Abstract
An important tenet of constructivism is that learning is an idiosyncratic, active and evolving process. Active learning, operationalized by cognitive, metacognitive, affective and resource management learning strategies, is necessary for students to effectively cope with the high level of demands placed on the learner in a constructivist learning environment. Case studies of two students detail contrasting passive and active learning behaviours. Examples of their strategic learning behaviours illustrate that having students involved in activities such as discussions, question answering, and seatwork problems does not automatically guarantee successful knowledge construction. The nature of students' metacognitive knowledge and the quality of their learning strategies are seen to be critical factors in successful learning outcomes.
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References
Anthony, G.: 1991, Learning Approaches and Study Patterns of Distance Education Students in Mathematics, unpublished MPhil thesis, Massey University, Palmerston North.
AnthonyG.: 1994a, ‘The role of worked examples in learning mathematics’, in A.Jones et al. (eds.), SAMpapers 1994, Centre for Science and Mathematics Education Research, University of Waikato, Hamilton, 129–143.
AnthonyG.: 1994b, ‘Learning strategies in the mathematics classroom: what can we learn from stimulated recall interviews?’, New Zealand Journal of Educational Studies 29(2), 127–140.
Anthony, G.: 1994c, Learning Strategies in Mathematics Education, unpublished PhD thesis, Massey University, Palmerston North.
Anthony, G.: (in press), ‘When mathematics students fail to use appropriate learning strategies’, Mathematics Education Research Journal.
Australian Educational Corncil.: 1991, A National Statement on Mathematics for Australian Schools, Curriculum Corporation, Melbourne.
BairdJ. R. and NorthfieldJ. R.: 1992, Learning from the PEEL Experience, Monash University Printing Services, Melbourne.
BereiterC.: 1990, ‘Aspects of an educational learning theory’, Review of Educational Research 60(4), 603–624.
BereiterC.: 1992, ‘Referent-centred and problem-centred knowledge: Elements of an educational epistemology’, Interchange 23(4), 337–361.
BereiterC. and ScardamaliaM.: 1989, ‘Intentional learning as a goal of instruction, in L. B.Resnick (ed.), Knowing, Learning, and Instruction: Essays in Honor of Robert Glaser, Lawrence Erlbaum Associates, Hillsdale, N.J., 361–282.
ChiM. T. and BassokM.: 1989, ‘Learning from examples via self-explanations’, in L. B.REsnick (ed.), Knowing, Learning, and Instruction: Essays in Honor of Robert Glaser, Lawrence Erlbaum Associates, Hillsdale, N.J., 251–282.
Cobb, P.: 1994, ‘Where is the mind? Constructivist and sociocultural perspectives on mathematical development’, Educational Researcher October, 13–20.
CobbP., WoodT., YackelE. and McNealB.: 1992, ‘Characteristics of classroom mathematics traditions: an interactional analysis’, American Educational research Journal 29(3), 573–604.
ConfreyJ.: 1990, ‘What constructivism implies for teaching’, in R. B.Davis, C. A.Maher and N.Noddings (eds.), Constructivist Views on the Teaching and Learning of Mathematics, National Council of Teachers of Mathematics, Reston, Va., 107–122.
DeCorteE.: 1995, ‘Fostering cognitive growth: A perspective from research on mathematics learning and instruction’, Educational Psychologist 30(10), 37–46.
DerryS. J.: 1990, ‘Learning strategies for acquiring useful knowledge’, in B.Jones and L.Idol (eds.), Dimensions of Thinking and Cognitive Instruction, Lawrence Erlbaum Associates, Hillsdale, N.J., 251–282.
DesforgesC. and BristowS.: 1994, ‘Reading to learn mathematics in the primary age range’, in P.Ernest (ed.), Constructing Mathematical Knowledge: Epistemology and Mathematical Education, The Falmer Press, London, 215–236.
ErnestP.: 1995, ‘The one and the many’, in L.Steffe and J.Gale (eds.), Constructivism in Education, Lawrence Erlbaum Associates, Hillsdale, N.J., 459–486.
