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Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students’ abstract thinking. However, in addition to research on cognitive processes, learners’ affective characteristics have largely remained unexplored in the context of teaching and learning group theory to date. In this paper, we contribute to closing this gap: We report on an empirical study investigating n=143 students’ affective characteristics within a two-weeks course program–the Hildesheim teaching concept. In our study, this concept was used to introduce pre-service primary teachers into group theory. A multiple linear regression analysis reveals that neither mathematics-specific ability self-concept nor subject interest are significant predictors of the achieved conceptual understanding of group theory after the intervention indicating that group theory is not reserved for only the mathematically interested students or students with a high mathematics-specific self-concept.
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EURASIA Journal of Mathematics, Science and Technology Education, 2022, 18(10), em2157
ISSN:1305-8223 (online)
OPEN ACCESS Research Paper https://doi.org/10.29333/ejmste/12417
© 2022 by the authors; licensee Modestum. This article is an open access article distributed under the terms and conditions of
the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).
veith@imai.uni-hildesheim.de (*Correspondence) girnat@imai.uni-hildesheim.de philipp.bitzenbauer@fau.de
The role of affective learner characteristics for learning about abstract
algebra: A multiple linear regression analysis
Joaquin Marc Veith 1* , Boris Girnat 1 , Philipp Bitzenbauer 2
1 Mathematics Education, Institute for Mathematics and Applied Computer Science, Stiftung Universität Hildesheim, Hildesheim,
GERMANY
2 Physics Education, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, GERMANY
Received 23 June 2022 Accepted 23 August 2022
Abstract
Recent research has boosted the inclusion of introductory group theory into secondary and
undergraduate mathematics education due to manifold potentials, e.g., with regards to the
promotion of studentsabstract thinking. However, in addition to research on cognitive processes,
learnersaffective characteristics have largely remained unexplored in the context of teaching and
learning group theory to date. In this paper, we contribute to closing this gap: We report on an
empirical study investigating n=143 studentsaffective characteristics within a two-weeks course
programthe Hildesheim teaching concept. In our study, this concept was used to introduce pre-
service primary teachers into group theory. A multiple linear regression analysis reveals that
neither mathematics-specific ability self-concept nor subject interest are significant predictors of
the achieved conceptual understanding of group theory after the intervention indicating that
group theory is not reserved for only the mathematically interested students or students with a
high mathematics-specific self-concept.
Keywords: mathematics-specific self-concept, subject interest, situational interest, group theory
INTRODUCTION
In recent years a body of research has emerged,
entirely dedicated towards exploring educational
aspects of abstract algebra (Wasserman, 2014, 2016, 2017,
2018) and group theory in particular (Melhuish, 2015,
2019; Melhuish & Fagan, 2018; Pramasdyahsari, 2020;
Veith & Bitzenbauer, 2022; Veith et al., 2022a, 2022b,
2022c). Even though group theory is mostly taught on
university level mathematics, numerous connections to
primary and secondary school mathematics have been
uncovered (cf. Even, 2011; Wasserman, 2016) and with it
the great potential it offers for mathematics educators in
all fields alike. Consequentially, many studies focused
on mathematics teachers and how they responded to
abstract algebra courses deepening their content
knowledge (cf. Veith et al., 2022b). The importance of
group theory in mathematics teacher education is
underpinned by a study conducted by Wasserman
(2014): With a mathematics for teachers course,
Wasserman showed that dealing with the concepts of
algebraic structures had a significant impact on the
participants beliefs and their practices of teaching. In
this article we want to enrich these findings by shedding
light onto how a conceptual understanding of group
theory might be connected to and influenced by affective
learner characteristics.
RESEARCH BACKGROUND
Learning and Teaching Group Theory
So far, two primary research interests of abstract
algebra education can be observed: On the one hand,
researchers investigated potential learning hurdles the
concepts of abstract algebra pose. On the other hand, it
was examined how knowledge of algebraic structures
can be of use for mathematics educators in all fields.
