# A cross-age study on secondary school students’ views of stars

Philipp Bitzenbauer<EMAIL_ADDRESS>Friedrich-Alexander-
Universität Erlangen-Nürnberg, Professur für Didaktik der Physik, Staudtstr.
7, 91058 Erlangen, Germany  Sarah Navarrete  Friedrich-Alexander-Universität
Erlangen-Nürnberg, Professur für Didaktik der Physik, Staudtstr. 7, 91058
Erlangen, Germany  Fabian Hennig  Universität Leipzig, Institut für Didaktik
der Physik, Prager Str. 36, 04317 Leipzig, Germany  Malte S. Ubben  Technische
Universität Braunschweig, Institut für Fachdidaktik der Naturwissenschaften,
Bienroder Weg 82, 38106 Braunschweig, Germany  Joaquin M. Veith
Stiftungsuniversität Hildesheim, Institut für Mathematik und Angewandte
Informatik, Samelsonplatz 1, 31141 Hildesheim, Germany

(August 28, 2024)

###### Abstract

Research in astronomy education has uncovered that many learners possess
limited and fragmented understanding of stars. The corresponding
misconceptions manifest in various areas such as star formation, size, the
relationship between stars and planets, and their position in space and have
been shown to persist across different age groups and educational settings,
highlighting the need for further investigation. This paper presents the
findings of an empirical study that examines secondary students’ views of
stars and their evolution throughout their secondary school careers.
Therefore, we designed and evaluated an instrument for assessing students’
views of stars in five domains (stars and the solar system, formation and
evolution of stars, properties of stars, (sub-)stellar objects, and spectral
aspects). The instrument creation process involved several steps, including
literature-based item development, an expert survey with faculty members, and
a quantitative pilot study with a sample of $N=390$ secondary school and
college students. This process led to a final version of the instrument that
exhibits good psychometric properties. We used this new instrument in a cross-
age study to investigate the alignment of secondary students’ ideas about
stars with scientific views across different stages of secondary education.
The sample of this main study comprised a total of $N=366$ learners, including
148 lower, 151 middle and 67 upper secondary school students. Our study
findings reveal a progressive development of students’ perspectives on star-
related topics throughout their school career: Using ANOVAs and conducting
pairwise post-hoc comparisons, we observed a statistically significant
increase in the proportion of responses aligning with scientific views across
all aspects of stars examined in this study, as students progressed from lower
secondary to upper secondary levels. We further report on widely held views of
stars among our study participants that oppose the scientific views, and
discuss the implications of our findings for both educational research and
practice.

Astronomy; Stars; Cross-age study; Student Views

##  I Introduction

Learning about astronomical objects poses a challenge for individuals due to
the limited, skewed, or lack of direct experience with these objects [1].
Currently, research on mental models in astronomy education is mostly focused
on topics related to celestial bodies such as the Sun, Moon, and Earth: For
instance, there exists a large body of research on the development of
students’ mental models of Earth [2, 3], the origin of seasons [4], the day-
and-night cycle [5] or lunar phases [6]. In contrast, research on more
elaborate and modern astronomy concepts is still in its infancy [7, 8],
although astrophysics research findings are increasingly making their way into
the spotlight of news broadcasts and newspaper articles due to recent
advancements in the field (e.g., see [9]), as evidenced by the multiple Nobel
Prizes awarded for astrophysical research in recent years (e.g., 2002 [10],
2006 [11], 2011 [12], 2015 [13], 2017 [14], 2019 [15] and 2020 [16]). However,
there is no need to rely solely on the number of Nobel Prizes to gather
unanimous support for the assertion that modern astrophysics is an
exceptionally captivating realm. Physics education research has found that
space and astronomy topics spark significant interest among both boys and
girls [17], and this comes as no surprise as argued in Ref. [18]: From an
early age, students are consciously confronted with astronomical questions
through the inevitable act of observing the sky [19]. Furthermore, their
curiosity about the origins of humanity leads them to seek scientific
explanations, highlighting the enduring allure and importance of astronomy and
astrophysics in the eyes of students and non-specialists alike. Consequently,
astronomy concepts are on the rise in K-12 physics education [20, 21].
Thereby, the topic of stars and their evolution holds significant potential
for physics education from various perspectives: Stars are objects whose
structure and life can be described through the interaction of different sub-
disciplines of physics (for an overview, see [22]). Through the application of
fundamental physics principles, a comprehensive understanding can be gained of
the formation and evolution of stars as well as their transition into compact
objects such as white dwarfs, neutron stars, or black holes, which occurs when
nuclear processes converting lighter elements (e.g., hydrogen and helium) into
heavier elements (including carbon, oxygen, and elements across the periodic
table up to uranium) cease. The example of stars offers a compelling
demonstration of the interconnectedness between observation (such as spectral
analysis) and theoretical description (for an overview, see [23]). Hence,
stars are not only a fundamental aspect of astrophysics but may also serve as
a central theme in astronomy education: They provide an excellent opportunity
for students to grasp core aspects of stellar evolutionary processes.
Additionally, the theory of star formation remains incomplete, with unresolved
questions, offering a platform for learning about the Nature of Science. For
example, the mechanisms leading to the collapse of interstellar clouds, and
hence to star formation, are still not fully understood [24].

