AD ALTA
JOURNAL OF INTERDISCIPLINARY RESEARCH
EXAMINATION OF TEACHER STUDENTS’ INDUCTIVE THINKING ABILITY
a
PÉTER TÓTH,
b
KINGA HORVÁTH,
c
GYÖRGY JUHÁSZ
J. Selye University, Bratislavská cesta 3322, SK-94501
Komárno, Slovakia
email:
a
tothp@ujs.sk,
b
horvathki@ujs.sk,
c
juhaszg@ujs.sk
This research has been supported by the project titled „VEGA-1/0663/19 Analysis of
science and mathematics education in secondary schools and innovation of teaching
methodology”.
Abstract: Available literature on researching inductive thinking ability is really rich.
Our study presents three types of approaches: it is (1) a constructive element of
intelligence, (2) the decisive method of human learning, (3) a key competence playing
an important role in understanding. The main objectives of our research were to (1)
determine the development level of the inductive, and within that the abstract and
analogue thinking of the teacher students starting their studies in higher education, (2)
find the background variables by means of which significant differences can be found
between the various student groups, (3) respond to the question whether any
conclusions regarding the performance expected in the inductive test can be drawn
based on the time spent on solving the tasks. The students’ analogue reasoning and
rule induction are more developed than their diagrammatic thinking. One of the
preconditions of a good result achieved in the inductive test is the full utilization of the
available time frame. Introducing the ide of specific performance we found that the
students having achieved the best results were studying at teacher specialization in full
time training, lived in cities and had parents with a degree. The students could be
properly grouped according to the time used for problem solution: (1) negligent and
superficial, (2) reflective but not persistent enough; (2) persistent and diligent.
Knowing the type of training and specialization of the students helps
defining/understanding the clusters.
Keywords: inductive, analogue and diagrammatic reasoning, teacher training, specific
learning performance, task solution time
1 Background
The students’ intellectual capacities to meet university
requirements is one of the most significant risk preliminaries
identified by the relevant literature (O'Neill et al., 2011; Stewart
et. al., 2015; Sarra et al., 2018). The justification of focusing at
the vulnerability of university studies (Sosu- Pheunpha, 2019) is
directly connected to the policies of the world’s governments the
objective of which is to achieve equity and social justice in the
access to higher education (UNESCO, 2015). However, the
impact of this vulnerability is not deterministic; it is in close
connection with psychological factors like self-efficiency and
self-control that are important indicators of university
persistence (Richardson et al., 2012; Respondek et al., 2017).
The papers focusing at the learning results reveal the fact that an
integrated learning of the education content leads to better
conceptual understanding, improves cooperation skills, the
students’ capacities to solve problems and critical and inductive
thinking at all levels of school education (Roberts, 2009;
Cervetti et al., 2012; Darwish, 2014
; Zahatňanská – Nagy,
2020). The results of several studies have declared close
connection between abstract reasoning and educational results
(Bennedsen - Caspersen, 2006; Armoni, Gal-Ezer, 2007;
Roberts, 2009). Abstract reasoning is inevitable to comprehend
and interpret scientific concepts (Darwish, 2014).
Inductive reasoning and thinking can be explained from three
various points of view.
The first idea reckons the ability of inductive implication and
reasoning among the elements of intelligence (Wilhelm, 2005).
Intelligence can be defined as using intentional mental
operations to solve new problems. These mental operations
include implications, the creation and classification of the
concept, generation and testing of the hypothesis, identification
of the relations, understanding the consequences, problem
solution and the extrapolation and transformation of information
(Dumontheil, 2014). Thus intelligence is closely connected to
inductive reasoning and thinking (Ferrer et al., 2009). It is
thought that intelligence is a basic constituent of cognitive
development (Goswami, 1992) and provides as the base for
gaining various capabilities in various fields in childhood and
adolescence, as well (Blair, 2006; Ferrer et al., 2009). Childhood
intelligence is an apt indicator to forecast cognitive school
performance (Gottfredson, 1997; Primi et al., 2010). So
intelligence is a predictor of learning effectiveness, especially in
new and complex situations.
The second view comprehends inductive reasoning, and within
that abstract thinking, as an important method of human
cognizance. By means of this we become able to extract the
essence from complicated and abstract issues and to realize the
interconnections. This is particularly essential in understanding
knowledge in natural sciences. Abstract reasoning and thinking
plays an important role in drawing conclusions, forming
opinions, recognizing rules and regularities, i.e. in logical
thinking as well as in concept creation (Inhelder, Piaget, 1958;
Schwank, Schwank, 2015; Brendefur, Rich, 2018; Devi, 2019).
Researchers have proved that the pupils quitting the nursery
school in lack of the basic competencies in mathematics would
face serious difficulties at primary and secondary schools, as
well (Duncan et al., 2007; Jordan et al. 2009; Morgan, Farkas,
Wu, 2009). It is, however, important to emphasize the fact that
the development of inductive reasoning and thinking is
influenced by several other biological, psychological, social and
cultural factors, too (Amsel, Moshman, 2015).
According to the third approach, inductive reasoning is a key
competence (Kramer, 2007) in achieving learning successes and
results and in comprehension, which is mainly stressed by the
teachers of mathematics, computer sciences and natural sciences
(Iqbal, Shayer, 2000; Kuhn et al. 1977; Adey, Shayer, 1994;
Szőköl – Nagy, 2015). Puberty appears as the critical phase of
the reorganization of regulatory systems (Steinberg, 2005).
Blakemore (2012) has shown that puberty is a period of
permanent neurological development that may last longer than
that suggested by Inhalder and Piaget’s (1958) and Piaget’s
theory (Piaget, 1972). This was also proved by the examination
of pupils’ skills to solve simple algebraic equations. The gained
results showed that younger students were less precise and were
slower when solving the equations with letters and symbols than
they were when using numbers. Küchemann (1981) reported
that most of the students under 15 do not know algebraic letters
(symbols) as unknowns or universal numbers, which can be
expected of operative thinkers. This difference disappeared with
older pupils (aged 16-17), which refers to the fact that they
reached an abstract level of argumentation (Markovits et al.,
2015). Similar conclusions were drawn based on the analyzation
of their strategies, which indicates that the younger pupils had
mostly used strategies like the embedment of numbers while
older students had generally followed more abstract and rule-
based strategies. Kusmaryono et al. (2018) reported that none of
the pupils aged 14-15 had reached the quality stadium of
inductive reasoning. Darwish (2014) presented similar results
and also stated that only 42 percent of the first-grade teacher
students at natural scientific specializations were capable of
formal cognition, which shows that university students are late in
cognitive development (Cohen, Smith-Gold, 1978) or in
reaching the expected level of abstract thinking. These
outcomes, too, point to the fact that the development of algebraic
cognition is a process taking long time to evolve (Susac et al.,
2014).
During the latest 25-30 years, many researches examined the
inductive reasoning of teacher students (Astin, 1997; Bowman,
2010; Darwish, 2014). These on one hand prove that dealing
with natural sciences needs a high level of inductive and abstract
reasoning, which may ease the proper teaching of abstract
theories (Darwish, 2014); on the other hand, they emphasize the
importance of teachers’ vocational development (Brendefur et
al., 2016; Brestenská et al., 2019), and highlight the most
effective elements of vocational development (Koellner et al.
2011; Desimone, 2011; Sztajn et al., 2011). Yoon et al. (2007)
write that most of the researches related to the vocational
development of mathematics disproved an improvement in the
pupils’ performance as the characteristics and competencies
necessary to change the teachers’ practice were lacking.
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