The first aspect is comprised of learning difficulties
primarily located in the fundamental basics of group
theory. For example, learners have trouble with the
newly presented vocabulary of group theory (cf. Veith et
al., 2022a), especially composition and operation are
potentially confusing terms that were shown to lead to
Veith et al. / The role of affective learner characteristics
2 / 10
fundamental misunderstandings. Additionally,
generalizing the notion of inverses from inverse functions
to inverse elements in algebraic structures revealed to be a
non-trivial step for students dealing with abstract
algebra for the first time (cf. Wasserman, 2014). Most
pronounced, however, were learning difficulties that are
tied to the binary operations of groups, namely
associativity and commutativity. Here, learners tend to
conflate and overgeneralize these properties as shown
by Melhuish and Fagan (2018) as well as Larsen (2019).
This is substantiated by an earlier study where in the
context of an in-service professional development course
the participating teachers showed to have trouble
distinguishing between both properties and to some
extend are even convinced, they are logically dependent
on one another (cf. Zaslavsky and Peled, 1996).
As for the second aspect, a comprehensive and
detailed summary is provided by Wasserman (2018).
This summary can be viewed as an extension of his 2016
study, where he explored the potential of abstract
algebra for the teaching of school algebra: By outlining a
progression line across elementary, middle, and
secondary mathematics he demonstrated how
knowledge of algebraic structures may transform
teachers elementary conceptions of number and
operation as related to early algebra concepts
(Wasserman, 2016, p. 31). Regarding elementary
education, for example, he explored how the teaching of
arithmetic properties is influenced by knowledge about
abstract algebra. The importance of this exploration is
twofold: Firstly, as mentioned beforehand, these
arithmetic properties have shown to be the most
problematic aspect when entering abstract algebra.
Secondly, Chick and Harris (2007) found that primary
school teachers displayed unsatisfying knowledge of
how the mathematics they teach build the foundation for
later algebra. They further argued that this deficit might
be caused by the educational background primary
teachers are presented with and thus demanded to
bridge this gap by additional learning opportunities.
This conclusion was also derived by Wasserman (2016)
who saw the need to foster teachersunderstanding of
algebraic structures to enhance their ability to reflect on
elementary mathematics content.
In conclusion, the literature suggests that pre-service
primary teachers abstract algebra education is to be
improved, especially regarding introductory aspects of
group theory such as inverses, binary operations,
associativity, and commutativity. In order to better
facilitate abstract algebra education, however, we need
to know how it is connected to affective learner
characteristics. As mentioned earlier, Wasserman (2014)
already provided evidence for the educational impact of
group theory by exploring the transformation of
teachersbeliefs and teaching practices by arguing that
teachers should engage with abstract algebra to help
them more fully understand the vertical development
from arithmetic properties to algebraic structures and
gain an understanding of the mathematical horizon,
which is an important knowledge component for
teaching (Wasserman, 2014, p. 210). And in another
survey by Even (2011) mathematics teachers
participating in an advanced mathematics course
explained how deepening their algebraic knowledge
resulted in a deeper knowledge of what mathematics
actually is. These observations result in a multitude of
pressing questions: Do primary pre- service teachers
experience group theory as a relevant part of
mathematics education? Do they perceive it as a difficult
branch of mathematics and is their success in
understanding these abstract concepts dependent on
their subject interest?
While the psychological constructs occurring in these
questions are already well operationalized in the
literature, namely as relevancy of content, ability self-
concept, subject interest, and situational interest, the
clarification of these questions require
(a) a teaching concept for primary pre-service
teachers dedicated to group theory and
(b) a test instrument to assess conceptual
understanding of group theory. Both
requirements are met by the literature, and we
will present them in the following.
The Hildesheim Teaching Concept
A teaching concept specifically designed for the
aforementioned target group is presented by the
Hildesheim teaching concept. The Hildesheim teaching
concept aims at introducing secondary school students
and first semester students to introductory group theory.
It is derived from the literature (cf. Veith & Bitzenbauer,
2020), merging viewpoints from the new math era (i.e.,
Griesel, 1965; Kirsch, 1965; Steiner, 1966) as well as
contemporary works on abstract algebra education (i.e.,
Contribution to the literature
Exploration of affective learner characteristics in the context of group theory. The results are situated in
the body of prior research and linked to results regarding cognitive charcteristics, allowing for a holistic
perspective on group theory education.
