Some Correct Strategies Are Better Than Others: Individual Differences in Strategy Evaluations Are Related to Strategy Adoption

Why do people shift their strategies for solving problems? Past work has focused on the roles of contextual and individual factors in explaining whether people adopt new strategies when they are exposed to them. In this study, we examined a factor not considered in prior work: people's evaluations of the strategies themselves. We presented undergraduate participants from a moderately selective university (N = 252; 64.8% women, 65.6% White, 67.6% who had taken calculus) with two strategies for solving algebraic word problems and asked them to rate these strategies and their own strategy on a variety of dimensions. Participants' ratings loaded onto two factors, which we label quality and difficulty. Participants' initial evaluations of the quality of the strategies were associated with whether they used the strategies at posttest, and this effect held even when controlling for individual and contextual factors. However, people's evaluations of the difficulty of the strategies were not consistently associated with their later adoption of those strategies. We also examined individual and contextual predictors of strategy ratings and strategy adoption. Participants' need for cognition and their spatial visualization ability were associated with their strategy evaluations, and the framing of the story problems was associated with their strategy adoption. The findings highlight that strategy adoption depends on multiple interacting factors, and that to understand strategy change, it is critical to examine how people evaluate strategies.

[1]  M. Alibali,et al.  Symbolizing algebraic story problems: Are diagrams helpful? , 2021, Applied Cognitive Psychology.

[2]  Jon R. Star,et al.  Comparing and Discussing Multiple Strategies: An Approach to Improving Algebra Instruction , 2021, The Journal of Experimental Education.

[3]  Martha B. Makowski,et al.  “Bold Problem Solving”: A New Construct for Understanding Gender Differences in Mathematics , 2021 .

[4]  Sarah A. Brown,et al.  Strategy adoption depends on characteristics of the instruction, learner, and strategy , 2019, Cognitive research: principles and implications.

[5]  Sarah A. Brown,et al.  Understanding Strategy Change: Contextual, Individual, and Metacognitive Factors. , 2019, Advances in child development and behavior.

[6]  V. de Gardelle,et al.  Confidence as a Priority Signal , 2018, bioRxiv.

[7]  Martha W. Alibali,et al.  Relational Equity and Mathematics Learning: Mutual Construction During Collaborative Problem Solving , 2018, J. Numer. Cogn..

[8]  Nicole M. McNeil,et al.  Perceptual support promotes strategy generation: Evidence from equation solving , 2018, The British journal of developmental psychology.

[9]  Sarah A. Brown,et al.  Promoting Strategy Change: Mere Exposure to Alternative Strategies Helps, but Feedback Can Hurt , 2018 .

[10]  V. de Gardelle,et al.  Metacognitive ability predicts learning cue-stimulus associations in the absence of external feedback , 2018, Scientific Reports.

[11]  Markus Brauer,et al.  Linear Mixed-Effects Models and the Analysis of Nonindependent Data: A Unified Framework to Analyze Categorical and Continuous Independent Variables that Vary Within-Subjects and/or Within-Items , 2017, Psychological methods.

[12]  M. Alibali,et al.  Does it matter how Molly does it? Person-presentation of strategies and transfer in mathematics , 2017 .

[13]  B. Rittle-Johnson,et al.  Developing Mathematics Knowledge , 2017 .

[14]  Julie L. Booth,et al.  Support for Struggling Students in Algebra: Contributions of Incorrect Worked Examples. , 2016 .

[15]  P. Sterzer,et al.  Mesolimbic confidence signals guide perceptual learning in the absence of external feedback , 2016, eLife.

[16]  Lisa K. Fazio,et al.  Strategy use and strategy choice in fraction magnitude comparison. , 2016, Journal of experimental psychology. Learning, memory, and cognition.

[17]  Julie L. Booth,et al.  Simple Practice Doesn’t Always Make Perfect , 2015 .

[18]  B. Rittle-Johnson,et al.  Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics , 2015, Educational Psychology Review.

[19]  Martha W. Alibali,et al.  Leave Her out of It: Person-Presentation of Strategies is Harmful for Transfer , 2015, Cogn. Sci..

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

[21]  Nicole M. McNeil A Change–Resistance Account of Children's Difficulties Understanding Mathematical Equivalence , 2014 .

[22]  David H. Uttal,et al.  Exploring and Enhancing Spatial Thinking , 2013 .

[23]  Jan Boom,et al.  Microgenetic patterns of children's multiplication learning: confirming the overlapping waves model by latent growth modeling. , 2012, Journal of experimental child psychology.

[24]  Mike Stieff,et al.  The role of spatial ability and strategy preference for spatial problem solving in organic chemistry , 2012 .

[25]  Mary Hegarty,et al.  The Cognitive Science of Visual-Spatial Displays: Implications for Design , 2011, Top. Cogn. Sci..

[26]  D. Lubinski,et al.  Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. , 2009 .

[27]  Rainer Bromme,et al.  Coherence Formation when Learning from Text and Pictures: What Kind of Support for Whom? , 2009 .

[28]  John R. Anderson,et al.  The strategic nature of changing your mind , 2009, Cognitive Psychology.

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

[30]  B. Rittle-Johnson,et al.  Flexibility in Problem Solving: The Case of Equation Solving. , 2008 .

[31]  J. Rieskamp,et al.  SSL: a theory of how people learn to select strategies. , 2006, Journal of experimental psychology. General.

[32]  Roberto Araya,et al.  A computational model of conscious and unconscious strategy discovery. , 2005, Advances in child development and behavior.

[33]  J. Grice Computing and evaluating factor scores , 2001 .

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

[35]  R. Siegler,et al.  The rebirth of children's learning. , 2000, Child development.

[36]  M. Hegarty,et al.  Types of visual–spatial representations and mathematical problem solving. , 1999 .

[37]  Susan Goldin-Meadow,et al.  Illuminating Mental Representations Through Speech and Gesture , 1999 .

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

[39]  Marsha C. Lovett,et al.  Task representations, strategy variability, and base-rate neglect , 1999 .

[40]  M. Alibali How children change their minds: strategy change can be gradual or abrupt. , 1999, Developmental psychology.

[41]  Jeff Shrager,et al.  SCADS: A Model of Children's Strategy Choices and Strategy Discoveries , 1998 .

[42]  Mary Hegarty,et al.  Individual differences in use of diagrams as external memory in mechanical reasoning , 1997 .

[43]  R. Siegler,et al.  Four aspects of strategic change: contributions to children's learning of multiplication. , 1995, Journal of experimental psychology. General.

[44]  K. Crowley,et al.  Constraints On Learning in Nonprivileged Domains , 1994, Cognitive Psychology.

[45]  M. Hegarty,et al.  Individual differences in mental animation during mechanical reasoning , 1994, Memory & cognition.

[46]  F. Paas,et al.  Variability of Worked Examples and Transfer of Geometrical Problem-Solving Skills: A Cognitive-Load Approach , 1994 .

[47]  C. J. Sadowski,et al.  Internal Consistency and Test-Retest Reliability of the Need for Cognition Scale , 1992 .

[48]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

[49]  C. F. Kao,et al.  The efficient assessment of need for cognition. , 1984, Journal of personality assessment.

[50]  J. Cacioppo,et al.  The need for cognition. , 1982 .

[51]  M. Scheerer,et al.  Problem Solving , 1967, Nature.

[52]  R. Adamson Functional fixedness as related to problem solving; a repetition of three experiments. , 1952, Journal of experimental psychology.

[53]  A. Luchins Mechanization in problem solving: The effect of Einstellung. , 1942 .