The conceptual interface between secondary and university mathematics: A schema-based analysis

In this paper I provide a theoretical analysis of difficulties experienced by students in having to transfer concepts they have learnt in high school to university mathematics. This analysis is based on the assumption that mathematical knowl­ edge can be represented in the form of organised structures called schemas. The organisational quality of students’ mathematical schemas is a function of spread of network and strength of links between pieces of information. Well-developed schemas are argued here to facilitate assimilation of university mathematical con­ cepts and the use of this new information in the solution of novel problems.

[1]  H. Möller.  ICMI Study on the Teaching and Learning of Mathematics At University Level , 1998 .

[2]  Mohan Chinnappan,et al.  Generative Activity During Geometry Problem Solving: Comparison of the Performance of High-Achieving and Low-Achieving High School Students , 1994 .

[3]  Allen Newell,et al.  Human Problem Solving. , 1973 .

[4]  R. Catrambone.  The subgoal learning model: Creating better examples so that students can solve novel problems. , 1998 .

[5]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[6]  Jeremy Kilpatrick,et al.  International handbook of mathematics education , 1997 .

[7]  M. Chinnappan.  Schemas and mental models in geometry problem solving , 1998 .

[8]  Guershon Harel,et al.  The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical Concepts , 2002 .

[9]  Zvia Markovits,et al.  Functions Today and Yesterday. , 1986 .

[10]  John Sweller,et al.  Cognitive technology: Some procedures for facilitating learning and problem solving in mathematics and science. , 1989 .

[11]  Tommy Dreyfus,et al.  IMAGES AND DEFINITIONS FOR THE CONCEPT OF FUNCTION , 1989 .

[12]  Gaea Leinhardt,et al.  Functions, Graphs, and Graphing: Tasks, Learning, and Teaching , 1990 .

[13]  Jeanette R. Palmiter,et al.  Effects of Computer Algebra Systems on Concept and Skill Acquisition in Calculus. , 1991 .

[14]  R. B. Davis,et al.  The Notion of Limit: Some Seemingly Unavoidable Misconception Stages. , 1986 .

[15]  David Tall,et al.  Advanced Mathematical Thinking , 1994 .

[16]  P. Alexander,et al.  The Interaction of Domain-Specific and Strategic Knowledge in Academic Performance , 1988 .

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

[18]  Richard C. Anderson,et al.  Schooling and the Acquisition of Knowledge , 1978 .

[19]  David B. Pisoni,et al.  Cognitive Theory. Vol. 2 , 1978 .

[20]  Norman Frederiksen,et al.  IMPLICATIONS OF COGNITIVE THEORY FOR INSTRUCTION IN PROBLEM SOLVING , 1983 .

[21]  John R. Anderson.  Cognitive Psychology and Its Implications , 1980 .

[22]  Richard C. Anderson.  The notion of schemata and the educational enterprise , 1977 .

[23]  Guershon Harel,et al.  Higher Mathematics Education , 1996 .