Rekenproject: de ‘reform movement’

Ben Wilbrink

rekenproject thuis
rekendidactiek
    ontwikkelingen in het rekenonderwijs
        pabo
        historisch: rekendidactiekhistorisch: rekenopgaven
        van HieleFreudenthalTreffers
        reform (internationaal)



Reform - progressivism


For progressivism see also constructivisme.htm




Alan H. Schoenfeld (2007). Problem solving in the United States, 1970–2008: research and theory, practice and politics. ZDM, The International Journal on Mathematics Education, 39, 537-551. abstract<--reform.htm-->


Abstract Problem solving was a major focus of mathematics education research in the US from the mid-1970s though the late 1980s. By the mid-1990s research under the banner of “problem solving” was seen less frequently as the field’s attention turned to other areas. However, research in those areas did incorporate some ideas from the problem solving research, and that work continues to evolve in important ways. In curricular terms, the problem solving research of the 1970s and 1980s (see, e.g., Lester in J Res Math Educ, 25(6), 660–675, 1994, and Schoenfeld in Handbook for research on mathematics teaching and learning, MacMillan, New York, pp 334–370, 1992, for reviews) gave birth to the “reform” or “standards-based” curriculum movement. New curricula embodying ideas from the research were created in the 1990s and began to enter the marketplace. These curricula were controversial. Despite evidence that they tend to produce positive results, they may well fall victim to the “math wars” as the “back to basics” movement in the US is revitalized.

Literature



Jo Boaler (2002). Experiencing School Mathematics. Revised and expanded edition. Erlbaum. site


De uitgever heeft een oorlogsverklaring op de achterkant van het boek gedrukt. Let wel: dit boek gaat over een onderzoek waarin driehonderd leerlingen gedurende drie jaar zijn gevolgd. Een heel bescheiden onderzoek dus, waargeen onbescheiden conclusies bij passen.

The book draws some radical new conclusions about the ways that traditional teaching methods lead to limited forms of knowledge that are ineffective in non-school settings.

tekst van de uitgever



Jo Boaler (1997). Equity, Empowerment and Different Ways of Knowing. Mathematics Education Research Journal, 9, 325-342. abstract, of meteeen maar de pdf


Een nogal ideologisch gekleurde — of moet ik zeggen: romantische? — slotverklaring:

In the UK, as in many other parts of the world, we are currently in the midst of a "ba~k to basics" political ... climate, characterised by support for traditional teaching methods (from Labour as well as Conservative politicians). A number of different research projects within mathematics education have contrasted open, progressive or meaning-based approaches to mathematics teaching with closed, traditional, algorithmic approaches (Keedy & Drmacich, 1994; Maher, 1991; Resnick, 1990; Sigurdson & Olson, 1992; ). These studies have all shown that progressive approaches to teaching result in increased attainment, even on traditional tests that are not compatible with the teaching approaches used. But such research is ignored in media and public debates, and schools in the UK are experiencing mounting pressure to conform to one standard model of mathematics teaching with classes set by ability, whole class teaching and procedural textbook lessons. Phoenix Park has now abandoned its project-based lessons and mixed ability groups in favour of textbook lessons and setted groups. The students who left Phoenix Park did so as active mathematical thinkers who liked to use their initiative and were flexible in their use of mathematics. Research suggests that future cohorts of students will not leave Phoenix Park with such positive mathematical capabilities. Nor will they leave the school having experienced the opportunity to work in equitable environments, that enable both separate and connected ways of knowing.


Boaler noemt hier een aantal ‘onderzoekprojecten’ die aangetoond zouden hebben dat reform-didactiek betere resultaten oplevert dan conventionele didactiek, alle andere omstandigheden gelijk zijnde. Ik vraag mij af of zij daarin gelijk heeft, en wil best even voor lief nemen dat zij deze drie projecten zelf heeft gekozen. Ik ga geen moeite doen om de volgende publicaties binnen te halen, het lijkt me dat Boaler wat onvoorzichtig is geweest met haar claim.


