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 blog will focus on a, b, and c of the fourth Kindergarten standard in Counting and Cardinality. Note that the Common Core Standards will appear in blue, followed by an ambient translation.
Counting and Cardinality K.CC
Count to tell the number of objects.
4. Understand the relationship between numbers and quantities; connect counting to cardinality.
a) When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
b) Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
c) Understand that each successive number name refers to a quantity that is one larger.
I must say that I’m having a bit of a brain freeze here. This is so intricately worded that it’s challenging for me to unravel and translate into kindergartenese. I would venture to guess that there is some of the same challenge as teachers and students alike attempt to hone each standard into a practical, workable format.
Ok, let’s see. Cardinality in number tells quantity or how many. Simple enough, but sorting that concept out from assigning each of the counting numbers its own name and identity is tricky. Disclaimer: as said earlier, until first grade a less intellectual or abstract approach is best. So better to keep it as concrete as possible.
The Math By Hand system uses beans for value coding ones, tens, and hundreds to teach place value in second grade. Black beans are ones, kidney beans are tens, and lima beans are hundreds. Without becoming too abstract, it may be possible to teach these standards’ concepts using the beans. Here’s the thought:
You’ll need black beans, kidney beans, and 20 small glass jars or clear plastic containers. For the first 10 jars, place 1 black bean in jar one, 2 in jar two, and so on up to 9 in jar nine. Place 1 kidney bean in jar ten, 1 kidney and 1 black bean in jar eleven, and so on up to jar nineteen. Place 2 kidney beans in jar twenty.
No need to label the jars with their numbers, since the number of beans inside says which each jar is. This builds a wonderful foundation for understanding place value as well, without getting too abstract. The jars themselves represent the number of objects, and the beans inside tell which is which. Now, you can line the jars up in order to see that each successive number name refers to a quantity that is larger, and if you mix jars one to five (for example) out of counting order, it’s plain that they can still be counted as 5 jars.
There’s a bit more of a Montessori than a Waldorf feel to this activity, but I like that sort of eclectic approach. That may be why, even though I taught in a Waldorf classroom, at heart I favor a more inclusive, blended method. And I do believe Waldorf homeschooling is an excellent venue for doing just that!
Always remember that 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. More Kindergarten tomorrow!