 A Year in the Life: Ambient Math Wins the Race to the Top!
Day 278

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.” Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. The CCSS math standards are listed here in blue followed by their ambient counterparts.

Measurement and Data 4.MD
Geometric measurement: understand concepts of angle and measure angles.
5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
a) An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
b) An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Geometry 4.G
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

In a word (or two): developmentally inappropriate.  Rather, it should be “sufficient unto the day” for your fourth grader to make reasonable strides in math within a sensible and methodical framework that includes mastery of the following concepts and skills: times tables, factoring, prime numbers, as well as fractions, decimals and the number line with positive and negative integers (including whole numbers, fractions, and decimals) applying 4 processes’ rules to all of the above, and a first look into beginning algebra.  All of this is included in both the Waldorf and Math By Hand Grade 4 curriculums.

The Common Core begins its harmful, abusive overreach in Pre-K and Kindergarden, and it continues to do so up through all of the lower school grades.  Waldorf covers geometry indirectly through form drawing until Grade 6 when it is formally studied, with instruments.  Children cannot be rushed into logic, reason, and abstract thinking before they are ready to make that leap.  This does not preclude building a solid foundation, however.  Which is exactly what form drawing does for geometry.  The posts over the next few days will be focused on form drawing.

Here is a youtube video of a brave New York State teacher who stood up for her sixth grade students against the Common Core’s developmentally inappropriate testing and teaching to the tests.  See below for another spectacular Grade 4 chalkboard form drawing from Catie Johnson’s page.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal.  Tune in tomorrow for more on form drawing in Waldorf and Math By Hand. 