Comments
To me, Common Core math, aka state standards, and Every Student Succeeds Act does not establish realistic goals because the kids who walk through the school door vary widely in math ability, knowledge, and motivation. Early exposure and practice, I believe, are a step in the right direction for developing achievement, but, likewise, to obtain better achievement requires ability, determination, and drill-for-skill. Unfortunately, US educators frequently downplay ability, trivialize drill-for-skill development, and focus too much on standardized testing. In the real world, some kids are better at math than others. That's life! Moreover, the one-size-fits-all dogma of Common Core and state standards is an inferior approach to math education.
Also, I believe the math education most kids get is full of gaps. If you get a 75% correct on a test, then you miss 25% of what you need to know, says Salma Kahn. "Concepts build on one another." Kids need a "good grasp of basics" to acquire a higher-quality achievement. But, many students never master the fundamentals of standard arithmetic. Instead, they are taught doses of test prep; (i.e., bits and pieces) and reform math, which sidelines or delays the standard algorithms and substitutes several, more complicated ways to perform simple arithmetic. Indeed, Common Core or state standards are often interpreted through the lens of reform math.
Focus on Developing Achievement
In education, everything seems to be about race and "illusions of fairness" rather than excellence and achievement. The focus should be on cultivating talent and developing achievement, but it isn't, regardless of the rhetoric and hype. Instead, there has been an anti-intellectualism movement in our culture. No Child Left Behind, now Every Student Succeeds Act, mantras such as Algebra for All, College for All, and ideas such as inclusion and one-size-fits-all are not what they seem to be. Also, included are Common Core (linked to testing and so-called Mathematical Practices), most math reforms (reform math), minimal guidance methods (discovery), group work, technology (i.e., the silver bullet), etc. All of these are smokescreens and part of an anti-intellectualism culture. Indeed, they are not credible because they are not supported by scientific evidence. I am not sure we can fix an anti-intellectualism culture that prescribes progressive ideas.
"We need nerds because they make the world a better place," writes David Hopkins. We need smart kids. We need smart, minority kids, too, but, in my opinion, the people in charge of our educational system (i.e., the progressives), seem bent on suppressing excellence and achievement, regardless of their deceiving rhetoric. "The Common Core standards initiative is part of the progressive push to centralize education, says the Heritage Foundation in a new report," writes Dr. Susan Berry. Note. Common Core has been renamed "state standards" with little change.
Proper instruction should increase differences, and, therefore, inequalities, explains Richard Feynman, Noble-prize winner in Physics. (Progressives: Well, we can't have that! It's racist.) “Equalizing downward by lowering those at the top” is an illusion of fairness that hurts bright blacks and Hispanics, observes Thomas Sowell (Dismantling America, 2010). Many low-income kids are smart and can be high achievers in math, but they seldom get the accelerated instruction that meets their needs. Our best students in math should be tracked starting in early elementary school. (Progressives: Well, we can't have that! It's racist.). In my opinion, inclusion policies and other progressive social policies in our schools interfere with the academic advancement of bright black and Hispanic students by lowering those at the top so that one size fits all.
I think it is absurd to deny better students algebra in middle school or fast track math in elementary school. If we can develop talent in music at an early age, then we can do it in mathematics, too. "Talent matters but motivation [commitment and passion] may matter more," writes Daisy Yuhas (Scientific American, Think Like A Genius). To develop ability in mathematics requires content acceleration and task commitment. Gaining knowledge is key to becoming proficient and an expert. American schools rarely fast-track mathematical ability. Opportunities for high-achieving students are often limited. Excellence has not been the focus of schooling for decades. Tracking, if it is implemented correctly, can help all achievers, including black and Hispanic students, by establishing manageable achievement benchmarks and code of excellence in our schools.
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| High-Achieving Students Need Acceleration |
"Today, researchers, policymakers, and teachers pay little to no attention to high-achieving students.... Many such students spend their days in school unchallenged--relearning material they have already mastered ... In academics, so far only in mathematics do we have reliable ways to detect potential talent early on ... High achievers may have exceptional task commitment, meaning they are willing to engage in study and practice that, though not necessarily enjoyable, is instrumental to improvement ... Acceleration significantly boosts both achievement and motivation in gifted students ... Schools hardly ever use acceleration strategies, yet acceleration should be a key part of gifted education." explain Subotnik, Olszewski-Kubilius, & Worrell (Scientific American, Think Like A Genius, November/December 2012). High-achieving math students need acceleration that advances them, not enrichment.
Scores Are Flat And Going Down
In reform math, the standard algorithm has been denigrated. For example, students are taught 3 or 4 nonstandard ways to multiply numbers, a reform math pedagogy that had not worked in the past. The multiple ways often confuse students, overload working memory, and alienate parents. Consequently, fewer students master the standard algorithm. The TIMSS (International) test scores show that US students are not improving like students in some other nations. Moreover, the 4th- and 8th-grade 2015 National Assessment for Educational Progress, or NAEP, math scores are worse than the scores from 2013. Tom Loveless (Brown Center Report) points out, “The bad news is that there also is no evidence that CCSS [Common Core State Standards] has made much of a difference during a six-year period of stagnant NAEP scores.” Apparently, what we consider good teaching and good practices are inadequate, inferior, and seriously flawed—e.g., reform math, minimal guidance, one-size-fits-all, Common Core, group work, test prep, technology hype, and inclusion, just to name a few.
