There is no substitute for knowledge in long-term memory
and the practice that gets it there.
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| "Drill to develop skill" is essential. |
[ Note: There are many beliefs in education that lack scientific evidence. Belief is not evidence. Anecdotal claims are not reliable because they are based on "personal accounts rather than facts or proper research." ]
Consequently, students do not master standard arithmetic and the standard algorithms to perform arithmetic. Moreover, the reformers have branded "Old School" ideas such as "memorization" and "drill to develop skill" as obsolete and bad teaching. Countering the reformists' claims, the Old School ideas worked well for most students. They are essential, not obsolete. Also, progressive reformers refuse to sort kids. It makes no sense to place high achieving students in math with low achieving students in the same math class via so-called inclusion or fairness policies. Thomas Sowell points out that "equalizing downward by lowering those at the top [is] a crazy idea taught in schools of education across the country." The high performing students need a different curriculum taught by an algebra teacher starting no later than the 2nd grade. Differentiated instruction within a classroom has never worked well. Chester Finn, Jr. and Brandon Wright write in EducationNext, "Rare is the teacher who can do right by her ablest pupils at the same time she provides slower learners in her classroom the attention that they need."
Click: My Contrarian Math Page
[ Special Insert
My Contrarian Math Page is a response to progressive pedagogy and its illogical reforms. Charles Payne, University of Chicago (So Much Reform, So Little Change, 2008), points out the Holy Postulates for progressives. Here is one: "The Only Pedagogy is Progressive Pedagogy, and Thou Shalt Have NO Other Pedagogy Before it. Drill and practice are always wrong. Real teaching is always inquiry-based, student-centered, and constructivist." The progressive assumptions are bunk. (Quote Source: Larry Cuban's blog)
Progressive pedagogy is an ideology, not a science of learning content. Evidence doesn't matter to progressives who trash the standard algorithms and put calculators in the hands of K-12 students for arithmetic and algebra. Memorization, imitation, repetition, review, and "drill to develop skill" are often downgraded or disparaged in progressive pedagogy or should I say ideology.
Examples of progressive pedagogy are reform math and state-mandated standards, which are primarily Common Core. A popular reform math curriculum is Everyday Mathematics. Group work and minimal guidance during instruction such as discovery/inquiry activities are characteristics of reform math. In 2015, U.S. 4th grade students outscored Finland 539 to 535 in the math content section of TIMSS, an international test, but the East Asian nations dominated with Singapore at 618, Hong Kong at 615, and S. Korea 608. How has the resurgence of reform math worked out? The U.S. TIMSS math scores for 2013 were better than the 2015 scores. Furthermore, by the 8th grade, 54% of Singapore students reached the Advanced TIMSS Level compared to 10% of U.S. students, which indicates that we are not teaching math at a world-class level starting in the 1st grade. The teaching of items on a test is a fragmented curriculum and not the same as standard arithmetic and algebra.
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Other illogical reforms include an obsession with technology as a panacea, the use of calculators in K-12 mathematics, the intense concentration on critical thinking without content, and the minimal guidance "constructivist" methods during instruction. Moreover, the popular Piagetian notion that kids learn best (naturally) through a child-centered discovery/inquiry approach without a formal curriculum is bogus and violates the basic tenets of the science of learning content. To learn something is to remember it from long-term memory, which requires memorization, imitation, repetition, review, and hard work. Kids need to "drill to develop skill" to learn arithmetic well, that is, they need to practice-practice-practice.
There is no substitute for knowledge in long-term memory and the practice that gets it there.
At the Brookings' Brown Center Chalkboard blog, I noticed that all the topics were about issues, such as teacher diversity, personalized learning, integrating schools, technology, teacher pay, graduate degrees, equal pay, but nothing about teaching, itself, which is what teachers are supposed to do.
One reason that most kids grossly underachieve is that educators do not teach the basics of arithmetic for mastery. Yes, it often is that simple. (There are other reasons, too!) The Reform Math frame-of-mind marginalizes the standard algorithms. The standard algorithms are not taught first if they are taught at all. They are not the top priority in reform math, but they should be! Progressive educators trash the standard algorithms saying kids don't need to learn the multiplication table or the mechanics of long-division and fractions because they can use calculators.
More is said than done. It is especially true in education. We say we want students to engage in "higher-level" thinking, yet we don't focus on lower-level thinking (i.e., knowing and applying content) that leads to higher-level thinking. Put simply: our actions do not support our goals. We say one thing, then do another. We say x causes y based on scant or anecdotal evidence when there is no cause-effect. Hence, education is loaded with false claims, junk science, and so-called "exemplary" reform math programs that do not work well. Moreover, kids are seated in small groups facing each other. Consequently, they are easily distracted and off task. Much instructional time is wasted.
Immanuel Kant wrote that thought (e.g., critical thinking, problem-solving, analysis, etc.) without content is empty. To learn something means remembering it from long-term memory such as the single-digit number facts and standard algorithms in arithmetic. Learning requires effort, memorization, drill to develop skill (practice-practice-practice), and review. Unfortunately, the focus has been on reform-math alternatives rather than the standard fundamentals of arithmetic that prepare students for Algebra-1.
By 8th grade, American students are at least two years behind their peers from some other nations; only 33% of them are proficient in math (NAEP 2015: The Nation's Report Card).
Moreover, teachers are often required to teach "items on the test" and use inferior methods of instruction; consequently, many students never master arithmetic. In effect, the math curriculum is fragmented and below world-class levels. The disparity begins in the 1st grade.
In Everyday Mathematics (EM), which has been a popular reform math program, "The addition algorithm is probably the best of the U.S. traditional computation algorithms," but "Everyday Mathematics does not focus on it." Why not? Also, Everyday Mathematics shows five algorithms for whole-number subtraction: "trade-first, counting up European, left-to-right, and partial-differences," but not the standard algorithm for whole number subtraction.
According to Everyday Mathematics, "Learning a single traditional algorithm for each operation, especially at an early stage, may inhibit the development of children's mathematical understanding." Wrong!!!
As Carl Sagan once said, "Extraordinary claims require extraordinary evidence" And, the supporting evidence just isn't there. The reform math claim is absurd! (FYI: Today, reform math ideas are prevalent in most K-8 classrooms.) Unfortunately, EM recommends four-function calculators for the early grades (K-3) and a scientific calculator starting in 4th grade. A keystroke sequence on a calculator is not the same as learning basic arithmetic in long-term memory.
If Reform Math had worked well, then our students would be at the top on international tests such as TIMSS and PISA, but they are not.
Last update: 10-12-17
©2017 LT/ThinkAlgebra
