Supporting Algebraic Reasoning through Personalized Story Scenarios: How Situational Understanding Mediates Performance

Context personalization refers to matching instruction to students' out-of-school interests and experiences. Belief in the benefits of matching instruction to interests is widely held in the culture of schooling; however, little research has empirically examined how interest impacts performance and learning in secondary mathematics. Here we investigate these issues with a series of problem-solving sessions where 24 Algebra I students were presented with story problems on linear functions, some of which were personalized to their interests. Our analyses focus on performance, strategy use, and mistake patterns. Results suggest that personalization supported situational reasoning (Nathan, Kintsch, & Young, 1992) about the actions and relationships in the scenario, improving performance for weaker students and on harder problems. However, personalized scenarios seemed to act as a distraction when stronger students in the sample worked on easier problems. Thus context personalization may have the potential to provide assistance and support performance as students learn new concepts.

[1]  Kaye Stacey,et al.  Learning the Algebraic Method of Solving Problems , 1999 .

[2]  David W. Carraher,et al.  Arithmetic and Algebra in Early Mathematics Education , 2006 .

[3]  Kenneth R. Koedinger,et al.  Teachers' and Researchers' Beliefs about the Development of Algebraic Reasoning. , 2000 .

[4]  J. Boaler.  When Do Girls Prefer Football to Fashion? An analysis of female underachievement in relation to ‘realistic’ mathematic contexts , 1994 .

[5]  Barry Cooper,et al.  Realistic Contexts, Mathematics Assessment, and Social Class: Lessons for Assessment Policy from an English Research Programme , 2009 .

[6]  湯淺 太一,et al.  20世紀の名著名論:Seymour Papert: Mindstorms:Children Computers and Powerful Ideas Basic Books New York 1980 , 2005 .

[7]  Candace Walkington,et al.  Using adaptive learning technologies to personalize instruction to student interests: The impact of relevant contexts on performance and learning outcomes. , 2013 .

[8]  Joanna O. Masingila,et al.  Mathematics learning and practice in and out of school: A framework for connecting these experiences , 1996 .

[9]  S. Herring,et al.  Situationally embodied curriculum: Relating formalisms and contexts , 2007 .

[10]  Evelyn C. Ferstl.  Learning from Text , 2001 .

[11]  David W. Carraher,et al.  Written and Oral Mathematics. , 1987 .

[12]  Torulf Palm,et al.  Theory of Authentic Task Situations , 2009 .

[13]  K. Ann Renninger,et al.  Effect Of Interest On Attentional Shift, Recognition, And Recall In Young Children , 1985 .

[14]  Richard Lesh,et al.  Problem Solving, Modeling, and Local Conceptual Development , 2003 .

[15]  Howard J. Sullivan,et al.  Effect of personalization of instructional context on the achievement and attitudes of hispanic students , 1992 .

[16]  Seymour Papert,et al.  The Children's Machine , 1993 .

[17]  B. Cooper,et al.  Making sense of realistic word problems: portraying working class ‘failure’ on a division with remainder problem , 2005 .

[18]  Barry Cooper,et al.  Anyone for Tennis? Social Class Differences in Children's Responses to National Curriculum Mathematics Testing , 1998 .

[19]  Leland S. Cogan,et al.  Who Takes What Math and in Which Track? Using TIMSS to Characterize U.S. Students’ Eighth-Grade Mathematics Learning Opportunities , 2001 .

[20]  J. Hox,et al.  Sufficient Sample Sizes for Multilevel Modeling , 2005 .

[21]  Mitchell J. Nathan,et al.  A theory of algebra-word-problem comprehension and its implications for the design of learning environments. , 1992 .

[22]  M. Stein,et al.  Algebra A Challenge at the Crossroads of Policy and Practice , 2011 .

[23]  Geoffrey B. Saxe,et al.  Candy Selling and Math Learning , 1988 .