In this paper, we report on a cross-age study investigating secondary
students’ views of stars and their evolution throughout secondary school
careers. Building on previous research on student learning of astronomy
concepts in general, and stars in particular (see Section II), we formulate
our research questions in Section III, and describe the design and evaluation
of the research tool used in this study in Section IV. We present the findings
of our study in Section VI and discuss these results against the backdrop of
prior research in Section VII. Finally, we provide recommendations for both,
future research and practice in astronomy education at the secondary school
level (see Section IX).

##  II Research Background

###  II.1 The big ideas of astronomy education research

#### Topics covered and target groups addressed

Lelliott and Rollnick [25] conducted a comprehensive review of peer-reviewed
astronomy education studies published between 1974 and 2008. Their review
highlighted that the majority of these studies focused on teaching and
learning of five big ideas, “all involving the Earth in relation to its
satellite and the Sun” [25] (p. 1777): (1) Earth [2, 3, 26, 27, 28, 29, 30, 2,
31], (2) gravity [26, 27, 30, 2, 31, 32], (3) the day-and-night cycle [5, 33,
34], (4) the seasons [4, 35, 36, 37, 38], and (5) the Earth-Sun-Moon system
[39, 28, 40]. However, there is a scarcity of studies exploring student
learning in other areas of astronomy, such as the Big Bang [41, 20, 42, 43],
black holes [7], stars [44, 45], and aspects related to sizes and distances of
astronomical objects [1]. A recently published review article by Salimpour
[46] further highlights the development of “a fertile landscape for research
into Cosmology Education” (p. 819). It is noteworthy that research in the
field of astronomy education sketched above has focused on questions regarding
the teaching and learning of astronomy concepts in various target groups:
These groups range from students, including school-aged students [47, 4, 48,
34, 1], as well as college and university students [45, 49, 50, 51, 52], to
pre- and in-service teachers [53, 54, 55, 56].

#### Tools to assess students’ conceptions of astronomy topics

To assess students’ conceptual understanding and students’ conceptions of the
aforementioned astronomy topics, a number of concept inventories have been
developed and evaluated, e.g., the Lunar Phases Concept Inventory [57], the
Moon Phases Concept Inventory [58], the Light and Spectroscopy Concept
Inventory [59, 60], the Astronomy Diagnostic Test [61, 62, 63], the Test of
Astronomy Standards [64] or the Star Properties Concept Inventory [65].
However, in Ref. [66], the authors emphasize the necessity of developing
further instruments that allow for the valid assessment of students’
conceptions of more advanced topics such as black holes [7] or the Big Bang
[20] on the one hand, and stars, especially with regard to aspects beyond
their basic properties, on the other. The development of such diagnostic tools
seems necessary to address the gap in the existing literature concerning
students’ understanding and students’ conceptions of a broad range of facets
related to the topic of stars. In the upcoming subsection II.2, we will
provide an overview of astronomy education research results on this topic.

