Advantages, Disadvantages, and Applications of Constructivism

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In the space of a month, I went from not knowing what constructivism is to producing this term paper for a course taken in '08. Advantages and limitations of constructivist theory are surveyed, moderation is endorsed, and a short lesson plan for high school chemistry is included. For an essay written for the same course after viewing "A Private Universe and a couple of lesson plans, please visit http://assumetheopposite.com/Articles.html

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Advantages, Disadvantages, and Applications of Constructivism

  1. 1. ADVANTAGES, DISADVANTAGES, AND APPLICATIONS OF CONSTRUCTIVISM Marjorie E. Steakley University of Tennessee at Martin TCED 712 Principles of Learning and Instruction July 1, 2008 Copyright © 2008 by Marjorie E. Steakley
  2. 2. ADVANTAGES, DISADVANTAGES, AND APPLICATIONS OF CONSTRUCTIVISM ABSTRACT: 25 years after the National Commission on Excellence in Education issued its report, American schools are still losing ground compared to those of other developed countries, especially in math and science. Cognitive psychologists have responded with the theory of constructivism, which postulates that knowledge is actively constructed in the minds of students rather than being passively transmitted from lectures. Educational advantages include (1) involvement of students in their own education, (2) relevancy to real life, (3) remediation of past demographic injustice, and (4) prevention of discipline problems. Epistemological disadvantages include (1) idealism, (2) empiricism, and (3) relativism, which can wreak havoc if taken to postmodernist extremes. Moderation is recommended, and a sample high school chemistry lesson plan is included. Over the past 40 years, American schools have been sharply falling behind those of Europe and the Pacific Basin, particularly in math and science (National Commission on Excellence in Education, reported in Skinner, 1987). Ill-conceived government reforms, such as No Child Left Behind, have turned many early childhood and elementary classrooms into mind-numbing, soul-destroying test-score mills, in which reading is continuously drilled for most of the day, at the expense of all other subjects, a militarist ploy that invariably backfires and further escalates functional illiteracy (Pate, P., personal communication). Policymakers, steered by their ruling-class campaign benefactors, have systematically designed policies that have condemned the schools—as well as other institutions—to failure (Liu and Hanauer, 2008). Racism is a major motive for this sabotage of national institutions, including education (Kozol, 1991; Steakley, unfinished manuscript). One obvious way in which schools are sabotaged is through large class sizes, which deprive students of individual attention and Copyright © 2008 by Marjorie E. Steakley
  3. 3. tutoring (Skinner, 1989, pp. 85-86). Public schools typically have class sizes ranging from 25 to 40 students, while private schools, where the children of the ruling class are invariably educated, have classroom sizes of a single digit. Exacerbating matters is a fundamental disconnect between school and the real world. The public classroom is an artificial environment separated from external reality that is expected to prepare students for a future that cannot be foreseen (Skinner, 1989, pp. 87-88). This disconnect has become even more acute amid the emerging Second World Depression and its consequences, i.e. the danger of the United States becoming a failed state. Consequently, urban schools are primarily driven by punishment (Skinner, 1968, 1989), under pressure from business to furnish “a trained workforce” (Kozol, 1991) that will submit to its elitist, punishment-driven “culture.” This predominance of punishment is yet another guarantee of educational failure, as punishment cannot produce positive long-term results and inevitably breeds frustration and resentment (Skinner, 1953, 1968). Teachers, placed in a hopelessly untenable position by malevolent policymakers and weary of failed nationalist ideology and failed behaviorist theories, have been desperate for educational and philosophical theorists to produce an alternative epistemology with effective classroom applications. The Rise of Constructivism The roots of constructivism lie in the developmental theories of Piaget and the social and historical theories of Vygotski. Piaget's proto-constructivist concept is that a student's consciousness is not a vessel to be filled with informational content (Ferriero, 2001, p. 215), but is a partner in active experimentation, especially in mathematics and science (Piaget, 1973, p. 104). Ernst von Glasersfeld (1990) characterizes this personal constructivism as “minimal constructivism,” because it represents no actual innovation; curricula have been designed to progress from the simple to the complex via active exploration since the advent of Jerome Bruner's post-Sputnik curriculum reform (e.g. Bruner, 1961, p. Copyright © 2008 by Marjorie E. Steakley
