Encouraging Sixth-Grade Students’ Problem-Solving Performance by Teaching through Problem Solving

Abstract This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students’ problem-solving performance and performance on a unit test were analyzed. The intervention had a positive effect on students’ problem-solving performance whereas the comparison group experienced no changes. ANCOVA analyses suggest that intervention students solved more problems on the posttest than their peers, but the comparison group outperformed the intervention group on the unit test.

[1]  Lieven Verschaffel,et al.  Teaching realistic mathematical modeling in the elementary school. A teaching experiment with fifth graders , 1995 .

[2]  Candice L. Ridlon.  Learning Mathematics via a Problem-Centered Approach: A Two-Year Study , 2009 .

[3]  M. Stein,et al.  Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning. , 1997 .

[4]  C. W. Tate.  Solve it. , 2005, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[5]  H. Meserve.  Understanding understanding , 2005, Journal of Religion and Health.

[6]  S. Stein.  What's All the Fuss About? , 1996 .

[7]  J. Bostic.  Model-Eliciting Activities for Teaching Mathematics , 2013 .

[8]  Michael Shaughnessy,et al.  Focus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability , 2009 .

[9]  Jo Boaler,et al.  The Role of Contexts in the Mathematics Classroom: Do They Make Mathematics More "Real"? , 2016 .

[10]  Michelle Drouin,et al.  Alphabet Knowledge in Preschool: A Rasch Model Analysis. , 2012 .

[11]  L. James,et al.  Estimating within-group interrater reliability with and without response bias. , 1984 .

[12]  Griet Van Vaerenbergh,et al.  Learning To Solve Mathematical Application Problems: A Design Experiment with Fifth Graders. , 1999 .

[13]  Frank K. Lester,et al.  Musings about Mathematical Problem-Solving Research: 1970-1994. , 1994 .

[14]  Franz W. Peren.  Arithmetic , 1903, Nature.

[15]  J. Linacre,et al.  Sample size and item calibration stability , 1994 .

[16]  M. Segers,et al.  Effects of problem-based learning: a meta- analysis , 2003 .

[17]  Torulf Palm,et al.  Word problems as simulations of real-world situations : A proposed framework , 2006 .

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

[19]  dkk Donald Ary.  Introduction to research in education , 1972 .

[20]  J. Boaler,et al.  Creating Mathematical Futures through an Equitable Teaching Approach: The Case of Railside School , 2008, Teachers College Record: The Voice of Scholarship in Education.

[21]  Jeremy Kilpatrick,et al.  Adding It Up: Helping Children Learn Mathematics , 2013 .

[22]  Lyn D. English,et al.  Problem solving for the 21st century , 2010 .

[23]  C. Hirsch.  Curriculum and Evaluation Standards for School Mathematics , 1988 .

[24]  Bessie Davis Cooke,et al.  Mathematical Communication in the Classroom: A Teacher Makes a Difference , 2005 .

[25]  Lieven Verschaffel,et al.  Reconceptualising Word Problems as Exercises in Mathematical Modelling , 2010 .

[26]  Margaret S. Smith,et al.  5 Practices for Orchestrating Productive Mathematics Discussions , 2011 .

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

[28]  Christina Kluge,et al.  Making Sense Teaching And Learning Mathematics With Understanding , 2016 .

[29]  Ralph T. Mason,et al.  Problem Solving and Mathematics Learning. , 1994 .

[30]  Subashan Perera,et al.  Rasch analysis of a new stroke-specific outcome scale: the Stroke Impact Scale. , 2003, Archives of physical medicine and rehabilitation.

[31]  Edie Ronhovde,et al.  Making Sense of Word Problems , 2009 .

[32]  M. Dunne,et al.  Assessing Children's Mathematical Knowledge: Social Class, Sex and Problem-Solving , 1999 .

[33]  Randall I. Charles,et al.  An evaluation of a process-oriented instructional program in mathematical problem solving in Grades 5 and 7. , 1984 .

[34]  Alan H. Schoenfeld,et al.  How We Think : A Theory of Goal-Oriented Decision Making and its Educational Applications , 2010 .

[35]  Examining instructional practices in Core-Plus lessons: implications for professional development , 2006 .

[36]  J. Boaler.  Learning from Teaching: Exploring the Relationship between 'reform' Curriculum and Equity , 2022 .

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

[38]  Irene Bloom,et al.  Measuring Reform Practices in Science and Mathematics Classrooms: The Reformed Teaching Observation Protocol , 2002 .

[39]  Jonathan D. Bostic,et al.  Effects of Minute Contextual Experience on Realistic Assessment of Proportional Reasoning , 2013 .

[40]  Margaret S. Smith,et al.  Mathematical Tasks as a Framework for Reflection: From Research to Practice , 1998 .

[41]  Penelope L. Peterson,et al.  Teachers ' Pedagogical Content Knowledge of Students ' Problem Solving in Elementary Arithmetic Author ( s ) : , 2007 .