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| Merry Christmas Be Well! |
"Outcomes" is a collection of compelling and/or often contrary cogitations regarding Common Core and education. [Last changes made on December 24, 2014]
See my latest reflections and random thoughts about education:
Click Reflections.
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 students need to be taught traditional arithmetic starting in 1st grade--not Common Core reform math. Furthermore, we must kick out accountability testing. Note. Sometimes, Feynman would write equations on the board during a lecture on cutting-edge physics, then suddenly exclaim--this makes no sense. This is the way it works out, but I don't understand it.
Moreover, Paul Thomas (in his blog, The Becoming Radical) says that Common Core is the problem, which has drained billions from the public schools to pay testing and technology companies, money that should have been spent on essential school resources, textbooks, science equipment, etc. Moreover, as many writers have stated before, the new testing is designed to fail at least half of the kids. Why design tests that fail half of the kids? Thomas writes, "The Common Core advocacy is market-driven, benefiting those invested in its implementation. But ... [the] market success is at the expense of the very students who need our public schools." I should add that kids are taught [Common Core] reform math, not tried-and-true traditional arithmetic. Common Core reform math does not prepare students for algebra in middle school, puts capable students behind, and wastes valuable instructional time by teaching inefficient, alternative operations that lead nowhere. Common Core reform math looks like arithmetic, but it is not the real thing.
Common Core reform math claims it teaches understanding better than traditional arithmetic. I guess, it must be by magic because the claim has no basis in evidence. Common Core advocates predict that learning different ways to calculate will pay off when students get to higher math, but there is absolutely no proof that this is the case. In fact, the opposite is true. In contrast, traditional math, which involves the memorization of number facts, the fluent use of paper-pencil standard algorithms through practice, and the application of arithmetic to solve routine word problems, has been a tried-and-true method for centuries. Indeed, factual and efficient procedural knowledge in long-term memory are required to solve problems. When taught well, traditional arithmetic prepares students for algebra-one by middle school, especially if the Core Knowledge K-8 math sequence is taught well. In essence, Common Core methods make simple arithmetic difficult and more complicated than it is. This is The Common Core Way: Let's not simplify arithmetic; let's complicate it. Bad idea.
Common Core claims it emphasizes critical thinking, but, as Immanuel Kant wrote, "Thoughts [critical thinking] without content [knowledge] are empty...." The leaders or so-called masterminds in education lack wisdom, which cannot be taught. They also lack knowledge in mathematics and cognitive science. Hippocrates wrote, “There are in fact two things, science and opinion; the former begets knowledge, the latter ignorance.” This is what we have in education today: ignorance and progressive ideology. Evidence does't matter.
What cognitive science research reports is that doing math starts the process of understanding it, which grows gradually over the years with practice, repetition, and experience. There are no short cuts. In contrast, the basic idea in Common Core reform math and 21st Century Skills is that children can become problem solvers without building a solid knowledge base in long-term memory, stating in 1st grade. How? Apparently, by working in groups to collaborate, by doing inquiry/discovery activities with minimal teacher guidance, and by learning inefficient, alternative methods to calculate (reform math). It's total nonsense, of course! Also, our best college students don't want to be teachers or go into STEM; they go into finance or other fields to make money. Many of the financial fields require calculus. Some higher-level college math courses are required in many majors--not just STEM. Finland's education system is often promoted as a model for the US. But, it should be noted that, according to the most recent math scores from TIMSS, Finnish 4th and 8th graders are about the same in math achievement as American 4th and 8th graders. Moreover, both Finnish and American students are left in the dust compared to the scores of students in Asian nations or regions. Moreover, Paul Thomas (in his blog, The Becoming Radical) says that Common Core is the problem, which has drained billions from the public schools to pay testing and technology companies, money that should have been spent on essential school resources, textbooks, science equipment, etc. Moreover, as many writers have stated before, the new testing is designed to fail at least half of the kids. Why design tests that fail half of the kids? Thomas writes, "The Common Core advocacy is market-driven, benefiting those invested in its implementation. But ... [the] market success is at the expense of the very students who need our public schools." I should add that kids are taught [Common Core] reform math, not tried-and-true traditional arithmetic. Common Core reform math does not prepare students for algebra in middle school, puts capable students behind, and wastes valuable instructional time by teaching inefficient, alternative operations that lead nowhere. Common Core reform math looks like arithmetic, but it is not the real thing.
Common Core reform math claims it teaches understanding better than traditional arithmetic. I guess, it must be by magic because the claim has no basis in evidence. Common Core advocates predict that learning different ways to calculate will pay off when students get to higher math, but there is absolutely no proof that this is the case. In fact, the opposite is true. In contrast, traditional math, which involves the memorization of number facts, the fluent use of paper-pencil standard algorithms through practice, and the application of arithmetic to solve routine word problems, has been a tried-and-true method for centuries. Indeed, factual and efficient procedural knowledge in long-term memory are required to solve problems. When taught well, traditional arithmetic prepares students for algebra-one by middle school, especially if the Core Knowledge K-8 math sequence is taught well. In essence, Common Core methods make simple arithmetic difficult and more complicated than it is. This is The Common Core Way: Let's not simplify arithmetic; let's complicate it. Bad idea.
Common Core claims it emphasizes critical thinking, but, as Immanuel Kant wrote, "Thoughts [critical thinking] without content [knowledge] are empty...." The leaders or so-called masterminds in education lack wisdom, which cannot be taught. They also lack knowledge in mathematics and cognitive science. Hippocrates wrote, “There are in fact two things, science and opinion; the former begets knowledge, the latter ignorance.” This is what we have in education today: ignorance and progressive ideology. Evidence does't matter.
Note. Please excuse typos, misspellings, grammatical errors, etc. I rearrange ideas and often digress. I am not a writer. I add, move, rewrite, delete, and repeat text. Please excuse redundancies. I write about Common Core, mathematics, education, science, reforms, and other odds and ends. LT, ThinkAlgebra.org. I can be reached at ThinkAlgebra@cox.net. It's not that our kids are dumb; it's that they aren't taught to master content like kids in top-performing nations. For decades, US math instruction has been lousy, and I fear that Common Core will make it worse.
Physical exercise and learning new things have impact on cognitive ability. The lack of recess, physical education, the arts and music has hurt kids. The lack of focus on knowledge and essential skills, especially in mathematics and science has hurt students. Ninety-minute periods in middle school and high school are absurd. Often, students are placed into higher level math classes or AP classes without the proper background knowledge, skills, and experience. Typical students don't take calculus to learn to be creative. They take calculus to learn calculus and how to apply it. It should also be noted that most of the students who take AP calculus don't develop insight or a good understanding of the math. It requires memorization, repetition, and extensive practice.
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| My Teach Kids Algebra (TKA) Class: 3rd Grade. Kids can learn more math than K-8 teachers are prepared to teach. |
In contrast, American kids [starting in 1st grade] simply are not taught to automate fundamentals, especially the memorization of number facts, the fluent use of standard algorithms, and the application of factual and efficient procedural knowledge to solve routine word problems (applications) to build a strong storehouse of factual and procedural knowledge in long-term memory to use for problem solving. To accomplish these, extensive practice and repetition are necessary, yet, for decades, memorization and practice have fallen out of favor in progressive classrooms. Instead of traditional arithmetic that advances capable kids to algebra-one by middle school, under the one-size-fits-all Common Core dictate, American kids are taught questionable, unverified, confusing, inefficient, alternative methods called reform math, along with test prep. Kids aren't educated; they are coached to take tests.