  4. 4. 22). While Piaget focused on the intellectual development of the individual, Vygotski, now better understood through improved translations from the Russian following the fall of the Soviet empire, examined the social and historical environment in which learning takes place. Some of his areas of interest included the influence of symbols upon thinking, such as language and numerals (Vygotski, 1997, p. 62), and cultural influences of people in the immediate environment on cognitive development (Vygotski, 1978). A wide, diverse, and still-evolving spectrum of forms of constructivism has been arising from Piaget's and Vygotski's theories, which are far too many to enumerate here. However, several major types will be presently examined. Some Major Types of Constructivism Radical constructivism Radical constructivism, an outgrowth of Piagetian theory (Glasersfeld, 1990), argues that external reality, although not nonexistent, is inscrutable and unknowable. Instead, each individual progressively synthesizes one's own perception of reality based upon one's experience, and traditional notions of “truth” are replaced with those of “viability” (Glasersfeld, 1989, p. 124). No one individual can ever know exactly how many possible constructs can exist (Glasersfeld, 1987, p. 199). Learning takes place when a new experience conflicts with one's preexisting construct, forcing it to change in order to accommodate the novel occurrence. As each person's construct is going to be inevitably different, constructs need not be identical in order for people to be able to communicate with others. As long as there are no surprises, it is sufficient for one individual's construct to be “compatible” with the other's, in order to maintain the illusion of shared meaning without either person's construct being compromised (Glasersfeld, 1990). Social constructivism Copyright © 2008 by Marjorie E. Steakley
  5. 5. Social constructivism is an outgrowth of Vygotski's social-historical theories; acknowledging and utilizing the immediate social environment in which learning takes place (i.e. the classroom). Social constructivism places equal value on the role of individual consciousness and that of the collective consciousness of the entire class. Teaching of mathematics, for example, is no longer merely transmission of informational content from the teacher to the students, but the cultivation of mathematical ideas from the evolving collective practices of the class (Cobb, 1994). Furnishing correct answers to problems is subordinated by collaboration, discussion, and activities that are personally meaningful to the students. Collaboration involves pairs or small groups of students listening to, agreeing, and disagreeing with each other, and devising their own solutions to mathematical problems (Wood, Cobb, and Yackel, 1995). Cultural constructivism Cultural constructivism is a natural expansion of the scope of social constructivism, examining cultural influences from beyond the immediate classroom upon the students and the subject matter. The short documentary “A Private Universe” has already offered a dramatic example of how textbook design and format can influence the learning or mislearning of scientific content. Furthermore, the nature of language itself represents a major force which profoundly impacts the shaping and apprehension of ideas. For example, the English language has lost virtually all of its inflection as a result of Britain having survived or repelled so many invasions from the European mainland. Consequently, English has inherently and decisively moved towards gender inclusivity, greatly facilitating the development of feminist thought, and by natural extension, that of broader issues of human rights. In contrast, it is very difficult to advance a feminist agenda in countries where the language is highly inflected and consequently gender noninclusive, arbitrarily assigning genders to inanimate objects (Anshelevich, O., classroom communication). Cultural constructivism recognizes Copyright © 2008 by Marjorie E. Steakley
  6. 6. that cultural artifacts permeate every body of knowledge, fundamentally shaping and transforming thinking and learning. Newborn infants are immediately thrown into a vat of cultural and historical artifacts, including but by no means limited to parents' expectations of them. All physical and psychological actions, including scientific research, stemming from such artifact-laden thinking are inescapably culturally, historically, and institutionally mediated (Cole and Wertsch, 1996). Critical constructivism Such ubiquitous presence of cultural, historical, and institutional artifacts in the body of scientific knowledge should be deeply disturbing to any serious scientist, student, or concerned citizen. Most dramatically, health care has long since become a cesspool of misogynist, racist, elitist, capitalist, and pro-industry artifacts, condemning nearly the entire U.S. population to years of unnecessary suffering and deprivation of decades of life, and threatening to bankrupt the country (e.g. Mendelsohn, 1979; Breggin, 1991; Abramson, 2004). Critical constructivism directly addresses sociopolitical bias in the classroom, allowing students to cultivate the critical thinking and confidence to recognize and reform cultural, historical, and ideological artifacts in mathematics and science at large. Critical constructivism acknowledges the vulnerability of the student to social, cultural, and