According to Mercedes K. Schneider (Common Core Dilemma), "Common Core is the nucleus for test-driven reform." She says that Phil Daro, William McCallum, and Jason Zimba were the leading writers of the math standards, and that all three were or became part of Student Achievement Partners (SAP). The core mission of SAP is to help teachers implement Common Core. In short, Common Core is SAP's bread and butter. Also, contrary to popular belief, classroom teachers were not in decision making roles in Common Core, says Schnieder. More later. Read Common Core Dilemma.
[Note. This is a random collection of compelling and/or often contrary cogitations regarding Common Core and education: December 2014 to July 2015.]
Richard Feynman used to say that you don't understand anything until practiced. Even then, your "understanding" could be minimal not only because "understanding" is an indeterminate idea that is difficult to measure, but also because "understanding" develops slowly over years of study. Incidentally, "understanding" does not produce mastery; practice does! Furthermore, kids should not calculate single-digit number facts, they should memorize them starting in 1st grade, so they stick in long-term memory. If we want to jumpstart kids in math then they need to be taught traditional arithmetic starting in 1st grade--not Common Core test-driven reform math. Furthermore, we must kick out accountability testing.
The test-based NCLB law failed. In many schools, the curriculum focuses too much on test-prep. (If it is not in Common Core, then skip it.) Sadly, the government keeps funding its own failures--from Head Start, to Title 1, to NCLB, etc. Common Core is a political narrative, not an education narrative. Common Core is intrinsically linked to test-based reform (NCLB), which, in my opinion, downgrades children to numbers [test scores]. A child is not a data point. The main assumption under NCLB was that test-based reforms would work with consequences built in (sanctions and punishments). The fundamental assumption was wrong.
Walk into most any elementary school classroom and you will find students with a wide range of ability and achievement--fast and slow learners together. For decades the elementary school classroom is like the old, inefficient one-room schoolhouse. The status-quo solution has been differentiated instruction within the same classroom (more inefficiency), but the best solution is common sense, that of putting faster learners together (tracking) with an accelerated, challenging math curriculum. ["Oh, we can't do that." It goes against the progressive ideology of fairness. But, what's fair about holding our best students back?] Common Core means that everyone gets the same, which is like the old inefficient one-room schoolhouse. The caveat is that kids are not the same. Putting high achievers in math and low achievers in the same math classroom has been a recipe for underachievement and a regression to mediocrity. The kids who learn math faster get bored and the kids who struggle stay behind. In my view, mainstreaming [inclusion] for math class has led to underperformance at all levels. In short, the system of heterogeneous classes for math is deeply flawed. Moreover, the Common Core standards, themselves, are flawed, especially when the curriculum distilled from them is taught as reform math. Starting in 1st grade, we should arrange kids into homogeneous math sections by achievement [knowledge] with different teachers. Don't worry about their self-esteem. Worry about their competency!
“[At a conference] The subgroup I was in was supposed to discuss the ethics of equality in education,” writes Richard Feynman (Surely You’re Joking, Mr. Feynman!). He writes, “In education you increase differences. If someone’s good at something, you try to develop his ability, which results in differences, or inequalities. So if education increases inequality, is this ethical?” Feynman is right. A good education should increase differences and inequalities, but the contemporary education mind-set seems narrowly focused on closing gaps, not boosting individual achievement.
Our schools slow down the learning and achievement of many bright children, including minority students. Several elementary school teachers told me that they were glad I gave algebra lessons to their self-contained classes because they didn’t know what to do with the brighter kids. For example, in my 3rd, 4th, and 5th grade classes, I used an idea from mathematician Ian Stewart to show that division by zero results in a counterexample. Ian Stewart (In Pursuit of the Unknown) writes, “Division by zero is not an acceptable operation in arithmetic, because it has no unambiguous meaning. For example, 0 x 1 = 0 x 2 [true], since both are 0, but if we divided both sides of this equation by 0, we get 1 = 2, which is false.” In short, division by zero leads to false statements.
[Note. Our best students are shortchanged in self-contained elementary school classrooms. The advanced kids in math are mixed with low achieving math students, which is a recipe for mediocrity. Common Core means everyone gets the same.]
[Note. It is incorrect to blame classroom teachers for the state of affairs. Teachers did not create the gaps (achievement), policies (inclusion), mandates (NCLB), standards (Common Core), and testing culture (Achieve) we have in our public schools. Who did? Think reformists, politicians, departments of education, special interest groups, organizations, pundits, opportunists, "experts" (non-educators), governments (state and federal), and big money.]
In a recent post, Katharine Beals writes good math instruction is the “kind done in countries that outperform us in math.” She says that basics must be taught first and learned to mastery. Good math instruction, she says, begins with “basic arithmetic facts and procedures to automaticity.” Teachers should should focus on one efficient method to do each operation, and push ineffective, alternative strategies to the background where they belong. “The best math classes focus on standard arithmetic and algebraic algorithms rather than drawing of groups of objects, digit splitting, skip counting, number bonds, repeated action, repeated subtractions, landmark numbers, and lattices.” Furthermore, students must gain background knowledge to do math and teachers should stick to content and practice it.
I don’t think we can equalize gaps in academic ability, knowledge, and skills. Kids come to school vary widely in academic ability, motivation, industriousness, background knowledge, etc. Schools cannot come close to compensating for all the differences, nor should they. It is not their job to be parents. One prevalent solution has been to equalize down (a socialist dogma), says Thomas Sowell, which is a pernicious idea, to make everyone the same, that is, bring down the kids at the top—not bring up the kids at the bottom.
Of course, there are limits to what kids with lower IQs can learn, but this seems to escape educators. No matter, I think most kids can learn standard arithmetic and introductory algebra, but gaps will always exist. And, as Richard Feynman said that when you spot someone with an ability, you try to nourish that ability and increase the child’s knowledge and skills. There will always be students who will not learn algebra or even arithmetic, no matter how hard they try. And, there will be always be students who don’t want to learn.
Will Fitzhugh writes, “Skills have taken the place of content [not only in History, but also in science and math]. Content, after all, can be such a pain. What if someone asks you something and you don't know what they are talking about? Now you can just say ‘I was educated in critical thinking skills, and we moved far beyond content in my day.’ Another advantage is that with the content largely removed, the hard work of choosing what the content of a curriculum should be no longer needs to be faced (addressed).” The reformists say that content is no longer important, yet content knowledge is the foundation for critical thinking and problem solving. In short, you can't solve chemistry equilibria problems unless you know content, can apply it, and are able to calculate equilibria in equations.
To comment, email ThinkAlgebra@cox.net.
©2015 LT/ThinkAlgebra