In 2009, I wrote that Common Core was not for STEM students. In short, Common Core math standards do not prepare kids for the many careers that involve STEM or parts of STEM. Moreover, starting in 1st grade, the new math standards are not world class and below many Asian benchmarks. Common Core has left high achievers in the gutter, which is another reason that Common Core and its testing regime should be tossed in the waste can of bad ideas. It makes little sense to punish achievers with a non-challenging curriculum. Through top-down, one-size-fits-all Common Core, laws, mandates, and regulations, the federal government, big money, such as Bill Gates and others, and powerful corporations, such as Pearson, are in control of education--not the states, not the school districts, and not the teachers. It is tragic that the American school system chases after mediocrity and equalizes downward.
Outcomes" is a collection of compelling and/or often contrary cogitations regarding Common Core, testing, and education. Understanding does not produce mastery; practice does. Early on, kids are not mastering basic arithmetic. For decades our best kids have been ignored and bored. Moreover, for decades, educators have been training kids to take tests, but that's not education. Equalizing performance (outcomes) is the central theme of Common Core. Talent and individualism cannot flourish under such an ideology, which focuses on group work, inquiry-discovery and other reform or progressive pedagogy. Even our best math students underperform under this regime. They are merely average, if that, compared to their peers in Singapore or South Korea.
Marc Tucker (Fixing Our National Accountability System), writes "High stakes tests in the top performing countries are used to hold students, not teachers, accountable, the obverse of what happens in the United States." Today's students don't study enough, read books enough, write essays enough, learn math and science enough, or exercise enough. Teachers need to stop inflating grades and using ineffective instructional methods, starting in 1st grade. Parents and teachers should stop fixating on a child's self-esteem and worry more about the child's competency.
There has been a shift of power in America "from ordinary Americans to the corporate and financial elite," says Bob Herbert ( Losing our Way). This is especially evident in education in which there is no equality of funding. Poor school districts stay poor and lack resources. The people making huge profits under Common Core are corporations, such as Apple, Microsoft, Pearson and other technology, publishing and testing companies, etc., along with powerful hedge fund managers and their investors. Furthermore, nearly every writer of the Common Core standards, almost all of whom were from special interest groups (e.g., ACT, College Board, Achieve, etc.), is cashing in--one way or another. These people want power, not truth. Common Core has never been shown to work, yet it is promoted by the US Department of Education and backed by government money, big money from Bill Gates who financed Common Core, and others. Many influential business people, politicians, governors, and powerful heads of institutions (e.g., AFT, NCTM, NEA, think tanks, academia, etc.) were asked to endorse Common Core--although they never read the document.
Our schools should not copy schools in other nations, such as Finland, South Korea, Singapore, etc. [Singapore math works in Singapore. In math, Singapore tracks less-able students in 1st and 2nd grade and again in 4th to 6th grade. The Singapore 6th grade exit test determines which "level" of secondary school the child attends next. In short, Singapore prudently tracks students. The system works well in Singapore, but for decades, the US has been diametrically opposed to tracking, which, I think is a mistake because kids vary widely in academic ability. Finland's international test scores (TIMSS) are about the same as US 4th and 8th graders. Also, only 28% of Finnish 9th graders correctly calculated 1/6 x 1/2 in research conducted by Dr. Olli Martio, University of Helsinki.]
The fact is that Finnish K-8 students are not any better in math than American K-8 students. In contrast, top-performing Asian nations, which have from about 40% to 50% of 4th and 8th grade students scoring at the Advanced Level in TIMSS, leave Finnish and American students in the dust. Only 7% of our 8th grade students reach the Advanced Level and only 4% of Finnish 8th graders make that level. In short, US & Finnish students underperform.
The so-called "transformative," progressive reforms in American education, such as test-based reform, have not leapfrogged our students, either. For decades there have been only modest gains, if that, not rapid improvement, says Diane Ravitch. Children have been trained to take tests, not educated, explains Linda Perlstein (Tested). We don't need to transform education; we need to restore it. The top-down, one-size-fits-all reform model [Common Core] of standards>standardized testing>data collecting>punishment) is the road of mediocrity, littered with bad ideas, ill-founded fads (often called innovations), and junk science. Teachers need to take back education. One major step forward is to teach arithmetic as arithmetic (memorizing number facts and learning standard algorithms, starting in 1st grade) and not as reform math, such as in Common Core with its "strategies" approach, which looks like arithmetic but isn't the real thing. Understanding does not produce mastery; practice does. Another major step is to bring back "McGuffey-Reader-style curriculum [from which] American kids learned not only the basics, but also values such as honesty and patriotism, and immigrant kids assimilated by learning our language, laws, and customs (Eagle Forum)."
Bad ideas, fads, myths, whims, and pseudo-science have corrupted traditional arithmetic and have impeded US math achievement for decades. Furthermore, test-based reforms do not foster quality. In fact, in my opinion, states have not been accountable. Statism has not provided most children with a high-quality education for decades. Children are still subjected to contentious top-down, one-size-fits-all reforms that have failed to produce rapid improvement. Children vary widely in academic ability, yet all students are fed the same Common Core curriculum in the name of fairness. In short, no child gets ahead. It makes no sense. It is a recipe for mediocrity.
The fact is that Finnish K-8 students are not any better in math than American K-8 students. In contrast, top-performing Asian nations, which have from about 40% to 50% of 4th and 8th grade students scoring at the Advanced Level in TIMSS, leave Finnish and American students in the dust. Only 7% of our 8th grade students reach the Advanced Level and only 4% of Finnish 8th graders make that level. In short, US & Finnish students underperform.
The so-called "transformative," progressive reforms in American education, such as test-based reform, have not leapfrogged our students, either. For decades there have been only modest gains, if that, not rapid improvement, says Diane Ravitch. Children have been trained to take tests, not educated, explains Linda Perlstein (Tested). We don't need to transform education; we need to restore it. The top-down, one-size-fits-all reform model [Common Core] of standards>standardized testing>data collecting>punishment) is the road of mediocrity, littered with bad ideas, ill-founded fads (often called innovations), and junk science. Teachers need to take back education. One major step forward is to teach arithmetic as arithmetic (memorizing number facts and learning standard algorithms, starting in 1st grade) and not as reform math, such as in Common Core with its "strategies" approach, which looks like arithmetic but isn't the real thing. Understanding does not produce mastery; practice does. Another major step is to bring back "McGuffey-Reader-style curriculum [from which] American kids learned not only the basics, but also values such as honesty and patriotism, and immigrant kids assimilated by learning our language, laws, and customs (Eagle Forum)."
Bad ideas, fads, myths, whims, and pseudo-science have corrupted traditional arithmetic and have impeded US math achievement for decades. Furthermore, test-based reforms do not foster quality. In fact, in my opinion, states have not been accountable. Statism has not provided most children with a high-quality education for decades. Children are still subjected to contentious top-down, one-size-fits-all reforms that have failed to produce rapid improvement. Children vary widely in academic ability, yet all students are fed the same Common Core curriculum in the name of fairness. In short, no child gets ahead. It makes no sense. It is a recipe for mediocrity.
Note. I recall a lesson (written in a university journal as a model) in which middle school kids in groups were discussing whether the 3D object on their desks was a cylinder, or a pyramid, or something else. And, the "researchers," who were students (education majors), just let the kidsgo on and on. What a waste of time! The discussions of the different groups were recorded, and a sample of one group's dialog (4 kids) was in the journal. ("I think Jane is right. It's a pyramid, and she's always right.) What irks me is that this lesson serves as a model for other teachers to follow. The idea is that a good teacher should watch the groups and not intervene. It's a bad idea. (Incidentally, the object was a cylinder. Any good first grade student would know that. When I find the journal in one of my boxes, I will print the entire conversation.)
