Learning from “Didactikids”: An impetus for revisiting the empty number line

This article discusses students’ perceptions as a source for understanding education. It addresses what didactically experienced children, called “didactikids”, taught us about the empty number line as a didactical model for teaching whole number calculations. The article mainly reports on a student consultancy study carried out in the Netherlands. The findings are similar to what was revealed in an Australian study. Both studies explain what can go wrong when the number line is applied rigidly and wrongly implemented.

[1]  Anne Cockburn,et al.  Understanding the Mathematics Teacher: A Study of Practice in First Schools , 1987 .

[2]  E. L. Klein,et al.  “What do you do in child care?” children’s perceptions of high and low quality classrooms , 2001 .

[3]  Marja van den Heuvel-Panhuizen,et al.  Children learn mathematics : a learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school , 2001 .

[4]  H. Freudenthal.  Mathematics as an Educational Task , 1972 .

[5]  J. Campbell,et al.  Personal and Class Forms of Classroom Environment Instruments , 1998 .

[6]  Hans Freudenthal,et al.  Weeding and Sowing: Preface to a Science of Mathematical Education , 1977 .

[7]  Adrian Treffers.  Meeting innumeracy at primary school , 1991 .

[8]  Lisa A. Wing.  Play is Not the Work of the Child: Young Children's Perceptions of Work and Play. , 1995 .

[9]  W. Hagborg.  Student and teacher perceptions of classroom instructional methods and evaluation procedures , 1994 .

[10]  Vicki Steinle,et al.  Confusions between decimals, fractions and negative numbers: a consequence of the mirror as a conceptual metaphor in three different ways , 2001 .

[11]  Gary P. Barkhuizen,et al.  Discovering Learners' Perceptions of ESL Classroom Teaching/Learning Activities in a South African Context , 1998 .

[12]  B. Kumaravadivelu,et al.  Language learning tasks: teacher intention and learner interpretation , 1991 .

[13]  M. Heuvel-Panhuizen.  Realistic Mathematics Education as work in progress , 2002 .

[14]  B. Fraser.  Science Learning Environments: Assessment, Effects and Determinants , 1998 .

[15]  A. Treffers,et al.  Proeve van een nationaal programma voor het reken-wiskundeonderwijs op de basisschool. Deel 2: Basisvaardigheden en cijferen , 1990 .

[16]  Mary Spratt,et al.  How good are we at knowing what learners like , 1999 .

[17]  Theodore A. Mork,et al.  Young Children , 1949, Nature.

[18]  Doris Bergen,et al.  Play as a medium for learning and development : a handbook of theory and practice , 1988 .

[19]  Gunilla Dahlberg,et al.  Beyond Quality in Early Childhood Education and Care: Languages of evaluation , 1999 .

[20]  L. Streefland,et al.  Young children (6–8)-ratio and proportion , 1979 .