Math & Music
Many Asian parents guide their children into math and music. From the beginning, children are taught that math is important. Asian parents also push early musical training (playing piano or violin) because they believe that learning to play a musical instrument helps with learning math. Incidentally, musical talent can be spotted in kids aged 2 to 4. Also, Asian parents frequently teach basic arithmetic (e.g., addition facts) to their preschool children. Even after their children have started regular school (1st grade), parents continue math lessons at home using workbooks. Students practice math at school and at home. Also, after school, many Asian students go to cram schools to prepare for consequential exams. For example, in Singapore, the 6th-grade primary (math) exit exam determines which secondary school (7th-12th) the child can attend, aka tracking.
In Singapore, tracking students starts in the 1st grade with a pull-out program for incoming students who lack numeracy skills. (Note. Public school in Singapore starts in 1st grade.) The catch-up program lasts for two years and works well. Tracking starts again in the 4th grade when math becomes harder. Some students are placed in a different textbook with a separate teacher. [Note. The Singapore curriculum and instructional methods are not perfect in my opinion. The curriculum relies too much on bar models rather than on writing equations to model problem situations. The early curriculum should include number lines and negative numbers in 1st grade. Moreover, 1st graders should learn functions (input-output model), built tables of values, and graph linear equations in Q-I. Students should do more measuring in 1st grade: mass in grams, liquid volume in milliliters and liters, solid volume in cubic centimeters, length in centimeters and meters. Also, in 1st grade, the curriculum should include perimeters of squares and rectangles (addition) and areas of squares and rectangles (counting).]
US Math Achievement Is Stalled
Curriculum & Instruction Are Weak!
Math achievement has been stalled for years. US students, on average, are mediocre compared to their peers in some other nations (TIMSS). Indeed, on international tests, our students are not achieving as fast as students in some other countries. The latest indicator is that the 2015 National Assessment for Educational Progress (NAEP) math scores for 4th and 8th graders are lower than in 2013. As stated above, the math curriculum, instructional methods, and progressive social policies are seriously flawed.
The strength of a math program is found at the Advanced Benchmark level of TIMSS, an international test. At the 8th grade level, 48% of Singapore students reached or exceeded the Advanced Benchmark compared to 7% of US students. At the 4th grade level, 43% of Singapore students reached or exceeded the Advanced Benchmark compared to 13% of US students. Roughly half of the Singapore students learn content significantly above their grade level. The TIMSS Advanced Benchmarks show that American math programs are weak both in curriculum and instruction. The rote-leaning kids in Asian nations not only master math but also dominate in problem-solving. [Advanced Benchmark data from 2011 TIMSS; PISA]
Good instruction should increase differences.
Richard Feynman, a Noble-prize winner in Physics, writes about the ethics of equality in education, “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?” (“Surely You’re Joking, Mr. Feynman” by Richard Feynman, 1985) The idea that instruction should increase differences conflicts sharply with the prevailing progressive ideology of inclusion and sameness and with Common Core's one-size-fits-all tenet, aka every student gets the same instruction regardless of the achievement level. Indeed, "equalizing downward by lowering those at the top," in the name of fairness, is an "illusion of fairness" and a twisted idea. (Note. "equalizing downward..." and "illusion of fairness" by Thomas Sowell)
Failed!
Many failed ideas and assumptions, practices and pedagogies, and theories and conjectures in education don’t get junked overnight. They hang around for decades and decades. Some are repackaged and start anew, such as the resurgence of reform math. Similarly, like the failed programs of the past, the newest trends and fads (often called innovations) are not supported by the cognitive science of learning. In short, the claims of effectiveness lack scientific evidence.
Squandering Talent
Starting in elementary school, our best students in math and science are not only underserved and underfunded, but they are pushed to the back burner and left to fend for themselves as if they don’t exist. Much of our potential talent is squandered in the American system. Many low-income kids are smart and can be high achievers in math, but they seldom get accelerated instruction that meets their needs. Parents of high achieving kids should be outraged.
Tom Loveless, a Brookings Institute researcher, writes, "You need to cultivate talent over time in mathematics." Indeed, high-achieving minority students should be tracked into advanced groups, starting in lower elementary school. Ther best math students of all races should be tracked. Jill Barshay (Hechinger Report, Education by the Numbers, March 28, 2016) writes, "Loveless's research raises an age-old question of whether excellence is sacrificed by well-intended efforts to promote equity." The fairness policies, which are illusions of fairness, hurt low-income black and Hispanic kids in urban schools. Black and Hispanic kids have every right to be in advanced and honors classes. But, their talent must be spotted early enough and cultivated through tracking. Unfortunately, most American educators believe that tracking exacerbates inequality, even if it means denying high-achieving minority students the opportunity and boost they need. I don't believe that tracking--when done properly--increases inequality or makes students feel bad. I have been hearing these excuses for over 40 years. Even 1st-grade students know which kids are brainy. It is absurd to deny better students algebra in middle school or fast track math in elementary school.
