A CRITICAL APPROACH TO SCHOOL MATHEMATICAL KNOWLEDGE - THE CASE OF “REALISTIC” PROBLEMS IN GREEK PRIMARY SCHOOL TEXTBOOKS FOR SEVEN-YEAR-OLD PUPILS - Volume 4 - Number 1 - 2011

Oct 15, 2026

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The educational role of “realistic” problems that accompany mathematical instruction in early grades is central yet complex, requiring consideration of pedagogical, sociological, and psychological parameters. This paper analyzes selected tasks from a Greek 2nd-grade mathematics textbook, solved and commented on by 27 postgraduate students. Results indicate that the empirical reference contexts used in these problems create substantial difficulties in deciphering, making their pedagogical role problematic.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Abstract

1. Introduction

2. Theoretical observations

Volume 4, Number 1, 2011 A CRITICAL APPROACH TO SCHOOL MATHEMATICAL KNOWLEDGE: THE CASE OF “REALISTIC” PROBLEMS IN GREEK PRIMARY SCHOOL TEXTBOOKS FOR SEVEN-YEAR-OLD PUPILS Konstantinos Zacharos, Gerassimos Koustourakis Abstract: The reference contexts that accompany the “realistic” problems chosen for teaching mathematical concepts in the first school grades play a major educational role. However, choosing“realistic” problems in teaching is a complex process that must take into account various pedagogical, sociological and psychological parameters. This paper presents a selection of problems from the new mathematics textbook of the 2nd grade of Greek primary school which were solved and commented upon by 27 postgraduate students. The results of our research showed that the empirical reference contexts put forward in these problems create many difficulties in their “deciphering”, which leads us to conclude that their pedagogical role is problematic. Key words: Mathematics education, early years, reference contexts. 1. Introduction School mathematical knowledge is the product of a process of “didactical transposition”(Chevallard, 1992) or, in other words, processes of recontextualisation (Bernstein, 1990) . In order to shape it, knowledge is selected from the scientific field of mathematics, and then simplified and adapted to the age of the pupils to whom it is addressed. The final shaping of the content of textbooks is also influenced by the choices made regarding pedagogical and didactic knowledge management. These emanate from the epistemological acknowledgements of official pedagogical discourse which, in every curriculum reform, are linked to specific theories of instruction (Morais, Neves and Fontinas, 1999) . Αccording to the new primary school curricula which were implemented in 2006 and are in force to the present day, problem solving is one of the main objectives of mathematical education in Greek schools. Indeed, the solving of problems contained in textbooks may constitute an autonomous learning objective, aimed at activating children’s mental functions in order for them to develop the ability to identify connections and synthesise the parameters involved in a problem; or it may constitute a means by which to teach particular topics in school mathematics. In any event, the interest of textbook authors is focused on the introduction of suitable problems, which will make sense to the children and will engage their interest by drawing on pre-existing knowledge and experiences (Siegel and Borasi, 1992) . Moreover, in order for a problem to be manageable by a child, it should be on – or adjoining – the level of its cognitive capabilities. According to Vygotsky (1978), the problem should lie in the child’s zone of proximal development. Thus, the new information and new knowledge incorporated by mathematics problems should guide the pupil to enrich the way in which he/she thinks and works (Grugnetti and Jaquet, 2005) . In the first school grades, mathematics problems are introduced through the use of suitable reference contexts. In particular, by utilizing these contexts, an effort is made so that the way in which Received 5 March 2011, accepted 20 March 2011., published 30 March 2011. mathematics problems are presented engage children’s interest and that, through the solving process, children are able to assimilate the school mathematics being taught. In this paper, we examine a selection of problems from the 2nd grade textbook of Greek primary school which is intended for seven-year-old pupils, and we investigate aspects of the educational context that accompanies them, in order to assess the possibility of their pedagogical management. 2. Theoretical observations The way in which pupils learn the meaning of mathematical concepts is related to the semiotics of teaching (Radford, 2006) . In the context of this semiotic process, emphasis is placed on the central role of the cultural environ

FAQs

What is the focus of the paper regarding “realistic” problems in early math teaching?

It examines how the reference contexts accompanying “realistic” problems influence learning and considers why selecting such problems is pedagogically complex.

How was the study conducted and who evaluated the problems?

A selection of problems from the Greek 2nd-grade mathematics textbook was solved and commented on by 27 postgraduate students.

What did the research find about the reference contexts used in these textbook problems?

The empirical reference contexts create many difficulties in deciphering, leading to the conclusion that their pedagogical role is problematic.

Oct 15, 2026

Uploaded by Putri