SYLLABUS OF MONTESSORI THEORY & METHODS UNIT 5 ARITHMETIC & MATHEMATICAL MIND DAY 13 – 14
Pre Home Assignments
Learning Activity 1: Read passage & Meditate (as home assignment): Should read the passages in this unit minimum 3 times. After reading each paragraph, close your eyes & think about the paragraph content in a few minutes.
All students should do all preparations and practices with fullest effort for the live class session too.
Learning Activities for Live Class Session:
Learning Activity 1: Pair talk: Two pupils sit face to face and talk regarding the memories of mathematics class in their school and sharing their experiences regarding various mathematics practices learned from their teachers.
Learning Activity 2: Casual Discussion: Arrange a casual discussion about arithmetic mind in the class by forming trainees into 7 or 8 members groups.
Learning Activity 3: TV Shoot & Interview: Divide trainees into 7 or 8 members group and conduct an Imaginary TV shoot & Interview in a Montessori House of Children by giving roles like, anchor, Montessori directress, student, parent etc. They are asking and telling about the specialties of Mathematics study in Montessori school.
Learning Activity 4: Imaginary Activity practice/ Visualization with closed eyes: Sub: Arithmetic activities in Montessori House of Children by using all five imaginary senses.
Learning Activity 5: Group Discussion: Arrange a Group Discussion like in TV. All students are participating in the discussion.
Round 1: Purpose and objectives of learning and practicing the content in this theory unit
Round 2: How to apply the knowledge and the ideas in this unit in your life, career and in society.
Learning Activity 6: Pair talk: Two pupils sit face to face and talk about their plan and techniques for teaching Mathematics if they get a chance to teach Mathematics in KG or Primary class.
Learning Activity 7: Learning activity as per students’ choice. Conduct a learning activity as per the choice of lesson activities coordinating group.
Self-Home Assignments & with classmates:
Learning Activity 1: Self Speech in front of Mirror: About Learning Mathematics in a Montessori School. Talk about it in 5-10 minutes.
Learning Activity 2: Pair talk: Two pupils sit face to face and talk regarding the memories of mathematics class in their school and sharing their experiences regarding various mathematics practices learned from their teachers. Faculty prepare the list & put it in the group.
Learning Activity 3: Face to face Interview: Two pupils sit face to face like a TV interview. One acts as Dr. Maria Montessori. The other one asks questions to her regarding the Mathematics learning system following in her school, imagining that she is Dr. Maria Montessori. Faculty prepare the list & put it in the group.
Learning Activity 4: Pair talk: Two pupils sit face to face and talk about their plan and techniques for teaching Mathematics if they get a chance to teach Mathematics in KG or Primary class. Faculty prepare the list & put it in the group.
Individual & pair learning activities as Post Home Assignments:
Learning Activity 1: Chart: Write the main concept in arithmetic (12 points) introduced in a Montessori School in a Chart paper in an attractive way.
Learning Activity 2: Talk with school children: Talk with 5 KG or Primary class children near to your house and discuss with them regarding the way of Mathematics teaching in their schools and write that experience in 1 A4 page in your Assignment Book.
Learning Activity 3: Prepare List: Prepare a list of learning activities in 2A 4 pages suitable for preschool children to improve their Arithmetical mind.
Learning Activity 4: Discussion: Discuss briefly about Dr. Montessori’s ideas of teaching mathematics with an English fluent Mathematics teacher of any good school and write that experience in 1 A4 page in your Assignment Book.
Learning Activity 5: Small Project work: Many children face difficulty in studying Mathematics during their school days. Conduct a study regarding this subject and prepare a small project report containing your solutions to solve the difficulties of Mathematics study in not less than 4 A 4 pages in your Assignment book. You can include Dr. Montessori’s ideas in the report.
Mathematics is the head of all sciences. It is part and parcel of our life and therefore very essential. It is an abstract science which makes it possible to evaluate different parts and aspects of things and thus compare with precision the relationship between things and their entities.
Mathematics is a product of man’s intellect. It is not a natural science. As Pascal said “Man’s mind is mathematical by nature. Knowledge and progress comes from accurate observation”. The child is with us before the age of 3. During this period we offer him various concepts, where indirectly we aim at systematic study of mathematics. The capacity to observe, compare and when exerted with aspects like dimensions, shapes and forms of matters, it is referred to as geometry. These aspects are available to our senses that is why geometry is offered to children in the House of Children. Working with the geometrical insets, the Binomial cube etc. help the child to prepare himself for various branches of mathematics.
