CLASSIFYING: COMPREHENSION OF STUDENTS AND TEACHERS OF PRIMARY SCHOOL

Abstract

Throughout its history, mankind has created classifications for various ends. Classifying is a habitual process for people, one which is not only part of their daily routine, but also present in divers learning situations in various areas, including scientific research. Nowadays, because of the importance given to research at every level of learning, the importance of the act of classifying and creating classifications is being recognized, given that in any investigative activity categorization is necessary, as is the organization of data in groups for objective interpretation. Taking this into consideration, this study investigates how students, future teachers, and teachers of primary school create criteria to classify a group of elements. The results reveal difficulties, but not the impossibility of learning, even with very young children.

Full text

13th International Congress on Mathematical Education
Hamburg, 24-31 July 2016
1 - 1
CLASSIFYING: COMPREHENSION OF STUDENTS AND TEACHERS OF
PRIMARY SCHOOL
Gilda Guimarães
Universidade Federal de Pernambuco, Brazil
Izabella Oliveira
Université Laval, Canada
Throughout its history, mankind has created classifications for various ends. Classifying is a
habitual process for people, one which is not only part of their daily routine, but also present in
divers learning situations in various areas, including scientific research. Nowadays, because of the
importance given to research at every level of learning, the importance of the act of classifying and
creating classifications is being recognized, given that in any investigative activity categorization is
necessary, as is the organization of data in groups for objective interpretation. Taking this into
consideration, this study investigates how students, future teachers, and teachers of primary school
create criteria to classify a group of elements. The results reveal difficulties, but not the
impossibility of learning, even with very young children.
CLASSIFICATION
Statistics plays a fundamental role in education for citizenship. It can be also considered an
important tool for carrying out projects and investigations in various areas, being used for planning,
data collection and analysis, in inferences for decision making with the intent to support statements
in various areas, such as health, education, science, and politics. When students carry out research,
they may reflect autonomously and, as a consequence, be capable of interpreting reality through
their own data systems or of interpreting the data systems of others critically. To this end, knowing
how to classify is a fundamental ability.
Studies geared toward investigating how children and adults create categories to classify a group of
elements are rare in the literature. We have found studies that investigate how adults and children
build concepts based on classifications (Deák & Bauer, 1995; Nguyen & Murphy, 2003; among
others) or in studies with very young children or babies on the relation between thought and
language (Mareschal & French, 2000; Vieillard & Guidetti, 2009; among others).
In order to contribute to the field of statistics, the present study investigates how students, future
teachers, and teachers of primary school create criteria to classify a group of elements.
Logical-mathematical concepts of classification
Classifying is a natural and very early activity for humans. From a very young age children classify
objects according to analyses based on similarities and differences (Vergnaud, 1991). For Piaget
and Inheilder (1983), classifying can be defined as a procedure which allows one to attribute a
category to all the elements of a certain collection, according to the criteria defined. For a
classification to be correct, the categories must exhibit exhaustiveness (they represent all possible
facts and occurrences) and exclusiveness (coherence such that any result can be represented in only
one manner); in other words, categories must be able to exhaust all the possibilities and, at the same
time, be mutually exclusive. We would further add that it is fundamental to point out that the

Guimarães & Oliveira
1 - 2
classification criteria adopted depend on the context in which the classifications take place,
including the historic moment and the person’s needs. Thus, it is possible to find as many
classification systems as there are classifiers.
Studies on classification
1
Barreto and Guimarães (2015) carried out Piagetian clinical interviews with 20 children (age 5),
seeking to investigate the strategies used in three different activities which involved classifications:
a) based on a given criterion; b) identifying the classification criterion; c) creating a classification
criterion. The authors observed that 95% of the children were successful in the classification
activity based on a given criterion (a). This type of activity is conceptually easier and very common
in textbooks for young children, as Cruz (2013) points out. In the b (20%) and c (35%) activities,
the students had more difficulty. It is important to point out that these activities are considered more
difficult and that, even so, some 5-year-old children were able to solve them.
Guimarães, Gitirana and Roazzi (2001) investigated how 107 students from the 4th grade in primary
school (aged 9-10) created categories to classify a group of animals. The authors observed that most
students (64%) did not develop a correct classification, presenting a great variety of understandings
about classifying. They describe distinct properties which made it impossible to set a descriptor or
they attributed one property to each element, used one or more categories in the same attempt to
classify, such as using the descriptor “where they live” and creating classes such as “jungle” and
“flying,” implying alternately classifying an animal’s living space as “jungle” and its means of
locomotion as “flying,”.
Leite, Cabral, Guimarães and Luz (2013) investigated the knowledge of 30 3rd (age 8) and 5th (age
10) primary school students creating categories to classify, and a potential improvement in
performance based on a teaching intervention. This intervention was carried out over two days,
during which it was proposed that students, in pairs, classify groups of pictures, then present these
to the class and, together with the teacher, reflect on the criteria used. The results show that students
in both grades had difficulty classifying; however, the reflections in class allowed significant
improvement in their understanding of classifying, showing the possibility of quick learning.
These studies show differences in children’s understanding when they seek to create a classification
criterion. Might adults, given the fact that they experience, on a daily basis, a world that is already
classified, present different concepts?
Guimarães and Oliveira (2014) investigated how 113 future teachers in Recife, Brazil; Quebec,
Canada, and Burgos, Spain, created criteria to classify and used them in a free classification
activity. To this end, they gave each subject a group of cartoon characters to be classified. Half of
the students in each group classified them into two groups and the other half into three groups.
Although most students managed to reach a correct classification in two groups, when the activity
required three groups, performance was significantly weaker (X2 = 13.717, gl 1, p≤.000). Only
those who defined a descriptor were successful in their classification. Thus, knowing how to
classify appears to not be an ability learned solely through life experience.
Guimarães, Luz and Ruesga (2011) investigated how children of primary school and their teachers
created classification criteria. 48 students in the 3rd grade of primary school (age 8) and 16 teachers
participated in the study. The results show that most of the participants had a weak performance
(only 33% of students and 44% of the teachers succeeded in the task). Once again, in their attempts
to classify, participants would use more than one criterion (56% of students and teachers); in other
words, they would name a subgroup of pictures that had characteristics in common. In addition, few
participants made the descriptor explicit (29% of students and 44% of teachers); furthermore, many
1
The different studies carried out by our research group will be presented in order based on school level.

