Mathematical Arts: Geometry
Geometry holds a central place in Waldorf education’s mathematics curriculum and emerges out of form drawing which students begin in Kindergarten. In sixth grade, students move from creating flat two-dimensional geometric designs to kinesthetic art with curve stitching, which creates circles and curves from straight lines. They are colorful and beautiful and very visually interesting but do you wonder what they have to do with math?
Artistic, but also Technical
In order to construct and shade those drawings or string designs, the students need to have learned many things, including a knowledge and understanding of circles and polygons, how to use a compass and ruler with competence, and how to bisect an arc or a line or an angle. The students learn how to construct straight lines from a curved line by drawing exact polygons within a circle as they learn how to divide a circle into 2, 3, 4, 5, 6, 8, 10, 12, 16, and 24 divisions. Line and string designs show them the many ways that curved lines can be constructed from straight lines. The drawings done in sixth grade represent foundational Geometric concepts, presented beautifully and artistically, that are carried into the high school when students learn about Conic Sections, Trigonometry and Projective Geometry.
Engaging the Hands Creates a Deeper Understanding
Use of string art in learning geometry is a powerful method to ‘experience’ the facts and laws of geometric forms. The precision and beauty of these geometric forms lead the children to a deeper understanding of mathematics as they use their hands to illustrate concepts and develop skills.
These constructions offer abundant opportunity for students to learn mathematical vocabulary and concepts, and the ability to follow directions. String designs helps to improve spatial perception, encourages students to experiment, enriches their learning and lays a foundation for advanced Projective Geometry and the three-dimensional graphs and surfaces encountered in Calculus in high school and college.
The brain discovers what the fingers explore.
In sixth grade, geometrical rules are sought and formulated:
Geometrical proof of sums of angles of triangles
Construction of angles using compasses, bisecting angles
Congruent triangles and the four principle cases for congruency
Movement properties of triangles and quadrilaterals
Congruent shapes, construction of similar angles, complementary, supplementary and other angles
Construction of triangles, with altitudes, and angle and side bisectors
Why We Teach This Way Matters