Aan het eind van het boek (de laatste blz. 188) noemt Jo Boaler andere literatuur, en geeft in de laatste zinnen van haar boek nog eens glashelder haar ideologische positie weer, niet de resultaten van glashelder onderzoek:

“ . . . . the enormous wealth of research evidence, spanning over 60 years, that has shown the advantages of these approaches [‘an open apporach’’, i.e. problem-based learning. b.w.] (Baird & Northfield, 1992; Benezet, 1935a, 1935b, 1936; Charles & Lester, 1984; Cobb, Wood, Yackel & Perlwitz, 1992). Phoenix Park’ open, project-based approach has been eliminated, and there is a real possibility that the students who left the school in 1995 as active mathematical thinkers will soon be replaced by mathematics students who are submissive and rule-bound and who see no use for the methods, facts, rules, and procedures they learn in their school mathematics lessons . . . ”
  • J. R. Baird & J. R. Northfield (Eds.) (1992). Learning from the PEEL experience. Monash University. html [Dit mag amusant zijn, maar oo hier zie ik niet wat Boaler ermee wil aantonen, behalve die zestig jaar dan]
  • R. Charles & F. Lester, Jr. (1984). An evaluation of a process-oriënted program in mathematical problem solving in grades 5 and 7. Journal for Research in Mathematics Education, 15(1), 15-34. preview [Zie ook http://goo.gl/FEBHO ] [Dit is een experimentje met een cursus probleemoplossen klas 5 en 7, ik zie het verband met het werk van Boaler niet; over probleemoplossen is ondertussen wel het een en ander bekend, en echt iets anders dan wat in dit experimentje aan de orde is]
  • P. Cobb, T. Wood, E. Yackel & M. Perlwitz (1992). A follow-up assessment of a second-grade problem-centered mathematics project. Educational Studies in Mathematic, 23, 483-504. preview [constructivisme]

  • Alan Schoenfeld mag dit allemaal prachtig vinden, voor mij geven de laatste woorden van Jo Boaler getuigenis van een onwetenschappelijk onderzoekhouding. Die indruk wordt bevestigd door het merkwaardige literatuurlijstje hierboven, waaraan zij zo’n grote betekenis hecht (wat mij echt een raadsel is). Ik ben niet meer in staat om haar op haar woord te vertrouwen. Dat zal ook het gevoelen zijn geweest bij Bishop en Milgram, aan wie zij kennelijk ook in dit boek refereert (zonder de namen te noemen, een hinderlijke gewoonte die mij doet denken aan Hans Freudenthal) op blz. 187.



    Mary Kay Stein, Barbara W. Grover and Marjorie Henningsen (1996). Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms. American Educational Research Journal, 33, 455-488 abstract




    Mary Kay Stein, Barbara W. Grover & Marjorie Henningsen (1996). Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms. American Educational Research Journal, 33, 455-488. [nog geen pdf] abstract


    • The findings suggest that teachers were selecting and setting up the kinds of tasks that reformers argue should lead to the development of students’ thinking capacities.



    Erin R. Ottmar, Sara E. Rimm-Kaufman, Ross A. Larsen & Robert Q. Berry (2015). Mathematical Knowledge for Teaching, Standards-Based Mathematics Teaching Practices, and Student Achievement in the Context of the Responsive Classroom Approach. American Educational Research Journal, 52, 787-821. [researchgate.net] abstract




    Erin R. Ottmar, Sara E. Rimm-Kaufman, Robert Q. Berry, and Ross A. Larsen (2013). Does the Responsive Classroom Approach Affect the Use of Standards-Based Mathematics Teaching Practices?: Results from a Randomized Controlled Trial. The Elementary School Journal, 113, 434-457. researchnet.rtf




    Jan de Lange (1991). Hard tegen hart. Vernieuwing in het wiskundeonderwijs. Rede (hoogleraar in de didactiek van het wiskunde- en informaticaonderwijs)




    Alan J. Bishop & Helen J. Forgasz (2009). Issues in access and equity in mathematics education. In: F. Lester, Second handbook of research on mathematics teaching and learning 1145-1167. National Council of Teachers of Mathematics.