Common Core: In my opinion, educators have been conned and left out in the cold. The "powers that be" always win. Teachers have been cut off from the decision making process. This is what happens when an oligarchy rules education. The cult-like obsession with Common Core and its excessive standardized testing is illogical and hurts kids. Teachers are caught in a quagmire. They do what they are told to do to keep their jobs. Instead of teaching essential knowledge that kids must know to advance, standardized testing (NCLB) has become the centerpiece of US education, and Common Core is right in the middle. In my opinion, these top-down reforms have little to do with improving education. The new standards, themselves, the way they are taught (as reform math), and excessive standardized testing are counterproductive. Diane Ravitch has characterized No Child Left Behind as test and punish, which is an abhorrent policy. Peter Green (Curmudgucation blog) writes, “Why do we have these policies that don’t make sense? Why does it seem like this system is set up to make schools fail? Why do states pass these laws that discourage people from becoming teachers?"
Note. First Grade Common Core: "Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)." (Common Core 2014 website.) Notice that Common Core asks students to calculate single-digit sums, which is an epic error. Students should not calculate single-digits sums in working memory, they should automate them in long-term memory for instant use. Many of the strategies named above are a crutch and not needed. Read below.
➡ Students should not calculate single-digit facts (i.e., via strategies), they should memorize them so they are instantly usable in solving math problems. Price, Mazzocco, & Ansari (The Journal of Neuroscience), explain that students who memorize by rote single-digit math facts starting in 1st grade, rather than always calculating them, become good math students, and the benefits reach far into high school with much higher PSAT scores. Being able to retrieve 5 + 6 = 11 automatically from long-term memory is different from [and better than] calculating it using a strategy (e.g., 5 + 6 = 5 + 5 + 1 = 10 + 1 = 11), which is a different mental process that clutters working memory, leaving less space for problem solving.
In my view, the strategies approach, starting in 1st grade to teach arithmetic, makes little sense, and many of the strategies, themselves, are only tangentially related to arithmetic, that is, Common Core reform math is not the real thing. For example, if a 1st grade child knows 6 + 6 = 12, then 6 + 7 is one more than 6 + 6 or 13 [because 7 is one more than 6]. While this type of reasoning helps kids, but I would not call it a strategy. I call it mathematical thinking that a 1st grader can do; however, before the child can do "one more than" reasoning, the child must first memorize [automate in long-term memory] 6 + 6, which is not the goal, as far as I can tell, in 1st grade Common Core. (In contrast, it is the goal in Singapore 1st grade.) My argument is that if a child can memorize 6 + 6 = 12, then should not the child also be able to memorize 6 + 7 = 13, 6 + 8 = 14, etc.? The facts are obvious on the number line. Why waste time on strategies or inefficient alternative algorithms. Why not just memorize the number facts and learn efficient standard algorithms. Ah, but this is not the "Common Core Way." Furthermore, Common Core claims that its standards are pedagogy free, which is a total lie. Just read the 1st grade standard above--it's the Common Core Way to teach math and it goes against cognitive science according to researchers Price, Mazzocco, & Ansari.] Indeed, the overemphasis on conceptual understanding in Common Core has pushed aside the vital importance of factual and procedural knowledge that leads to understanding. Understanding comes from extensive practice of efficient procedures, such as standard algorithms, which require the memorization of number facts for instant recall from long-term memory. [Note. In the very early 70s, the best textbook for 7th grade was Concepts, Skills, and Applications (Scott Foresman, Publisher), so the idea of conceptual understanding is not new. Is it possible to do math with limited conceptual understanding? Yes, Isaac Newton invented a calculation method that solved physics problems (calculus). The methods always worked (agreed with experimental observations), so he knew how to apply the calculus, but he did not know why his calculus worked. It just did. The conceptual basis for his method would take another 200 years. Maybe, we should remember that kids are not little mathematicians. Understanding grows slowly over the years, and it is difficult to measure.]
Frankly, strategies should never replace or hinder the memorization of basic facts or the learning of standard algorithms through practice in first grade or any grade. Memorization and practice to gain factual and procedural knowledge in long-term memory do not squelch creativity and learning, as many say. Common Core is the latest version of reform math that downgrades memorization and practice for mastery in the early grades, which is a primary reason that our kids suck at basic math. The strategies were part of NCTM math standards and reform math pedagogy of the 90s, which failed.
[However, these strategies are not new. You can find some of them in old elementary textbooks, such as those in the 1950s, as Barry Garelick has pointed out, but in the 50s, as Garelick explains, kids also memorized the facts and learned standard algorithms to do arithmetic. Today, kids don't. In my opinion, some of the reform math strategies are enrichment or involve unnecessary, often confusing calculations that clutter working memory. In short, the strategies don't focus on or drive students to automate basic arithmetic facts in long-term memory. Common Core kids come into 3rd grade and can't add 231 + 47, a calculation my Title 1 urban 1st graders did well in the early 80s. Under Common Core, the standard algorithms, which are a function of place value and automated number facts, have been pushed aside.]
Note. Typical first grade students can memorize the addition facts and learn the standard algorithm. This is what is done in Singapore. I taught 1st grade self-contained in the early 80s under a deseg order at an urban Title 1 school. The children were good at memorizing and at using what they learned to solve word problems. They were pleased with themselves. More recently (2011) I taught algebra to over 40 minority 1st graders at a city Title 1 school in Tucson. In each case, I made up my own math curriculum. Very young children can learn more than teachers are prepared to teach. We have known this since the 1950s, even before.
The Common Core strategies may look like arithmetic, but they are not the real thing. This is not smart arithmetic education. Why make something that is not difficult, difficult? Also, in Common Core, words like "understanding" and "fluency" are vague or ill-defined. The word "mastery" or "automation" of essential arithmetic procedures and facts in long-term memory for use in problem solving is not mentioned. The concepts of addition and subtraction are easy for 1st graders to understand at their level using a number line. Understanding, which is difficult to measure, says Daniel T. Willingham, a cognitive scientist, changes over time and grows slowly, and it seems to be a product of practice. Richard Feynman used to say that you don't understand anything until practiced. Feynman, a Nobel Prize winner in Physics, is saying that understanding and insight come through practice, lots of it, not instantly. Feynman practiced calculus at breakfast, on this way to work, at lunch, at home at night, etc. It drove his 2nd wife crazy and ended in divorce. He was brilliant, yet he took time to review and practice fundamentals, which is what all talented people do. They go back to fundamentals.
A lot of K-12 students have just bits and pieces of understanding in arithmetic, if that, and the same is true for algebra because math fundamentals were not practiced to mastery. Indeed, many students who take AP calculus, AP statistics, or AP Physics never truly understand it. Common Core reform math will not change this.
As I stated years ago, Common Core is a political document intrinsically linked to the government's crumbling No Child Left Behind law, intrusive standardized testing, questionable data collection, and ill-advised policies. Education is ruled by an oligarchy. Educators have been conned and left out in the cold. The "powers that be" always win. Teachers have been left out of the decision-making process. Teaching under Common Core has become a exasperating chore for many classroom teachers rather than a delight, which is a sad commentary on education today. Teachers have to put up with government rules, regulations, policies, including NCLB, and reform after reform after reform. In addition, a few bad apples, poor working conditions, low prestige, and low pay have marred the teaching profession. Then, there is also Common Core that drives some of our best teachers out of teaching and prompts many parents to homeschool their kids. I am fortunate that I am not a teacher in the Common Core era. I left full-time teaching when it was no longer fun, and, a couple years ago, I stopped tutoring algebra and precalculus.
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| 3rd Grade: Teach Kids Algebra |
But, in 2011, I founded a unique algebra program, which was built on arithmetic and designed for little kids as a part-time guest teacher until Title I funding went to Common Core. The school district classified me as a College Prep Assistant. I wrote and produced my own materials. Algebra comes out of arithmetic.
Outcomes" is a collection of compelling and/or often contrary cogitations regarding Common Core and education. I think we ought to bury NCLB, Race to the Top grants, wavers, Common Core, and other blather coming from "high-IQ idiots" of the ruling class, who pretend to know what's best for kids [even though they have never been classroom teachers]. They believe ordinary people are too stupid to know what is good for students; consequently, over the years, they have produced a flimsy education system that equalizes downward. Common Core reform math screws up arithmetic, doesn't measure up to the Asian level or prepare capable students for Algebra 1 in 7th or 8th grade. This is moving backwards, not forward. Smart does not mean wise or prudent. We need leadership that is wise, but where is it? Apparently, there is very little wisdom in the top-down model of education.
