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. Before moving on to the four pairs of Mathematical Practice Standards, I’d like to take some time today to highlight the three principles that form the foundation of the CA CCSSM. These three principles will appear in blue, and their suggested ambient counterparts will follow.
1. Focus. Means that instruction should focus deeply on only those concepts that are emphasized in the standards so that students can gain strong foundational conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the mathematics they know to solve problems inside and outside the mathematics classroom.
Rudolf Steiner, the founder of Waldorf Education, said, “Receive the children with reverence, educate them with love, and send them forth in freedom.” Freedom is the hallmark of a true education, and it cannot find a place in the current strictures that demand the narrow focus stated above. These demands on teachers, parents, and children alike, strangle the flexibility and creativity that enables great teaching and learning. Faith and trust are implicit in a system that honors its teachers’ (and parents’ and children’s for that matter) judgment and ability to excel, employing the dynamic, exciting ideas that flower from a free and creative approach.
Cross curricular teaching and learning, in vogue at one time, seems to be frowned upon in light of the fact that “instruction must focus deeply on only those concepts that are emphasized in the standards.” the Waldorf method of introducing the numbers 1-12 in a personal way in the first grade via connections with a unique fairy tale and a geometric form for each one surely violates this idea of focus. But at the same time, an alternative sort of focus can enable an entirely different kind of depth, one that is multi-faceted, sparking a comfortable familiarity and confidence with numbers and math.
2. Coherence. Arises from mathematical connections. Some of the connections in the standards knit topics together at a single grade level. Most connections are vertical, as the standards support a progression of increasing knowledge, skill, and sophistication across the grades.
This concept resonates with the “spiral” method employed in most Waldorf schools. And this is a good, since it builds confidence and meaning. For instance, factors could be introduced very early on, colorfully and with a supporting story that goes something like this, “The King of Numbers is 12. It’s rich with many jewels. But 13 is poor!” An illustration shows 12’s factors (1, 2, 3, 4, 6, and 12) contrasted with 13’s factors (1 and 13). The story and image serve as anchors for the concept, and when factoring repeatedly returns, vertically with increasing knowledge, skill, and sophistication, it’s met with confidence and readiness. I would though, expand this to include connections across the curriculum with language, art, games and movement, in a much more concrete and much less abstract mode.
3. Rigor. Requires that conceptual understanding, procedural skill and fluency, and application be approached with equal intensity.
Rigor does not seem like a good thing in the early grades. I found three definitions for rigor in my little Mac dictionary: 1. strictness, severity, stringency, toughness, rigidity, inflexibility, intransigence. 2. meticulousness, thoroughness, carefulness, diligence, scrupulousness, exactness, exactitude, precision, accuracy, correctness, strictness. 3. hardship, harshness, severity, adversity; ordeal, misery trial; discomfort, inconvenience, privation. I am sure that #2 is the one espoused by the Common Core Standards. But I am uncomfortable with the fact that #’s 1 and 3 definitions are so close to #2’s. And if you look closely at #’s 1 and 3, you will notice a resemblance to a lot of the distress and disagreement coming forward from teachers, parents, and children in regard to teaching to these standards and then applying the accompanying difficult and rigorous tests.
As for the idea that an equal emphasis be placed on these three: understanding, skills and fluency, and application, it seems this balance would come about spontaneously with a method that embraces enthusiasm for the subject. Allow me an example from one of my Waldorf second graders. We had just experienced (with lots of lively movement, fun, and color) the patterns that the tables from 1-10 make on a 10 circle. The children were so surprised by and excited about the unusual patterns that occur on the circle, that many of them carried the idea home and created visual images of it. One boy brought in a very large paper with all of the patterns superimposed in different colors. His enthusiasm enabled all three of the above, without any special effort on my (or his) part. It flowed, and that’s what story, art, and movement will bring to math, every time.
In closing, a couple stories re the Common Core. Today I talked to a grandparent about her grandson’s parents’ choice of schools. She said that they were considering a new school that was rated 9 out of 10 based on test scores. However, they love his current school which is only rated 3 out of 10, again based on test scores. She added that when parents were asked to rate their schools using a 5-star system, the schools that ranked the highest happened to have the lowest test scores. What does this say, and shouldn’t we be listening?
Google delivers ads for things it thinks we want, on the sidebars of its web pages. I saw one today that said “Common Core Curriculum for Grade 2.” So I explored the site and found that the curriculum was all digital, applicable only to iPads, Android tablets, etc., strictly structured on standards content, and that it claimed to be engaging and interesting. (I question this about any activity if all it requires is staring at a screen and moving only your right index finger to click the mouse.) On checking some of the lesson samples, I found the pages were bare fact based, multiple choice, and with a robotic, computer voice over. I connected this with something President Obama is advocating, that all schools will be wired in the near future, and came up with this image. A roomful of 7-8 year olds sitting at their desks, each plugged into his/her own tablet with earphones, all day. No teacher needed . . . yikes!
Please remember that 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. On to Kindergarten Mathematical Practice Standards tomorrow!