    Paul Ernest (2009). New philosophy of mathematics: Implications for mathematics education. In Brian Greer, Swapna Mukhopadhyay, Arthur B. Powell & Sharon Nelson-Barber: Culturally responsive mathematics education. Routledge. fc


    Constructivisme van heb ik jou daar. Tjonge. Een tussenkopje als 'Mathematical knowledge as a socially constructed human invention' geven het al weg. Overal een kern van waarheid, maar dan een ideologische saus erover. Ik had er een kopie van, die heb ik weggeflikkerd. Ooit was ik gecharmeerd van werk van Paul Ernest, nog voordat ik met Daan en Sanne kennis maakte, zal ik maar zeggen. Verontrustend hoe aantrekkelijk romantiek blijkt te zijn! Ik heb overal op mijn website Paul Ernest verwijderd, of naar de constructivisme-pagina gedirigeerd. [Ernest geeft zelf een tijdschrift uit dat online op zijn website staat, voor de liefhebbers van constructivisme zal ik maar zeggen.] abstract



    Izzak Wirszup & Robert Streit (Eds.) (1991). Developments in School Mathematics Education Around the World Vol. 3. ICME Proceedings of the UCSMP International Conference on Mathematics Education. University of Chicago School Mathematics Project. National Council of Teachers of Mathematics. isbn 0873533569


    1. The Goal of Mathematics for All
      • Will everybody ever count? / Lynn Arthur Steen 3-13
      • Mathematics education: an indurstrial view / Keith W. McHenry 14-24
      • The popularization of mathematics / Jean-Pierre Kahane 25-34
      • Is there a real chance for "mathematics and science for all Americans"? / Christine Keitel 35-48
      • Higher order (un-)teaching / Jan de Lange 49-72
      • Mathematics for all students: technology and the power of visualization / Franklin Demana, Bert K. Waits 73-83
      • MAS-MATHICS: a curriculum for non-college bound students in Israel / Nitsa Movshovitz-Hadar
      • Equity, assessment, and thinking mathematically: principles for the design of model-eliciting activities / Richard Lesh, Mark Hoover, Anthony E. Kelly 104-132
    2. The Process and Evaluation of Reform Efforts
      • "America is likewise bestirring herself": a century of mathematics education as viewed from the United States / Jeremy Kilpatrick
      • The mathematical sciences education board: preparing for the twenty-first century / Linda P. Rosen
      • What does it mean to be modern in mathematics education? / Ubiratan D'Ambrosio
      • Reflections on the mathematics assessments of the national assessment of educational progress [NAEP] / Mary Montgomery Lindquist 163-185
      • Certifying accomplishments in mathematics: the new standards examining system / Lauren B. Resnick, Diane Briars, Sharon Lesgold 186-207
      • Assessing mathematics: enhancing understanding / John A. Dossey 208-222
    3. The Content of Reform
      • Toward a world class curriculum in the United States / Thomas A. Romberg
      • What are the goods and how do we deliver them? / Paul J. Sally, Jr.
      • Investigations in number, data, and space: a new elementary curriculum / Susan Jo Russell - The UCSMP elementary mathematics specialist project / Sheila Sconiers
      • Reflections on inservice work with U.S. teachers of mathematics / Jerry P. Becker
      • The effects of technology on the mathematics curriculum: what goes in? What goes out? / Wade Ellis, Jr.
      • Computers, understanding of concepts, and problem solving / Lars-Eric Björk, Hans Brolin
      • Getting students to function in algebra / Judah L. Schwartz
      • Statistics in the mathematics curriculum: why and what? / David S. Moore
      • Algorithmics in school mathematics: why, what and how? / David C. Johnson 330-345
      • Applications and modeling in school mathematics-directions for future development / Mogens Niss
    4. International Comparisons
      • -- The third international mathematics and science study: issues and questions / David F. Robitaille 365-386
      • School mathematics in the U.S. and U.K.: similarities and differences / David C. Johnson 387-404
      • School mathematics in Japan and the U.S.: focusing on recent trends in elementary and lower secondary school / Tatsuro Miwa 405-427
      • Results of U.S.-Japan cross-national research on students' problem solving behaviors / Jerry P. Becker 428-467
      • Some puzzling questions arising from mathematics education in China / Dianzhou Zhang 468-480
      • Competition and cooperation in school mathematics / Zalman Usiskin. 481-492
     



    Bert Zwaneveld (1974). Rapport over een vorm van wiskundeonderwijs waarbij differentiatie naar tempo centraal staat. Didactiek Commissie van de Nederlandse Vereniging van Wiskundeleraren NVvW.