"The only reform that almost no one in authority wants to see enacted: equalizing [K-12] funding nationwide," points out William Deresiewicz. There should not be rich school districts and poor school districts based on property tax, which has created a "class" inequality we see today. Even with equalizing funding, inequalities will still exist. Some kids are better at math than others, etc. Academic ability, conscientiousness, and hard work count!
There is a group of people who "believe" they are smart enough to make sweeping decisions, or reforms, or changes in education and can control [take over] education through government and big money--even though they have never been teachers in a K-12 classroom (the real world). [Why are non-educators making K-12 ed policies?] These people, who often claim a higher status than the rest of us, are dead wrong! Unfortunately, there are many self-serving high-IQ idiots in charge. William Deresiewicz writes, "We do need experts, to be sure, but we also need them not to be in charge." The idea that the "affluent and powerful have merit" and the rest of us don't matter that much is stupidity. The education system has created an underclass. "The poor are poor because they are inferior," the progressive elite say. Some teachers believe this, too. Such an assumption is rubbish. Who are these people? They are often politicians, corporate philanthropists, professors, economists, etc., along with many federal, state, and local officials--people who never taught K-12. There are exceptions, of course.
Dana Goldstein (The Teacher Wars) writes, "American teachers feel alienated from education policy making." If teachers don't matter that much in making education policy, then kids don't matter either. "It's for the kids" mantra is the ultimate deception. Telling kids they can be anything they want to be is another deception. Common Core is yet another reform forced upon teachers and kids with consequences--from an increased number of standardized tests and practice tests, instructional time stolen for test prep, not enough time [or money] for art, music, field trips, etc., says Dana Goldstein.
Quick Fixes: Hidden Danger
Evgeny Morozov (To Save Everything, Click, The Folly of Techological Solutionism) asserts, "The ballyhoo over the potential of new technologies to disrupt education--[such as online courses, etc.]--is a case in point. Digital technologies might be a perfect solution to some problems, but those problems don't include education--not if by education we mean the development of the skills [knowledge] to think critically about any given issue." Furthermore, we have been bamboozled into believing that the best way to improve education is to put more and more technology [Internet, computers, iPads, calculators, laptops, cell phones, smart boards, etc.] into our classrooms. The "quick fix" idea has never worked in education. We have had digital technology in our classrooms since the late 80s, and our test scores in math have remained relatively flat. Blackboards have been replaced by costly smart boards. Common Core has thrown out traditional arithmetic and cursive writing. Cognitive science has been marginalized and replaced by junk science. Teachers are told to teach the "Common Core Way." It's pathetic! "Schools concentrate all their efforts on improving test scores even if children learn much less as a result," explains Morozov. Technology and test-based instruction will not fix education.
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| Junking traditional arithmetic and replacing it with Common Core reform math was an epic error. Common Core reform math frustrates and confuses students and ignores basic cognitive science. |
Amy Chua & Jed Rubenfeld (The Triple Package), point out, "In short, education--like hard work--is not an independent, but a dependent variable. It's not the explanatory factor; it's a behavior to be explained. Successful groups in America emphasize education for their children because it's the surest ladder to success." A stress on education WITH high expectations, discipline AND hard work, and impulse control are cultural behaviors. It seems that many Americans may have lost these, say Chua & Rubenfeld. "America failed the marshmallow test."
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| Veruca Salt (Julie Cole) in Willy Wonka I Want It Now! |
Bad ideas plague K-12 education.
The first really bad idea was to junk traditional arithmetic and replace it with reform math ideology, such as in Common Core, which, in my opinion, is a regression to more mediocrity.
Furthermore, Kids are not the same so why feed them the same curriculum? Kids vary widely in math ability, yet they are placed in the same math class under the pretense of fairness, which is ambiguous. The kids who are better in math are bored with CC reform math and don't advance. The one-size-fits-all dogma of Common Core supports inclusion, not tracking. In contrast, Singapore tracks incoming 1st grade students who are weak in number skills (a pull out program), but, in my opinion, Singapore should also track (pull out) the very best math students, starting in 1st grade. Schools in the US don't track young children, which, I think, is a blind position. Mike Petrilli asserts, "The greatest challenge facing America's schools today isn't the budget crisis, or standardized testing, or teacher quality. It's the enormous variation in the academic level of students coming into any given classroom." The enormous variation, which is caused by inclusion [fairness] policies, has been a recipe for mediocrity in math education. Cognitive ability to learn math well, which varies widely, has been ignored. A child's academic ability and effort matter in learning arithmetic, algebra, and higher mathematics well.
We are living in "an age of diminished expectations," explains Ross Bouthat (New York Times Columnist). In my opinion, this is especially true in education. We underestimate the math and science content kids can [and should] learn, and we have become complacent with underperformance, which we judge as normal. Furthermore, the lack of critical thinking by those in charge of education, from local school boards and politicians to state and federal government agencies and officials and big money people like Bill Gates, has produced many inept policies, fads, myths, and bad ideas. Educators need to break free from a "standards-testing-data" mind set that has gripped schooling for decades. We don't need to transform education; we need to restore it. This is the antithesis of Bill Gates, Common Core, which Gates financed, and the progressive agenda of the US Department of Education and special interest groups that have profited hugely from Common Core.
The outcomes of K-12 Common Core are unknowable, yet billions of dollars have been put into Common Core. The outcomes (college/career readiness) claimed by Common Core reformers are speculation as there is no evidence they are true. If the math standards are inadequate, that is, not up to world-class benchmarks, which is the case, then the curriculum based on the Common Core standards would be ineffectual in that most students will continue to underperform.
Our schools may not be in decline as Diane Ravitch argues; however, they lag far behind in math and science education. The "We'll Try Anything" approach has failed again and again. The latest assumption is that our students need more technology in the classroom to raise test scores. Wrong! We have had computers and calculators in classrooms since the early 80s, yet math test scores have remained roughly flat. Is there a correlation here? Most Asian schools are low tech. In addition, the parents of Asian students pay for tutors, math lessons, and after-school cram schools. Typical American parents don't.
Michael E. Martinez (Future Bright) writes, "We recognize that some children display uncommon aptitudes for music, swimming, chess, mathematics, science, or art. Indeed, the entire field of gifted and talented education is premised on an assumption that some children are marked with unusual aptitude--so much so that the standard curriculum is an impediment to the child's development." An inclusion approach (everyone gets the same) has been a recipe for mediocrity, yet, it is a commonplace in our schools.
Our kids are not dumb. Indeed, better instruction, a focused curriculum, and teacher quality are important, but, according to Will Fitzhugh (Concord Review), "The most important variable in student academic achievement is not teacher quality, but the student's academic work." It's not the teacher's fault that a child is lazy or doesn't come to school prepared and ready to learn. Early on, parents should provide the environment for achievement and "teach their kids how to be successful in school," says Larry Winget. Mike Petrilli asserts, "The greatest challenge facing America's schools today isn't the budget crisis, or standardized testing, or teacher quality. It's the enormous variation in the academic level of students coming into any given classroom." The enormous variation, which is caused by inclusion [fairness] policies, has been a recipe for mediocrity in math education.
We have separated math from key applications, especially applications in science. Morris Kline (1973), a mathematician, writes, "Mathematics is not an isolated, self-sufficient body of knowledge. It exists primary to help man understand and master the physical, the economic, and the social worlds. It serves ends and purposes."
Prove Its Worth!
