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Last update: August 17, 2014
Zig berates the distastefulness results from the [Common Core] committee's strange notions of how children learn. "The [Common Core] standards clearly follow the Piagetian myth that children first manipulate then internalize the manipulations, which slowly grows into concrete operations, and later into abstractions or formal operations" (The Dreaded Standards, Zig Engelmann. Zig lambastes the Common Core Mathematical Practices for the early grades).
"It does not work that way, and manipulatives are an instructional nightmare in K [and the early grades]. The products--what children actually learn from manipulation activities--are trivial compared to what could be taught directly in the same amount of time," explains Zig.
Concrete models are often ineffective or detrimental. Symbols-only work better, conclude Mix, Prather, Smith, & Stockton (Mutli-Digit Number Names). Students should not make drawings (visuals) to perform arithmetic.
Every year, state test scores go up slightly, but this should not imply that cognitive abilities (e.g., abstract reasoning) go up too, say MIT neuroscientists. Anne Trafton, MIT News Office, writes, "The researchers found that educational practices designed to raise knowledge and boost test scores do not improve fluid intelligence, such as working memory capacity, speed of information processing, and the ability to solve abstract problems." Our schools, even the best ones (perception), are worse than we think. Furthermore, the highly praised constructivism in reform math and the irrational testing used to compare [judge] states, schools, teachers, and students are all ed talk gobbledygook.
The purpose of learning to do math is to get the right answer. Getting the right answer is just as important being able to figure out the problem types, select an efficient algorithm and calculate the right answer using it. James Shuls, Ph.D. says that "students display deep understanding by getting answers correct." The reformers say getting the right answer is not all that important. Since when?
Constructivism does not work in the classroom!
Kirschner, Sweller, & Clark in 2006 wrote an article for Edcuational Pyschologist called Why Minimal Guidance During Instruction Does Not Work: An analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. The pedagogy of minimal guidance during instruction comes with different names, but they are all basically constructivism. In math, they are often called reform math. K-S-C write, "The constructivist argument [minimal teacher guidance, such as that in reform math and now Common Core], has attached a significant following; however, the goal of this article is to suggest that, based on our current knowledge of human cognitive architecture, minimally guided instruction is likely to be ineffective." The current research supports direct guidance, which is explicit teaching, something Zig Engelmann emphasized in the 1960s with his symbols-only approach with pre-first-graders.
Traditional, explicit teaching with carefully selected worked-examples, which are expertly explained, is by far the best way to teach children arithmetic. The evidence seems overwhelming. On the other hand, reform math, laced in Piagetian theory (constructivism) and endorsed by ed schools for decades, has screwed up arithmetic instruction. Unfortunately, Common Core follows Piaget's constructivism approach.
The Canadian Study
Evidence that supports Kirschner-Sweller-Clark comes from a Canadian study that started in the early 2000s, when Quebec switched from traditional to constructivist reform math, which was designed after reform math instruction in the US. In the 2014 issue of Economics of Education Review (Haeck, Lefebvre, & Merrigan), the conclusion was that the reform math was a failure in more ways than one.
"The Quebec education program (MELS, 2001, 2003, 2007) relied on a socio-constructivist teaching approach, focused on problem-based and self-directed learning. This approach mainly moved teaching away from the traditional/academic approaches of memorization, repetitions and activity books, to a much more comprehensive approach focused on learning in a contextual setting in which children are expected to find answers for themselves." In short, students are asked to reinvent arithmetic, which is a really dumb idea.
"More specifically, the teaching approach promoted by the Quebec reform is comparable to the reform-oriented teaching approach in the United States. As of 2006, this approach was widely spread across the United States (although more traditional approaches remained dominant) and it was supported by leading organizations such as the National Council of Teachers of Mathematics, the National Research Council, and the American Association for the Advancement of Science."
The researchers (Haeck, Lefebvre, & Merrigan) observed, "We find strong evidence of negative effects of the reform on the development of students’ mathematical abilities." But, there is more to it than this. "We find that the [socio-consructivist] reform had negative effects on students’ scores at all points on the skills distribution and that the effects were larger the longer the exposure to the reform," explain the researchers."
(Note: Excerpts in "quotes" on the Canadian study are found at Kitchen Table Math)
Canada has gone back to direct instruction with excellent results. I think some US teachers see the clear benefits of explicit teaching of arithmetic and disregard the Common Core reform math approach (constructivism), which is inefficient, ineffective, and not backed by evidence. The reinventing of arithmetic in small groups does not work. We have known this for decades, but many teachers continue it. Common Core reform math continues it as well.
1. See Multiple Models (Different Strategies)
Students are taught inefficient, alternative strategies (reform math), which I call pretend arithmetic, instead of tried and true standard algorithms to do arithmetic.
2. See SingleDigit
Don't calculate single-digit math facts; memorize them.
3. See Memorization & Practice
US schools are a breeding group for mediocrity, not excellence. Early on, parents should provide an environment for achievement and teach their kids how to be successful in school. Early arithmetic at home pays off. Very young children can learn a lot more than we think or are prepared to teach. American children underperform in math!
4. See CommonCore
Common Core is part of the progressive agenda to downgrade American education. Every student gets the same. The government has taken over and controls education. Teachers are no longer in charge of education.
To comment, email LarryT: ThinkAlgebra@cox.net
To be continued.
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