Computer-based feedback in linear algebra: Effects on transfer performance and motivation

Two studies investigated the effects on students' perceptions (Study 1) and learning and motivation (Study 2) of different levels of feedback in mathematical problems. In these problems, an error made in one step of the problem-solving procedure will carry over to the following steps and consequently to the final solution. Providing immediate feedback after an error is made could prevent such carry-over effects. Feedback given on all problem-solving steps was hypothesized to yield higher motivation and better learning than feedback on the final problem-solving step. Study 1 investigated students' perceptions of three feedback types: 'on the final solution step'; 'on all the solution steps at once'; and 'on all the solution steps successively'. Feedback on all solutions steps was perceived by learners more positively than feedback on the final solution step. Study 2 investigated the learning and motivational effects of two types of feedback, namely, 'feedback on the final solution step' and 'feedback on all the solution steps'. The hypotheses that feedback on all problem-solving steps would lead to more effective learning and higher motivation than feedback on the final solution step were confirmed. Our results support current efforts to implement step-wise feedback. The implications for further research and for the design of feedback are discussed.

[1]  Fgmt Hans Cuypers,et al.  MESS: the MathDox Exercise System , 2009 .

[2]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[3]  J. Hattie,et al.  The Power of Feedback , 2007 .

[4]  Charles M. Reigeluth,et al.  Instructional Design Theories and Models : An Overview of Their Current Status , 1983 .

[5]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[6]  Jacquelynne S. Eccles,et al.  Development of achievement motivation. , 2007 .

[7]  John V. Dempsey,et al.  Interactive Instruction and Feedback , 1993 .

[8]  K. H. Canobi,et al.  Concept-procedure interactions in children's addition and subtraction. , 2009, Journal of experimental child psychology.

[9]  Malcolm L. Fleming,et al.  Instructional Message Design: Principles from the Behavioral and Cognitive Sciences , 1993 .

[10]  F. Paas.  Training strategies for attaining transfer of problem-solving skill in statistics: A cognitive-load approach. , 1992 .

[11]  P. Winne,et al.  Feedback and Self-Regulated Learning: A Theoretical Synthesis , 1995 .

[12]  Erica Melis,et al.  Global Feedback in ActiveMath. , 2005 .

[13]  F. Paas,et al.  Cognitive Architecture and Instructional Design , 1998 .

[14]  J. Michael Spector,et al.  Handbook of Research on Educational Communications and Technology, 3rd Edition , 2012 .

[15]  E. Mory.  Feedback research revisited. , 2004 .

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

[17]  Cathy L. Bruce-Hayter,et al.  A review of Computer Mediated Communication and the Online Classroom , 1995 .

[18]  Kent J. Crippen,et al.  The impact of web-based worked examples and self-explanation on performance, problem solving, and self-efficacy , 2007, Comput. Educ..

[19]  F. Paas,et al.  Instructional control of cognitive load in the training of complex cognitive tasks , 1994 .

[20]  John Sweller,et al.  Cognitive Load During Problem Solving: Effects on Learning , 1988, Cogn. Sci..

[21]  Orit Zeichner,et al.  Using Technology to Enhance Mathematical Reasoning: Effects of Feedback and Self-Regulation Learning , 2001 .

[22]  S. Derry,et al.  Learning from Examples: Instructional Principles from the Worked Examples Research , 2000 .

[23]  D. Jonassen,et al.  Enhancing relevance: Embedded ARCS strategies vs. Purpose , 1997 .

[24]  Abdel K. Halabi,et al.  Applying an instructional learning efficiency model to determine the most efficient feedback for teaching introductory accounting , 2006 .

[25]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[26]  J. Keller.  Motivational Design of Instruction , 1983 .

[27]  Liesbeth Kester,et al.  Dynamic task selection: Effects of feedback and learner control on efficiency and motivation , 2009 .

[28]  Peter Boon,et al.  DESIGNING DIDACTICAL TOOLS AND MICROWORLDS FOR MATHEMATICS EDUCATIONS , 2008 .

[29]  Roger Azevedo,et al.  A Meta-Analysis of the Effects of Feedback in Computer-Based Instruction , 1995 .

[30]  Regina Vollmeyer,et al.  A Surprising Effect of Feedback on Learning. , 2005 .

[31]  Adnan Baki,et al.  Evaluation of a web based mathematics teaching material on the subject of functions , 2008, Comput. Educ..

[32]  Erica Melis,et al.  Interactivity of Exercises in ActiveMath , 2005, ICCE.

[33]  Frank M. Pajares,et al.  The development of academic self-efficacy. , 2002 .

[34]  T. Gog,et al.  Optimising worked example instruction: Different ways to increase germane cognitive load. , 2006 .

[35]  F. Paas,et al.  Cognitive Load Theory and Instructional Design: Recent Developments , 2003 .

[36]  E. Deci,et al.  Motivation and Education: The Self-Determination Perspective , 2008 .

[37]  Jean-François Nicaud,et al.  Mixing Microworld and Cas Features in Building Computer Systems that Help Students Learn Algebra , 2004, Int. J. Comput. Math. Learn..

[38]  R. Catrambone.  Generalizing Solution Procedures Learned From Examples , 1996 .

[39]  Bernard Kolman,et al.  Introductory Linear Algebra: An Applied First Course , 2004 .