In math, we should show students "what mathematics accomplishes," and one enormous venture (Science--A Process Approach or SAPA) did this in 1967. In the 60s, SAPA taught mathematics in science. [I was fortunate to be a K-6 SAPA teacher.] K-6 SAPA taught the math kids needed to understand and do the science. In fact, 4 of the 6 processes taught in 1st grade (SAPA, Part B) were math or math related, such as numbers (arithmetic), measurement (metric), graphing, and geometry. Alfred North Whitehead (1912) said that educators need to prove mathematics, that is, "prove its worth!" Most ES teachers are weak in both math and science, so they can't do this. Indeed, many MS and HS math teachers don't have a science background. How many math teachers can actually show what mathematics accomplishes to prove its worth? The math education conundrum that existed 100 years ago in Whitehead's era, exists today! Why learn something when educators cannot prove its worth?
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| My 4th Grade Algebra Classes Doing Science 2012-2013 School Year Photo by LT |
In my Teach Kids Algebra (TKA) program, 4th graders did a ball bounce experiment from 5 different heights, 3 trials per height, recorded data, calculated averages, graphed it, figured out the best fit line, the slope, wrote a linear equation, and tested interpolated and extrapolated values. There was class discussion on measurement error.
Real scientists don't set out to prove their theories or equations right; they set up experiments to prove they were wrong. In this sense, science self-corrects itself. In short, science progresses through theories being falsified, says Karl Popper (1902-1994).
Science is highly mathematical, but you would not know it when you read elementary school science textbooks which are practically math-less, according to the late Richard Feynman, Nobel Winning Physicist. Perhaps, we should think like Max Tegmark, physics professor at MIT (Our Mathematical Universe), who writes, "Everything in our world is purely mathematical--including you." He says the Universe is not only similar to mathematical structure; it is mathematical structure. The physical world is described by mathematics; our reality is mathematics. Mathematics describes nature very well, and it is for this reason that young children should learn it well. Lastly, the world was lucky that Isaac Newton decided not to become a farmer as his mother insisted.
(Note. In TKA, no calculators were used. Also, it should be noted that the two classes of 4th graders I taught were Title 1 kids in a poor urban school district, 95% Hispanic.)
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| Mr. Wizard (Don Herbert) 1950s. Girl: Rita |
Mr. Wizard provided science instruction every Saturday morning for boys and girls. Today, we have nothing like Mr. Wizard, nothing to inspire children to get interested in real science. (Note. With the advent of test-based instruction, science faded out of the curriculum in many schools. It was never a priority in the first place.) Photo: Rita wrote equations for area. She thought the area of the inner white circle was larger than the the area of the outer white circle, but both turned out to be the same (9pi). "The next time you want to be accurate about something, make no judgements. Instead, measure and calculate." It is easy to fool our minds and get things wrong, so measure and calculate. Good advice for every math and science student and adult.
Bad ideas, fads, myths, whims, and pseudo-science have
corrupted traditional arithmetic and impeded math achievement.
Insert
In the New Math (1970s), the teacher asks, why is 9 + 2 = 11? A typical student should say 9 + 1 is ten (make 10) and one more is 11. The teacher says, “Wrong. 9 + 2 = 9 + (1 + 1) by the definition of 2. Thus, by the associative law, it becomes (9 + 1) + 1; therefore, 9 + 1 is 10 by definition of 10, and 10 + 1 is 11 by the definition of 11.” The New Math used number properties and definitions to do arithmetic. It is correct arithmetic, but it is also tiresome and confusing. (Reference: Why Johnny Can’t Add, Chapter 2, 1973, by Morris Kline, mathematician)
Today, the Common Core reform math teacher asks, “What is 8 + 5?” One student might answer 13. Another student might say the same as 5 + 8. The teacher says, “No. You didn’t tell why it's 13.” The teacher continues, “It is 10 + 3 = 13! You add 2 to 8 to make 10 and subtract 2 from 5 to make 3 [a double calculation], thus, it is 10 + 3 or 13," making a total of three calculations that clutter working memory. The Make Ten strategy changes an expression into another expression comprised of more compatible numbers that yield the same answer. The mathematical principles are not explained. It makes arithmetic overly complex, confusing, and perplexing to little kids. Make Ten and other reform math strategies have been major failures since the early 90s. Reform math strategies, such as make ten, are tangential, and should not be the primary or first method taught to kids for doing arithmetic. Note. Isaac Newton, a polymath, invented calculus, a fast way to get the right answer to physics problems, but the conceptual underpinnings of his calculation method didn't come for another 200 years. Newton knew that his fast method always worked [It agreed with observations]. He knew how to apply it, but he didn't know why it worked. Isn't getting the right answer to a problem the main purpose for learning mathematics? It was good enough for Newton. Nobel Prize winning physicist Richard Feynman often remarked that you don't understand something until practiced. In short, the how comes before the why.
In short, instead of memorizing basic facts, "make 10" and other strategies become the method of adding single digits, which is not practical or useful with larger numbers. Make 10 is not essential and leads nowhere. It's enrichment, if that. It is often confusing to young children and counterproductive.
This "make ten" approach is tedious, confusing, and not practical. Kids don't need to explain or write reasons why 8 + 5 is 13. It just is. Check it on a number line. It is obvious.
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| 8 + 5 = 13. It is obvious! It needs to be memorized to stick in long-term memory. There is no need to explain it, or write out the reasons why it is true, or make a drawing. And, there is no need to Make 10! |
The fact needs to be memorized. Kids don't have to prove that 1 + 2 = 3 or that 2 + 1 = 3. It is obvious! We accept it as a fact without proof. Likewise, students should not struggle through clever, complicated manipulations to show or prove that 8 + 5 = 13. We accept it as fact (8 + 5 = 13) and memorize it. In my opinion, Make Ten and many other Common Core reform math strategies lead nowhere and inhibit learning. Sadly, the strategies or models are commonplace in Common Core reform math. (It is the Common Core way.) Consequently, our kids cannot add because the mastery of basic number facts is not the actual goal. Furthermore, standard algorithms, which are excellent for practicing basic facts, have been shoved aside early on in Common Core reform math. Therefore, kids do not master basic arithmetic to prepare for algebra-one in middle school. Single-digit math facts should not be calculated; they should be automated for instant use.
1. Richard Feynman once wrote, "If you ever hear yourself saying, 'I think I understand this,' that means you don't." (Quote found in The Sense of Sytle by Steven Pinker. The late Dr. Feynman was a Nobel Winner in Physics.)
2. "The better you know something, the less you remember about how hard it was to learn." Teachers must know math, be good at explaining it, and prove its worth, starting in 1st grade. Understanding does not produce mastery; practice does. In short, students need explicit instruction (not inquiry/discovery based instruction in groups), along with memorization, repetition, practice, and lots of word problems. (Quote: The Sense of Sytle by Steven Pinker.)
3. The world was lucky that Isaac Newton decided not to become a farmer like his mother insisted. He hated farming. He went back to school at age 17 and started to study mathematics.
4. Common Core reform math looks like arithmetic, but it is not the real thing. Reform math doesn't get our kids where they need to be.
5. Alfred North Whitehead (1912), writes, "There can be nothing more destructive of true education than to spend long hours in the acquirement of ideas and methods which lead nowhere....Quadratic equations are part of algebra and algebra is the intellectual instrument for rendering clear the quantitative aspects of the world." Whitehead defends quadratic equations as important part of every child's education because they explain how the universe works, such as in Newton's laws of motion etc.
Common Core presents a flimsy "version" of arithmetic that lacks vision and doesn't get our kids to where they need to be. W. Stephen Wilson (mathematician) says that many kids never get to traditional arithmetic, much less master it, which, for centuries, has been the solid background needed for algebra. The reform math methods and strategies, which Dr. Wilson and many other mathematicians advise against, lead nowhere. We sent men to the moon using the slide rule; today we send kids who used calculators and taught reform math since grade school to remedial math.
