On Novice Loop Boundaries and Range Conceptions

The paper presents a study of novice difficulties with range conceptions in loop design. CS2 students were asked to solve four related enumeration tasks, which required various loop boundary specifications. The student solutions varied considerably in conciseness and efficiency. The solution diversity reveals significant differences in range partitioning insights. The solutions are categorized, analyzed, and discussed. The categorization and analysis illuminate a novel perspective of novices' lack of range conceptions in loop design. A set of guidelines is offered for addressing this deficiency, by underlining the mathematical and design links between range ends, range partitioning, and loop boundary specifications.

[1]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[2]  Kim B. Bruce,et al.  Why math? , 2003, CACM.

[3]  Derek Sleeman,et al.  Pascal and High School Students: A Study of Errors , 1986 .

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

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

[6]  Marcia C. Linn,et al.  Patterns and pedagogy , 1999, SIGCSE '99.

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

[8]  Donald E. Knuth,et al.  The art of computer programming, volume 3: (2nd ed.) sorting and searching , 1998 .

[9]  Richard E. Mayer,et al.  Problem-solving transfer. , 1996 .

[10]  Eric S. Roberts,et al.  Loop exits and structured programming: reopening the debate , 1995, SIGCSE.

[11]  Sandra P. Marshall,et al.  Schemas in Problem Solving , 1995 .

[12]  Derek H. Sleeman,et al.  A Summary of Misconceptions of High School Basic Programmers , 1984 .

[13]  G. Kane.  Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol 1: Foundations, vol 2: Psychological and Biological Models , 1994 .

[14]  Raffaella Borasi,et al.  Reconceiving Mathematics Instruction: A Focus on Errors , 1996 .

[15]  Benedict duBoulay,et al.  Some Difficulties of Learning to Program , 1986 .

[16]  Doug Baldwin,et al.  Striving for mathematical thinking , 2001, ITiCSE-WGR '01.

[17]  M. Linn.  The Cognitive Consequences of Programming Instruction in Classrooms , 1985 .

[18]  Landon P. Cox,et al.  Design patterns: an essential component of CS curricula , 1998, SIGCSE '98.

[19]  Celia Hoyles,et al.  Windows on Mathematical Meanings: Learning Cultures and Computers , 1996 .

[20]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

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