http://www.benwilbrink.nl/projecten/transfer.htm
‘Transfer’ is een psychologisch begrip, niet uit de psycho-analyse, maar gewoon in de cognitieve theorie. Anderson heeft er een boek over geschreven waarin een en ander bij elkaar is gebracht, binnen zijn ACT (Singley & Anderson, 1989). Mijn referentie is het recente boek van Ohlsson (2011), in het bijzonder zijn behandeling van het leren; in hoofdstuk 7: transfer (zie noten 40-43).
In diverse artikelen hebben Anderson, Reder & Simon (1996, 1998, 2000) al uitstekend aangegeven wat de typische misverstanden over transfer zijn, vooral in de wereld van he reken- en wskundeonderwijs. Wat dat betreft is mijn werk dus snel gedaan; ik kan daarnaar verwijzen. Voor Nederland wil ik dan toch nog wel specifiek in kaart brengen wie welke misvattingen met welk gevolg heeft verspreid. Denk vooral aan Freudenthal, Treffers, en Goffree, in de beginjaren van wiskobas en het realistisch rekenen, en aan hun navolgers en napraters die al helemaal niet meer weten waarover ze het hebben. Een interessant terrein. Opruimen van deze misverstanden rond transfer, onlosmakelijk verbonden met de thematiek van contexten, is absoluut een voorwaarde om weer terug te kunnen keren naar een gezonde didactiek voor het reken- en wiskundeonderwijs.
Wat realistisch rekenen betreft. Mijn opzet is om helder te krijgen wat de gedachten in zowel het IOWO (Wiskobas) als het FI zijn over transfer van rekenkennis, en wat dat dan zou betekenen voor de inrichting van het rekenonderwijs. De term ‘transfer’ wordt waarschijnlijk weinig gebruikt, zodat ik zelf goed op moet letten waar het onderwerp opduikt. Het duikt dus op bij de impliciete claim van het realistisch rekenen dat ‘handig’ rekenen van belang is, dat je dat later in het dagelijks leven zou moeten kunnen, en ook doen. De expliciete claim ben ik in dit boek van Treffers tot nu toe nog niet tegengekomen: dat het traditionele rekenonderwijs niet verhindert dat verworven rekenvaardigheden in het dagelijks leven uiteindelijk niet gebruikt blijken te worden, althans te vaak niet. En dat ‘rijk’ rekenonderwijs, onderwijs met contexten, lees: realistisch rekenonderwijs, daar iets aan doet.
Stellan Ohlsson (2011). Deep Learning. How the Mind Overrides Experience. Cambridge University Press.
Erik de Corte (Ed.) (1999). On the road to transfer: new perspectives on an enduring issue in educational research and practice. International Journal of Educational Research, 31, 553-654. contents
Paul Hager & Phil Hodkinson (2009): Moving beyond the metaphor of transfer of learning, British Educational Research Journal, 35:4, 619-638 abstract
Martin Packer (2001). The Problem of Transfer, and the, Sociocultural Critique of Schooling. Journal of the Learning Sciences, 10, 493-514. Learning and Instruction, 19abstract
“The debate over transfer rests on but obscures divergent views of the goals and aims of schooling. Both critique of schooling and calls for school reform presuppose conceptions of the kind of person we want children to be, and the kind of society we wish to foster.”
Alexander Renkl, Heinz Mandl & Hans Gruber (1996). Inert knowledge: Analyses and remedies. Educational Psychologist, 31, 115-121. abstract
“Knowledge, although seemingly available, is often not used for problem solving. That means it remains "‘nert.’”
Kevin J. Pugh & David A. Bergin (2006): Motivational Influences on Transfer, Educational Psychologist, 41:3, 147-160 abstract
Tinne Dewolf, Wim van Dooren & Lieven Verschaffel (2011). Upper elementary school children’s understanding and solution of a quantitative problem inside and outside the mathematics class. Learning and Instruction, 21, 770-780.
abstract We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils’ understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or a religion class. Afterwards, they had to evaluate several (fictional) answers for this problem. We compared the responses and evaluations from both groups and found that (1) in the mathematics class pupils preferred precise numerical answers, while in the religion class pupils had a preference for a verbal description of the solution; (2) pupils in the mathematics class preferred answers motivated by calculations, while in the religion class, pupils favoured non-numerical arguments; (3) the concept ‘fairness’ was interpreted and used differently in both conditions, leading to different preferential situational and mathematical models andsolutions.
Robert L. Goldstone & Uri Wilenski (2008). Promoting transfer by grounding complex systems principles. The Journal of the Learning Sciences, 17, 465-516. abstract
M. Bassok (1990). Transfer of domain-specific problem-solving procedures. Journal of Experimental Psychology: Learning, Memory, and Cognition, 16, 522–533.
Susan M. Barnett and Stephen J. Ceci (2002). When and where do we apply what we learn? A taxonomy for far transfer. Psychological Bulletin, 128, 612-637.