We need to cultivate talent at very young ages. The American excuse has been that practice to cultivate talent takes away from childhood. It's baloney. Also, the cultivation of young talent requires exceptional instruction. However, high-achieving, mathy kids are not likely to get the level of math instruction needed in elementary schools and many middle schools. Furthermore, students who do not take a high-quality, traditional Algebra-1 course in middle school, as defined by the National Mathematics Advisory Panel (2008), will likely be locked out of advanced math and science courses, such as algebra-based physics, in high school. Math talent needs to be identified, trained, and developed early on. If we can develop talent in music at a very young age, then we can do it in mathematics, too.
Stupidity
Some school districts are making stupid decisions based on Common Core’s one-size-fits-all mantra. One is kicking Algebra-1 out of middle schools, such as in the San Francisco Unified School District, according to Ana Tintocalis of KQED News. The SFUSD justifies its decision for two unverified reasons. One is that Common Core pushes algebra to 9th grade, which is a ruse. Common Core allows content to move up and down. The second is that tracking students, based on a student’s achievement in math, is wrong and a matter of social justice. No, the reason is that tracking doesn’t fit the entrenched progressive tenet (ideology) of “sameness,” which, Thomas Sowell (Dismantling America, 2010) has described as an illusion of fairness.
Inclusion policies lower those at the top.
Tracking students is not wrong! Not tracking students is equivalent to “equalizing downward by lowering those at the top,” which is a twisted tactic in many public schools and a “crazy idea taught in schools of education,” writes Thomas Sowell (Dismantling America, 2010). Tom Loveless (2016 Brown Center Report on American Education) writes, “Recent research indicates that high-achieving students may benefit from tracking…. Tracking is significantly correlated with performance on AP tests, which holds true for black, Hispanic, and white subgroups.”
Absurdity Reigns
It is absurd to deny better students algebra in middle school or fast track math in elementary school. The idea arises from the bent mentality of a one-size-fits-all dogma in Common Core and state standards. Both high achievers in math and low achievers are tossed together in elementary school classrooms (inclusion policy). The same goes for middle school math classes. All the kids, regardless of ability and achievement, get the same math content and work in groups (inclusion). In 9th grade, both high achievers and low achievers are in the same algebra class. Furthermore, in Common Core classrooms, students don’t need to drill-for-skill to learn math, which is idiocy raised to the nth power, if that was possible. The best math kids, starting in 1st grade, need a separate curriculum (acceleration) taught by an algebra teacher to cultivate their ability, which is malleable.
Opinion (Real World Problems)
The math reformists say that Common Core teaches math differently. The new math approach requires discussion of so-called real-world problems in small groups (inclusion) and reasoning that leads to deeper understanding. For example, students voice their opinions when comparing two advertisements from competitors (aka real-world problems) or the pros and cons of social issues. Students argue and defend their views based on the numbers, percentages, probabilities, averages, charts, graphs, and text of the ads (the given information). But, students have no way to figure out the correctness of the claims suggested in the ads. They don't have enough information. All ads are bent and misleading. Bias is everywhere, and it is easy to lie with statistics! "Data analysis is rarely simple and straightforward. It may be possible to draw more than one conclusion," writes Sherry Seethaler (Lies, Damned Lies, and Science, 2009). Furthermore, children do not know how to do costs benefits analysis.
Given a real-world problem in school, children are not expected to produce information (data) to find patterns that will help them make better choices and reduce risk. In fact, K-8 children probably do not understand risk-reward covariance. They don't realize that the possible choices are often false dichotomies. In my opinion, the so-called deep understanding that allegedly comes from the discussion in groups is merely juvenescent opinion and shallow thinking. In many cases, so-called real-world problems are oversimplified, superficial, and not the real world at all. Perhaps, it is better to teach kids personal finance and basic economics.
Moreover, many important decisions youth and adults make are subjective. Real decision making deals with uncertainty. There are risks. Often, we downplay or ignore the risks. Which college should I attend? Which major should I select? If I major in x, will I be able to find a job when I have a degree? Will I be able to pay off student loans? Should I get a degree online or attend a traditional university? Which smartphone should I buy? Which carrier is the best? Which car should I buy? Should I buy a used car or a new car? Should I pay cash or finance the car? Should I finance a new TV and furniture? Should I rent an apartment or buy a house? Is product x better than product y?
Incidentally, math, itself, is not a matter of opinion; it is a matter of fact.
Real World
The reality is that most high school graduates are not college-ready. And, there is no evidence that Common Core’s one-size-fits-all approach will magically make them college-ready, not even for community college.
©2016 LT/ThinkAlgebra.org
First Draft, To Be Revised
Please excuse typos and errors.
