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. As promised yesterday, this post will attempt to review and amplify (or ambientify) the Eight Common Core Standards for Mathematical Practice.
As stated in the California Common Core State Standards: Mathematics, “The CA CCSSM include two types of standards: Eight Mathematical Practice Standards (identical for each grade level, and Mathematical Content Standards (different at each grade level). Together these standards address both ‘habits of mind’ that students should develop to foster mathematical understanding, and expertise and skills and knowledge – what students need to know and be able to do.”
The CA CCSSM goes on to say that “The mathematical content standards were built on progressions of topics across grade levels, informed by both research on children’s cognitive development and by the logical structure of mathematics.” Most likely the Common Core research did not include Waldorf Education’s methodology and pedagogy. And that’s a very significant omit. Because it illuminates areas of consideration in child development that go beyond the merely scientific, the Waldorf philosophy presents the case for later learning and the need to ensconce all subjects, but most especially math, in the arts while also embedding them in lively physical movement.
If we proceed on the premise that these two elements (later learning and art as well as play/movement integration) are essential, then it’s incumbent upon us to hold the light of this premise to the Common Core and see what it reveals. According to the CA CCSSM, “The MP standards are not a checklist; they are the basis of mathematics instruction and learning. Structuring the MP standards can help educators recognize opportunities for students to engage with mathematics in grade-appropriate ways.”
Here are the Eight Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason Abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
These eight are further broken down into four categories:
1 & 6 = Overarching habits of mind of a productive mathematical thinker.
2 & 3 = Reasoning and explaining.
4 & 5 = Modeling and using tools.
7 & 8 = Seeing structure and generalizing.
It seems working with the four pairs of standards would be most effective, so the focus will be on them for the next four days. Allow me to reprint what appeared in this blog on Day 1, re the focus of the Common Core. I believe that the “back door” or indirect approach is a very effective teaching tool, especially with math. Most children will happily and eagerly take on any task presented in a friendly, warm, and meaningful way. The Race to the Top, as espoused by the Common Core Standards, is a most direct approach. This approach does not translate well, whether in the classroom or homeschool environment.
As Viktor E. Frankl says in Man’s Search for Meaning, “Don’t aim at success. The more you aim at it and make it a target, the more you are going to miss it. For success, like happiness, cannot be pursued; it must ensue, and it only does so as the unintended side effect of one’s personal dedication to a cause greater than oneself or as the by-product of one’s surrender to a person other than oneself . . .” In light of this, 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.
Tomorrow, Kindergarten Mathematical Practice Standards!