Results indicate that neither ability self-concept nor subject interest are significant predictors of conceptual
understanding of group theory contents.
Uncovering the central role of situational interest and its influence on developing group theory concepts.
EURASIA J Math Sci Tech Ed, 2022, 18(10), em2157
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Lee & Heid, 2018; Wasserman, 2014; Weber & Larsen,
2008), for example Larsens (2013a, 2013b) TAAFU
materials. It has been subject to both formative (Veith et
al., 2022a) and summative evaluation (Veith et al.,
2022c). The core idea lies in introducing learners to
groups from a geometric perspective by studying the
dihedral groups D3 and D4 as well as cyclical groups 𝑛.
This introduction is further motivated through a hands-
on approach, e.g., by working with triangles and squares
made from acrylic glass to reenact the transformations of
D3 and D4 in a haptic way (cf. Figure 1). It has been
shown that this approach is conducive to learning and
guides learners to an adequate conceptual
understanding of introductory group theory. The
formative evaluation further showed that the
instructional elements within the concept are well
accepted by Thus, our study used this teaching concept
as a guideline.
Measuring Conceptual Understanding of Group
Theory
In order to facilitate quantitative research into
educational aspects of group theory and enrich findings
from qualitative research (cf. Baldinger, 2018; Cook,
2018; Even, 2011; Suominen, 2018), two concept
inventories have been developed in recent time: the
GTCA (Group theory concept assessment) by Melhuish
(2015) and the CI²GT (Concept inventory for
introductory group theory) by Veith et al. (2022b),
respectively. Here, we conceive that conceptual
understanding reflects knowledge of concepts and
linking relationships that are directly connected to (or
logically necessitated by) the definition of a concept or
meaning of a statement(Melhuish, 2019, p. 2). While the
GTCA is focused primarily on undergraduate
mathematics students, the CI²GT is focused primarily on
secondary school students and pre-service mathematics
teachers. The latter assesses conceptual understanding
of introductory group theory namely by addressing the
definitional fundamentals (neutral element, inverses,
binary operations, associativity, and commutativity) as
well as Cayley tables and isomorphisms in the context of
the groups D3, D4, and 𝑛. In other words, the CI²GT
addresses precisely the contents covered by the
Hildesheim teaching concept.
Interim Conclusion
In total, we conclude that the need to foster pre-
service primary teachers algebraic education derived
from the literature can be tackled by combining the
Hildesheim teaching concept with the CI²GT. To further
investigate the aforementioned affective learner
characteristics, the CI²GT is to be complemented with
additional scales from the literature. In this regard, we
understand
1. relevancy of content as a student perception of
whether the course instruction/content satisfies
personal needs, personal goals, and/or career
goals(Frymier & Shulman, 1995)
2. (Ability) self-concept as mental representations of
persons about themselves (Baumeister, 1999),
3. subject interest as characterized by intrinsic desire
to understand a particular topic that persists over
time(Schraw et al., 2001, p. 24), and
4. situational interest as a spontaneous interest that
appears to fade as rapidly as it emerges and is
almost always place-specific(Schraw et al., 2001,
p. 24).
As part of a two-week program into introductory
group theory, we investigated the above-mentioned
constructs with a sample comprising n=143 pre-service
primary school teachers. The intervention of this
program was based on the Hildesheim teaching concept
and the CI²GT. While mathematics-specific self-concept
and subject interest are fairly stable variables, the
construct of situational interest is changeable and
partially under the control of teachers(Schraw et al.,
2001, p. 212) and therefore of great importance of
educators. Thus, we decided to feature it in both research
questions.
RESEARCH QUESTIONS
With this contribution, we approach a clarification of
the following research questions:
1. RQ1: How is group theory introduced via the
Hildesheim teaching concept perceived by
learners regarding
a. situational interest,
b. relevancy of content, or
c. perceived difficulty?
