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
Solve problems involving measurement and estimations of intervals of time, liquid volumes, and masses of objects.
1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
There’s that number line again. From the last blog post, “As for the number line, waiting until the full picture (negative numbers, the concept of zero, and the 4 processes on the number line) can be introduced is optimal.” Math By Hand introduces the number line with all of its complex concepts at the end of Grade 4. Partial work with it before then is counter-productive since it cannot be correctly understood without zero holding the middle, positive numbers to the right, negative numbers to the left, and a basic outline of how the numbers interact on it, within the 4 processes.
Time is one of our most engaging and pervasive every-day mysteries. Einstein certainly thought so, and pondering its nature resulted in some of his best work. Time should not be taught as minutes on a clock face or digital dial without first honoring its biography: how did it come to be and what words and elements form its essence? This can and should be related in an anecdotal manner, with generous doses of humor and wonderment. Here is an excerpt from the Math By Hand Grade 3 binder:
A good place to start is with the history of timekeeping and timepieces. Simply noting natural units of time measurement, made apparent by the sun and moon, could be the first reference. Then, going on from there, note the many different ways of measuring these units. In ancient Rome, priests announced the first day of the month with the appearance of the new moon. The Romans called this first day of the month Kalends from their word calare or “to proclaim.” This is where our word calendar comes from. The word clock is more direct, taken from the Latin word clocca or “bell,” since bells were the first means of announcing the time or marking the hours. And storytelling, as always, is the best cloak to wrap around these facts or anecdotes.
The teacher should research and learn these facts then present them in story form. Rather than going directly to the concept of the modern clock, which can be complex and dry, time should be presented as it evolved. Constructing a sun dial would be a wonderful hands-on project, tying time to the sun where it originated and making it more concrete than abstract. Examples of and instructions for making sun dials can be found at the library or online.
This one would be fairly easy to construct, using any variety of materials, and illustrates the morning and afternoon path of the sun. The hours are 6 to noon in the morning on the left, and noon to 6 in the afternoon on the right. Increments for the quarter and half hour could be indicated as well. No better foundation for learning about time exists than a child making a sundial like this, before moving on to navigating time in minutes.
Problems taken from real life are far better than abstract word problems, which can be boring at best and even worse, alienating and ineffective. Some examples of real-life time problems would be, “Let’s time how long it takes us to plant one row of carrots, then multiply that by the 5 rows we’re planting. Then let’s compare that to how long it takes us to mulch one row of strawberries times the 4 rows we’ve planted. We can then record all that information on the garden graphs we’re keeping.”
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.