xMath :: 69 
xTable of Contents: 

xIntroduction to the Decimal System 
'Our aim is not only to make the child understand, and still less to force him to memorize, but so to touch his imagination as to enthuse him to his innermost core.' With the first mathematics materials the child is introduced to the numbers one through ten. The materials that follow will develop the concept of the decimal system, that is, a numerical system based on ten. Maria Montessori called the decimal system the "cell of our system." To understand the decimal system is not easy for a child. It took humans many years to realize that the value of a numeral is dependent on the position it occupies. It was much later that the concept of zero was developed, and even later that the decimal point came into existence. Our decimal system (base 10) has nine numerals, one through nine. The presence of one or more zeroes allows us to create numbers beyond nine up to infinity. Thus, learning the numbers one through nine and their numerals, in addition to the concept of zero, is the only truly difficult part for the child. This he has already accomplished. Counting experiences (adding one more) up to 10 have preceded; now the child will learn to count beyond 10. In the hierarchical ordersones, tens, and hundreds of the simple class; ones, tens, and hundreds of thousands, and so on there are nine units: one through nine. No matter in which hierarchy the numeral one appears, the absolute value of one is one. The relative value depends on its position. The limit between one hierarchical order lies in the 'secret of ten' and in the exact value of the numerals one through nine. It is necessary that the child fixes in his mind the concept of the hierarchical orders and their values. The materials that follow enable the child to avoid the confusion and difficulties he may otherwise encounter. [top] 
xThe Great Lesson 
Prepare a broadly engaging, impressionistic story of the history of Mathematics. Card materials, timelines, and captivating stories will engage the child when offered with tales of early humans and their efforts to measure and quantify their universe. Explore early symbols of numeration, the history of 'zero', and prehistoric calendars. Study the precision of the Great Pyramids of Egypt. Delve into the navigation techniques of the ancient polynesians. Pursue this information enthusiastically and your students will become enthused, as well. Present this work graciously, and your students will express grace in their own studies. Their understanding of arithmetic within the context of human progress will grow. This understanding of how arithmetic evolved, and continues to evolve today, will inform an appropriate awe of our 'language of numbers'. Continue your 'Great Lesson' throughout the years, through attention to technology & current events and an ongoing expressed passion for the measurement of our world. This passion is a 'Fundamental Need', a common thread across cultures that ties humanity together. [top] 
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