“Despite a century's worth of research, arguments surrounding the question of whether far transfer occurs have made little progress toward resolution. The authors argue the reason for this confusion is a failure to specify various dimensions along which transfer can occur, resulting in comparisons of "apples and oranges." They provide a framework that describes 9 relevant dimensions and show that the literature can productively be classified along these dimensions, with each study situated at the intersection of various dimensions. Estimation of a single effect size for far transfer is misguided in view of this complexity. The past 100 years of research shows that evidence for transfer under some conditions is substantial, but critical conditions for many key questions are untested.”
Barnett & Ceci 2002
Mark K. Singley & John R. Anderson (1989). The transfer of cognitive skill. Harvard University Press site.
G. Salomon & D. N. Perkins (1989). Rocky roads to transfer: Rethinking mechanisms of a neglected phenomenon. Educational Psychologist, 24, 113-142.
Richard Lehrer and Joan Littlefield (1993). Relationship among cognitive components in Logo learning and transfer. Journal of Educational Psychology, 85, 317-330.
Earl C. Butterfield & Gregory D. Nelson (1991): Promoting Positive Transfer of Different Types. Cognition and Instruction, 8, 69-102.
Jan Terwel, Bert van Oers, Ivanka van Dijk & Pieter van den Eeden (2009). Are representations to be provided or generated in primary mathematics education? Effects on transfer. Educational Research and Evaluation, 15, 25-44. pdf
Jeff Evans (1999). Building bridges: Reflections on the problem of transfer of learning in mathematics. Educational Studies in Mathematics, 39, 1-21. http://www.springerlink.com/content/wj4480w188wk4770/
John R. Anderson, Lynne M. Reder, and Herbert A. Simon (1996). Situated learning and education. Educational Researcher, 25(4), 5-11. pdf
Anderson, J. R., Reder, L. M. & Simon, H. (1998). Radical constructivism and cognitive psychology. In D. Ravitch (Ed.) Brookings papers on education policy 1998. Washington, DC: Brookings Institute Press. pdf
Anderson, J. R., Reder, L. M., & Simon, H. A. (2000). Applications and misapplications of cognitive psychology to mathematics education. Texas Educational Review, 1, 29-49. pdf
Het is ongetwijfeld passend om Anderson, Reder & Simon (2000) te betrekken bij de theoretische analyse van de thematiek in de overweging van de motie Dijkgraaf - Van der Ham. De beweging van ‘het nieuwe leren’, ‘ontdekkend leren’, het constructivisme, en in Nederland specifiek ook het realistisch rekenen, hebben met elkaar gemeen dat het automatiseren van basale kennis en vaardigheden niet meer zo nodig wordt gevonden, en dat de tijd beter kan worden besteed aan het leren wiskundig te denken, problemen oplossen, en contextopgaven maken. Anderson, Reder & Simon zetten zich in scherpe bewoordingen af tegen deze vooral idealistisch geïnspireerde stromingen die in vele landen een sterke greep op het reken- en wiskundeonderwijs hebben gekregen, zoals in de VS (NCTM-standards) en Nederland (de invloed van het Freudenthal-Instituut die reikt tot en met de kerndoelen basisonderwijs, de referentieniveaus rekenen, en de rekentoetsen op F-niveau).
De auteurs van dit artikel zijn niet van de straat: zij zijn van Carnegie Mellon University. John Anderson is de auctor intellecualis van een van de sterkste — zo niet het sterkste — van de cognitieve modellen: het ACT-R model. Herbert Simon heeft de nobelprijs gekregen voor zijn werk op onder andere het gebied van probleemoplossen. Lynne Reder leidt nu het Memory Lab aan de genoemde universiteit.
E. L. Thorndike and R. S. Woodworth (1901). The influence of improvement in one mental function upon the efficiency of other functions (I, II, III). Psychological Review, 8, 247-261, 384-395. html I html II
Jose P. Mestre (Ed.) (2005). Transfer of learning: from a modern multidisciplinary perspective. San Francisco: Sage. commentaar en samenvatting
Willem Smit (15 juli 2011). Realistisch rekenen en transfer. BON forum blog 7821
G. Trelinski (1983). Spontaneous mathematization of situations outside mathematics. Educational Studies in Mathematics, 14, 275-284.
“In this study 223 graduate mathematics students were set the task of creating a mathematical model of a situation from outside mathematics. Their solutions and strategies were analyzed and the results are described. It was clear that the students found the task both difficult and unusual as only nine of them were able to succeed fully. The author draws significant conclusions for the teaching of applying mathematics.”
Trelinsky, abstract
John M. Love (1985). Knowledge transfer and utilization in education. In E. W. Gordon (Ed.) (1985). Review of research in education volume 12 — 1985. American Educational Research Association.
Corte, E. de (Ed.) (1999). On the road to transfer: New perspectives on an enduring issue in educational research and practice. International Journal of Educational Research, 29, 553-654. Themanummer. contents (op die webpagina ook abstracts van de artikelen) (niet specifiek gericht op reken- en wiskundeonderwijs)
Jo Boaler (1993). Encouraging the transfer of ‘school’ mathematics to the ‘real world’ through the integration of process and content, context and culture. Educational Studies in Mathematics, 25, 341-373. abstract
Greg A. Perfetto, John D. Bransford and Jeffery J. Franks (1983). Constraints on access in a problem-solving context. Memory & Cognition, 11, 24-31.
