😎Observations, Ideas, and Opinions on Math Education by a Contrarian in 2021, a Divergent View.
The latest: Sam Dorman of Fox News reports, In the name of equity, "the Virginia Department of Education (VDOE) is moving to eliminate all accelerated math options prior to 11th grade, effectively keeping higher-achieving students from advancing as they usually would in the school system." It is discrimination against kids who study hard to achieve. The VDOE should be dissolved. Education has run amok with crazy ideas from liberals. Idiots with power lurk everywhere in our education system, at the local, state, and federal levels. 4-22-21
For the latest: Click Cogitatus2.
Students who struggle in elementary school will likely continue struggling in middle school and then high school. Billions and billions and billions have been spent on students who have "poor attendance, suspensions, course failure, and failure to score at grade level...." They don't catch up or don't want to catch up. Many students don't study enough or take education seriously. They have the wrong attitude. Thomas Sowell explains, "There is no reason whatever to assume that education is valued equally by all individuals or groups. Not all groups value education or the behavior that leads to greater education successes, the same."
Thomas Sowell (Discrimination and Disparities, 2019) nails it: "Asian American students spend more hours studying than either white or black American students. How surprised should we be that academic outcomes show a pattern of disparities similar to the pattern of disparities in the amount of time devoted to school work?" 4-23-21
Knowledge is the goal of learning and the basis of critical thinking. Also, parents and educators need to know that thinking skills are domain-specific. What is happening? Our schools stress critical thinking, not the knowledge that enables it. Also, the status quo has downgraded memorization and practice of fundamentals starting in 1st-grade arithmetic. Educators are using standards that are not world-class, so our kids start behind and stay behind.
"Oh, we teach critical thinking, understanding, collaboration, and use alternative algorithms and manipulatives." What happened to traditional arithmetic or number lines? "It's so Old School. Our reforms are preparing students for the 21st century and the age of Google!" But critical thinking is domain-specific, not an independent skill, so how can you teach it without strong mathematical content? "We teach strategies such as building excitement, encouraging math talk, promoting teamwork, emphasizing hands-on learning, and so on. That's the way to teach math."
Really?
Why are American students at least two years behind their Asian peers in math by the 4th or 5th grades? I guess reform math strategies like engagement, teamwork, or using manipulatives are much more important than learning math content. Sadly, engagement has become a substitute for learning key content in long-term memory, but it is not the same as learning essential content. Is it any wonder that math has been taught awfully for decades? 4-22-21
Math is taught awfully!
Reform Math Failed, Again |
A decline in academics and a deteriorating curriculum have driven more parents to alternatives such as homeschooling and private schooling. After a decade of reforms, only 24% of 12th graders are proficient in math (NAEP 2019).
Reform Math Failed, Again! Parents and teachers must face the reality that math education has gone awry via the so-called math reforms, Common-Core-like state standards, strategies, and minimal guidance approaches (e.g., group work). For example, project-based learning, discovery learning, and other minimal guidance constructivist methods do not work with math, which is abstract and hierarchical.
Furthermore, the promises of Common Core (e.g., career and college readiness) and other reforms have failed! Although some will argue otherwise, poor performance on national and international tests indicates poor teaching related to a substandard curriculum and deficient instructional methods.
The "fairness solution" from the liberal education establishment has been to lower the math standards to close gaps. It is a "fallacy of fairness," explains Thomas Sowell. Also, Sandra Stotsky points out in The Roots of Low Achievement (2019) that gap closing is not a workable educational goal. Instead, upgrading the instruction for all students should be the goal. Thus, in my opinion, the "fairness crusades" have marginalized individual achievement, hard work, and excellence in our schools and are biased toward certain groups, such as Asian-Americans who "work harder, try harder, study harder, and perform better" than most other students. It is outright discrimination against Asians.
