Examining The Problem Solving Skills and The Strategies Used by High School Students in Solving Non-routine Problems

The main purpose of this study was to investigate how well certain students in a high school solve non-routine problems. These problem situation required the use of their conceptual understanding of mathematics and their procedural knowledge of the algorithm involved in the solution. Results of analysis of students’ solutions showed that each student employed at least three problem solving strategies. Nine out of the ten possible problem solving strategies were used at least once to solve the eight non-routine problems. The most frequently used strategies were making systematic list, looking for patterns, logical reasoning and making a model or diagram. Those who performed well were also proficient in the use of solution strategies.

[1]  Hope J. Hartman Metacognition in teaching and learning: An introduction , 1998 .

[2]  A. Schoenfeld Looking Toward the 21st Century: Challenges of Educational Theory and Practice , 1999 .

[3]  G. Pólya,et al.  How to Solve It. A New Aspect of Mathematical Method. , 1945 .

[4]  Rina A. Mabilangan,et al.  Problem Solving Strategies of High School Students on Non-Routine Problems , 2011 .

[5]  John Woodward Improving mathematical problem solving in grades 4 through 8: A practice guide , 2010 .

[6]  Adnan Baki,et al.  KAVRAMSAL VE İŞLEMSEL BİLGİ BAĞLAMINDA LİSE ÖĞRENCİLERİNİN CEBİR BİLGİLERİNİN KARAKTERİZASYONU , 2004 .

[7]  A. Schoenfeld Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint) , 2009 .

[8]  Chongde Lin,et al.  The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems , 2007 .

[9]  S. K. Teong The effect of metacognitive training on mathematical word-problem solving , 2003, J. Comput. Assist. Learn..

[10]  Alice F. Artz,et al.  Development of a Cognitive-Metacognitive Framework for Protocol Analysis of Mathematical Problem Solving in Small Groups , 1992 .

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

[12]  Ban Har Yeap,et al.  Mathematical Problem Solving: Yearbook 2009, Association of Mathematics Educators , 2009 .

[13]  S. Çepni Araştırma ve proje çalışmalarına giriş. , 2005 .

[14]  Ted Herr,et al.  Problem Solving Strategies: Crossing the River With Dogs and Other Mathematical Adventures , 1994 .

[15]  Yeap Ban Har,et al.  Mathematical Problem Solving in Singapore Schools , 2009 .

[16]  R. Mayer,et al.  Brief Note: A Comparison of How Textbooks Teach Mathematical Problem Solving in Japan and the United States , 1995 .

[17]  Torulf Palm,et al.  The relation between types of assessment tasks and the mathematical reasoning students use , 2010 .

[18]  Meir Ben-Hur,et al.  Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving , 2006 .

[19]  Merrilyn Goos,et al.  A money problem: A source of insight into problem solving action , 2000 .

[20]  A curriculum of non-routine problems in the middle school , 2004 .

[21]  Jan Wyndhamn,et al.  Word problems and mathematical reasoning—A study of children's mastery of reference and meaning in textual realities , 1997 .

[22]  Stephen Krulik,et al.  Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12: A Resource for the Mathematics Teacher , 2008 .