Comparing alternative sequences of examples and problem-solving tasks: the case of conceptual knowledge

ABSTRACT In cognitive load theory, the superiority of the Example-Problem sequence over the Problem-Example sequence has become a classic paradigm. The comparative effectiveness of these sequences, however, is subject to the influence of the factors of element interactivity and prior knowledge, and studies have examined these influences focused mostly on procedural rather than conceptual knowledge. This paper takes a deeper look at the effect of types of knowledge concentrating on conceptual knowledge. An experiment is reported comparing the Problem-Example and Example-Problem sequences on two levels of element interactivity, low versus high, which were associated with two types of conceptual knowledge (general principle knowledge and knowledge of principles underlying procedures, accordingly). Since there was no difference found between these sequences for either level of element interactivity, the paper discusses conditions of effectiveness of example-based instructions for different knowledge types in the broader context of Explicit Instruction First and Problem-Solving First approaches.

[1]  A. Renkl,et al.  How Effective are Instructional Explanations in Example-Based Learning? A Meta-Analytic Review , 2010 .

[2]  Barbara Flunger,et al.  Effects of problem–example and example–problem pairs on gifted and nongifted primary school students’ learning , 2019, Instructional Science.

[3]  Martha W. Alibali,et al.  Defining and measuring conceptual knowledge in mathematics , 2014 .

[4]  Ido Roll,et al.  Towards a Theory of When and How Problem Solving Followed by Instruction Supports Learning , 2017 .

[5]  Nikol Rummel,et al.  Delaying instruction: evidence from a study in a university relearning setting , 2012 .

[6]  J. Sweller,et al.  Effects of schema acquisition and rule automation on mathematical problem-solving transfer. , 1987 .

[7]  Ido Roll,et al.  Evaluating metacognitive scaffolding in Guided Invention Activities , 2012 .

[8]  Slava Kalyuga,et al.  The Expertise Reversal Effect is a Variant of the More General Element Interactivity Effect , 2017 .

[9]  J. Sweller,et al.  The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra , 1985 .

[10]  D. Krathwohl A Taxonomy for Learning, Teaching and Assessing: , 2008 .

[11]  Manu Kapur,et al.  Productive failure in learning the concept of variance , 2012 .

[12]  Slava Kalyuga,et al.  Problem-solving or Explicit Instruction: Which Should Go First When Element Interactivity Is High? , 2020, Educational Psychology Review.

[13]  Slava Kalyuga Expertise Reversal Effect and Its Implications for Learner-Tailored Instruction , 2007 .

[14]  Martin Reisslein,et al.  Encountering the expertise reversal effect with a computer-based environment on electrical circuit analysis , 2006 .

[15]  Manu Kapur,et al.  Designing for Productive Failure , 2012 .

[16]  B. Armstrong Wait for it. , 1992, The Health service journal.

[17]  Nikol Rummel,et al.  Knowing what you don't know makes failure productive☆ , 2014 .

[18]  Slava Kalyuga,et al.  Four Ways of Considering Emotion in Cognitive Load Theory , 2019, Educational Psychology Review.

[19]  Elsbeth Stern,et al.  When Problem-Solving Followed by Instruction Is Superior to the Traditional Tell-and-Practice Sequence , 2017 .

[20]  T. Gog,et al.  Effects of pairs of problems and examples on task performance and different types of cognitive load , 2014 .

[21]  B. Rittle-Johnson,et al.  Conceptual and Procedural Knowledge of Mathematics : Does One Lead to the Other ? , 2004 .

[22]  Slava Kalyuga,et al.  Exploring factors influencing the effectiveness of explicit instruction first and problem-solving first approaches , 2020 .

[23]  Benjamin S. Bloom,et al.  A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom's Taxonomy of Educational Objectives , 2000 .

[24]  Alexander Renkl,et al.  Toward an Instructionally Oriented Theory of Example-Based Learning , 2014, Cogn. Sci..

[25]  Gareth Roberts,et al.  Designs for learning about climate change as a complex system , 2017 .

[26]  Manu Kapur Productive Failure , 2006, ICLS.

[27]  L. R. Peterson,et al.  Short-term retention of individual verbal items. , 1959, Journal of experimental psychology.

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

[29]  Marci S. DeCaro,et al.  Exploring mathematics problems prepares children to learn from instruction. , 2012, Journal of experimental child psychology.