Daniel L. Schwartz (1999). Rethinking transfer: Simple proposal with multiple implications. In Review of Educational Research, volume 24, chapter 3, 60-100.
O. Jelsma, J. J. G. van Merriënboer & J. P. Bijlstra (1990). The ADAPT design model: towards instructional control of transfer. Instructional Science 19, 89-120. abstract
Lynn S. Fuchs, Douglas Fuchs, Robin Finelli, Susan J. Courey and Carol L. Hamlett (2004). Expanding Schema-Based Transfer Instruction to Help Third Graders Solve Real-Life Mathematical Problems. American Educational Research Journal, 41, 419-445. abstract
Mirte S. van Galen & Pieter Reitsma (2011). Transfer effects in children’s recall of arithmetic facts. Cognition and Instruction, 29, 330-348.abstract
Amy B. Ellis (2007). A taxonomy for categorizing generalizations: Generalizing actions and reflection generalizations.. The Journal of the Learning Sciences, 16, 221-262. abstract
Ference Marton (2006). Sameness and difference in transfer. The Journal of the Learning Sciences, 15, 499-535. abstract
James G. Greeno (2006). Authoritative, Accountable Positioning and Connected, General Knowing: Progressive Themes in Understanding Transfer. The Journal of the Learning Sciences, 15, 537-547. abstract
Robert L. Goldstone & Ji Y. Son (2005). The Transfer of Scientific Principles Using Concrete and Idealized Simulations. The Journal of the Learning Sciences, 14, 69-110. abstract
David Carraher & Analúcia D. Schliemann (2002). The Transfer Dilemma. The Journal of the Learning Sciences, 11, 1-24. abstract
Janet L. Kolodner (2002).Analogical and Case-Based Reasoning: Their Implications for Education. The Journal of the Learning Sciences, 11, 123-126. abstract
Catherine A. Clement (2002). Learning With Analogies, Cases, and Computers. The Journal of the Learning Sciences, 11, 127-138. abstract
Analogy and reflective thought. Clearly reasoning with analogies engages students in a high level thinking skill: Drawing a systematic correspondence between disparate domains requires analytic and often creative thought. Further, analogical thinking provides a way for students’ knowledge to be productive, that is, it is a mechanism for existing knowledge to be extended to grasp new situations. However, Holyoak and Thagard point out that when used improperly, analogies can be used to avoid reflective thought about a concept or problem. For example, when students rely on examples to solve problems in such areas as math or physics, they can engage in a kind of mindless pattern matching, in which they map low-level problem elements, and fail to map higher order relations that illuminate the problem. Further, Holyoak and Thagard distinguish good analogies from “intuition pumps,” that do not legitimately support a conclusion and are impossible to justify. Such analogies may “provoke an unreflective judgment.” Educators should be wary that for a student, even a good analogy may be treated as merely an intuition pump. That is, a student may accept either a legitimate or illegitimate analogy without seeking further justification. The analogy may then create an illusory sense of understanding.
Janet L. Kolodner (2002). The “Neat” and the “Scruffy” in Promoting Learning From Analogy: We Need to Pay Attention to Both. The Journal of the Learning Sciences, 11, 139-152. abstract
Together, their models of learning and reasoning can help us understand how reasoning and learning happen, how we might promote better reasoning and transfer, and some of the difficulties we can expect learners to have as they navigate new territory. These two sets of foci, from case-based and analogical reasoning, provide a complementary set of suggestions about educational practice: CBR sets up a big framework of what the learning environment ought to look like, how to orchestrate it, and a set of roles for teachers, peers, and software; analogical reasoning suggests difficulties learners might have and suggests other roles for the teacher and for software. If we take this big picture view seriously as we design curriculum approaches and educational software, our community may indeed be able to have a powerful positive influence on education.
Martin Packer (2001). The problem of transfer, and the sociocultural critique of schooling. The Journal of the Learning Sciences, 10, 493-514.
Shaaron Ainsworth, Peter Bibby & David Wood (2002). Examining the effects of different multiple representational systems in learning primary mathematics. The Journal of the Learning Sciences, 11, 25-61. abstract
Fred G. W. C. Paas en Jeroen J. G. van Merriënboer (1992). Training voor transfer van statistische vaardigheden: toepassing van een vier-componenten instructie-ontwerpmodel. Tijdschrift voor Onderwijsresearch, 17, 17-27. Herdrukt in de laatste jaargang van dit tijdschrift: 2000. Dit tijdschrift is per jaargang gescand beschikbaar op http://objects.library.uu.nl/reader/object_list.php?lan=nl
Jan Terwel, Bert van Oers, Ivanka van Dijk & Pieter van den Eeden (2009). Are representations to be provided or generated in primary mathematics education? Effects on transfer. Educational Research and Evaluation, 15, 25-44. pdf.
Jill H. Larkin (1989). What kind of knowledge transfers? In Lauren B. Resnick (Ed.) (1989). Knowing, learning, and instruction (283-306). Erlbaum.
http://www.benwilbrink.nl/projecten/transfer.htm