A Year in the Life: Ambient Math Wins the Race to the Top!
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. Today’s standard will be listed in blue, followed by its ambient counterpart.
Reason with shapes and their attributes.
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Form drawing! It fills the bill nicely. With the exception of the beginning and end, this standard is totally appropriate for Grade 2 (beginning with “reason” and ending with “cubes”). At this age, foundations are built for future learning, with an eye toward the concrete rather than the abstract. And since reasoning is by nature abstract, it doesn’t fit.
Cubes are a whole different genre than flat, 2 dimensional shapes. The latter is nicely addressed with form drawing, but drawing 3-dimensional shapes needs to come later. A playful approach to solid geometric forms could continue. Math By Hand offers materials to make a cube ball (see below). Similar 3-dimensional shapes could be sewn, sculpted, or knitted. But technically correct, 3-dimensional geometric drawings are way too complex for now.
Math By Hand offers a comprehensive progression of form drawings through the grades. The collection of 16 drawings for each of the grades 1-4 is included in a book with grade level stories. See this slideshow overview of the Stories / Form Drawing books.
Form drawing could be taught in a block of one to three weeks at the beginning of the year and brought back as a main lesson once a week. It’s a valuable discipline for many reasons, including building confidence, flexibility, and creativity.
See below for examples of a triangle, quadrilateral, hexagon, and pentagon/gram, all associated with numbers and fairy tales in the Math By Hand / Grade 1 / Quality of Numbers block. The exposure through form drawing to varied geometric forms begins in Grade 1 and continues, becoming more complex with each grade, until formal geometry in Grade 6.
As always, it’s movement, story, art and playfulness that win the math day! Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.