Wednesday, April 13, 2011

The Mathematical Mind

In light of all of the recent Math activity in the classroom, I thought it would be prudent to share some thoughts about Montessori's ideas regarding mathematics.  One such concept is the 'Mathematical Mind' of the child and  how the prepared environment naturally stimulates mathematical thinking.

Maria Montessori’s use of the term, ‘The Mathematical Mind’ refers to the unique tendencies of the human mind. She was familiar with Blaise Pascal, a French philosopher, physicist, and mathematician, who theorized that “man’s mind was mathematical by nature and that knowledge and progress came from accurate observation” (The Absorbent Mind, 17, pg. 169).  Montessori designed the specialized Math apparatus to incorporate the spontaneity and natural capabilities of a child’s mathematical mind.  The Early Childhood classroom offers children order, precision, and exactness through the manipulation of materials.  Consequently, their understanding of the surrounding environment is built on a foundation which is mathematical by nature.  “In our work, therefore, we have given a name to this part of the mind which is built up by exactitude, we call it the ‘mathematical mind’ (The Absorbent Mind, 17, 169).  Montessori emphasized the importance of this concept in relation to the child’s developing views toward the study of mathematics.  She proposed that the introduction of mathematics during the period of the absorbent mind (0-6 years) enables the child to form positive associations with numbers which can be carried on throughout life.  Montessori expands, “The results we obtain with our little ones contrast oddly with the fact that mathematics is so often held to be a scourge rather than a pleasure in school programs.  Most people have developed ‘mental barriers’ against it.  Yet all is easy if only its roots can be planted in the absorbent mind” (The Absorbent Mind, 17, pg. 170).
The concepts within the mathematical mind do not simply refer to common associations with math such as basic operations.  Instead, Montessori believed that the human tendencies lead one to be mathematical in thought.  That is, basic human tendencies such as order, orientation, exactness, repetition, activity, and manipulation of objects, all lead to the development of a mathematical process of thought.    “The child perceives, without conscious reasoning, patterns of relationships:  things to things, things to people, people to people…The mathematical mind [therefore] is a power to organize, classify and quantify within the context of our life experience” (Helfrich, The Mathematical Mind).  Additionally, Montessori believed that this manifests itself naturally within each person.  For this reason, the study of mathematics should follow a similar organic process and be considered a natural progression of educational growth.   Interestingly, it is no accident that the basic materials of the Sensorial apparatus are based on the quantity of ten.  Likewise, the area of Practical Life nurtures the mathematical mind of the child through its precision and order.  Furthermore, one can surmise that the entirety of the Prepared Environment is a foundation for the mathematical mind of the child.
At a certain point in development, namely the emergence of the sensitive period for numbers, an awakening occurs in the child’s mathematical nature.  “The child spontaneously begins to awaken consciously to the patterns of the world” (Helfrich, The Mathematical Mind).  He graduates form purely sensorial explorations to specific measuring and counting.  Typical questions are “how much?” or “how many?”  The child must attain a certain level of intellectual maturity that cannot be taught, but rather intrinsically absorbed. 

Montessori discovered that a child who could successfully comprehend the numbers one through ten was also capable of working with 100’s and 1000’s at the same level.  Moreover, if a child can count from one to nine, he can just as easily count from ten to 90.  In order to present the material in this manner, 90 simply had to be divided into nine equal parts.  Thus, Montessori developed the ten-bead bar.  Similarly, 100 could be presented in the form of a hundred square, made of ten ten-bead bars.  The 1000 cube was formed by joining ten 100 squares together. 
After developing this material based on the decimal system, children who could count to ten could just as easily count to 2,867 using, for example, two 1000 cubes, eight 100 squares, six tens, and seven ones.
Montessori demonstrated that if a child has access to concrete mathematical equipment in his early years, he can joyfully acquire many facts and skills of arithmetic.  On the other hand, these same skills and facts may require long hours of laborious work if introduced later in abstract forms.  Having observed children’s interest in counting and manipulating objects, Montessori designed concrete materials to represent all types of quantities. The Montessori setting not only enables a child to see the symbol for 1 or 1000, but also allows him to hold the corresponding quantities in his hand.  Later, by combining this equipment, separating it, counting it, and comparing it, he can demonstrate to himself the basic operations of arithmetic.  These activities allow a child to experience the satisfaction of learning through self-discovery.
Montessori’s understanding of the child’s natural inclinations toward mathematics is a guiding principle throughout all areas of the curriculum.  The Montessori materials and curriculum areas further enhance the child’s natural exploration and development within the mathematical mind. During the sensitive period for numbers, the specialized didactic materials allow the child to form concrete impressions of the world of mathematics.  This in turn, allows him to experience mathematics with positive associations while constructing self-knowledge in the subject matter.  The learning, therefore, is truly the child’s own and cultivates the spirit of a life-long love of learning.