Morris Kline adds, "The average schoolteacher is obliged to follow a curriculum that is laid out for him. He would not be allowed to depart from the syllabus." Kline asserts, "All talk about modern society requiring a totally new kind of mathematics is sheer nonsense." Kline, a noted mathematician, wrote these things in 1973, which, uncannily, describes today's Common Core reform math uproar. Not much has changed. Dumb ideas last because they are repackaged again and again and sound great!
Bad ideas, such as reform math, minimal teacher guidance methods, group work, Common Core, NCLB, mandated testing, RttT grants, wavers, fads, myths, pseudo-science, etc., which have infiltrated education and dictated policy, have not produce bright, high achieving students. Our kids suck at math because we made them that way. The way we think about education has been contaminated with bad ideas, junk, fads, myths, and pseudo science. It's pathetic. Moreover, our kids don't study enough, read literature and books enough, write essays enough, learn math and science enough, or exercise enough. Furthermore, many students often lack industriousness or do just enough to get by, but this isn't the teacher's fault. This is not only a schooling problem, it is also a parenting problem. American parents gladly shell out money for video games, gadgets, sports and lessons, but not for tutors. In short, many parents give education lip service. Education is not the top priority in many families today--sports, the newest technology, celebrities, and entertainment are. It is called pop culture.
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Common Core reform math looks like arithmetic, but it is not the real thing! The outcomes are that it makes simple arithmetic difficult and doesn't focus on mastery. Under Common Core and the reform math programs that came before, students do not master basic arithmetic to prepare for algebra in middle school. "In reform math, students use different strategies [that] are inefficient and won't help students advance," writes Laurie H. Rogers (Betrayed).
Steven Strogatz (Mathematician at Cornell) writes, "If we only teach conceptual approaches to math [i.e., reform math] without developing skill at actually solving math problems, students will feel weak. Their mathematical powers will be flimsy. And if they don’t memorize anything, if they don’t know the basic facts of addition and multiplication or, later, geometry or still later, calculus, it becomes impossible for them to be creative." (Strogatz's quote from The Atlantic in an article by Jessica Lahey)
Barry Garelick, in an Education News article ("Mathematics Education: Being Outwitted by Stupidity") writes, "The de-emphasis on mastery of basic facts, skills and procedures has met with growing opposition, not only from parents but also from university mathematicians. At a recent conference on math education held in Winnipeg, math professor Stephen Wilson from Johns Hopkins University said, much to the consternation of the educationalists on the panel, that the way mathematicians learn is to learn how to do it first and then figure out how it works later." Reform math is just the opposite and a reason our kids suck at math.
"Barbara Oakley, an engineering professor at Oakland University in Rochester, Mich., says the key to mathematics expertise is practice, not conceptual understanding as some common-core proponents would have educators believe."
Understanding does not produce mastery; practice does.
In my opinion, Common Core math standards should be used only as guidelines and "applied judiciously rather than robotically." [But, they are not used as a guide; they are used as dogma.] Instead of Common Core's dogma, students need achievable objectives that should be reshaped or modified as needed by teachers because academic ability varies widely and the background knowledge in vocabulary and arithmetic of students who walk through the school door diverges significantly. Consequently, CC's doctrine of "one size fits all" and its mandated testing are unintelligent and misguided ideas. There have been many bad ideas imposed on classroom teachers without their input. Common Core is one of the latest. I don't think one can fix Common Core. Teachers should trust the sensible Core Knowledge K-8 math sequence as a guide to write their own instructional objectives and refocus on essential factual and efficient procedural knowledge. Students need to learn arithmetic, not reform math.
Note. I think educators take Common Core literally. It should not be dogma, and it should not be interpreted as ideology or doctrine and taught as reform math, which, I think, are bad ideas. The standards equalize downward; i.e., everyone gets the same or one size fits all--another bad idea. In contrast, teachers should be empowered to ignore CC and write achievable objectives for the students who walk through the school door. In addition, teachers ought to junk reform math and bring back standard algorithms, which require the memorization and automation of math facts, and ask kids to do a lot of word problems. This [mastery] process requires a lot of practice and starts in 1st grade. For centuries, old-fashioned arithmetic, when it was taught well, has proved to be a reliable and trustworthy preparation for algebra and higher math. So why toss it out or marginalize it? Downplaying crystallized intelligence [factual and procedural knowledge in long-term memory] in arithmetic has failed for decades, which is a primary reason that our students suck at math. Teachers have been bombarded by bad reform after bad reform. They have no input. Top-bottom reforms, such as Common Core, don't work.
Starting in 1st grade, Common Core seems to justify inefficient, alternative algorithms to do operations or drawings or writing to "show" or "explain" understanding (?) by arguing, in my view, that not all students can memorized math facts needed for the standard algorithms. Really? Yet, in my opinion and experience, almost all students are good at memorizing. Memorization of single-digit number facts has not been a problem in other nations, and it wasn't a problem in the early 80s, when I taught first grade. Today, memorization of essential number facts is a problem, say the Common Core reform math advocates, perhaps, because memorization and drill [practice] do not conform to progressive ideology and have fallen out of favor in most classrooms. But, I should point out that this is not a new problem. Kids haven't been mastering arithmetic for decades. They are not taught to think in terms of symbols that convey concepts. "Barbara Oakley, an engineering professor at Oakland University in Rochester, Mich., says the key to mathematics expertise is practice, not conceptual understanding as some common-core proponents would have educators believe." Understanding evolves slowly and changes over time. What is more important, as Oakley points out, is to shift essential factual and efficient procedural knowledge into long-term memory through practice and practice and practice in order to maximize problem solving in math, especially word problems. You cannot apply something you don't know well.
Consequently, the outcome has not been good for crystallized intelligence in long-term memory, which is hugely important and prerequisite for problem solving in mathematics. Michael E. Martinez points out, "[It's] a mistake to downplay crystallized intelligence in favor of fluid intelligence." In short, you don't solve math problems without extensive math knowledge and practice. Downplaying crystallized intelligence in math has failed for decades. In short, kids are not taught to truly master traditional arithmetic. And, the same [downgrading traditional arithmetic] seems to be happening with Common Core reform math. Classroom teachers have been bombarded with reform after reform. Almost all were bad ideas and failed. Common Core reform math and the way it is taught do not match reality and ignore cognitive theory.
Michael E. Martinez (Future Bright) writes, "One domain of study might have been pivotal in the cultivation of fluid intelligence--mathematics....Early mathematics achievement now appears to have surprising power to predict student academic achievement in high school--both in mathematics and reading....Intelligence is...the product of education." It is a basic outcome of education when mathematics is taught well. My take on Common Core, however, is that the math is not taught well. In Common Core classrooms, what is taught looks like arithmetic, but it is not the real thing. Early on, little kids don't memorize math facts for mastery or focus on fast, efficient algorithms for basic operations (i,e., standard algorithms). Students can build fluid intelligence through problem solving in mathematics, which is the reason that word problems are so important, starting in 1st grade, but students must know basic arithmetic facts and standard algorithms to calculate answers to word problems. Furthermore, they must learn to recognize key patterns in word problems to know which operation or operations are needed (planning). All of this requires a lot of experience and practice, which has fallen out of favor in progressive classrooms. "As teachers teach, students become smarter," says Martinez. In short, teachers should teach directly, not facilitate.
Some kids, for whatever reasons, will always be better than others in math, but a widespread educational dogma taught in many ed schools is to equalize downward to narrow gaps, that is, let no child get ahead. However, kids are not the same in ability, so why feed them the same curriculum? It's a daft idea! We can never have equal outcomes. There will always be achievement gaps because good education creates inequalities, says the late Richard Feynman. Students who study more, practice more, pay attention in class, are more industrious, can delay gratification, and have an optimistic attitude create inequalities, etc. To excel in school mathematics, students need academic ability, realistic goals, and the persistence and conscientiousness to achieve through practice-practice-practice.
