Note: For years, U.S. high schools have inflated graduation rates via bogus credit recovery, grade inflation, and substandard courses.
Richard Rusczyk (the Art of Problem Solving) says that there is no reason we can't. He explains that calculus is for average high school students who are prepared. The conundrum is that our students are poorly prepared even in 1st grade. Students are novices, not little mathematicians. They need to learn content that is world-class to support problem-solving, but they don't under reform math.
(Note: Singapore 1st-grade students learn much more key content than American 1st-grade students. For example, Singapore students memorize addition facts, write equations from word problems in three operations (+ - x), drill to develop skill, learn formal algorithms, practice multiplication as repeated addition, and much more.) We don't do any of these in most 1st-grade classrooms.
The major textbook companies such as Pearson dictate the math curriculum, which is reform math. Instead of standard or traditional arithmetic and its standard algorithms, students are introduced to a hodgepodge of inefficient, alternative algorithms (aka reform math). Rather than teaching content for mastery (i.e., competency), the grade 3-8 teachers are told to teach to "items on the state test," which is a fragmented curriculum. Professor Milgram stated in a 2016 interview that the reform math textbooks, programs, and methods are "a total waste of time for your average, above average, and accelerated students. Just a complete waste." After reading parts of a 1st-grade enVision textbook and other textbooks from Pearson, I think he is right.
Most of the math class time is misdirected into group work, discovery/inquiry or other minimal guidance methods. The content is lean. Kids are encouraged to use calculators. Also, little time is given for practice, review, and feedback. Students do not memorize or drill-to-develop-skill because the mastery of fundamentals in long-term memory is not the primary goal of reform math. Consequently, in the real world, 54% of Singapore 8th-grade students score at the Advanced Level compare to only 10% of U. S. 8th-grade students (TIMSS). The great majority of students who want to go to community college will likely end up in remedial math because they have not mastered basic arithmetic and algebra. (Note: This has been the case for at least a decade or two, probably longer. Sufficient content is lacking in many so-called college-prep algebra courses in high school.)
If "learning is remembering" from long-term memory, then as Zig Engelmann points out, "You learn only through mastery" (i.e., practice-practice-practice). And, he is right! While other nations focus on mastery of fundamentals, many American educators complain that the content is developmentally inappropriate. Why is the content inappropriate here and not in the high achieving countries? The U. S. followed Piaget, even though much of his developmental theory had been refuted. Many other nations, including East Asians, did not follow Piaget.
Note: R. Barker Bausell, Too Simple To Fail, wrote that the work of Jean Piaget would ultimately wind up having no recognizable application to classroom instruction. Unfortunately, many teachers still hold to Piaget's claims that children grow into math and abstraction. The reason young children don't know much math isn't a matter of age or development but a matter of not being exposed to it (National Math Panel 2008).
The crux is that under reform math, which dominates American classrooms, "children do not practice math skills to mastery" (Laurie Rogers, Betrayed). Simply, reform math with its different strategies (i.e., inefficient alternative algorithms) does not work. Also, children might enjoy discovery activities, group work, and other minimal guidance methods, which are time-consuming, but they aren't learning enough math. Skills should come first, but not in reform math.
In contrast to American elementary schools, students in other nations such as Russia learn the standard algorithms for multiplication (e.g., 4987 x 6) and long division (e.g., 4987 ÷ 8) no later than the 3rd grade through practice-practice-practice. In Singapore, multiplication starts in the 1st grade, half of the multiplication table is memorized in the 2nd grade, and the rest in 3rd grade. Unfortunately, we have a barrage of math educators, teachers, professors of education, administrators, reformers, and so-called experts who denigrate standard arithmetic and want to abolish algebra as a requirement for college.
Parents don't seem concerned that their kids are 2 or 3 years behind in learning math content and problem-solving. The bottom line is that many students do not master basic arithmetic or algebra. Calculators disrupt mastery and camouflage weak math students. Parents say that education is a priority, but it isn't in practice. They gladly put out money for the latest gadgets, video games, smartphones, kids' sports programs, lessons, TV service, and so on but seldom for Kumon math lessons or a private math tutor.
Peg Tyre (The Good School) writes that (in the 60s) Singapore rejected Piaget's notion of kids growing into math and abstraction, but American educators eagerly adopted Piaget's progressive theory, which was a colossal mistake. In contrast to Piaget's notions, East Asian countries and other nations embraced the views of Jerome Bruner "who argued that kids are capable of learning nearly any material so long as it is organized, sequenced, and represented in a way they can understand." (Note: Bruner's quote is from Tyre's book.)
Moreover, the National Math Advisory Panel (2008) rejected the claims of Piaget. Kids do not grow into abstract thinking. The reason our "children often don't know math at an early age is not that the content is developmentally inappropriate but that they haven't been exposed to it."
In short, U.S. kids are not taught math they should learn. They underachieve compared to their peers in some other nations. Many primary teachers de-emphasize traditional arithmetic and its standard algorithms and, instead, teach reform math. The elementary teachers, themselves, are weak in arithmetic and algebra. Also, teachers try to make math fun, but learning math is hard work. Students need to memorize and drill to develop skill. American educators and parents need to wake up about what it takes to improve math performance.
©2017 LT/ThinkAlgebra