###  II.2 Students’ conceptions of stars

Agan’s study [67] shed light on students’ ideas about stars across various
educational levels, revealing a multitude of little elaborate ideas: These
encompass the twinkling nature of stars or the students’ idea that Polaris
(the North Star) would be the brightest star. Notably, a significant number of
students fail to recognize the Sun as a star, harbor the notion that stars are
immortal, and mistakenly assume that all stars end in supernovae. Moreover, an
erroneous view persists among students that all stars in the celestial sphere
are equidistant from Earth [68, 69]. Further research has unveiled that
students often describe stars as round objects without edges [68] and perceive
them as motionless entities in the night sky while recognizing the Sun’s
apparent motion during the day [33, 70]. Their comprehension of daily
celestial motion and knowledge of significant celestial objects, such as
Polaris and the ecliptic, also display limitations [71, 72]. Additionally,
misconceptions regarding the size of stars persist among learners [73].

To (a) address these persistent ideas opposing the scientific view and (b)
enhance students’ learning experiences of astronomy concepts, researchers have
explored the impact of out-of-school learning, particularly through
planetarium visits. Lelliott [74] and Dunlop [75] conducted investigations
into the effects of planetarium visits on secondary school students’
understanding of astronomy topics. Lelliott’s study [74] hints at different
cognitive levels of students’ knowledge, with planetarium visits leading to
changes in their initial ideas and a shift towards more scientifically
accurate notions of celestial motion.

###  II.3 Research desiderata

To succinctly summarize, research in astronomy education has revealed that
many learners possess limited and fragmented ideas about stars. Prevailing
students’ ideas opposing the scientific views encompass various aspects such
as star formation, size, their relationship to planets, and their position in
space. These challenges persist across diverse age groups and educational
settings, underscoring the need for further investigation. Specifically, two
key research desiderata emerge:

  1. 1.

Comprehensive analysis of students’ views of stars: The studies presented in
subsection II.2 have predominantly focused on isolated aspects of stars,
leaving some areas unexplored. Consequently, there is a dearth of instruments
capable of capturing students’ views comprehensively, encompassing the
multifaceted nature of the topic [66]. A comprehensive analysis and
identification of students’ views of stars, spanning the various sub-aspects
(e.g., from star formation to spectral aspects), remains elusive. Recognizing
the prevalent ideas among learners that contradict current scientific views,
however, is vital, as it enables the development of targeted instructional
interventions. Thus, a pressing research need exists to develop an instrument
that can holistically assess learners’ views on different aspects related to
stars.

  2. 2.

Cross-age exploration of students’ learning about stars: Although existing
cross-age studies in astronomy have examined students’ learning during limited
periods of their school careers [76, 77], a comprehensive overview of
students’ learning about stars across their entire secondary school careers is
lacking. Understanding the evolution of students’ views of stars over time is
crucial for designing instructional strategies that align with their cognitive
development and evolving needs. By gaining insights into the progression of
students’ views throughout their secondary education, educators and curriculum
developers can tailor interventions that effectively address conceptual
challenges at different stages.

In this article, we tackle both of these research desiderata: On the one hand,
we aim at developing an instrument to economically asses learners’ views of
different aspects regarding stars. On the other hand, we use this new
instrument to explore the development of secondary school students’ views of
stars throughout their secondary school careers, and hence, aim at gaining a
comprehensive overview of widespread students’ ideas of stars opposing the
current scientific views.

##  III Research Questions

The first research objective of this paper is to develop an instrument that
can economically assess learners’ views on various aspects of the stars and
that performs well psychometrically on a sample of secondary school students.
The second research objective is to gain insights into secondary school
students’ views of stars by examining their continuous development throughout
secondary education and identifying widespread ideas that contradict the
current scientific views. Hence, we aim at clarifying the following research
questions:

  1. RQ1:

How do the proportions of students’ ideas about stars aligning with the
scientific views compare among lower, middle and upper secondary school
students?

  2. RQ2:

What ideas opposing the scientific view on various aspects of stars are
widespread among secondary school students?