Dr. Richard Feynman ("Surely You're Joking, Mr. Feynman!" 1985) is a Nobel Winner in Physics. 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 made this blunt statement at an ethics in education conference. We need another Richard Feynman today, but we don't have one. Stephen Hawking has popular books, but he was not a Nobel Prize winner like Feynman. A Feynman comes along once in a lifetime, like Einstein and Newton.
Common Core's one-size-fits-all and top-down creed and ideology cannot close or eliminate the achievement gaps. The Common Core is a political document written in stone--not a flexible, feasible educational blueprint for positive change in math education. And, NCLB testing, which is part of the Common Core Package, should be buried, too. We cannot reform education unless we empower teachers, says Dana Goldstein (The Teacher Wars). Common Core does just the opposite and does not permit variation. It is imposed on teachers and students by government.
Common Core math is simply another edition of reform math [repackaged], which has not worked in the past. It looks like arithmetic, but it isn't the real thing. Common Core is not traditional arithmetic, and it is not taught the same way traditional arithmetic is taught.
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| Common Core 3rd Grade Lesson Counting Up Method for Subtraction From Erick Erickson Diary |
Common Core is not proven, tested, or reliable. It is a test-based reform. Moreover, the one-size-fits-all Common Core reform math standards, in my opinion, have been thrust into our schools by the powers that be and big money. States adopted the new standards before the final version was written or the costs calculated--an epic error in judgement, critical thinking, and common sense. A major consequence is that our kids suck at basic arithmetic because they are not actually learning arithmetic for mastery, but this is nothing new. Dr. Richard Feynman used to remark that you don't understand anything until practiced. I don't know why Common Core people make arithmetic instruction substandard [not up to Asian benchmarks] or needlessly difficult. Under Common Core, kids often have to "demonstrate understanding" using visuals, which they draw.The approach is nonsense. Understanding varies from student to student because academic ability and instruction vary widely. There is one thing for sure. Insight or understanding is the result of achieving essential knowledge in long-term memory [mastery]. Truly, you don't understand something until practiced, practiced, and practiced.
You don't make drawings to do arithmetic.
Who does that? It's another bad idea!
(Below) No wonder our kids are weak in arithmetic. They are not taught the real thing, that is, traditional arithmetic. Also see MultipleModels.
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| Area drawing for multiplication of two decimals. It is total nonsense! You don't make drawings to do arithmetic. (Image: Kaplan, 5th Grade Common Core) |
Knowledge of traditional arithmetic built up in long-term memory (mastery) through lots of practice (memorization and repetition) fosters understanding. It is tried and true and trustworthy, so why have schools changed to Common Core, which is the latest "form" of reform math, when the outcomes have no basis in evidence? Large scale, top-down, abrupt changes (often called reforms or innovations) have not worked well in the US public school system. Teaching Common Core as repackaged reform math is just the latest of countless fads and bad ideas that have crept into education.
Some outcomes, however, are knowable. I was talking to a 3rd grade teacher who said the kids this school year were taught Common Core last year. The results are easy to predict. She said her incoming 3rd graders could not add or subtract larger numbers, have no sense of place value, have not automate single-digit math facts, know nothing of standard algorithms, etc. In short, the students cannot calculate to solve problems, which is the main purpose for studying arithmetic. What will become of these kids? They don’t know arithmetic, and our reform math programs made them that way. Incoming Common Core third graders don't know number facts and efficient procedures that 1st graders easily learn in Singapore. Our kids are about 2 years behind because reform math programs do not require kids to practice fundamentals to mastery; consequently, there is little understanding. Professor W. Stephen Wilson says that students don't get to actual arithmetic when taught constructivist reform math programs, such as 5th grade Investigations/TERC. He calls it "pre-arithmetic." Common Core follows the same road.
Common Core Reform Math
It looks like [or pretends to be] arithmetic, but it's not the real thing. And, it is hindering students from mastering essential arithmetic. Here is an example.
Tell how to make 10 when adding 8 + 5. The student writes that you can't. The teacher responds and writes the "correct" answer, "Yes you can. Take 2 from 5 and add it to 8 (8 + 2 = 10), then add 3. The item above was found on Joanne Jacobs blog.
It is not a joke as some "commenters" suggested on her blog. It is not the teacher's fault, either. US teachers are told to teach Common Core reform math, which, I think, is a waste of time for most students because there are many variations that can confuse beginners, such as breaking 8 into 2 + 2 + 2 + 2 and 5 into 2 + 1 + 1 + 1. Add the 2s to get 10, then add the 3 ones. This does not lead to memorizing math facts for auto recall, which is essential. Kids are novices, not little mathematicians or experts. They need to practice and memorize basic math facts and get good at using standard algorithms to calculate starting in 1st grade. Mastery should be the goal because mastery leads to understanding. Understanding does not produce mastery; practice does.
Other commenters say this type of problem (make 10) is commonplace in Singapore math in K and 1st grade. Wrong! The Singapore primary syllabus makes no mention of it. To the contrary, the syllabus specifies that kids should memorize math facts in grade 1 and practice standard [formal] algorithms--not demonstrate proficiency by making tens, which is a reform math strategy (pedagogy) found in Common Core. What does "demonstrate proficiency" mean? What does "proficiency" look like? In fact, Singapore public schools start with 1st grade, not K, so there are no Singapore math standards for K. Singaporean parents have the option to pay tuition for private K schools, but the academic quality varies widely at these schools. They are not dependable. Indeed, many students skip K and go straight into 1st grade when they are old enough. In addition, roughly 2/5 to 1/2, perhaps more, of the incoming 1st grade Singapore students do not have an English speaking environment at home, yet they learn to speak, read, and write English in school.
Note. Make 10 is an inefficient reform math strategy. It clutters up working memory. Instead of memorizing single-digit facts for auto recall, like Singapore 1st graders, US students are asked to make 10, that is, to calculate single-digit number facts, which eats up a lot of working memory space. It is not necessary or beneficial. Why practice make ten at all? Why not simply memorize 8 + 5 = 13 for auto recall? Kids certainly don't need to write an explanation that 8 + 5 are 13. 8 + 5 = 13 is a true equation because it is obvious by inspection. [The left side {13} and the right side {13} name the same point on the number line and therefore are equal by the transitive law of equality: 13 = 13. A weakness in teaching young children arithmetic is that they never learn why an equation is true or false.]
Children should not calculate basic math facts in working memory, which takes up mental space that should be used for problem solving; they should memorize them for auto recall from long-term memory starting in 1st grade. But, this is not happening in reform math. Early on, starting in 1st grade, American teachers teach strategies rather than drill math facts for auto recall, or practice place value using standard algorithms, or teach kids when to add, subtract, or multiply to solve word problems, or teach kids how to write equations that are solutions to word problems. The student cannot become efficient at using standard algorithms without automating math facts. The math that students learn today, if it can be called that, such as in Common Core, takes the form of constructivist reform math, which is flawed.
"In reform math, students use different strategies [that] are inefficient and won't help students advance," writes Laurie H. Rogers (Betrayed). The Common Core/NCLB/RttT reforms have many unintended consequences, that is, "huge collateral damage in the form of a narrowed curriculum, loss of classroom creativity, and the rise of teaching to the test," writes Andy Hargreaves. But, the major consequence is that our kids stink at basic arithmetic because they are not actually learning arithmetic for mastery. Mastery is gained through practice, which leads to understanding. As Darren Miller writes, "Understanding is key...[and] comes with the mastery gained through practice." Not the other way around. The late Dr. Richard Feynman used to remark that you don't understand anything until practiced.
Dr. W. Stephen Wilson, who teaches mathematics at Johns Hopkins University, according to his assessment of 5th Grade Investigations/TERC (constructivist reform math), asserts that kids never get to arithmetic. What they learn looks like arithmetic, but it isn’t the real thing. It's constructivist reform math. Kids should learn the real thing!