political manipulation and disempowerment, and aggressively seeks avenues of cultural reform in the classroom (Taylor, 1996). A major vehicle for such reform is communicative ethics, which seeks to foster optimal conditions for the establishment of dialogue towards achieving mutual understanding. These conditions are (1) the establishment and maintenance of empathetic, caring, and trusting interpersonal relationships; (2) conscientious maintenance of bilateral dialogue towards mutual understanding of interests, objectives, and standards; and (3) raising consciousness and criticism regarding subtexts and unwritten rules of the classroom itself and of society at large (Taylor, 1998). Communicative ethics offers an alternative to students being force-fed a predetermined mindscape fabricated by the ruling Copyright © 2008 by Marjorie E. Steakley
  7. 7. class in order to serve its ulterior purposes. It also encourages a rational assessment and deconstruction of the often fraudulent claims made by self-serving social institutions, as well as that of historical bias from millennia of male and Nordic domination (Taylor, 1996). Educational Advantages of Constructivism Involvement of students in their own education Bruner's (1961) and Piaget's (1973) calls for children’s learning of science by experimentation, Cobb's principle of bottom-up cultivation of mathematical practices (1994), and Taylor's principle of communicative ethics (1998) clearly call for students to be active participants in their own education. This approach does not improve the learning of simple factual information. However, students who utilize simplified versions of the tools and methods of professionals in the subject area to actively construct their own knowledge have superior generalization skills and transfer of learning to novel contexts (Cobb, 1999). Furthermore, students who cooperate in small groups develop superior critical thinking and have longer retention of learning than those working alone (Johnson and Johnson, 1986). Clearly, letting students work either with a partner or in a small group is significantly helpful in overcoming the aforementioned problems associated with large class sizes. Relevancy to real-life situations Constructionism is the idea that constructivism works best when students make something that is tangible to others (Harel and Papert, 1991). This refinement helps to bridge the aforementioned gap between the classroom and the outside world. An example of constructionism is students in a physics class building their own electrical circuits. An example of a real-life application of a scientific principle is using the gas laws to predict that car tires will need inflation upon the outbreak of colder weather, to avoid uneven wear and extend tire life. Copyright © 2008 by Marjorie E. Steakley
  8. 8. Correction for past demographic injustice A major objective of Taylor's principle of communicative ethics is to empower the subjugated majority and break the cycles of misogyny, Norse domination, and poverty (1998). Furthermore, improved relevancy to real life makes science more accessible to girls, peoples of color, and the poor, and is an important start towards demystification. Relevancy of science studies to real life also equips graduates to recognize ideological and pro-industry sources of bias in scientific research that perpetrate discrimination and jeopardize public health and safety. Prevention of discipline problems Based upon recent classroom observations, students who are engrossed in dialogue and activities are unlikely to create disturbances or to strike up conversation about the sports and entertainment industries. Furthermore, students with more highly developed critical thinking and prefrontal function will have a better understanding of what is at stake and will be less likely to cut up or be disruptive. Arguably, the most important educational objective of all is for prefrontal function to remain online all the time. Most likely, such mental function brought on by active student involvement in lessons will translate into improved taste in non-school activities. Epistemological Disadvantages Despite these educational advantages, there is significant vitriolic opposition to constructivism. At first glance, this hostility seems openly partisan, driven by blatant ecophobia and utter disdain towards alternative medicine (e.g. Hirsch, 1996). Nationalists are threatened by the intellectual empowerment of women, peoples of color, and the poor; corporations are threatened by the servile “trained workforce” (Kozol, 1991) being replaced by free-thinking social critics, and internal construction of knowledge directly threatens the blind post-Confederate obsession with the Johannine Gospel (Jn. 3:16) that dominates the ignorant dogma of the megachurches. Partisan opposition to Copyright © 2008 by Marjorie E. Steakley