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  97. You came here to know how to get ssc result 2020 full marksheet. Wellcome to Lekhapora and the post SSC Result 2020. Here you are going to get some information like: About SSC Result 2020, SSC Result Online, SSC Result SMS, SSC Exam Result, SSC Result with Marksheet. Moreover, you are going to know about SSC Madrasha Board Result 2020.

    SSC Institution Result 2020: EIIN refers to Educational Institute Identification Number. Every school and college has its own EIIN Number. One can get all the information and JSC, SSC & HSC Result by this EIIN Number. If anyone wants to all the SSC results of any school then he/she can try the SSC Result EIIN Method.

    But unfortunately, most of the Muslim children go to general education from their childhood instated of Madrasah education. So, Details of Dakhil Result 2020 is shared below.

    SSC Result Bangladesh is near to the door. It is very important for the students of SSC Exam, Dakhil Exam, and Vocational Examination in 2020. SSC stands for Secondary School Certificate which is the most significant for every student. Though it is the third board exam of a student it still has the most significant on a student’s life. Before the 2013 SSC Exam was the first board exam on a student’s life.

    SSCExmResults.com is significant for who sat for the SSC or Dakhil or Vocational Examination in the year of 2020. In our counry Bangladesh, SSC or Secondary School Certificate examination is hard for a Secondary level students.

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  98. This comment has been removed by the author.

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  99. Hello Friend, Thank you for this outstanding post.
    PSC Result 2020 will be published after few days. If you want to see Full marksheet SSC Result 2020 click here.
    Full Marksheet also can see here at SSC Result 2020
    SSC Result 2020 by SMS

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  100. SSC Result 2020 will publish in the first week in June 2020! That’s Attractive and Great news for all SSC Examinee and Their Guardians. The Secondary Education Board, Bangladesh, Technical Education Board and Madrasa board announced that they’ll publish the SSC Result 2020 as soon as possible and it will be the first week of June. And BTEB SSC Vocational Result 2020 also published now you can check Check BTEB SSC Vocational Result 2020 With Marksheet Download. On the other hand Madrasa board authority also published Check Dakhil Result 2020 Marksheet Download with Number. Check Education Board SSC Result 2020 All Board With Number. You also can check এসএসসি রেজাল্ট ২০২০ Bangla post.

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  101. A large Number of SSC Examine and other People don’t know how to check SSC Result Fast. SSC Result Online Checking system will available on BD Exam Help Official Website, Teletalk SSC Result Website and also on SSC Result 2020 By Mobile SMS. If you are reading this post, don’t worry about checking PSC Exam Result 2019. Here are the complete Information and Guideline about HSC Scholarship Result 2020 of Madrasah Education Board Bangladesh.

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  102. In the world a lots of Muslim people are living. They are Everyday performing salat for the prayer of Allah. From here You can Collect the Rules of Salat/Namaz Porar Niom And we are all aware about that Ramadan month is going to start soon. Here we are also published Ramadan Calendar in Bangladesh 2020. You can also collect Sehri & Ifter schedule 2020 from here.
    People also searching the proper rules of Tarabi Salat for Ramadan Month. They can see all rules of The Regulatory of Tarabi Salat. After finish Ramadan Month we will celebrate Eid day. On that day we will download all wishing things. Just Click here and collect Eid Wish SMS, Image, HD Picture Free Download (New Pic 2020). So wishing everybody and enjoy Eid day with your friends and family.

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  103. SSC Result 2020 has been published by Bangladesh Education Board Authority Today on their Official Website. It also can download with marks from here. Anybody can check their Secondary school Certificate Result from us website. The exam starts on the first week of February, 2020. The exam is arranged by 9 general and One Madrasa and One Technical education boards. This year more than 2.5 million students have taken part in the SSC Exam.
    1. SSC Result 2020 Comilla Board
    2. SSC Result 2020 Barisal Board
    3. SSC Result 2020 Jessore Board
    4. SSC Result 2020 Chittagong Board
    5. SSC Result 2020 Mymensingh Board

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  104. Online is one of the most popular processes to check any Result. In Bangladesh, All public exam result publishes the result online. Additionally, the authority also publishes the result on the alternative process. The SSC Examinee 2020 Can Check their SSC Exam Result 2020 from the Internet (Online). There are too many Online Methods are available to check public Exam result of Bangladesh.
    SSC Result 2020 Dhaka Board
    SSC Dakhil Result 2020
    SSC Result 2020 Chittagong Board
    SSC Result 2020 Rajshahi Board
    SSC Result 2020 Barisal Board

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  105. ALL Education Board SSC Result 2020 has been published by Bangladesh Education Board. The result can be downloaded with marks. Anyone can check their SSC Result from here. The exam starts on February, 01 2020. The exam is conducted by nine general and One Madrasa and One Technical education boards. This year more than 2.5 million students have taken part in the SSC Exam.
    1. SSC Result 2020 Dhaka Board
    2. SSC Result 2020 Rajshahi Board
    3. SSC Result 2020 Sylhet Board
    4. SSC Result 2020 Dinajpur Board

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