2. RQ2: How may affective learner characteristics
such as
a. mathematics-specific self-concept,
Figure 1. Example image of the hands-on learning material
in the Hildesheim teaching concept
Veith et al. / The role of affective learner characteristics
4 / 10
b. subject interest, or
c. situational interest
or prior knowledge be used as predictors of students
conceptual understanding of group theory acquired by
participating in the Hildesheim teaching concept?
METHODS
Study Design and Sample
To clarify the research questions, a field study in a
pretest-posttest design was conducted. The sample
comprised n=143 pre-service primary school teachers in
their first academic year who were introduced to group
theory via the Hildesheim teaching concept. None of the
participants had participated in any course on abstract
algebra prior to the intervention.
Instruments
The participants conceptual understanding of
introductory group theory was assessed using the
CI²GT–a concept inventory consisting of 20 dichotomous
items. Its internal consistency expressed by Cronbachs
alpha is α=0.76 and the development and analysis of the
CI²GT is documented in Veith et al. (2022b). The 20 items
are designed in a two-tier way: In the first tier the
respondent has to select exactly one of three answer
options. And in the second tier, the respondent has to
rate the confidence in their given answer on a 5-point
rating scale (1=guessed, 2=unsure, 3=undecided,
4=confident, and 5=very confident). A point is awarded
if and only if the correct answer option was selected and
the respondent was confident or very confident. An
example item is provided in Table 1.
In addition, we assessed five affective variables using
5-point rating scales (1=lowest trait level and 5=highest
trait level), which were adapted from the literature (cf.
Appendix A). The questionnaire containing these scales
was administered alongside the CI²GT such that the
participants in a first step responded to said scales before
moving on to the group theory items provided by the
CI²GT. The internal consistencies of the scales used to
assess the affective learner characteristics are presented
in Table 2. It is noteworthy that the perceived difficulty
was obtained by the pre-service teachersratings of the
difficulty of each sub-domain of group theory included
in the Hildesheim teaching concept. As such, this does
not represent a psychometric scale.
Data Analysis
Analysis carried out to answer RQ1
To explore the interaction between affective learner
characteristics and conceptual understanding of group
theory, we applied a correlation analysis to the data. As
the data is ordinally scaled we used Spearmans
correlation coefficient ρ. According to Hemphill (2003),
correlations ρ with
1. | ρ|<0.20 are considered as weak.
2. 0.20<| ρ|<0.30 are considered as medium.
3. | ρ|>0.30 are considered as strong.
Analysis carried out to answer RQ2
To explore possible predictors for the assessed
conceptual understanding of introductory group theory,
we investigated multiple linear regression models.
Therefore, the CI²GT score in the post-test serves as the
dependent variable. The model under investigation
includes the following variables: mathematics-specific
self-concept, subject interest, situational interest, and
prior knowledge expressed by the CI²GT score in the
pre-test. To check the underlying assumptions of the
resulting models, we followed Bitzenbauer (2020) and
1. examined linear dependence of the included
variables via scatterplots.
2. ruled out multicollinearity of the variables by
ensuring that tolerance ≥0.2 and variance inflation
factor VIF<5 (Kutner et al., 2004).
3. verified normal distribution of residuals via a P-P-
diagram (Michael, 1983).
Table 1. Example item of the CI²GT
Item 4: Let G=(M,
) be a non-abelian group and a, b
M. The inverse of a
b is
b-1
a-1
a-1
b
a-1
b-1
Very confident
Confident
Undecided
Unsure
Guessed
Table 2. Overview of adapted scales for this research as well as their internal consistencies expressed by Cronbachs alpha.
Construct
Number of items
α
Adapted from
Mathematics-specific self-concept
7
0.72
Hoffman et al. (1998)
Subject interest
6
0.81
Hoffmann et al. (1998)
Situational interest
5
0.77
Pawek (2009)
Relevancy of content
4
0.71
Winkelmann (2015)
Perceived difficulty
1 per sub-domain of CI²GT
-
-
Note. The items of the scales can be found in Appendix A.
EURASIA J Math Sci Tech Ed, 2022, 18(10), em2157
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4. checked for homoscedasticity of the residuals by
plotting standardized residuals against the
(unstandardized) predicted values.
