Abstract:

A- What is the main ideas of the Montessori Pedagogy?
“Montessori is an approach to education with the fundamental belief that a child learns best within a social environment which supports and respects each individual’s unique development. The materials in the Montessori environment are designed to isolate one concept at a time in a very concrete manner. Children work with materials that are self-correcting, thus allowing for auto-education. “Errors” are viewed as a necessary and helpful part of the learning process. The Montessori materials provide a bridge from the known to the unknown, allowing children to evolve gradually from concrete, experience-based learning toward increasingly abstract thought.” [1]

B- Why is Montessori so effective?
“We know there is an indisputable link between movement and cognition, with the former actually enhancing the latter. We know that people of all ages need to feel a sense of control over their lives and that lack of control leads to depression and learned helplessness, which inhibits learning. We know from a huge body of research that extrinsic rewards and punishments don't work and can actually adversely affect intrinsic motivation. Research tells us all of these things, yet students at conventional schools are still confined to their desks, with rigidly scheduled days, receiving grades for every aspect of their learning and behavior. In contrast, students in a Montessori classroom are free to move about the room and are provided varying types of work spaces . They're given large blocks of time -- generally around three hours -- in which they choose their work. The children are taught how to test themselves or each other so they can know if they've really mastered something, such as math facts. There are some things that do need to be memorized!” [2]


C- What kind of Montessori's material I have created?
C.a-First example
The Montessori’s method uses forms of color to make some parsing. A geometrical shape and a color is associated to every word nature. There are many colors which the human being can differentiate but few forms (triangles, square, circle, rectangle). So for all which relates to the nominal group, the used form is the triangle and in order to differentiate a name, a determiner or a pronoun, various colors are used.
Inspired by this methodology, I adapted this concept to the units MKSA in physics in order to verify the formulae homogeneity. We use a different form for every single MKSA unit (we can introduce the basis notion because we can express all other units with these forms). Colors having not much importance, primary colors can be used (always to insist on this basis notion).

C.b-Second example
In the Montessori’s method, there is a Pythagorean table which is a kind of Puzzle with squares and rectangles of different different colors and sizes. Every form group having the same color forms a bigger and bigger rectangle which thus verifies the the most known Pythagoras’ relation.
Inspired by this methodology, I suggest using baguettes of various colors and different length (4 groups) as well as several angular sectors. With a adequat methodology, the student can understand the definition of all trigonometric lines and apply them in vectors projection.

References:
[1] http://www.schoolinthehills.com/montessori/montessori-ground-rules/
[2] http://www.huffingtonpost.com/laura-flores-shaw/montessori-education-debate_b_1237451.html

Keywords:

Montessori, middle school, Pythaogus,, equation homogeneity.