    • Op het Ignatiuscollege te Amsterdam wordt sinds 1969 op de onderbouw van de atheneum-havo-afdeling een vorm van wiskundeonderwijs in praktijk gebracht, waarbij de leerlingen van een bepaalde klas in groepjes van twee in hun eigen tempo de leerstof doorwerken.

    blz. 1



    NVvWL; NLO/SLO Samenwerkingsgroep (1982). Examen anders bekeken




    Martin Kindt e.a. Hewet Project: Eindverslag. Voorwoord: Van der Blij. OW & OC




    Magdalene Lampert & Deborah Loewenberg Ball (1998). Teaching, Multimedia, and Mathematics. Investigations of Real Practice. Teachers College, Coumbia University. isbn 0807737577 info


    As reformed as reform can be ;-) Quite interesting is that these researchers are ractising teachers themselves (Lampert in grade five, Ball in grade three). The project is bout the mathematics teaching specifically.

    • The pedagogy of investigation is at the heart of current efforts to improve schools. Whether students are studying temperature or democracy or poetry or probability, they are to learn from investigating practice, that is, from working on problems, talking with others about potential solutions, building on their own ways of thinking about concepts, and engaging with significant disciplinary ideas.

      p. ix



    Walter G. Secada, Elizabeth Fennema & Lisa Byrd Adajian (Eds.) (1995). New Directions for Equity in Mathematics Education. Cambridge University Press. info


    • All three projects [chapters 1-3, b.w.] are cognizant of the reform movement in mathematics education as exemplified, in part, by recent publications of the National Council of Teachers of Mathematics (1989, 1991) and the National Research Council (1989), and they provide evidence that it is possible to teach in ways that the reformers endorse, as well as in ways that make mathematics come alive to a wide range of students.

      p. 2-3

      The chapters by Keynes and Campbell are set firmly in out-of-school settings that provide different perspectives on ways by which those settings might inform efforts to make learning in-school more like learning out-of-school (Resnick, 1987).

      p. 4

      Also, there are tensions across these chapters and we invited Michael Apple, who has written about the current school mathematics reform movement (Apple 1992a, 1992b), to end this book with his reflections on some of those tensions.

      p. 4

      1. Edward A. Silver, Margaret Schwan Smith & Barbara Scott Nelson: The Quasar project: equity concerns meet mathematics education reform in the middle school 9-56

      2. Harvey B. Keynes: Can equity thrive in a culture of mathematical excellence? 57-92

      3. Deborah A. Carey, Elizabeth Fennema, Thomas P. Carpenter & Megan L. Franke: Equity and mathematics education 93-125

      4. Gloria Ladson-Billings: Making mathematics meaningful in multicultural contexts 126-145

      5. Walter G. Secada: Social and critical dimensions for equity in mathematics education 146-164

      6. Marilyn Frankenstein: Equity in mathematics education: class in the world outside the class 165-190

      7. William Tate: Economics, equity, and the national mathematics assessment: are we creating a national tollroad? 191-2007
      8. Gilah C. Leder: Equity inside the mathematics classroom: Fact or artifact? 209-224
      9. Patricia B. Campbell: Redefining the 'girl problem in mathematics' 225-241

      10. Suzanne K. Damarin: Gender and mathematics from a feminist standpoint 242-257

      11. George M. A. Stanic & Laurie E. Hart: Attitudes, persistence, and mathematics achievement: qualifying race and sex differences 258-277

      12. Lena Licón Khisty: Making Inequality: Issues of Language and Meanings in Mathematics Teaching with Hispanic Students 279-297
      13. Beth Warren & Ann S. Roseberry: Equity in the future tense: redefining relationships among teachers, students, and science in linguistic minority classrooms 298-328

      14. Michael W. Apple: Taking power seriously: new directions in equity in mathematics education and beyond 329-347



    Jo Boaler (2015). Mathematical mindsets. Jossey-Bass. isbn 9780470894521 info




    Marcus Nührenbörger ao (2016). Design Science and Its Importance in the German Mathematics Educational Discussion free
















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