Wednesday, October 25, 2017

Progressive Ideas Litter Education

Progressive Ideas Litter the Education Playground
The claim that teaching kids math discriminates against children of color is the latest progressive gobbledygook. Professor Gutierrez's remarks are ludicrous and biased. We need to keep politics out of schools. (See Alert below)

E. D. Hirsch Jr. writes, "Critical thinking does not exist as an independent skill. The domain specificity of skills is one of the most important scientific finds of our era for teachers and parents to know about, but it is not widely known in the school world.”

The idea that learning "standard arithmetic" is not that important stems from the progressive self-esteem crusade and reformers who think calculators are a substitute for learning basic arithmetic. Furthermore, progressive reformers also believe that critical thinking and problem-solving skills should be taught independent of content. They are WRONG

Children of color can excel in math when it is taught and practiced for mastery. But, this is often not the case. Also, Mark Manson points out that we have grade inflation, participation awards, and bogus trophies "to make low-achieving kids feel better about their lack of achievement." In my opinion, all teachers should teach standard arithmetic and standard algorithms rather than reform math. 
(See Alert below)

Peter W. Cookson Jr., a sociologist, wrote about the future: "Teachers will need new pedagogies and curricula for their students that emphasize problem-solving, higher-order skills, access to machine intelligence, teamwork, and lifelong learning." It's the same old junk from progressive ideologues that failed in the past. Cookson seems to ignore the critical importance of content knowledge in long-term memory needed for problem-solving, learning, and innovation.

Cookson claims that "inquiry skills" will drive learning; however, inquiry learning and similar minimal guidance methods are inferior to explicit teaching, according to Kirschner, Sweller, and Clark, who equate minimal guidance with minimal learning. Also, Cookson stresses "skills without content," which is not possible. Critical thinking or problem-solving is domain-specific. You have to know some trig to solve trig problems. 

Cookson is in a fantasyland. He talks about preparing kids (the digital natives) for an upcoming innovation era, but we have been in a technological innovation era since the invention of the transistor in 1947. Before that, the V-2 rocket that launched the space age. Then, there was Einstein.

The progressive narratives are everywhere in education. Most reforms have failed to turn education around. (I know it will work; we just need more funding, more resources, more tech, more innovation, etc.) Also, teachers are trained in progressive schools of education, so many misconceptions hang around decade after decade. Old ideas that failed in the past are revived with fresh language such as reform math.  

Cognitive skills are important. "The cognitive skills of the labor force as measured by math and science scores are extremely important in an economic sense." There is a link between the scores in math and science, and economic growth says Eric A. Hanushek. In short, school quality impacts economic growth. Progressive ideologues talk a lot about school quality then downgrade knowledge and individual achievement. Knowledge and skills go together. (Quote from The 4% Solution)

The bottom line is that students need to upgrade their math skills to move forward. But, the progressive narrative from the National Council of Teachers of Mathematics (NCTM 1989) is for students to use calculators early on, including in kindergarten children. We are told by reformers that with calculators, the central role of learning standard arithmetic is no longer that important. WRONG! In contrast, Ian Stewart writes (The Story of Mathematics), "Without internalizing the basic operations of arithmetic, the whole of mathematics will be inaccessible to you ... You won't learn to think sensibly about numbers by relying on a calculator." The fact is that standard arithmetic (e.g., standard algorithms, auto recall of math facts, etc.) is not taught well in our schools. Kids don't learn basic arithmetic well because it is not taught well.

Alert, Alert, Alert...  
An "education" professor claims that teaching kids math discriminates against children of color. How stupid! Comment: "Why would anyone think that minorities would be less able to do math than anyone else?"

Rochelle Gutierrez, an education professor, not a mathematician, claims that teaching kids algebra and geometry discriminates against students of color and perpetuates white "unearned privilege." She is wrong! In contrast, I go into urban 4th-grade classrooms to teach little kids algebra basics once a week. Virtually 90% of the students are children of color; most are Hispanic. I volunteer as a guest algebra teacher to provide opportunities for young students that expand their knowledge of mathematics. Indeed, factual and procedural mathematical knowledge in long-term memory is an asset to any learner regardless of color. 

Gutierrez says her work is "scholarly," but how can that be if her premise is weaker than gravity and the so-called investigators are offering only their biased opinions. It is not the cognitive science of learning. "This white paper represents the impressions and insights of Sanchez, Kastberg, Tyminski, and Lischka, [principle] investigators (PI) ... The opinions included in this paper represent those of the PIs as of November 5, 2015." (Gutierrez used the wrong word for PI. She wrote the "principle investigators" rather than the "principal investigators.")

Students need higher-level math courses to expand their career choices later on. Some students may dislike math, but this attitude should not govern their education priorities. Saying algebra is discriminatory is like saying tests discriminate against those who do not study.

Unfortunately, the typical methods--discovery or inquiry math activities in small groups--hold kids back because the curriculum and instructional practices do not optimize the early mastery of standard arithmetic. The constructivist minimal guidance methods are inefficient compared to the explicit explaining of worked examples in math. Also, there is no substitute for drill-to-develop-skill. 

Unfortunately, the minimal guidance methods are the same practices that progressive reformers, policymakers, and professors in schools of education advocate. Consequently, kids don't learn basic arithmetic well because it is not taught well.

Often, classroom teachers are asked to teach "items on the state test" using inferior methods. The state standards are Common Core rebranded. 

©2017 LT/ThinkAlgebra
October 25, 2017. 10-28-17, 10-30-17

Sunday, October 8, 2017

Against Reforms

There is no substitute for knowledge in long-term memory 
and the practice that gets it there.

"Drill to develop skill" is essential.
My Contrarian Math Page is a response to far-reaching, progressive reforms that for decades have twisted and trashed standard arithmetic into "something" I call "reform math." The reformers say that "drill and practice are always wrong. Real teaching is always inquiry-based, student-centered, and constructivist." These claims and other progressive notions are bunk! 

​[ 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.
End Insert ]

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