let's examine the big picture of what we want to develop in our Foundation.

Our learning philosophy is completely different from what is done today in the Educational System. In fact, we are not offering to directly help students to improve their grades in the school. That will happen as a consequence of our approach, but it is not our main objective. We believe that the essence of education is to inspire young people to become mature individuals, able to find their own path toward a meaningful life. This means that education should contribute to the discovery of excitement and creativity in the work that they choose, which will lead them to success, and, ultimately, to an enjoyable life.

To accomplish such a goal, we first begin by learning as much as possible from our own students' interest to link with the new knowledge needed to advance in society. And here is precisely where we diverge from the current educational system. Contrary to the standard instructional methodology, we choose the selective one: are we saying that some kind of natural selection occurs in our brain? Indeed! Our brain only pays attention to new knowledge if the new knowledge is connected to something that already exists in our long memory.

Mathematics, the most beautiful subject that humanity ever discovered! It is the one that opens our horizon to acquire any other knowledge needed to face life in society. The power of its logical construction becomes a profound tool that provokes our curiosity, creativity, and excitement to reach into unknown.

Let’s begin with perhaps the very first mathematical notion that every child gets exposed: the counting of objects that are surrounding us, but most of all nature. And precisely, here begins our basic difference with the standard education. Children should have a significant period of time where they observe nature, ask questions, play games, and do extensive physical activities. In the middle of this, we may expose kids to the idea of counting objects as a mental activity with no writing and no mathematical symbols at this stage of their life. In fact, we should let them create their own symbols if the need arises.

During this early stage, there are couple things that we want to accomplish. One, is the concept of a number, what it represents, and understanding that the number is not the symbol. Two, corporal participation either by drawing, cutting, or touching, which is critical for the brain to absorb new knowledge. For instance, we call the number 2, the class of all sets with two objects, which can initially be represented with || (two sticks).

Once the student understands the correspondence between a number and the number of objects in a set, we are ready to talk about comparing the size of two sets. In other words, we begin exploring the notion of more than or less than. This means, we need to know when a set has more objects than another set. I must say that here we are hiding a profound mathematical concepts that kids may, actually, get familiar in an earlier stage of their life.

Kids of the age one or two have some understanding of the notion of more than or less than. This allows us to begin with a definition how to determine whether a set S₁ with one object or a set S₂ with two objects has more objects. This basic idea will help us to derive that the number two is greater than the number one. Moreover, we can also discover that when we gather the objects of two sets, each containing one object, into a single set, we obtain a set of two objects.

In summary, let’s recollect the concepts learned in this short presentation, including the atmosphere to develop the learning activities.

1. Begin by exploring nature and develop a friendly group interaction.
2. Introduce the concept of a number, and the conclusion that the symbol 2 is not exactly the number two.
3. Inculcate the ability to count objects of various nature by establishing a one-to-one correspondence between sets of objects and numbers.
4. Introduce the relations greater than and less than.
5. Provide a basic introduction to Set Theory, like what is the union of two sets.
6. Using the concept of the union of two sets, have the students learn that “one and one makes two.”

Observe that the above lesson used almost no mathematical symbols, only 2, S₁, S₂. Finally, observe how the lesson incorporated the basic features of a meaningful learning experience.

1. Deep learning, profound creativity, and intense joy.
2. No reward and punishment approach of learning.
3. No memorization as a tool of learning.
4. Learning at each individual pace.
5. Integrated learning.

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