Guimarães & Oliveira
1 - 3
times the descriptor did not match the classification criterion used. Vieillard and Guidetti (2009)
had already observed that adults and children would name the groups and not the criterion they had
used.
This difficulty faced by both students and teachers can be partially explained by the absence of any
systematic school work on classification. Guimarães and Gitirana (2006), analyzing the collection
of math textbooks for the earliest school years approved by Brazil’s National Textbook Program
(PNLD 2004)
2
, show a lack of importance given to the theme of classification in the textbooks. In
this same vein, Silva (2013) found that, when analyzing the math and science textbook collections
used in Brazil in the primary school, in only 1% of the activities is it proposed that students create a
criterion of classification, since in the other activities the classes are already defined, and all the
students need to do is distribute the elements in the pre-defined groups.
CONCLUSIONS
In this article we sought to show the understanding of creating classification criteria of students in
pre-school and primary school (ages 5 to 10), undergraduate students in Education, and teachers of
primary school based on various published research papers by our research group.
These studies show the difficulty people with different educational backgrounds have in creating
criteria to carry out a classification. We believe this difficulty can be at least partially explained by
the lack of familiarity with this type of ability both in everyday life and at school. From a very
young age, people interact with a world organized hierarchically in classes and subclasses;
however, they are generally asked to classify given pre-defined criteria instead of creating the
criteria themselves. Barreto and Guimarães (2015) have shown, however, that from a very young
age some children can solve certain activities even if these are not widely present in their textbooks
and school everyday practice. Furthermore, Leite, Cabral, Guimarães and Luz (2013) demonstrate
the quick possibility of teaching these skills to students in primary school.
If current teachers and future teachers have difficulty classifying, how will they be able to teach
their students? The process of forming teachers needs to lead them on a systematic reflection which
allows them to learn to create criteria to classify a given group of objects, respecting both
exhaustiveness and exclusiveness. It needs to go beyond activities in which classes are already
defined and the student has only to distribute the elements. Developing students’ independence in
creating classifications will allow them to classify and analyze whatever data they wish, be it in
school or in their daily lives, in a relevant manner.
It is fundamental for an effective right to citizenship that everybody knows how to analyze the
criteria chosen for a classification, and how to create criteria to classify a group of data they wish to
analyze.
REFERENCES
Barreto, M. & Guimarães, G. (2015). A compreensão de crianças da educação infantil sobre classificação.
Trabalho de conclusão de curso de Pedagogia, Universidade Federal de Pernambuco.
Cruz, D.P. Classificação na Educação Infantil: o que propõem os livros e como é abordada por professores.
Dissertação de Mestrado em Educação Matemática e Tecnológica - Universidade Federal de Pernambuco,
Recife, 2013.
Deák, G. & Bauer, P. J. (1995). The effects of task comprehension on preschoolers’ and adults'
categorization choices. Journal of experimental child psychology, 60, 393–427.
2
The National Textbook Program is a program from Brazil’s Education Ministry which analyses textbooks to be
acquired by the government for distribution in public schools.

Guimarães & Oliveira
1 - 4
Guimarães, G. & Gitirana, V. (2006). Atividades que exploram gráficos e tabelas em livros didáticos de
matemática nas séries iniciais. Anais do III SIPEM, Aguas de Lindóia/Brasil.
Guimarães, G., Gitirana, V. & Roazzi, A. (2001). Interpretando e construindo gráficos. Anais da 24ª
Reunião da ANPED, Caxambu/Brasil.
Guimarães, G., Luz, P. & Ruesga, P. (2011). Classificar: uma atividade difícil para alunos e professores dos
anos iniciais do Ensino Fundamental? Anais da XIII Conferencia interamericana de Educação matemática
– CIAEM, Recife/ Brasil.
Guimarães, G. & Oliveira, I. Does future teachers of primary school know how to classify? 38th Psychology
of Mathematics Education (PME 38), Vancouver, Canada from July 15 to July 20, 2014.
Leite, M.; Cabral, P.; Guimarães, G &; Luz, P. O Ensino de Classificação e o Uso de Tabelas. Caderno de
Trabalhos de Conclusão de Curso de Pedagogia. Recife, UFPE, 2013.
Mareschal, D. & French, R. (2000). Mechanisms of Categorization in Infancy. Infancy, 1(1993), 59–76.
Nguyen, S. P. & Murphy, G. L. (2003). An apple is more than a fruit: Cross-classification in children's
concepts. Child Development, 74, 1–24.
Piaget & Inheilder, B. (1983). Gênese das Estruturas Lógicas Elementares. 3ª Ed. Rio de Janeiro: Zahar
Editores.
Vergnaud, G. (1991). El Niño, Las Matemáticas y La Realidad: Problemas de La enseñanza de Las
Matemáticas en La Escuela Primaria. México Trillas.
Vieillard, S. & Guidetti, M. (2009). Children’s perception and understanding of (dis)similarities among
dynamic bodily/facial expressions of happiness, pleasure, anger, and irritation. Journal of Experimental
Child Psychology, v. 102 p.78–95.