FlavellJ. H.: 1976, ‘Metacognitive aspects of problem solving’, in L. B.Resnick (ed.), The Nature of Intelligence, Lawrence Erlbaum Associates, Hillsdale N.J., 231–235.
FlavellJ. H.: 1987, ‘Speculations about the nature and development of metacognition’, in F. E.Weinert and R. H.Kluwe (eds.), Metacognition, Motivation, and Understanding, Lawrence Erlbaum Associates, Hillsdale, N.J., 21–29.
GlesneC. and PeshkinA.: 1992, Becoming a Qualitative Researcher: An Introduction, Longman, New York.
HennessyS.: 1993, ‘Situated cognition and cognitive apprenticeship: Implications for classroom learning’, Studies in Science Education 22, 1–41.
HerringtonA. J.: 1990, ‘Strategies for developing mathematical understandings’, in K.Milton and H.McCann (eds.), Mathematical Turning Points: Strategies for the 1990s, Australian Association of Mathematics Teachers, Hobart, Tasmania, 325–340.
HiebertJ.: 1992, ‘Reflection and communication: Cognitive considerations in school mathematics reform’, International Journal of Educational Research, 17, 439–456.
KyriacouC. and MarshallS.: 1989, ‘The nature of active learning in secondary schools’, Evaluation and Research in Education 3(1), 1–5.
LederG. C. and GunstoneR. F.: 1990, ‘Perspectives on mathematics learning’, International Journal of Educational Research 14(2), 105–120.
LeinhardtG. and PutnamR. T.: 1987, ‘The skill of learning from classroom lessons’, American Educational Research Journal 24, 557–587.
MayerR. E.: 1992, ‘Cognition and instruction: Their historic meeting within educational psychology’, Journal of Educational Psychology, 84, 405–412.
Ministry of Education: 1992, Mathematics in the New Zealand Curriculum, Learning Media, Wellington.
NoddingsN.: 1990, ‘Constructivism in mathematics education’, in R. B.Davis, C. A.Maher and N.Noddings (eds.) Constructivist Views on the Teaching and Learning of Mathematics, National Council of Teachers of Mathematics, Reston, Va., 7–18.
NoddingsN.: 1993, ‘Constructivism and caring’, in R.Davis and C.Maher (eds.), Schools, Mathematics, and the World of Reality, Allyn and Bacon, Boston, 35–50.
NolenS.: 1988, ‘Reasons for studying: Motivational orientations and study strategies’, Cognition and Instruction 5, 269–287.
PerkinsD. N.: 1991, ‘What constructivism demands of the learner’, Educational Technology 31(9), 19–21.
PetersonP. L.: 1988, ‘Teaching for higher-order thinking in mathematics: The challenge for the next decade’, in D. A.Grouws and T. J.Cooney (eds.), Research Agenda for Mathematics Education: Perspective on Research on Effective Mathematics Teaching, National Council of Teachers of Mathematics, Reston, Va., 2–26.
ThomasJ. W. and RohwerW. D.: 1993, ‘Proficient autonomous learning: Problems and prospects’, in M.Rabinowitz (ed.), Cognitive Science Foundations of Instruction, Lawrence Erlbaum Associates, N.J., 1–32.
vonGlasersfeldE.: 1991, Radical Constructivism in Mathematics, Kluwer Academic Publishers, Dordrecht.
von Glasersfeld, E.: 1995, Learning Mathematics: Constructivist and interactionist theories of mathematical development, [Review of the book Learning Mathematics: Constructivist and Interactionist Theories of Mathematical Development, P. Cobb (ed.)], in Zentralblatt für Didaktik der Mathematik 4, 120–122.
WangM. C., HaertelG. D. and WalbergH. J.: 1993, ‘Toward a knowledge base for school learning’, Review of Educational Research 63, 249–294.
WeinsteinC. E. and MayerR. E.: 1986, ‘The teaching of learning strategies’, in M. E.Wittrock (ed.), Handbook of Research on Teaching, Macmillan, New York, 315–327.
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Anthony, G. Active learning in a constructivist framework. Educational Studies in Mathematics 31, 349–369 (1996). https://doi.org/10.1007/BF00369153
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DOI: https://doi.org/10.1007/BF00369153