Practice Enables Successful Learning Under Minimal Guidance

Two experiments were conducted, contrasting a minimally guided discovery condition with a variety of instructional conditions. College students interacted with a computer-based tutor that presented algebralike problems in a novel graphical representation. Although the tutor provided no instruction in a discovery condition, it constrained the possible actions sufficiently that students could always discover the algebraic transformations they needed to learn. In Experiment I, with ample practice for each new transformation, students performed better in the discovery condition than any instructional condition. In Experiment 2, with only a little practice for each transformation, students performed worst in the discovery condition. The authors suggest that the high levels of practice in the 1st experiment made students more efficient at discovering the algebraic transformations. When the cognitive demands were manageable, the discovery students may have more often encoded the algebraic transformations in mathematically correct ways.

[1]  Davida Charney,et al.  Goal Setting and Procedure Selection in Acquiring Computer Skills: A Comparison of Tutorials, Problem Solving, and Learner Exploration , 1990 .

[2]  Neil T. Heffernan,et al.  Expanding the Model-Tracing Architecture: A 3rd Generation Intelligent Tutor for Algebra Symbolization , 2008, Int. J. Artif. Intell. Educ..

[3]  Vincent Aleven,et al.  An effective metacognitive strategy: learning by doing and explaining with a computer-based Cognitive Tutor , 2002, Cogn. Sci..

[4]  Vincent Aleven,et al.  Toward Meta-cognitive Tutoring: A Model of Help Seeking with a Cognitive Tutor , 2006, Int. J. Artif. Intell. Educ..

[5]  G. Hermann Learning by Discovery: A Critical Review of Studies. , 1969 .

[6]  Richard E. Clark,et al.  Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching , 2006 .

[7]  Alexander Renkl,et al.  Expertise reversal effects in writing-to-learn , 2010 .

[8]  C. Hmelo‐Silver,et al.  Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006) , 2007 .

[9]  R. Rosner Computer software , 1978, Nature.

[10]  T. P. Carpenter,et al.  Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics , 1996 .

[11]  J. Bruner The act of discovery. , 1961 .

[12]  D. Ausubel,et al.  Learning by discovery , 1961 .

[13]  B. Rittle-Johnson,et al.  Promoting transfer: effects of self-explanation and direct instruction. , 2006, Child development.

[14]  J. Tuovinen,et al.  A comparison of cognitive load associated with discovery learning and worked examples , 1999 .

[15]  Glendon W. Blume,et al.  Cases and perspectives , 2008 .

[16]  D. Krantz,et al.  The effects of statistical training on thinking about everyday problems , 1986, Cognitive Psychology.

[17]  Stephen K. Reed,et al.  Use of examples and procedures in problem solving , 1991 .

[18]  Albert T. Corbett,et al.  Cognitive Tutor: Applied research in mathematics education , 2007, Psychonomic bulletin & review.

[19]  Lorna J. Morrow,et al.  The Teaching and Learning of Algorithms in School Mathematics. 1998 Yearbook. , 1998 .

[20]  John R. Anderson,et al.  Cognitive Tutors: Lessons Learned , 1995 .

[21]  T. P. Carpenter,et al.  Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction. , 1997 .

[22]  A. Corbett,et al.  The Cambridge Handbook of the Learning Sciences: Cognitive Tutors , 2005 .

[23]  R. Mayer Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction. , 2004, The American psychologist.

[24]  Olivia N. Saracho,et al.  Handbook of Research on the Education of Young Children , 2005 .

[25]  John R. Anderson How Can the Human Mind Occur in the Physical Universe , 2007 .

[26]  D. Kuhn,et al.  Direct instruction vs. discovery: The long view , 2007 .

[27]  Sofie M. M. Loyens,et al.  Problem-Based Learning is Compatible with Human Cognitive Architecture: Commentary on Kirschner, Sweller, and Clark (2006) , 2007 .

[28]  Albert T. Corbett,et al.  Why Students Engage in “Gaming the System” Behavior in Interactive Learning Environments , 2008 .

[29]  Kelly S. Mix,et al.  The Development of Young Children’s Early Number and Operation Sense and its Implications for Early Childhood Education , 2006 .

[30]  K. Holyoak,et al.  Pragmatic versus syntactic approaches to training deductive reasoning , 1986, Cognitive Psychology.

[31]  E. Glasersfeld Radical Constructivism: A Way of Knowing and Learning. Studies in Mathematics Education Series: 6. , 1995 .

[32]  Peter Hilton,et al.  The Algebra ℝ I , 1970 .

[33]  Richard Mayer,et al.  Multimedia Learning , 2001, Visible Learning Guide to Student Achievement.

[34]  Milena K. Nigam,et al.  The Equivalence of Learning Paths in Early Science Instruction: Effects of Direct Instruction and Discovery Learning , 2022 .

[35]  Slava Kalyuga,et al.  When problem solving is superior to studying worked examples. , 2001 .