[30]  Hyun-Jeong Lee,et al.  The effects of worked examples in computer-based instruction: focus on the presentation format of worked examples and prior knowledge of learners , 2009 .

[31]  Nelson Cowan,et al.  Metatheory of storage capacity limits , 2001, Behavioral and Brain Sciences.

[32]  Kurt VanLehn,et al.  Rule-Learning Events in the Acquisition of a Complex Skill: An Evaluation of Cascade , 1999 .

[33]  Stacy Wood,et al.  Prior Knowledge and Complacency in New Product Learning , 2002 .

[34]  Jeffrey D. Karpicke,et al.  The Testing Effect Is Alive and Well with Complex Materials , 2015 .

[35]  John Sweller,et al.  Effectiveness of Combining Worked Examples And Deliberate Practice for High School Geometry , 2014, ICLS.

[36]  Slava Kalyuga,et al.  Rethinking the Boundaries of Cognitive Load Theory in Complex Learning , 2016 .

[37]  Manu Kapur,et al.  Is having more prerequisite knowledge better for learning from productive failure? , 2017 .

[38]  David A. Sears,et al.  Effects of Innovation versus Efficiency Tasks on Recall and Transfer in Individual and Collaborative Learning Contexts , 2006, ICLS.

[39]  Michael Wolmetz,et al.  Conceptual knowledge representation: A cross-section of current research , 2016, Cognitive neuropsychology.

[40]  John Sweller,et al.  Relations between the worked example and generation effects on immediate and delayed tests , 2016 .

[41]  Slava Kalyuga,et al.  Element interactivity as a factor influencing the effectiveness of worked example-problem solving and problem solving-worked example sequences. , 2019, The British journal of educational psychology.

[42]  J. Hiebert,et al.  Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis , 1986 .

[43]  G. A. Miller THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[44]  Vincent Hoogerheide,et al.  Effects of different sequences of examples and problems on motivation and learning , 2019, Contemporary Educational Psychology.

[45]  John Sweller,et al.  The worked example effect, the generation effect, and element interactivity. , 2015 .

[46]  Slava Kalyuga,et al.  When should guidance be presented in physics instruction , 2015 .

[47]  Manu Kapur,et al.  Productive Failure in Learning Math , 2014, Cogn. Sci..

[48]  T. Gog,et al.  Effects of worked examples, example-problem, and problem-example pairs on novices learning , 2011 .

[49]  John Sweller,et al.  Cognitive Load Theory , 2020, Encyclopedia of Education and Information Technologies.

[50]  Alexander Renkl,et al.  Learning from direct instruction: Best prepared by several self-regulated or guided invention activities? , 2017 .

[51]  K. VanLehn,et al.  Why Do Only Some Events Cause Learning During Human Tutoring? , 2003 .

[52]  Daniel M. Belenky,et al.  Motivation and Transfer: The Role of Mastery-Approach Goals in Preparation for Future Learning , 2012 .

[53]  John Sweller,et al.  When Instructional Guidance is Needed , 2016 .

[54]  Bethany Rittle-Johnson,et al.  Wait for it . . . Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study , 2014, J. Probl. Solving.

[55]  B. Rittle-Johnson,et al.  Conceptual and procedural knowledge of mathematics: Does one lead to the other? , 1999 .

[56]  Jeremy Mayall,et al.  The Magical Number Seven, Plus or Minus Two - PLUNGE , 2016 .

[57]  Michael J. Jacobson,et al.  Does sequence matter? Productive failure and designing online authentic learning for process engineering , 2017, Br. J. Educ. Technol..

[58]  Jeffrey N. Rouder,et al.  Default Bayes factors for ANOVA designs , 2012 .

[59]  Alexander Renkl,et al.  Inventing a solution and studying a worked solution prepare differently for learning from direct instruction , 2015 .

[60]  T. Gog,et al.  Example-Based Learning: Integrating Cognitive and Social-Cognitive Research Perspectives , 2010 .

[61]  Manu Kapur Productive failure in mathematical problem solving , 2010 .

[62]  Vimla L. Patel,et al.  Explanatory Models in the Processing of Science Text: The Role of Prior Knowledge Activation Through Small-Group Discussion , 1989 .

[63]  Nikol Rummel,et al.  The impact of guidance during problem-solving prior to instruction on students’ inventions and learning outcomes , 2014 .

[64]  K. A. Ericsson,et al.  Long-term working memory. , 1995, Psychological review.