[24]  Gregory Schraw,et al.  Situational Interest: A Review of the Literature and Directions for Future Research , 2001 .

[25]  John D. Bransford,et al.  The Jasper Project: Lessons in Curriculum, Instruction, Assessment, and Professional Development , 1997 .

[26]  Magdalene Lampert,et al.  Teaching Problems and the Problems of Teaching , 2001 .

[27]  Michelle Perry,et al.  Activation of Real-World Knowledge in the Solution of Word Problems , 1989 .

[28]  Liora Linchevski,et al.  A cognitive gap between arithmetic and algebra , 1994 .

[29]  Robert Moses.  Radical Equations: Math Literacy and Civil Rights , 2001 .

[30]  Kenneth R. Koedinger,et al.  Seeing language learning inside the math: Cognitive analysis yields transfer , 2010 .

[31]  S. Hidi,et al.  The Four-Phase Model of Interest Development , 2006 .

[32]  T. Rojano,et al.  Solving Equations : the Transition from Arithmetic to Algebra , 2014 .

[33]  Lynda R. Wiest,et al.  Impact of Personalization of Mathematical Word Problems on Student Performance , 2004 .

[34]  Gary R. Morrison,et al.  The Role of Rewording and Context Personalization in the Solving of Mathematical Word Problems. , 1991 .

[35]  Kenneth R. Koedinger,et al.  Trade-Offs Between Grounded and Abstract Representations: Evidence From Algebra Problem Solving , 2008, Cogn. Sci..

[36]  William B. Borgers.  DEMOCRACY AND EDUCATION. , 1919 .

[37]  H. Simon,et al.  How to Study Thinking in Everyday Life: Contrasting Think-Aloud Protocols With Descriptions and Explanations of Thinking , 1998 .

[38]  D. Kibler,et al.  Exploring the Episodic Structure of Algebra Story Problem Solving , 1989 .

[39]  R. Reber,et al.  Effects of Example Choice on Interest, Control, and Learning , 2009 .

[40]  Daniel Chazan,et al.  Beyond Formulas in Mathematics and Teaching: Dynamics of the High School Algebra Classroom , 2000 .

[41]  Martha W. Alibali,et al.  BRIDGES AND BARRIERS TO CONSTRUCTING CONCEPTUAL COHESION ACROSS MODALITIES AND TEMPORALITIES:: CHALLENGES OF STEM INTEGRATION IN THE PRE-COLLEGE ENGINEERING CLASSROOM , 2014 .

[42]  Helen Cooper.  THE WORD AND THE WORLD , 2009 .

[43]  T. P. Carpenter,et al.  Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction , 1996, The Elementary School Journal.

[44]  M. Lepper,et al.  Intrinsic motivation and the process of learning: Beneficial effects of contextualization, personalization, and choice. , 1996 .

[45]  M. Mitchell.  Situational interest: Its multifaceted structure in the secondary school mathematics classroom. , 1993 .

[46]  Walter G. Secada,et al.  New directions for equity in mathematics education , 1995 .

[47]  Jeremy Roschelle,et al.  SIMCALC : Accelerating Students’ Engagement With the Mathematics of Change , 2000 .

[48]  S. Hidi.  A reexamination of the role of attention in learning from text , 1995 .

[49]  J. Harackiewicz,et al.  Different Strokes for Different Folks: How Individual Interest Moderates the Effects of Situational Factors on Task Interest. , 2007 .

[50]  Etienne Wenger,et al.  Situated Learning: Legitimate Peripheral Participation , 1991 .

[51]  Ryan Shaun Joazeiro de Baker,et al.  The Difficulty Factors Approach to the Design of Lessons in Intelligent Tutor Curricula , 2007, Int. J. Artif. Intell. Educ..

[52]  K. A. Renninger,et al.  Individual interest as context in expository text and mathematical word problems , 2002 .

[53]  Harvey Goldstein,et al.  New Statistical Methods for Analysing Social Structures: an introduction to multilevel models , 1991 .