  9. 9. constructivism is typically linked to open hostility towards special education practices, as well as the legitimate affirmation of the failure of whole-language instruction. 1 From the rhetoric, one would think that (1) constructivism, (2) facilitated communication, (3) least restrictive environment, (4) inclusion, and (5) whole language instruction are major planks of the Democratic Party platform, and that Ernst von Glasersfeld is already Barack Obama's running mate. However, closer inspection reveals a separate corps of academic critics with legitimate epistemological concerns, including some from overseas. These detractors never digress to special education practices and never couch their arguments in ecocidal and allopathic terms. Tellingly, these epistemological opponents are conspicuously absent from the nationalists' citations and reference lists, and vice versa. These nonpartisan academic reservations will presently be examined. Idealism In epistemological terms (as opposed to colloquial terms), idealism is the claim that external reality is a figment of one's imagination. Although radical social constructivists generally deny being idealists, their summary rejection of rationalism is inescapably idealist (Slezak, 2000). Despite radical social constructivism's claim of progressiveness, its idealism withers under the stark glare of family abuse. No one is going to ever “construct” such a childhood unless it exists in external reality, and victims who escape into fantasy too much risk psychological damage far worse than post-traumatic stress. Furthermore, anyone espousing radical social constructivist rhetoric (e.g. “knowledge is experience,” “reality is unknowable”) outside of academia would be instantly slapped with a psychiatric label (Slezak, 2000). Thus, exercise of this epistemological perspective clearly represents class privilege and white privilege. Moreover, idealism inescapably negates the entire body of 1 As a classical musician, I am not surprised by the functional illiteracy spawned by this approach, having long witnessed the similar consequences of the Suzuki Violin School and its spinoffs. University music departments and conservatories have been forced to provide remedial instruction in reading music to “Suzuki victims” for half a century. In my opinion, whole language instruction should be characterized as the Suzuki Elementary School. Copyright © 2008 by Marjorie E. Steakley
  10. 10. scientific research, and makes any further work pointless (Phillips, 1997); and any attempt at science education would be tantamount to political indoctrination (Slezak, 2000). In effect, radical social constructivism would decisively end the Enlightenment, sending the Western world back to its predecessor, the antiscientific theology and philosophy of Augustine of Hippo (Shelley, 1995, pp. 312-314). Ironically, epistemological postmodernism would condemn the world to another millennium of medieval superstition, with consequences to women and sexual minorities once again measured in megadeaths. Empiricism Closely related to idealism is empiricism, another theory discredited by the scientific revolution that had deposed Augustine as the erstwhile sage of the ages (Shelley, 1995, p. 124). Although radical social constructivists claim to be summarily rejecting empiricism, their epistemology has all of its hallmarks: (1) knowledge is fabricated and evaluated by individuals, (2) all claims of knowledge are based upon experience, and (3) the external world is epistemologically inaccessible, especially once one is aware of one's thinking (Matthews, 1994). If children in a constructivist classroom place nails in different places to watch them rust, no amount of probing questions from the teacher could ever lead them to the concept that rusting is a chemical reaction between iron, oxygen, and water, producing the novel substance iron oxide. Furthermore, no amount of facilitated group discussion could ever come anywhere near the scientific view (Scott, Asoko, Driver, and Emberton, 1994). Children will never be able to independently recreate abstract scientific concepts that took scientists centuries to formulate; the only way they can learn counterintuitive concepts like gene regulation, thermodynamics, and valency is by actually being taught (Matthews, 1997). Moreover, such a group-dominated, implicit approach would saddle children with learning difficulties, low English proficiency, or living in poverty with additional barriers not found in direct instruction, imposing the will of the majority and exacerbating Copyright © 2008 by Marjorie E. Steakley
  11. 11. pre-existing racism and elitism (Cobb and Bowers, 1999). Relativism Initial impressions of the term relativism tend to evoke nationalist notions of misogyny, racism, and homophobia. However, upon closer inspection, the threat of relativism to progressive thought becomes clear. For example, it would be impossible to negate the pseudoscience of eugenics and the Hitlerian racist ideology it spawned, because that would be just another mental construct (Slezak, 2000). If there is no ontological truth, then global dialogue and debate about serious threats, such as global warming, ozone depletion, mass extinction, and war would become exercises in futility (Matthews, 1994). Moreover, relativism would dash all hope of addressing the blizzard of real ideological artifacts in health care, and millions will continue to needlessly suffer and die every year. Relativism would not only dismantle science, but also human rights, because nationalists would then have a carte blanche to do anything they want to their victims, just because doing so would seem “right” to them at any particular