For example, the major claims made by the Common Core (CC) people were bogus, such as readiness for college and world-class benchmarks. Beginning in the 1st grade, U.S. students are not learning world-class math. Also, parents may clamor for small class sizes, but the evidence doesn't support it. Remarkably, students don't need to start at the concrete level to get to the abstract level. The 1st-grade equation n + 7 = 12 is already abstract and can be used to solve countless situations that are concrete. Another issue is that equity trumps achievement in the classroom, hurting all children, including children of color. Moreover, costly technology in the school has not transformed education.
Over the years, I have found several precocious children in my algebra classes, children who can deal with abstraction better than others.
1. Abstract
We have been told that children get to the abstract only through concrete experiences and developmental stages (Piaget), so teachers ask kids to use manipulatives such as cubes and images in textbooks to demonstrate math ideas. But, what if we go from abstract to concrete, which is what I do in my elementary school algebra classes?
In 1st grade, I want children to learn the core of a concept, which means that the base of the concept of addition, for example, is not linked to counting cubes or manipulatives, or images in books. Concepts (i.e., ideas) are abstract, so are numbers, operations, equality, rules, and algorithms, too. Students don't need to start at the concrete level to get to the abstract level. Equation 3 + 7 = 10 is already abstract and can be used to solve countless situations that are concrete.
In my Teach Kids Algebra (TKA) program, 1st-grade students used symbols for unknown numbers and ideas and solved simple equations using arithmetic knowledge and reasoning. Ordinary 1st-grade students also built x-y tables and drew pictures of linear functions (i.e., make a graph in Quadrant-1). I created TKA as a reaction against Common Core. I fused algebra to standard arithmetic.
The equations x - 5 = 12 and y = x + x - 2 are abstract. For example, in the second equation, 1st-grade students were asked to find y given several x values, build a table of values, and make a graph of the equation. Find y when x = 1 corresponds to the point (1, 0) on the coordinate plane. Find y when x = 2, which is the point (2, 2). Find y when x = 3, which is the point (3, 4), and so on. Also, if y = 12, then what is x? {using guess-and-check reasoning, x is 7 because 7 + 7 - 2 = 12} Even 1st-grade students follow the algebraic rule for substitution.
2. Not College Prep
What irks me is that many schools offer kids so-called "college-prep" courses in math, but when they apply to a community college, for example, they are placed in noncredit remedial math courses, mostly the equivalents of middle school prealgebra and Algebra-1 and high school Algebra-2. Indeed, beginning in the 1st grade, kids are not learning world-class math. Common Core and state standards based on it are not world-class math. Our kids start behind and stay behind.
3. Not College-Career Readiness
The primary claim of Common Core has been college or career readiness without remediation in college, but there seems little consensus on how to do this, writes Alyson Klein. Klein explains that readiness is judged by what has been done in high school, not after high school. College readiness “will not mean that students enter college, or enter college without remediation,” says Phillip Lovell of the Alliance for Excellent Education. It is a bad idea to extrapolate beyond known data and say students are ready for college.
In Alyson Klein's article ( Education Week), she quotes Allison Timberlake: "You could have fairly high graduation rates but still pretty high remediation rates when kids go onto to postsecondary studies. And that's a problem, right?" said Allison Timberlake, the state's deputy superintendent for assessment and accountability (Georgia Department of Education).
The schools in the Tucson area have high graduation rates, but, depending on the school district, from 74% to 88% of the students applying at a local community college are placed in remedial math.
Okay, then what was the purpose of implementing Common Core (CC) and state testing? Common Core math standards were interpreted as a version of reform math that failed in the past. Reform math emphasizes group work and minimal guidance methods such as discovery learning, not the mastery of the fundamentals in math, i.e., factual and procedural knowledge. So, what was the purpose of CC? Many of the CC writers are cashing in.
Reference: Alyson Klein, Education Week. https://www.edweek.org/ew/articles/2019/01/23/states-using-post-high-school-readiness-as-essa.html
4. Not Internationally Benchmarked
The second main claim was that the math standards of CC were benchmarked internationally. But, as I pointed out in 2011, it is not the case. The 1st-grade students in Singapore learn much more standard arithmetic than CC 1st-grade standards.
For example, 1st-grade students in Singapore start multiplication, memorize addition facts, learn rules, and practice standard algorithms. By 4th or 5th grade, American students are at least two years behind their peers from top-performing nations.
5. Class Size
Robert Plomin (Blueprint) asserts that class size makes little difference in achievement. "It is widely assumed that children learn more in classrooms containing fewer children." But the effect size is small, only 1% of the variance is class size, says Plomin. In contrast, 60% of the differences in school achievement is genetics. Only 1% is class size.
6. Equity
"An analysis of state ESSA plans finds that many states are prioritizing equity over performance," writes Dr. Elizabeth V. Primas (From The 74). Inclusiveness, for the sake of equity, has created major problems in the classroom. There is no reason to mix low achieving math students with high-achieving math students in the same math class. Also, the one-size-fits-all concept of Common Core and state standards is not fair to most students, including students of color. Furthermore, it is anathema to sort kids for math class according to their achievement.
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| Thomas Sowell |
Indeed, equity often has dominated over achievement in school policy. Thomas Sowell says it is false equity ("the fallacy of fairness"). He writes, "Equalizing downward by lowering those at the top ... is a crazy idea taught in schools of education across the country." Equity overachievement is a liberal ideology in which "achievement is equated to privilege," says Sowell, a black economist.
Note. I volunteer at a K-8 Title-1 school where 85% of the students are of color. Over the years, I have found many children of color who excel in my weekly algebra lessons. This school year, I have two 4th-grade classes. In late February (2019), I started to give algebra lessons to a 2nd-grade class.
7. Reform & Innovation
Most of the reforms today are linked to a business or organization trying to sell its materials and ideas to the schools. It is lucrative for the sellers, but the students do not get any better. Unfortunately, some of the Common Core writers are cashing in, too. Most reforms fail.
Incidentally, almost all the innovations funded by the U.S. Department of Education (a whopping 82%) have failed to improve achievement. Furthermore, costly technology and software in the classroom have not transformed education and, often, is more of a distraction than a help. Larry Cuban, (Stanford Graduate School of Education) writes, "The fact is that many teachers continue to struggle in integrating devices and software into their lessons." Teachers, I think, waste valuable class time and energy attempting to fit technology into lessons as dictated by the school district. Sadly, they do not have much choice in the matter.
Unfortunately, time-on-task for math, reading, history, and science and the mastery of content through practice are less important in today's classrooms to make room for tech use, doubtful reforms, and social-emotional learning (SEL), which is self-esteem, revisited. The idea is that students need high levels of self-esteem before they can learn. It's nonsense, of course.
©2019 - 2020 LT/ThinkAlgebra
Last update: 2-11-19, 2-12-19
