Children need strong, teacher-guided instruction.
Minimal-guided instruction has been an epic flop.
Traditional arithmetic works well when taught well. Students become better at mental math because they have memorize basic number facts. Furthermore, the standard algorithm always works. We keep forgetting that little kids are novices. They don't think like adults. Children need to memorize and practice to put mathematical knowledge, both factual and procedural, into long-term memory for instant use in problem solving. Students cannot do mathematics without knowing some mathematics. Also, understanding is a slow process. It does not produce competency, practice does. Do not expect instant understanding or hold kids back because their understanding is partial or incomplete. Furthermore, Jason Zimba, one of the two major writers of CC math standards, explains, "The standards also allow for approaches in which the standard algorithm is instructed in grade 1, and in which only a single algorithm is taught for each operation." Note. Isaac Newton invented a fast way to calculate answers to physics problems, called calculus. It always worked (i.e., it was consistent with experimental data), but he didn't understand why the calculus worked; it just did. The "why" would take another 200 years. 3-9-15
Explicit teaching, which uses a carefully-planned sequence of worked examples, let's say in math, works well for almost all students. Students learn concepts through examples, lots of practice, and repetition, says Zig Engelmann. However, since the 60s, teacher-led instruction has been called "old school" or the opposite of “good” teaching. Explicit, teacher-led instruction—using examples, practice, and repetition—“contradicts much of what educators are taught to believe about good teaching,” writes J. E. Stone (Clear Teaching).
Stone says that explicit teaching [the teacher is the academic leader that leads instruction by explaining examples on the board, etc.] has not been popular in K-8 schools, not because it didn't work but because it goes against progressive reform ideology taught in schools of education. The Progressive Era revolution of the 60s affected education by attacking teacher-led exercises, scripted lessons, skill grouping, choral responding, repetition, etc., says Stone. “Thus, education professors and theorists denigrate teacher-led practice as ‘drill and kill,’ its high expectations as ‘developmentally inappropriate,’ and its emphasis on building a solid foundation of skills as ‘rote learning’.” Kids have not been taught a solid foundation of arithmetic for decades and decades.
Today we have teachers as facilitators, not academic leaders; mainstreaming (inclusion); a weak, incoherent, downgraded curriculum; low expectations for students; popular reform methods of instruction (i.e., minimal guided, not teacher-led) that do not work; reforms such as Common Core, intrinsically linked to standardized testing; etc. Education is no longer a "work hard and achieve" narrative; it is a political, money-driven narrative.
Note. I have quoted this study [Kirchner-Sweller-Clark (Why Minimal Guidance During Instruction Does Not Work...)] since it first appeared in Educational Psychologist in 2006. The instructional methods in classrooms across the US--mostly group work activities with minimal teacher guidance or no teacher guidance--have failed our students for decades. The minimal guidance instructional methods (e.g., discovery, constructivist, problem-based, inquiry-based, etc.), which are championed in schools of education, extend to Common Core. They are part of the progressive movement in education, starting with Dewey. Kids do a lot of group work, use manipulatives, etc. Their desks are in groups of 3 or 4, so kids face each other. The teacher is not the academic leader in the classroom. The teacher's role has diminished to a "facilitator" of learning. In short, the teacher no longer teaches.
Kirchner-Sweller-Clark (Why Minimal Guidance During Instruction Does Not Work...) write, "Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described."
Kirchner-Sweller-Clark write, "Cognitive load. Sweller and others (Mayer, 2001; Paas, Renkl, & Sweller, 2003, 2004; Sweller, 1999, 2004; Winn, 2003) noted that despite the alleged advantages of unguided environments to help students to derive meaning from learning materials, cognitive load theory suggests that the free exploration of a highly complex environment may generate a heavy working memory load that is detrimental to learning. This suggestion is particularly important in the case of novice learners, who lack proper schemas to integrate the new information with their prior knowledge."
© 2015 LT, ThinkAlgebra,org