5. conducted a Durbin-Watson test to check
autocorrelation. With a value of DW=1.76 for the
Durbin-Watson statistic, autocorrelation can be
ruled out according to Stoetzer (2017).
RESULTS
Descriptives and Correlation Analysis
The descriptives on the assessed affective learner
characteristics are provided in Table 3 and are
summarized in Figure 2.
The correlations among the affective learner
characteristics themselves are provided in Table 4.
Remarkably, all observed correlations are significant
(p<0.05) with the exception of the one between the
mathematics-specific self-concept and the relevancy of
content and, according to Hemphill (2003), they can
mainly be classified as strong.
Alongside Table 3, the correlation analysis allows for
a first insight into how these constructs interact with
respect to learning about group theory.
Multiple Linear Regression Analysis Results
An overview of the multiple linear regression model
is presented in Table 5. An F-test verifies statistical
significance of the model [F(4, 132)=5.81,p<0.001,
ω²=0.02]. The effect size ω²=0.02 indicates a small effect
according to Cohen (1988). With R²=0.15 the model
explains 15% of variance in the dependent variable.
It can be observed that mathematics-specific self-
concept and subject interest are not significant
predictors, while pre-test score (i.e., students prior
knowledge), and situational interest are statistically
highly significant predictors.
Table 4. Correlation coefficients among the affective learner characteristics
SuI
SiI
PD
MSSC
0.48
0.32
-0.33
SuI
1
0.36
-0.25
SiI
1
-0.46
RC
-0.29
PD
1
Note. MSSC: Mathematics-specific self-concept; SuI: Subject interest; SiI: Situational interest; RC: Relevance of content; & PD:
perceived difficulty
Figure 2. Box plots of the data for each affective learner characteristic
Table 3. Mean values (µ) of the assessed constructs alongside the standard deviations (σ) as well as each correlation
coefficient (ρ) to the CI²GT score in the post-test.
Construct
µ
σ
ρ
Mathematics-specific self-concept
3.38
0.44
0.18
Subject interest
3.65
0.57
0.05
Situational interest
3.35
0.63
0.23
Relevancy of content
3.72
0.68
0.12
Perceived difficulty
2.88
0.50
-0.24
Note. 5-point rating scales used to measure the constructs were adapted so that 1 represents the lowest trait level and 5 the highest
Veith et al. / The role of affective learner characteristics
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DISCUSSION
Discussion of RQ1
All affective learner characteristics are above the
center of the scale (cf. Figure 2). The students possessed
proper mathematics-specific celf-concepts (µ=3.38) and
subject interest (µ=3.65). Moreover, the values for
situational interest (µ=3.35) and relevancy of content
(µ=3.72) lay above the center of the scales, and indicate
that the intervention based on the Hildesheim teaching
concept was able to
(a) invoke situational interest in the concepts of
group theory and
(b) provide plausible evidence for learners that
applications of group theory are manifold both
inside and outside of mathematics.
In addition, the perceived difficulty was well below
the center of the scale (µ=2.88), insinuating that the
abstract concepts of algebra (cf. Veith & Bitzenbauer,
2022) were didactically conveyed in a comprehensible
manner and did not evoke a sense of overload.
The performance in the CI²GT is connected with the
affective learner characteristics, expressed by the
correlations in Table 3. For example, the perceived
difficulty correlates negatively at ρ=-0.24. This is not
surprisingthe more challenging the concepts are
perceived the more cognitive load (cf. Sweller et al.,
2011) is required to comprehend the mathematical
problems and thus the test performance declines. A
similar but positive correlation is observed regarding the
situational interest (ρ=0.23) which is, as mentioned
earlier, changeable and partially under the control of
teachers(Schraw et al., 2001, p. 212). This suggests that
a higher test performance in the CI²GT is connected to
engaging teaching concepts and learning materials. This
connection has already been found in other studies (cf.