moment. Resolution: Moderation via an Asymptotic Approach to Objective Reality Clearly, constructivism represents a double-edged sword. Cultural and critical aspects promise to alert the public about existing (e.g. health care) and potential (e.g. interference in environmental science by the executive branch) political and ideological artifacts that threaten the human species and the biosphere. However, radical postmodernist idealism and relativism, by denying ontological reality, threaten to scuttle these very reforms before they ever get off the ground. Reversion to behaviorism is not the answer any more than that to Augustine, especially as the epistemological reign of behaviorism had been sunk by none other than Noam Chomsky (Slezak, 2000), who is now arousing the wrath of nationalists as one of the best peace writers in the world. Clearly, the most progressive route to take is one of moderation. Phillips (1995) indicated that it is possible and desirable to have active Copyright © 2008 by Marjorie E. Steakley
  12. 12. participation by the learner without wallowing in the wretched excesses of postmodernism. The trajectory of physics over the past 200 years has outlined an asymptotic approach to objective reality. The challenge to humanity is to preclude such an approach of science at large from being derailed by corporations, ruling elites, and managerial elites only concerned with massaging their dysfunctional egos with racism and the maintenance of their pipeline of uninterrupted addictions. Sample Lesson Plan Discovering Chirality through Building Models of Organic Compounds While the school laboratory experiment is a time-honored vehicle of student participation, this classroom exercise is an innovative way of introducing an advanced concept with significant nutritional implications. Earlier in the year, there would have been a prior similar exercise to teach stereochemistry, which also has significant nutritional implications. Materials: a ball-and-stick molecular modeling set for each pair of students. There needs to be plenty of color-coded balls for hydrogen, carbon, oxygen, and chlorine, as well as plenty of sticks signifying single bonds. There will be no double or triple bonds in the exercise. Although space-filling models are more accurate representations of what the molecules look like, it is much easier for students to see the molecular structures in ball-and-stick models. The students also will need paper and writing implements for note-taking. An honors or advanced placement class would instead build models of glucose and/or tocopherol (vitamin E), towards the same goal. Instructions to students: Join with your lab partner and get a modeling set. First, build a model of ethane (CH3 CH3). Then, set down the ethane model and build as many different molecules as you can that have these substitutions. More than one molecule is possible! Copyright © 2008 by Marjorie E. Steakley
  13. 13. H Cl | | H—C—C—H | | H OH After the students have built two different molecules with the substitutions, proceed with discussion, punctuated with direct instruction. Direct instruction is enhanced by writing the new terms on the board, having the students write them down in their notes, and saying them aloud as a group, to engage as many abilities as possible. How many forms of ethane were you able to build? [Just one] How many different forms were you able to make of the molecule that had the substitutions? [Two] How are the two substituted molecules different from each other? [They are mirror images of each other; one looks “right-handed” and the other seems “left-handed”] Carbon chemists have a name for compounds that can be either right-handed or left-handed. These substances are called chiral. Is ethane symmetrical? Are both of its carbons symmetrical? [Yes] Is the chiral molecule symmetrical? [No] All chiral molecules are asymmetrical. Are both of its carbons asymmetrical? [No, the carbon in the methyl group is symmetrical; only the carbon with the chloro and hydroxy substitutions is asymmetrical] Chiral compounds have chiral carbons and can also have non-chiral carbons. Carbon chemists call the pairs of right-handed and left-handed molecules enantiomers. Who remembers how enzymes from a living organism recognize the molecules they're supposed to bind to and react with? [The molecules fit into the active site, just like a key fits in a lock or a hand fits in a glove] Copyright © 2008 by Marjorie E. Steakley
  14. 14. Would an enzyme be able to recognize both enantiomers? [No, only one molecule would fit, and the other would be like putting a left hand into a right-handed glove or vice versa. The fit would be awful] [Show a transparency or power point with the structural formula of glucose] Is glucose chiral? Do you see any asymmetrical carbons? [Yes] Do you think most nutrients and vitamins would be chiral? [Probably] Would it matter for your health which enantiomer the vitamin is? [Absolutely! Only one would fit your enzymes; the other would be useless] If you made this hydroxychloroethane in a reaction flask, would you get the right-handed form, the left- handed form, or both? [Both] Once you've made it, could you separate out the two enantiomers? [No, they have the same melting point, the same boiling point, the same