Davis Waldorf School
Curriculum

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Mathematics Curriculum
Before formal arithmetic study begins in the grades, the child's first experiences with order and rhythm are based in daily, weekly and monthly rhythms. Songs, poems, verses and repeated stories also give the child a sense for order and structure.

Early arithmetic is focused on understanding the quality of the numbers and counting. First the child experiences one-to-one correspondence when learning to count their fingers and toes and then learning to count to 100. While the children are learning to do this, they also begin rhythmical work with clapping, stepping, jumping and so on.
 
In first grade, the number study begins with the whole, the divine unity out of which all other numbers are born. Working from the whole to the parts has a salutary effect on the children's soul development. The quality of the numbers one through twelve is explored, based always in the children's experience of themselves and their natural surroundings. "Oneness" is the whole self; "Twoness" is demonstrated through having two hands, or two feet, or two eyes while "Threeness" is the upper arm, lower arm and hand, for example. Roman numerals are often initially taught, as they are closer to the bodily experience of the number than the Arabic numerals, though the Arabic numerals are introduced early in the year. Mathematical operations are introduced imaginatively, with the "feeling" of each operation given character and humanity: "Polly Plus" is always collecting things, "Mister Minus" loses or gives things away, "Tara Times" likes to add groups of things very quickly, while "Daniel Divide" shares things evenly with everyone, and "Queen Equalus" makes sure that what happens over here has the same effect as what happens over there (2 + 3 = 1 + 4). The name of the character may change, but the inherent quality of the character's operation does not. Actual figuring is done initially with manipulatives. The children solve the problem and then learn to write the equation that represents it. Rhythmical counting activities combined with active movement reinforce the learning of the counting sequences, and the sequences for the one, two, five, and ten tables are learned. Other sequences may be learned as well. Place value for individual units, tens and hundreds is explored, with the zero not representing emptiness, but instead is a sack in which the first nine numerals are contained. Additionally, an incipient sense of geometry is awakened through form drawing.

In second grade, intensive practice continues with counting sequences and full times tables, structured from the whole to the parts and back to the whole (10 is 2 x 5, 2 x 5 is 10). Practice in solving problems and writing the equations that represent them continues. A change is made from writing equations for all four processes horizontally to vertically. Carrying and borrowing is explored. Place value is expanded, possibly as far as the millions place. A basic sense of geometry emerges through the balance of above and below, or right and left, in form drawing.

In third grade, arithmetic remains connected to the practical things in life. Main lesson subjects provide excellent opportunities to explore measurement of American units of length, weight, and volume. Time is a key concept and the children practice using clocks and calculating times. The basic units of American coin and paper currency are learned and often explored through a fun "store" activity. Constant practice with the times and division tables continues, and place value is expanded at least to the billions. Two and three digit numbers multiplied or divided by one or two digit numbers are practiced. Finding balance across four quadrants or inner and outer forms is explored through increasingly complex form drawings.

The fourth grade curriculum reflects the changing consciousness of the children as they begin to see the world in a more compartmentalized way. The goal is that, by the end of fifth grade, the children will be able to "move among whole numbers, fractions and decimal fractions, doing calculations freely and easily."[1] Every child must have the times tables completely memorized out of order so that this freedom to move among the numbers may happen. Factoring is developed out of the work with the times tables. Through concrete experiences, wholes are broken into fractions and built up again, and fractions are expanded and contracted. Calculations using the four processes with fractions are practiced. Area and perimeter are introduced using familiar places and objects in the children's environment. Estimation, rounding, and finding averages are explored. Complicated interweaving forms are drawn in form drawing, enhancing the children's "development of the feeling for space in order that the children's capacity for feeling and mental picturing be trained."[2] In the later middle school years, the children will be asked to mentally picture and rotate geometric figures, a capacity based on the early work with form drawing in the first three years of school. "Thus, geometry brings the transition from what begins with taking up forms and space through the will to describing and understanding through thinking that which is observed."[3] Beginning with the lawful relationships inherent in numbers found in the human body and in nature and moving ever onward toward sense-free thinking, the math curriculum develops flexible and independent thinking. Moral development is supported by the lawful, exact quality of numbers, and the repeated discovery that there are many ways to come up with a correct answer. Abundant opportunities to physically engage with mathematical ideas are woven throughout the curriculum. Opportunities to experience spatial thinking through form drawing exercises commence on the first day of first grade and continue regularly throughout the lower school years. These ultimately lead to formal geometric drawing and visual proofs of ideas.


[1] Steiner, Rudolf. Discussions with Teachers. Barrington, MA: Anthroposophic Press, 1997. Pg. 57.
[2] Kellman, Staley and Schmitt-Stegman 60
[3] Kellman, Staley and Schmitt-Stegman 60

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