Hidi, 1990; Vainikainen et al., 2015) and it has been
demonstrated that situational interest is a significant
predictor of learning outcome. Thus, regarding group
theory the question arises as to which affective factors
are connected to situational interest. A first insight into
this question is provided by Table 4. Here, with ρ=0.59 a
strong correlation can be observed between situational
interest and relevancy of content, hinting at the
importance of emphasizing the use of group theory and
its applications. As a mathematical model of symmetry,
the applications are multifaceted even outside of
mathematics, i.e., in chemistry, physics, computer
science and even musical set theory. We argue that
expounding those connections might enrich this abstract
theory with meaningfulness which in turn increases the
situational interest as empirical results suggest.
Additionally, the strongest negative correlation can be
observed between situational interest and perceived
difficulty (ρ=-0.46). Thus, teaching group theory should
focus on adequate didactic reduction and low threshold
learning opportunities to further facilitate the
development of situational interest.
Lastly, the data suggest that subject interest is nearly
uncorrelated to the test score in the CI²GT. On a positive
note, this could be interpreted as group theory not being
a domain solely accessible for mathematically interested
students.
This result is especially important for motivating the
demands to foster pre-service teachersabstract algebra
education by Chick and Harris (2007) and Wasserman
(2016) as it demonstrates that large intrinsic
mathematical interest does not constitute a requirement
for making sense of the notions of group theory. In other
words, even though group theory vastly remains a topic
taught to mathematicians only, it is accessible for other
audiences as well. And, as outlined by Wassermans
(2016) study, group theory may well serve to deepen the
understanding of arithmetic properties which is
precisely what primary mathematics teachers teach.
Discussion of RQ2
The results (cf. Table 5) show that neither
mathematics-specific self-concept nor subject interest are
significant predictors of achieved conceptual
understanding of group theory after the intervention.
This indicates that these constructs do not play a crucial
role in learning environments regarding group theory.
This finding is of particular interest as it suggests that
group theory is not reserved for only the mathematically
interested students or students with a high mathematics.
However, as the effect of these two control variables is
not statistically significant more research needs to be
done to empirically substantiate this finding.
On the other hand, prior knowledge expressed by the
pre-test score and situational interest have been revealed
to be highly statistically significant predictors of
achieved conceptual understanding of group theory
after the intervention. This is in line with the findings
regarding RQ1, where this construct showed first signs
of being very influential for student learning about
Table 5. Multiple linear regression model with estimates B and standardized estimates β
Predictor
B
SE
β
Lower
Upper
t
p
Intercept
0.55
2.62
--
--
--
0.21
0.833
Mathematics-specific self-concept
0.63
0.80
0.08
-0.11
0.26
0.78
0.446
Subject interest
-0.35
0.61
-0.05
-0.24
0.13
-0.57
0.570
Situational interest
1.58
0.51
0.27
0.10
0.44
3.09
0.002
Pre-test score
0.30
0.11
0.23
0.06
0.40
2.70
0.008
EURASIA J Math Sci Tech Ed, 2022, 18(10), em2157
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group theory. Situational interest has the highest
correlation to the post-test score and with the highest
weighted value B=1.58 in the linear regression model
also contributes the most. The pre-test score is significant
but its contribution to the post-test score is relatively low
at B=0.30 This underpins our earlier findings where the
learning gain in two groups (one with prior knowledge,
one without) was comparable (cf. Veith et al., 2022c).
In conclusion, the results of the multiple linear
regression analysis align well with the correlation
analysis: Instructors of group theory should focus on
invoking a high situational interest in the learners as this
revealed to be the most contributing factor to an
adequate conceptual understanding of this
mathematical theory.
Limitations of This Study
The results in this article allow for a first exploration
of the interaction of various affective learner
characteristics in the context of group theory and how
they are connected to a conceptual understanding. In
this respect, our results may not be regarded
independent from the specific intervention we used,
which is a common obstacle in educational research.
Additionally, the results are further limited in three
aspects: Firstly, the presented study is a field study and
as such the data gathered is strongly dependent on the
sample. Secondly, our results are not meant to yield set
causal relationships. Instead, the results obtained from
our exploratory study conducted in the field setting
allows for the formulation of hypotheses. These may be
the starting point for future investigations in the
laboratory setting where the effects can be investigated
and distinguished from dark noise. Lastly, no similar
research has been conducted yet (to the best of our
knowledge) so the results cannot be compared with
findings from the literature. Thus, this contribution
should be seen as a pure exploration study to set a course
for future research in this field.
