Developing the Mathematical Mind in the Montessori Environment

The highest form of pure thought is in mathematics. ~Plato
Maria Montessori believed that human intelligence is no longer based on natural intelligence but on mathematical intelligence. Humans have moved beyond the innate survival instincts of early humans and moved toward an analytical awareness of the world. Math is more than math facts and computations. It deals with shape, space, patterns, symbols and the relationships found therein. Mathematics: Birth to Age Three

Learning about patterns occurs in utero: the cycles of day and night, activity and inactivity, the patterns of the mother and the family. The developing child also hears the patterns of speech and music around him. Music is thought to enhance the development of the mathematical mind due to the fact that the neural pathways of learning music are very similar to those for mathematics and may help with the mylinization of those neural pathways. Montessori observed that humans tend to be attracted to order. After birth, consistency with [pic]routines and activities such as feeding, bedtimes, bathing and playing help the child establish an early sense of order and sequence. Babies learn to think logically and know what to expect. Deviations from the expected order can cause confusion and cause upset. This early tendency towards mathematics causes the child to observe others and to compare, contrast, and classify objects in his environment. Consistency helps the child make sense of the world around him. Using clear, precise language also helps develop the mathematical mind. As children are beginning to order their world, we use mathematical terms such as big, small, more, some, few, many, to help them learn to quantify. Mathematics: The Preschool Years

Although preschool students have had several years working with numbers and mathematical concepts, children do not immediately begin working with the math materials in the Montessori...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...concrete model.
Looking on the locality of the paper, I highly acknowledge the fact that the researchers described the current state of math education in the Philippines. They emphasized the fact that we are more focused on procedural knowledge rather than the more desired conceptual knowledge. That is our disadvantage because we usually train students to perform math without understanding or making connections on what they are doing. By mentioning this, the readers would really have an idea that the paper itself could be a solution to the problem mentioned. Moreover, it makes the thesis more realistic.
To sum up everything that was tackled, I could say that the thesis served to have an important purpose in the current state of Mathematics Education in the Philippines. It is very informative and feasible. Since it is a small study because it only involved 6 average students, we could propose more studies rooting from this which would have a bigger scope such as implementing the same study but now comparing it to the results gathered from high and low performing students....

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

...The Mind of a Child Thief
If you get in the habit of stealing I believe it always starts out in people as they are young adults or children. It’s greatly enforced by peer pressure, or in some cases, just wanting to have everything you couldn’t. For me once I got in it, it was hard to get out and almost became a routine and a drug to steal, such as my case making me a kleptomaniac. The need to do it for my case came from the thrill and adrenaline I got from doing it every time as well as having such a reputation that I could do these things. It was greatly influenced by my friends to keep doing it as well as my own inability to stop myself. Only after getting caught twice as a child, I was able to learn my lesson and turn my bad habits around with the help of my mother and the court system.
Stealing was an everyday thing for me, sometimes even twice a day. It hadn’t really taken off until my friends and I had access to transportation like one of our friends getting a car, and then we had no limits as to where we could go or how many stores we could go to. I also was trying to grab as much stuff as I could every time I went, trying to set a record for some obscene reason. I also was not the only one in my group that did this; I always had multiple friends join me and help me which only aided my bad habits.
I have been caught three times stealing. All which had great distances in-between First, I was nine years old stealing...

...In the Mind of a Child
By Diosa Bernadette M. Retig
As the life of some Filipinos become harder, several solutions are being tried out by the family, especially the parents, to be able to pay the electric and water bills, to put food on the table, to meet the needs of every member, to make life as comfortable as possible, and to give their children the greatest treasure that they can give—education. Some parents would have multiple jobs, apply for work abroad, borrow money to relatives, and sadly, some engage in illegal transactions and commit crimes just for their family. Unfortunately, some children are being forced by their own parents to work but some children choose to work just to help out their parents. It is common in our society to hear about college students working as call center agents and fast food employees to be able to have money for their schooling expenses but who would think that this similar kind of thinking is already instilled in a 13 year old boy’s mind?
Jericho Castro, fondly called Kong by his family and friends, is a grade six pupil and at the same time, a magbobote. He is second among the five siblings and at the present, he and his mother, Reginaria “Naria” Castro who is a laundry woman, are the ones providing for their family after his father, a construction worker, died because of ulcer last January. Being a working student, Jericho admits that it’s hard for him to understand the lessons...

...The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[19] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.Evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time – days, seasons, years.[20]
More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[21] The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time.
In Babylonian mathematics elementary arithmetic (addition, subtraction, multiplication and division) first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]
Between 600 and 300 BC the Ancient Greeks began a systematic study of mathematics in its own right...

...mother of Europe's languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity... of self-government and democracy. In many ways, Mother India is the mother of us all."
- Will Durant, American Historian 1885-1981
Mathematics is an important field of study. Mathematics is essential as it helps in developing lots of realistic skills, in fact study of mathematics itself include the concepts related to the routine lives of human. It not only develops mathematical skills and concepts, it also helps in developing the attitudes, interest, and appreciation and provides opportunities to develop one’s own thinking. So, mathematics is undoubtedly a discipline which is imperative to know and study. Figure 1 clearly specifies all the skills that are developed by the mathematics. Mathematics starts from simple things and linear thinking that lead towards the more complex things and higher order thinking skills. Mathematics has taken centuries to develop in its present form and that’s why it will be really fruitful to know about its development.
Fig. 1, Importance of MathematicsC:\Users\naveen\Desktop\Untitled.png
Mathematics has played a very significant role in the progress and expansion of Indian culture for centuries. Mathematical ideas that originated in the Indian subcontinent have had a...

...components there will be no new inventions in the realm of science and business and all of a sudden there will be no difference human and animals. Without maths the whole world will go mad and economy will be badly affected. If there is no maths, we cannot do anything in our life. Maths is the only thing which develops our mind and which teaches to reach our goal. Maths teaches us to utilize our resources with lesser and lesser wastage of efforts. Its maths which allows humanmind to plan the concept of development. Today man has reached on the moon and even it is planning to look beyond the sun, do you think it would have been possible without the knowledge of 1 + 1 =2.All mathematical concepts are real life experiments. The peano postulates, the density theorem, the Pythagoras theorem, components of trigonometry all plays vital part in modern era engeering.The whole progress of humanity will reduce to ashes if maths is removed somehow.
Conclusion-Maths plays a very important role in our daily life so without maths even it is impossible to think about life. Life is not possible without maths. Maths promotes logical thinking which inturns develops ones mind and mindset which is the key component for basic human development. If there is no maths then there will be no life.
As one shlok of ancient Indian manuscript “VEDANG JYOTISH” says-
maths has supreme position among all the science...