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.
The CCSS Standards for Mathematical Practice are meant to be used throughout the year, applied to all lessons and skills practices. The wording is pretty dense and unapproachable, certainly not child friendly and possibly not even teacher friendly. There have been attempts at translation, but the examples I’ve seen still tend to be somewhat dry. Here’s my attempt, with a Grade 4 focus and a Waldorf lens. The CCSS standards are in blue, followed by their ambient counterparts.
1. Make sense of problems and persevere in solving them.
Mathematically proficient students in grade 4 know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.
Math is the underpinning of all life. By nature it likes to remain hidden, as a mystery that’s all the more compelling when discovered. Children understand this instinctively, much more than we as adults do, with our more empirical mindsets. From this perspective, math in a Waldorf fourth grade takes a back seat to the rich tapestry of ever-expanding subjects and activities that fill each day. But from that back seat, it presents itself beautifully as the universal bottom line. The meaning of a problem may be expressed through many practical examples such as mapping the neighborhood, sketching a cross stitch pattern on graph paper, noting and comparing animal characteristics, etc. Discussing how a problem was solved takes a back seat to the process and the finished product. Besides which, discussion is antithetical at this age, which is a few years shy of being comfortably conversant with logic and reasoning. A fourth grader’s main lesson book drawing of a compass rose, from the blog mud between our toes, is a freehand geometric 8-point construction that takes a back seat to orienting a hand-drawn neighborhood map.
2. Reason abstractly and quantitatively.
Mathematically proficient fourth graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.
A Waldorf fourth grade student would have mastered this concept in first grade. Math By Hand introduces the Roman and then the Arabic numerals in depth, in the first Grade 1 math block. The abstract nature of the numbers we use is circumvented by the imaginative, pictorial, and historical treatment of the numbers as symbols. Introduce and extend whole number understanding to fractions with the Math By Hand clay plaque, shown below. The Math By Hand Grade 2 place value block teaches the meaning of 1’s, 10’s, 100’s, and 1,000’s and their relationship to each other, in depth, including estimation and rounding.
3. Construct viable arguments and critique the reasoning of others.
In fourth grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain their thinking and make connections between models and equations. They refine their mathematical communication skills as they participate in mathematical discussions that the teacher facilities by asking questions such as “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
A fourth grade local geography mapmaking project would be an ideal application here. Students literally construct arguments by working together and combining ideas and solutions as the project proceeds. Having seen Common Core videos of classroom scenarios where this is put into practice, the teacher’s questioning as listed above often takes on an artificial tone. If however, the explanation of and responses to thinking occur in a project context, i.e., through the modification of techniques, measurements, and specifications, the resulting teaching and learning is much more effective and successful. For example, a relief map of California could be started on a grid as a scaled up version of a smaller, gridded map. Math practice (and even new concepts) could be embedded in this project.
4. Model with mathematics.
Mathematically proficient fourth grade students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make sense.
Waldorf students experience this sort of broad, varied approach to math from first grade on. Flexibility of thinking is paramount to math success, and it gets off to a flying start as the 4 processes are introduced side by side in first grade. In both the Waldorf and Math By Hand systems, students and teachers alike experience a full spectrum of math expression.
Waldorf handwork is one of the best practical examples of experiencing math principles. For all who practice it regularly, knitting or crocheting engenders the best of math practice, by casting on and off, counting stitches, and creating geometric patterns. Most importantly, it stimulates neuron health and balance in the right and left brain, while enhancing eye hand coordination, by the repetitive and detailed use of the right and left hands. And all children most decidedly thrive on it. Here’s an idea that includes handwork, math, and community: a granny square blanket group project!
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 the last of the Grade 3 CCSS math standards and their ambient counterparts.
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