CONTENTS - Dipartimento di Matematica e Informatica

Graeber, Tanenhaus (1993) propose an informal approach to fractions designed to give
them a concrete sense, using fractions as numbers for measuring sizes and thereby
building an informal knowledge.
Brown (1993) emphasizes the necessity to find common theories and models in order to
overcome the fragmentation of the research into learning difficulties.
Giménez (1994) proposes a distinction between “divide” in everyday language and
“fraction” in Mathematics, using accounts of experiences and various stimuli together
with classroom discussion designed to create greater integration between different
situations of use of fractions.
Groff (1994) is one of numerous researchers who believe that fractions should be
banished from the first years of schooling. Others argue the contrary, sustaining that
informal construction of the idea of fraction should begin in the Infants school. I
personally believe that the latter position is correct, while it is clearly necessary to
proceed with caution.
Mariotti, Sainati Nello, Sciolis Marino (1995) examine the skills that students say that
possess at the moment of passage from Middle to Secondary school, discovering that
they generally believe that different sets of numbers and unconnected and that the
written form used determines the nature of the number.
Kamii, Clark (1995) consider the classic question of the difficulty of understanding the
relation of equivalence between fractions, a question which will be of interest when
considering teaching approaches.
Pitkethly, Hunting (1996) provide an extremely wide and useful critical summary of
many of the directions of research in this field, obviously without explicit educational
practical suggestions. The present study is a modest attempt to participate in the
construction of a similar summary for the period up to 2005.
Sensevy (1996a) describes a teaching-learning experience with fourth and fifth year
primary pupils concerning the constant negotiation of meanings and construction of
formal models in the classroom during the handling of problems involving fractions.
The objective was that of achieving effective communication. Meanings and formal
models were based on appropriate semantic tools designed to enable shared meanings.
New social norms give rise to a new form of didactic contract. The study is based on a
doctoral thesis (1994).
Sensevy (1996b) is also responsible for an experimental teaching activity called “The
Journal of Fractions”, conducted over a period of two years in fourth and fifth year
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