Note: Cogitatus is Latin for the act of thinking. April 16, 2021
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Special: Jill Barshay, writing in The Hechinger Report, cites a new study by Redding & Grissom ("Do Students in Gifted Programs Perform Better?" 2021) that shows students in gifted programs are not getting much of an academic bang, if at all. When I taught in TAG (Talented & Gifted), the program was an enrichment model; however, I implemented accelerated math, computer programming in LOGO, photojournalism, and advanced writing at a primary city school, grades 2 and 3.
The major flaw in gifted programs and schooling in general, I think, has been that teachers believe in "all-purpose critical thinking skills" that work for all subjects. There is no such thing. E. D. Hirsch (Why Knowledge Matters, 2016) writes, "Thinking skills cannot readily be separated from one subject matter and applied to other subject matters. The domain specificity of skills is one of the firmest and most important determinations of current cognitive science." Yet, most educators and parents are unaware of it, says Hirsch. In short, thinking without content is empty (I. Kant). I know a lot of smart kids who test well but lack content knowledge. Indeed, knowledge does matter for better thinking!
According to the study by Redding & Grissom, "Children in gifted programs are learning only a tiny bit more than they would without them." The report points out that "the disappointing academic results may reflect that most teachers of gifted students don't emphasize advanced topics but instead focus on "enrichment activities," such as fun projects." If this is true, why are there gifted programs in schools where acceleration in academic subjects is not the primary goal? You can not "think" your way to a solution in trig without substantial knowledge of trig in long-term memory and experience solving trig problems. Likewise, you cannot translate Ovid's works without substantial knowledge of Latin vocabulary, conjugations, declensions, and experience translating.
In my opinion, acceleration is the primary justification for gifted programs, not Johnny is bored. While teaching in gifted programs, I found that the same enrichment activities benefited most students, not just students in the gifted program. I wrote Joseph Renzulli about this. A few years later, he published a book aimed at parents, stating that all children are gifted and benefit from enrichment lessons. But CTY has a different view on identifying talented children, especially in the math and verbal areas.
CTY's Talent Search: To gain access to online or in-person courses from the Johns Hopkins Center for Talented Youth (CTY), students take a test called the School and College Ability Test or SCAT) that is grade levels above. SCAT has a verbal part and a quantitative (math) part. Middle school students (under age 13) can be admitted if they have qualifying SAT or SCAT scores. (FYI: Several of my 7th-grade math students qualified with high SAT scores. Today, they would qualify for Study of Exceptional Talent or SET at Johns Hopkins.) Incidentally, the CTY admission rate is about 8%. CTY is for talented and gifted students, not enrichment. Most kids placed in school districts' gifted programs, such as TAG or GATE, are intelligent but not talented by CTY standards; however, they would benefit from accelerated math, science, reading, vocabulary, and writing. They should take Honors courses and AP courses. Talent Search is the gateway to CTY's online and summer classes.
Unfortunately, most gifted programs focus on enrichment, not acceleration. Placing a 2nd grader into a 3rd-grade math textbook is not acceleration. Why? The 3rd-grade book is for average kids. Kids who are genuinely gifted in math need a totally different math curriculum, but they also need to master the fundamentals, starting with arithmetic drills, just like Einstein. Also, I think it is nonsense to tell kids they are "gifted." Many bright kids in gifted enrichment programs across the United States do not reach the CTY standards. Math League kids, especially those who take advanced courses from the Art of Problem Solving, are advanced and often score very high in math. Unfortunately, some parents often brag, "Oh, my Veronica is in the gifted class!" Really? One of my 4th graders, who was classified as gifted, began to cry when other students solved a math problem first. He was good at math but not exceptional. Kids widely vary in academic ability.
Unfortunately, many gifted programs focus on enrichment, not acceleration. Placing a 2nd grader into a 3rd-grade math textbook is not acceleration. Why? The 3rd-grade book is for average kids. Kids who are truly gifted in math need a totally different math curriculum, but they also need to master the fundamentals, starting with arithmetic drills, just like Einstein. Also, I think it is nonsense to tell kids they are "gifted." There are many bright kids in gifted enrichment programs across the United States who do not reach the CTY standards. Math League kids, especially those who take advanced courses from the Art of Problem Solving are advanced and often score very high in math. Some parents often brag, "Oh, my Veronica is in the gifted class!" Really? One of my 4th graders, who was classified as gifted, began to cry when other students solved a math problem first. He was good at math but not exceptional. Indeed, kids widely vary in academic ability, even among the best.