[54]  N. Koblitz,et al.  Radical Equations: Math Literacy and Civil Rights 328 Notices of the Ams Volume 49, Number 3 Radical Equations: Math Literacy and Civil Rights , 2022 .

[55]  S. Hidi,et al.  Interest, Learning, and the Psychological Processes That Mediate Their Relationship. , 2002 .

[56]  Chris S. Hulleman,et al.  Enhancing interest and performance with a utility value intervention. , 2010 .

[57]  Larry Cuban.  Rethinking education in the age of technology: The digital revolution and schooling in America , 2010 .

[58]  B. Greer.  Modelling Reality in Mathematics Classrooms: The Case of Word Problems. , 1997 .

[59]  D. Johanning.  Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies , 2004 .

[60]  Noriyuki Inoue,et al.  The Realistic Reasons behind Unrealistic Solutions: The Role of Interpretive Activity in Word Problem Solving. , 2005 .

[61]  K. Koedinger,et al.  Designing Knowledge Scaffolds to Support Mathematical Problem Solving , 2005 .

[62]  Patricia A. Alexander,et al.  Interest and Learning From Text , 1991 .

[63]  Mark A. McDaniel,et al.  The effects of text-based interest on attention and recall. , 2000 .

[64]  L. Schauble,et al.  Structuring Error and Experimental Variation as Distribution in the Fourth Grade , 2003 .

[65]  Moving beyond Teachers' Intuitive Beliefs about Algebra Learning. , 2000 .

[66]  Mitchell J. Nathan,et al.  The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning , 2004 .

[67]  Charles R. Fletcher,et al.  Understanding and solving arithmetic word problems: A computer simulation , 1985 .

[68]  최영한,et al.  미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론 , 2002 .

[69]  Wolff-Michael Roth,et al.  Where is the Context in Contextual Word Problems?: Mathematical Practices and Products in Grade 8 Students' Answers to Story Problems. , 1996 .

[70]  E. Kazemi.  Exploring test performance in mathematics: the questions children’s answers raise , 2002 .

[71]  Maxine Eskénazi,et al.  Personalization of Reading Passages Improves Vocabulary Acquisition , 2010, Int. J. Artif. Intell. Educ..

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

[73]  Ozlem Cakir,et al.  A comparative analysis of the effects of computer and paper-based personalization on student achievement , 2010, Comput. Educ..

[74]  Joseph J. Stevens,et al.  The Role of Choice and Interest in Reader Engagement , 2004 .

[75]  Martha W. Alibali,et al.  Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y-intercept , 2012 .

[76]  Richard Lesh,et al.  Model development sequences , 2003 .

[77]  James J. Kaput,et al.  Teaching and Learning a New Algebra with Understanding. , 2000 .

[78]  Torulf Palm,et al.  Impact of authenticity on sense making in word problem solving , 2008 .

[79]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[80]  David H. Jonassen,et al.  Designing Research-Based Instruction for Story Problems , 2003 .

[81]  Suzanne Hidi,et al.  Interest and Its Contribution as a Mental Resource for Learning , 1990 .

[82]  Kaye Stacey,et al.  Teaching Linear Functions in Context with Graphics Calculators: Students’ Responses and the Impact of the Approach on Their Use of Algebraic Symbols , 2004 .

[83]  Padma G. Anand,et al.  Using computer-assisted instruction to personalize arithmetic materials for elementary school children , 1987 .

[84]  W Kintsch,et al.  Understanding and solving word arithmetic problems. , 1985, Psychological review.

[85]  K.P.E. Gravemeijer,et al.  Context Problems in Realistic Mathematics Education: A Calculus Course as an Example , 1999 .

[86]  Kurt Reusser,et al.  Every word problem has a solution—The social rationality of mathematical modeling in schools , 1997 .

[87]  Seymour Papert,et al.  Mindstorms: Children, Computers, and Powerful Ideas , 1981 .