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. CCSS math standards are listed here in blue, followed by ambient math suggestions.
Measurement and Data 3.MD
Geometric measurement: understand concepts of area and relate area to multiplication and addition.
6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
7. Relate area to the operations of multiplication and division.
a) Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
b) Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c) Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b plus c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.
d) Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
8. Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
I chose to list and address the rest of the measurement standards in one go because I feel that the application is similar for all. As said in yesterday’s post, a bit of reality goes a long way, and the reality needs to be really real. A fake reality just will not do. One online lesson plan suggested having a group of third graders collaborate in designing a fictional clubhouse. Such ruses are easily seen through and disaffection sets in, making understanding and successful learning elusive if not impossible.
So be real. Design garden plots in shapes that fulfill the requirements of the standards, then build your garden using various units of measurement, first on paper, then for real. Or design a game with a shape that fulfills the standard’s requirements, and draw it with sidewalk chalk on the pavement, then play the game! Cut the required shapes out of fabric and sew a quilt that you and the children will be measuring as you go along.
The possibilities are endless, and it’s vitally important to ground learning in life. A lifelong love of learning is built on just this sort of solid ground. Worksheets, apps, and applets alienate. They remove human interaction from the mix. There may be a fear-driven motivation to consume (most workbooks are termed “consumable”) reams of standards-aligned worksheets to insure that when the questions show up on the high-stakes tests they will be recognized, and answered correctly.
But what lives beyond this sort of fear? Faith. A belief that if the concept is covered globally and holistically, just once or twice, it will stick. And it will translate when the relevant questions appear on the test. Out of such stuff the kind of heroes needed to address the towering challenges awaiting them in this fragile, cliff-hanger of a world are built. Let love and humanity trump fear. Give your children the gift of real things, not virtual, digital, or computerized.
Norman Davidson, Director of Teacher Training at the Waldorf Institute in Spring Valley, NY, summed it up with this. “Go to the library, get what you need to teach the lesson, and then enliven it.” Using the most mundane sources so your teaching is grounded, apply love and creativity to translate lessons into the language your child needs and understands: that of love and beauty.
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 Grade 3 math CCSS and their ambient counterparts.