Johns Hopkins CTY
- Students in grades 2-3 take the Elementary SCAT designed for students in grades 4-5.
- Students in grades 4-5 take the Intermediate SCAT designed for students in grades 6-8.
- Students in grades 6 and above take the Advanced SCAT designed for students in grades 9-12.
My experience has been that intelligent kids can learn advanced material in mathematics such as trig in 6th or 7th grade when prepared and taught explicitly. But, I also know that most children as young as 6 (1st grade) can learn some basic ideas in algebra when it is fused to standard arithmetic in my Teach Kids Algebra (TKA) program, which requires memorization, practice, and review. Students must overlearn math facts, so they are instantly shifted to working memory to do calculations and solve problems. Kids need to develop retrieval strength, writes Sanjay Sarma, MIT (Grasp, 2020), which comes from practice-practice-practice. To learn more about TKA, click here. 04-19-20-2021
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Comment: We need to upgrade math instruction for all students by returning to traditional arithmetic. Also, I know we can fuse algebra ideas (e.g., Equation/Table/Graph) to standard arithmetic because I have done it in grades 1-5. I'm a guest algebra teacher at a city school with almost all minority students and plan to continue once-a-week sessions when the 2021-2022 school year begins in early August.
Algebra in 1st grade: Teach Kids Algebra Project Stresses Traditional Arithmetic. |
Comment: After eight years of Common-Core-based reform math, only 24% of 12th graders were proficient in math (NAEP 2019), an awful statistic. Common Core and state standards have failed to deliver career and college readiness for 3/4 of the students.
Traditional Arithmetic Forms the Basis of Higher Math!
2nd Grade 1973 Math Drills Cursive Writing, Too. |
"Mathematics is different. It endures. It's still correct today," writes Ian Stewart (Significant Figures 2017). It is a powerful tool for solving problems because it is abstract. For example, an abstract fact like 3 + 5 = 8 can apply to hundreds of problems.
Comment: You don't start at the top of Bloom's pyramid. You start at the bottom to enable critical thinking or problem-solving later on when you have a sufficient knowledge base. Students must learn math content.
- Key facts should be learned and memorized for automaticity.
- Standard algorithms should be taught and practiced for fluency.
- You learn to do math problems by doing math problems.
- Common Core math standards and the Next Generation Science standards do not prepare students for STEM.
- Reform math is pointless.
The standard algorithm implies place value.
Simple combinations such as 3 + 5 = 8 can be manipulated on a 0-20 number line. Nothing fancy. The number line is mathematics. Students acquire a number-line understanding of addition. Basic combinations (i.e., addition facts) should be stored systematically in long-term memory via memorization and be instantly available for problem-solving.
US Kids Lag Behind, Starting in 1st Grade.
Beginning in the 1st Grade, Common Core's one-size-fits-all math standards (aka state standards) are not world-class. They are often interpreted as reform math and taught in "inclusive" or mixed classrooms without regard to individual achievement or ability. These are three strikes against American K-8 students.
Furthermore, our better students are penalized by a so-called "fairness" approach that lowers those at the top, which is a progressive idea of "sameness" (aka a "fallacy of fairness," says Thomas Sowell), and the flawed thinking behind the one-size-fits-all Common Core, now the state standards. (Note. The Common Core math standards have been rebranded as the state standards with some changes.)
The old 1997 California math standards indicated that primary students should learn the standard algorithms for addition, subtraction, multiplication, and division by the end of 3rd Grade. Still, the Common Core-based state standards do not come close to achieving it. Contrary to typical instruction today, there is no reason not to teach the standard algorithm for addition in the first marking period of 1st Grade. But it's not the Common Core way, say the reformists.
Common Core Way: Delay, Delay, Delay!
