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 features the Common Core Grade 3 overview in blue, followed by its ambient counterpart as practiced by Waldorf Education and Math By Hand.
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
Understand properties of multiplication and the relationship between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations and identify and explain patterns in arithmetic.
The 4 processes are taught and learned side by side from the very beginning, so a relationship has been established, between and among all 4. Equations are written horizontally at first in Grade 1, as number sentences. Single digits totaling no more than 20 are worked with in addition, subtraction, multiplication, and division. After briefly reviewing the Grade 1 content at the beginning of Grade 2, the horizontal format is changed to vertical, using double digits with no regrouping, in all 4 processes up to 100. Since multiplication and division have been worked with so extensively, their long forms can be taught mid to end of Grade 3. A great emphasis is placed on math patterns in both the Waldorf and Math By Hand curriculums.
Number and Operations in Base Ten
Understand place value.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Place value was taught in Grade 2 using hands-on materials and manipulatives, and used primarily in regrouping with addition and subtraction. Regrouping was also used with short multiplication and division. In mid-Grade 3 the long versions of both are taught with hands-on materials and manipulatives. Multi-digit arithmetic has been performed with regrouping in all 4 processes from mid-Grade 2 on.
Number and Operations – Fractions
Develop understanding of fractions as numbers.
Fractions do not appear until Grade 4 in both the Waldorf and Math By Hand systems, since both place a great emphasis on developmental appropriateness. In the growth process, things need to be broken down and broken apart slowly and carefully. Wholeness is retained in all that’s taught until the child is ready to accommodate the fracturing that occurs with complex, abstract concepts. There’s not a full readiness for abstract learning until age 11 or 12, so teaching must be as concrete as possible until then. Meanwhile, the introduction to abstract learning through reasoning should be gradual and incremental. No rush! Fractions can wait, but foundational lessons can be applied wherever possible.
Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Il’s time! Time and measurement can be taught now in Grade 3, as the child has left the relatively timeless world of childhood to the extent that these concepts can be meaningfully grasped. Both time and measurement are introduced slowly, carefully, and creatively through anecdotal historical stories and lots of hands-on, real, and experiential application. Data can remain informal, through collections and notebook recording (no Excel spreadsheets just yet). Area and perimeter wait until Grade 5. I remember struggling with my daughter over these concepts in Grade 6! We used the kitchen floor tiles as examples again and again. Mastering times tables and other basics is far more important in Grade 3 than forcefully forging ahead to inappropriate and far too advanced subjects. This is just one of Common Core’s mistaken principles, that if advanced concepts are pushed down to lower grades, math proficiency will more likely be achieved. False! This sadly mistaken notion is what’s brought us all-day Kindergartens, with 4 and 5 year olds struggling through hours of worksheet seat work, both at school and at home. Slowing down with generous slices of play all through the grades, while also getting the basics solid, is so key!
Reason with shapes and their attributes.
As has been previously shown, form drawing is more than adequate to address all aspects of this standard. Here’s one example of many Grade 3 form drawings from this Pinterest page.
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.