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 post will feature the next Grade 2 Common Core Math Standard listed in blue, followed by its ambient counterpart as practiced by Waldorf Education and Math By Hand.
Number and Operations in Base Ten 2.NBT
Use place value understanding and properties of operations to add and subtract.
7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
The Math By Hand place value materials and methods thoroughly cover this standard. As stated in yesterday’s post, numbers reach into the several thousands using three- and four-digits. Another huge advantage is that the 4 processes are worked with side-by-side, which among other things allows greater opportunities for exploring the relationships between all 4.
The concrete models used are two sets of color-coded columns, one for table top and one for floor use. The table top set is paired with a beans bank: 3 pouches holding 3 kinds of beans, color-coded with the columns. The red pouch holds black beans and goes with the red ones column. The yellow pouch holds kidney beans and is matched with the tens column. The blue pouch holds lima beans and goes with the hundreds column.
Beans are cashed in when they go over 10 in the ones column or over 100 in the tens column (10 black beans are cashed in for 1 kidney bean, while 10 kidney beans are cashed in for 1 lima bean). Thus the process of composing and decomposing is experiential, using concrete models to make abstract concepts doable and understandable for 7-8 year olds. The beans can be easily translated to coins, using pennies, dimes, and silver dollars.
After the table top columns are used for some time, focus switches to the floor columns, which include the thousands place. For these, five large index card number sets of the numbers 0-9 are created beforehand and kept handy in stacks. Smaller carrying/borrowing number cards are created as well. The addition or subtraction problem is written on the board or large paper then it is transposed to the columns using the large cards. Each column is added or subtracted, and if there’s a regrouping number, it’s physically jumped to the top of the next column.
After the floor columns have been used for some time, practice in all 4 processes resumes, now including regrouping. Numbers can be quite large, up into the several thousands, now that the regrouping skill has been mastered. Because long multiplication and division are not taught until Grade 3 however, these problems are kept to their short forms for now, with three- or four-digit numbers multiplied or divided by times tables up to 12. See below for examples of this as well as explorations of 4 processes’ inverse relationships.
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 Common Core, and its ambient, Waldorf/Math By Hand counterpart.