Comparison of the various qualities can be done with sensorial activities. It may not be precise and accurate. The child is no longer interested or happy with vague expressions. He wants more precise and accurate information and results. The child has the capacity to appreciate the quality of things but he reaches a stage when he needs to take a quantitative point of view. The child is exposed to quantity when he works with sensorial material but the quality aspects are in the forefront. The child has the capacity to appreciate the quality of things. When a child is familiar with the qualitative aspects it is also a quality.
We can offer the child one more quality aspect that is numbers. This will help the child to distinguish how much more and how much less. What the child appreciates sensorial he needs to express precisely. So arithmetic becomes the answer offered according to what he needs, in the manner he needs for the purpose of his self-formation. The relationships, ideas, generations and the concomitant skills are all mathematical in nature and from this fact instruction in arithmetic derives its second aim, namely a mathematical aim.
As the intent of the social aim is to make arithmetic clearly useful to children, just so the intent of mathematical aim is to make it sensible and ready for use. Experience with numbers needs to be meaningful to children. They are to attain the mathematical aim, just as they must be significant to children if they are to attain the social aim. The stage when the child is not happy with just this qualitative phenomenon but becomes exacting or in other words the tendency for accuracy and precision is observed and we call it the awakening of the ‘Mathematical Mind’. The need for arithmetic is clearly expressed. The child is no longer happy with vague expressions. He must have a very clear knowledge of quantity. This is when we offer arithmetic to the child’s hands and senses. That is, activities the child can work as quantitative aspects of all the things he sees. Offering arithmetic to the child’s hands and senses is what Dr. Montessori calls “Psycho Arithmetic”. Psycho arithmetic helps the child to understand the basic concepts of Arithmetic and also look at the world from a different point of view and apply the concepts in his everyday life. Unlike the exercise of practical life and sensorial activities, the child is offered a different concept.
In arithmetic the child is taken into a land of abstractions which are not familiar to him. He may have heard the names of the numbers but may not know what it really means. Hence we take the child step by step like every time he uses the unit he should know what to and how to internalize. At such an early age he needs to use his intelligence. Every area of knowledge we have has some basis. Written arithmetic becomes the basis element. Without the knowledge of arithmetic we will not be able to understand the other branches of mathematics and also the branches of science like physics, chemistry, cooking, astronomy, astrology etc. Every field requires arithmetic. Arithmetic is a very important aspect of human life and the basis of every area of learning. Every area of knowledge has some basis. Written Arithmetic becomes the basis element.
Counting is the basis of arithmetic. Finding out how many units we have in a quantity is counting. Quantity is something we can count, something that can be perceived as the sensorial of a unit. It is the very first step we have as well as intellectually. What to count is the concept of a unit. It is the very first step we have to take if we have to count. Having a concept of the units alone is not enough. We need numbers. We offer the child the numbers 1 – 10, their names and also their relationship to the unit or quantity. We also need to offer him the symbols for writing. Numbers 1 – 10 are offered to the child because 10 is the base for the decimal system of numeration. We need to give the child all he needs to know regarding the numbers from 1 – 10.
The significance of Zero as a symbol, the mutual relationship between the units and the rest of the numbers and also the mutual relationship between numbers. Some mathematical concepts are given below:
A ‘mathematical mind’ is a special merit and ability in children. It is a clear sign of intelligence. It is manifested in children in various ways; the Directress should take advantage of it. Children show the innate tendency for exactness. They need to do calculations in favor of precision. They have a passionate love for order. Most children have the spirit of enquiry, objective observation. They arrive at tentative conclusions.
If the Directress provides more opportunities to the child to perform activities precisely, he will benefit more, and he will strengthen his aptitude for precision and exactness. The Montessori Apparatus and the method take cognizance of difficulties one may face in understanding the whole process, and help the child surmount them at his pace and joyfully so. When the child crosses all his difficulties confidently, arithmetic ceases to be a bugbear. The final result is that the knowledge of shapes and colors, weights and dimensions, smells and tastes become orderly and classified.
The main concepts in arithmetic introduced in a Montessori School are following:
• Determination of a Unit
• Relationship between names and quantities.
• Relationship between names and symbols.
• The association of quantities and symbols via the names.
• Arithmetic of variables and arithmetic of groups.
• The concepts of Zero as absence of quantities and as part of numbers when written.
• The succession of the natural numbers.
• The relationship of the unit with other numbers up to ten.
• The mutual relationship of the numbers above one to ten.
• The four arithmetical operations.
• The steps leading the child to abstraction.
• The laws of the decimal system.
Edited & his Methodology applied by: Baba Alexander, New Delhi