CONCLUSION AND OUTLOOK
In summary, a coherent picture emerges from the
data: Instructions in group theory should focus on
fostering learners situational interest of the
mathematical objects as it strongly predicts to which
degree conceptual knowledge of group theory can be
developed. Due to its high correlation to relevancy of
content our findings suggest that fostering such interest
can be attained by laying out the various applications
groups offer both inside and outside of mathematics. On
a positive note, as mentioned before this is precisely
within the scope of action of mathematics instructors.
And variables outside of the instructorsreach such as
mathematics-specific self-concept do not seem to be
relevant in group theory learning environments.
However, as pointed out before, these findings are
limited by statistical significance. Thus, in future
research the results are to be substantiated and
complemented by increasing sample size and expanding
the linear regression model, i.e., by including the
learners self-efficacy and beliefs. Lastly, we want to
emphasize that introductory group theory was
perceived as a highly relevant part of mathematics by the
participating pre-service primary teachers and also
evoked situational interest regarding the notions of
dihedral and cyclical groups, independently of general
subject interest. We therefore argue in favor of
enhancing group theory education for this audience to
(a) better address their deficits outlined in prior
research and
(b) leverage the opportunities and benefits uncovered
in the presented literature.
Author contributions: JMV & PB: Writing and editing; BG:
supervision; & JMV, BG, & PB: conceptualization and data
analysis. All authors have agreed with the results and conclusions.
Funding: This study was funded by the open access fund of the
Friedrich-Alexander-University Erlangen-Nuremberg.
Declaration of interest: No conflict of interest is declared by
authors.
Data sharing statement: Data supporting the findings and
conclusions are available upon request from the corresponding
author.
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APPENDIX A
Table A1. Adapted scale for the Construct Mathematics-specific Self-Concept (1 = I do not agree, …, 5 = I agree)
1.1
I understand mathematical contents well.
1
2
3
4
5
1.2
I can remember mathematical contents well.
1
2
3
4
5
1.3
In school I participated in mathematics classrooms very frequently.
1
2
3
4
5
1.4
My performances in mathematics are good in my opinion.
1
2
3
4
5
1.5
I believe my peers think I am very good in mathematics.
1
2
3
4
5
1.6
I expect my future scores in mathematics to be very good.
1
2
3
4
5
1.7
I think I am gifted in mathematics.
1
2
3
4
5
Table A2. Adapted Scale for the Construct Subject Interest (1 = I do not agree, …, 5 = I agree)
2.1
I find mathematics interesting.
1
2
3
4
5
2.2
I think doing mathematics is fun.
1
2
3
4
5
2.3
I am interested in mathematical connections.
1
2
3
4
5
2.4
I like mathematics puzzles and riddles.
1
2
3
4
5
2.5
It is important for me to learn about mathematics.
1
2
3
4
5
2.6
I like to engage with mathematics in my spare time
1
2
3
4
5
Table A3. Adapted Scale for the Construct Situational Interest (1 = I do not agree, …, 5 = I agree)
3.1
I would like to learn more about Group theory.
1
2
3
4
5
3.2
I would like to learn more about applications of Group theory.
1
2
3
4
5
3.3
I would like to learn more about other algebraic structures.
1
2
3
4
5
3.4
I feel like I understood the contents of the past two weeks
1
2
3
4
5
3.5
The contents of the past two weeks have been very interesting.
1
2
3
4
5
Table A4. Adapted Scale for the Construct Relevancy of Content (1 = I do not agree, …, 5 = I agree)
4.1
I feel like Group theory is a very important part of mathematics.
1
2
3
4
5
4.2
I feel like Group theory is very important for science in general.
1
2
3
4
5
4.3
Engaging with Group theory enabled a deeper look into mathematics.
1
2
3
4
5
4.4
Group theory made me see mathematical connections that were not
oblivious to me.
1
2
3
4
5
https://www.ejmste.com
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