In my view, the "many levels" in the same math class, an overemphasis on group work and inquiry learning, calculator use, multiple fads, minimal guidance instructional methods, inefficient strategies for calculating, and making drawings, have led to widespread underachievement and unintended consequences. Asian kids are superior in math compared to American kids (TIMSS, PISA). It's not that Asian kids overachieve; it's that American kids underachieve. In the US, it has been a mistake not to focus on mastery of fundamentals of arithmetic, a bad idea that has been part of progressive ideology for decades. Instead of mastering fundamentals in the early grades like kids in top performing nations, US students are taught inefficient strategies or models that make simple arithmetic needlessly difficult. Also, kids in the early grades are not taught the standard algorithms, which are efficient and always work. In short, constructivist reform math screws up arithmetic. "In reform math, students use different strategies [that] are inefficient and won't help students advance," writes Laurie H. Rogers (Betrayed). Gaining conceptual understanding is not mastery. Practice (memorization and repetition) is needed for mastery and to move students forward. Students don't need complete understanding either. There is no such thing because understanding grows slowly over time.
Darren Miller writes, "So repeat and repeat and repeat until the repetition begets memorization. That’s what Mrs. Barton [Miller's 3rd Grade teacher] did until every one of her students knew the multiplication tables. Don’t allow a pet pedagogical theory to harm students’ ability to calculate. Teach them what works. Give them the most efficient tools out there." Common Core doesn't give kids the most efficient tools, but traditional arithmetic does.
Kids need achievable learning objectives, but the one-size fits-all Common Core doesn't not allow for variation, which is deeply disturbing. Moreover, the learning objectives need to be specific, observable, measurable, and adjustable to meet the needs of the students who walk through the school door.
The biggest problem I have tutoring high school students is that they will often say they understand the concepts but can't work the exercise problems, much less the word problems. This means they don't truly understand the concepts and/or have not mastered some of the important arithmetic and pre-algebra fundamentals (knowledge gaps) when they were in elementary and middle school. They are products of reform math.
Walter Mischel (The Marshmallow Test), a psychologist, writes, "The ability [of preschoolers] to delay immediate gratification for the sake of future consequences in an acquirable cognitive skill. This skill set is visible and measurable early in life and has profound long-term consequences for people's welfare and mental and physical health over the life span." Anyway, this is Mischel's theory, but there is little evidence that it is true. Even longitudinal studies don't account for unmeasured traits that may affect the outcome. The feedback from the adults was self-reported, so the data is hardly scientific. We know that the brain is malleable or capable of change, but malleability is an inexact idea. You cannot turn a student with average IQ into a Ph.D. in mathematics or physics no matter how much the student studies and practices. Rather, executive function can help create competent math students, which is a worthy goal, but brain plasticity and ability have limits. You can increase IQ up to a point, but it can also decrease. Smart people often make stupid decisions, says Mischel, and he is right. Think about it! Who controls education? {smart non-educators} No wonder education is a mess of bad ideas. Another outcome is that teachers who criticize Common Core on social media are often reprimanded and written up. Test-based reform failed under NCLB, yet Common Core is an intrinsic part of test-based reform. The outcome isn't going to change.
Elementary teachers spend too much time on understanding rather than on practicing basic arithmetic for mastery. Liana Heitin (Curriculum Matters) writes, "Barbara Oakley, an engineering professor at Oakland University in Rochester, Mich., says the key to mathematics expertise is practice, not conceptual understanding as some common-core proponents would have educators believe." Mastery means instant recall from long-term memory that 5 x 5 = 25, which takes practice. You don't arrange beans in a 5 by 5 array to demonstrate that 5 x 5 = 25. That's a crutch, which can impede understanding, not mastery, says Oakley. She writes, "Having students stop to continually check and prove their understanding can actually impede their understanding, in the same way that continually focusing on every aspect of a golf swing can impede the swing." Mastery also implies that students have some understanding of the math and are able to apply it to solve problems. But understanding is a relative term and develops slowly over time. Unfortunately, reform math procedures in Common Core, such as counting up for subtraction needlessly complicate arithmetic and do not lead to understanding (no evidence) or the standard algorithm. In short, they are not practical; they are useless. Common Core justifies them by saying that not all students can memorized math facts needed for the standard algorithms. Yet, in my opinion, almost all students are good at memorizing. Memorization of single-digit number facts has not been a problem in other nations, and it wasn't a problem in the 80s, when I taught first grade. Suddenly, now, memorization of essential number facts is a problem.
Note. Many speak of equal opportunity, which is not a possibility because the students who come through the doors of different schools have different vocabulary and math backgrounds. Students vary widely in academic ability and knowledge; consequently, the curriculum should adjust to meet the needs of students, but Common Core does not allow variation. Kids need achievable learning objectives. But, many educators underestimate the content very young children can learn with explicit teaching, memorization, and practice, especially in essential arithmetic, starting in 1st grade.Instead of teaching traditional arithmetic using tried and true methods, Common Core tells teachers to use reform math methods. Thus, the outcomes will be totally different.
Notes.
Kids need achievable "behavioral learning objectives" (Robert Mager), and, because academic ability varies widely, the learning objectives should vary or be flexible from school to school, even from classroom to classroom, according to the students who walk through the school door. But, Common Core does not allow for variation. Since the 70s, educators have switched from behavioral learning objectives, which specify conditions and criteria for acceptable performance, to nonspecific or less specific objectives such as understands concepts, solves problems, acquires fluency, is proficient, or know from memory, which are unclear, ambiguous, and ill-defined. "Teachers rarely specify conditions and criteria in their objectives," says Pearson Education, so the learning objectives are fuzzy and vague. In math, teachers often say they teach "understanding," yet understanding is indeterminate without specifying the conditions and criteria. On the other hand, Mager's behavioral learning objectives specify the conditions and the criteria for acceptable performance. According to Mager, acceptable performance is observable and measurable and must be stated clearly--both conditions and criteria. Mager is not talking about rubrics, which are subjective. Without the conditions and the criteria for acceptable performance, teachers don't know what acceptable performance looks like. In short, there must be an observable behavior that is measurable. Also, under the Common Core, teachers are told to teach multiple strategies (constructivist reform math) rather than traditional arithmetic. But, in my view, they need to cut out the trivial and go straight to basic [traditional] arithmetic (the real thing). This is difficult with Common Core because it is a repackaged "strategies" approach and doesn't go straight to essential arithmetic. Consequently, teachers focus on strategies, not traditional arithmetic, which is built on concepts, basic facts, efficient algorithms, and routine applications. In Common Core, all students get the same, which is a shabby approach to education because academic ability varies widely. Common Core cannot narrow achievement gaps without equalizing downward. In short, most kids are not learning enough basic arithmetic that is essential for algebra-one in middle school. It's a conundrum. The effectiveness of Common Core or any set of standards taught as constructivist reform math has always been questioned and strongly criticized by mathematicians and scientists. In addition, the lack of word problems, applications, and arithmetic used in science in the US elementary school math curriculum have been grounds for concern since the 70s when Professor Richard Feynman read elementary school math and science textbooks and called them "lousy." Read more about Feynman and his conclusions on MultipleModels.
[On a personal note, I stayed in the classroom because teaching was fun and retired when it became a chore. I no longer tutor high school mathematics, such as precalculus, and, sadly, my Teach Kids Algebra guest teacher program has gone unfunded for the past two years because of district budget problems. Teaching under Common Core and a host of other government regulations, including NCLB, has become a chore for many classroom teachers rather than a delight, which is a sad commentary on education today. I feel fortunate that I am not a teacher in the Common Core era. It is clear, at least to me, that the wrong people are in charge of education; consequently, the public schools have been losing some of its best teachers who are fed up.]
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