density, the same molecular size, and the same charge. There's no way you can separate them; you'd be stuck with the mixture] Carbon chemists call this mixture racemic. When buying vitamins, how can you be sure that you're getting the right enantiomer? [Buy a natural vitamin, because an organism had made it with enzymes, and it would be all be the same enantiomer] [Challenge question for smart students] Is it possible for you to make a vitamin in a flask that is all the right enantiomer? [Yes; you make it with live enzymes rather than with ordinary reagents] References Abramson, J. (2004). Overdo$ed America: The broken promise of American medicine; How the pharmaceutical companies are corrupting science, misleading doctors, and threatening your health. New York: Harper Collins. Breggin, P. R. (1991). Toxic psychiatry. New York: St. Martin's. [The section on autism has become outdated; please disregard it.] Bruner, J. S. (1961). The act of discovery. Harvard Educational Review 31, 21-32. Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher 23 (7), 13-20. Copyright © 2008 by Marjorie E. Steakley
  15. 15. Cobb, P., & Bowers, J. (1999). Cognitive and situated learning perspectives in theory and practice. Educational Researcher 28 (2), 4-15. Cobb, T. (1999). Applying constructivism: A test for the learner as scientist. Educational Technology Research & Development 47 (3), 15-31. Cole, M., & Wertsch, J. V. (1996). Beyond the individual-social antimony in discussion of Piaget and Vygotski. Human Development 39, 250-256. Ferriero, E. (2001). On the links between equilibration, causality, and prise de conscience in Piaget's theory. Human Development 44, 214-219. Glasersfeld, E. von, (1987). Construction of knowledge. Salinas, CA: Intersystems Publications. Glasersfeld, E. von, (1989). Cognition, construction of knowledge and teaching. Synthese 80 (1), 121-140. Glasersfeld, E. von, (1990). An exposition of constructivism: Why some like it radical. In R. B. Davis, C. A. Maher, & N. Noddings (Eds), Constructivist views on the teaching and learning of mathematics, pp. 19-29. Reston, Virginia: National Council of Teachers of Mathematics. Harel, I. & Papert, S. (1991). Constructionism, research reports and essays, 1985-1990. Norwood, NJ. Hirsch, E. D. Jr. (1996). The schools we need and why we don't have them. New York: Doubleday. Johnson, R. T., & Johnson, D. W. (1986). Action research: Cooperative learning in the science classroom. Science and Children 24, 31-32. Kozol, J. (1991). Savage inequalities: Children in America’s schools. New York: Crown. Liu, E., & Hanauer, N. (2008). The true patriot. Seattle, WA: Sasquatch. Matthews, M. R. (1994). Science teaching: The role of history and philosophy of science. New York: Routledge. Matthews, M. R. (1997). Introductory comments on philosophy and constructivism in science education. Science & Education 6, 5-14. Mendelsohn, R. S. (1979). Confessions of a medical heretic. Chicago: Contemporary. [Written from a socially conservative perspective; a few details have become outdated.] Phillips, D. C. (1995). The good, the bad, and the ugly: The many faces of constructivism. Educational Researcher 24 (7), 5-12. Phillips, D. C. (1997). Coming to grips with radical social constructivisms. Science and Education 6, 1-2. Piaget, J. (1973). To understand is to invent: The future of education. New York: Grossman. Scott, P., Asoko, H., Driver, R., & Emberton, J. (1994). Working from children’s ideas: planning and teaching a chemistry topic from a constructivist perspective. In P. Fensham, R. Gunstone, & R. White (Eds), The content of science: A constructivist approach to its teaching and learning. London: Falmer Press, pp. 201-220. Shelley, B. L. (1995). Church history in plain language, 2nd ed. Nashville, TN: Thomas Nelson. Copyright © 2008 by Marjorie E. Steakley
  16. 16. Skinner, B. F. (1953). Science and human behavior. New York: Macmillan. Skinner, B. F. (1968). The technology of teaching. New York: Appleton-Century-Crofts. Skinner, B. F. (1987). Upon further reflection. Upper Saddle River, NJ: Merrill/Prentice Hall. Skinner, B. F. (1989). Recent issues in the analysis of behavior. Upper Saddle River, NJ: Merrill/Prentice Hall. Slezak, P. (2000). A critique of radical social constructivism. In D. C. Phillips (Ed), Constructivism in education: Ninety-ninth yearbook of the National Society for the Study of Education. Chicago: University of Chicago Press, pp. 91-126. Taylor, P. (1996). Mythmaking and mythbreaking in the mathematics classroom. Educational Studies in Mathematics 31, 151-173. Taylor, P. (1998). Constructivism: Value added. In B. Fraser and K. Tobin (Eds), The international handbook of science education. Dordrecht, Netherlands: Kluwer Academic. Vygotski, L. S., (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Vygotski, L. S., (1997). Research method. In R. W. Rieber (Ed), History of the development of the higher mental functions, vol. 4. Collected works, pp. 27-63. New York: Plenum. Wood, T., Cobb, P., & Yackel, E. (1995). Reflections on learning and teaching mathematics in elementary school. In L. P. Steffe & J. Gale (Eds), Constructivism in education, pp. 401-422. Hillsdale, NJ: Lawrence Erlbaum. Copyright © 2008 by Marjorie E. Steakley

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