"Multiple strategies, versus a single algorithm, are taught. Common Core expects students to understand math conceptually." Really? The so-called "understanding" tactic is the same old NCTM reform math scheme that failed in the past. You cannot "get" addition without being able to add and apply it to word problems. First-grade students should use the standard vertical algorithm based on place value to add 67 and 85 by Christmas. The conceptional understanding of arithmetic is in the doing of arithmetic. Also, it is fantasy to believe that reasoning and understanding will magically automate factual and standard procedural knowledge to long-term memory for instant use in learning new concepts and problem-solving. In contrast, repetition will. Indeed, practice improves performance.
First-Grade Standard Arithmetic by Christmas |
Put simply, students are taught convoluted reform math that screws up basic arithmetic, not straightforward standard arithmetic needed to advance. With its nonessential extras, complex nonstandard procedures, and unrealistic progressive ideology of sameness, reform math has been a grave error in judgment. Yet, it influences much of math instruction today. Reform math confuses young students and equally alienates parents.
What's worse is that reform math dogma slows the pace of learning standard arithmetic and is why US students are about two years behind their peers as early as the 4th or 5th grade.
You learn to do math problems by doing math problems!
Science without math is not science. It's pretend science!
And I quote: "Climbing Down extensively documents the failures of the NGSS [Next Generation Science Standards], but also provides eleven steps parents, teachers, and school boards should take to correct the deficiencies in this curriculum. They include using the Fordham Institute’s A-graded science standards as a template; allowing, encouraging, or requiring students to begin algebra in 8th grade rather than 9th; replacing Common Core State Standards (CCSS) mathematics with higher-level standards, such as the excellent and highly rated pre-CCSS California mathematics standards; and ensuring that science standards steer students toward the full range of scientific careers, especially those that serve the American national interest."
The scientific method was left out, as was the intrinsic link between science and mathematics. Note: The core authors of the "Climbing Down" were Jennifer Helms and James Nations. The report appeared on the National Association of Scholars (NAS) website. David Randall took part in the revision. 4-8-21. Simply, the new standards do not prepare students for college-level courses in chemistry, physics, or mathematics.
"The Next Generation Science Standards sacrifice content (what you know) for performance (what you can do), with project learning being central to the science classroom. Hands-on projects are important and make learning enjoyable, but a disproportionate focus on project learning results in a haphazard teaching and learning process." Also, just like Common Core, the Next Generation standards were not field-tested. Like CC, NG has already failed.
I quote from the report, "The entire NGSS document is written as inquiry-based standards (a.k.a. “problem-based learning,” “experiential learning,” “discovery learning,” and “constructivist learning”)." These methods were shown to be ineffective in math and science by Kirschner, Sweller, and Clark: Minimal Guidance = Minimal Learning.
Just as in math, and I quote: The NGSS’s revealed preference is to eliminate the “achievement gap” by removing all difficult material that produces said “gap.” It's the same old equalizing downward by lowering those at the top, a fallacy of fairness, says Thomas Sowell.
I wrote about the new science standards several times. My views have not changed. I am glad that a new report ("Climbing Down") restates the lack of science content in the standards. "Here, the NGSS commit themselves to eliminate science achievement gaps across all identity groups by removing challenging science content. They reduce rigor to produce more “equitable” educational outcomes among students — a remarkable coercive expression of the soft bigotry of low expectations. In the name of equity, the NGSS leaves all students equally unprepared for STEM undergraduate majors or STEM careers."
The same is evident in mathematics.
Lower the math standards to close the gaps.
What do you think "same for all" Common Core was all about?
Did it work? No!
Thomas Sowell, in Dismantling America 2010, a collection of essays, explains that the "equalization crusades" were about "equalizing downward, by lowering those at the top. Fairness strikes again! It is a crazy idea taught in schools of education across the country." Sowell calls the lowering of content standards a "fallacy of fairness." It's a disgrace, not only in math but also in science. 4-14-21
The new standards combined chemistry with physics, which diminished or restricted content, but kept biology by itself. It should not surprise us because the framework committee was mostly from the social sciences or education.
the better I can think and solve problems. WOW, isn't cognitive science great?