##  IV Design and Evaluation of the Instrument

In this section, we provide an overview of the development and evaluation of
an instrument suitable for the assessment of learners’ views of various
aspects of stars. This endeavor aligns with the research objective outlined in
the previous section (see Section III) and, hence, contributes to the validity
and reliability of the research findings put forth in this paper.

###  IV.1 Design of the instrument

#### Determination of target group and question format

Research question 1 addresses the evolution of learners’ views of stars
throughout their secondary school careers. Hence, the primary target group are
secondary school students. To allow for the economic identification of
widespread student ideas of stars that are opposing the scientific views on a
large scale (see Research question 2), the use of rating scale items seems a
sensible approach which has been used in prior research that aimed at the
economic assessment of students’ views in science education research [78, 79].
Consequently, in our instrument we decided to include statements about
different aspects of stars alongside a four-point rating scale (1 corresponds
to ”I do not agree”, 2 to ”I rather do not agree”, 3 to ”I rather agree” and 4
to ”I agree”). We decided to include a response option for abstaining to
ensure that participants were not compelled to choose either agreement or
disagreement when uncertain. Additionally, this reduces the likelihood of
participants guessing their responses (for similar arguments see [80]).

It is crucial to emphasize that the ratings provided by the participants for
the statements in the instrument were not assigned as either ’true’ or
’false.’ Instead, we employed a categorization approach to classify the
students’ ratings into the following distinct categories: (a) “in line with
the scientific view”, (b) “opposing the scientific view”, and (c) “abstained
from voting”. This categorization decision is well-justified given the dynamic
nature of research on stars and their formation, which continues to grapple
with unresolved questions in the field, as thoroughly discussed in the
introduction of this article (cf. Section I). However, we refrain from a more
fine-grained categorization that takes into account the degree of
(dis)agreement among students, since the meaning assigned to the rating
options is highly subjective and may therefore vary from person to person. For
example, if a questionnaire item contained a statement that deviated from the
currently accepted scientific view of stars, and a student selected the
response option ’I rather agree,’ we categorized the student’s rating as
’opposing the scientific view.

Lastly, we highlight that we deliberately ask for students’ views or students’
ideas instead of students’ conceptions in the research questions underlying
this study. The term conception would refer to representations and notions
that people give to phenomena or their underlying patterns [81]. However, we
assume that in this study we also collect ad hoc triggered mental connections
of the learners, which are provoked by the items of the research instrument
developed in this study, and which would not have been expressed without the
input. These are then not internalized conceptions, but we refer to those as
students’ views or ideas that potentially are more superficial in nature. The
distinction of the terms students’ views or ideas from the term students’
conceptions is in line with diSessa’s knowledge-in-pieces perspective on
learning (e.g., see [82, 83]) in which students’ views or ideas are regarded
the “product of occasional mismatches between p-prims and contexts” ([84], p.
10).

#### Description of the content domain

With our instrument, it should be possible to capture students’ understandings
of all aspects of stars relevant for astronomy education at the secondary
level. Therefore, the aspects to be included were initially identified based
on (German) secondary school curricula. Additionally, we used typical
undergraduate textbooks (e.g., [18, 85, 86]) as well as scientific articles on
astronomy education research that cover student learning (e.g., see [43, 67,
87, 88, 75]) for the description of the relevant content domains. This
procedure led to the identification of five thematic domains covering the
relevant aspects of stars:

  * •

Domain 1: Stars and solar system. This domain covers the Earth-Sun-Moon
relationship as well as their classification as celestial objects.

  * •

Domain 2: Formation and Evolution of Stars. This domain covers topics such as
stars’ origin, age, life and death.

  * •

Domain 3: Properties of Stars. This domain includes key properties of stars,
such as size or apparent motion.

  * •

Domain 4: (Sub-)Stellar objects. This domain comprises main aspects of binary
stars, brown dwarfs, white dwarfs and pulsars.

  * •

Domain 5: Spectral aspects. This domain covers questions on stars’ specific
colors and their brightness.

In the initial iteration, we meticulously devised a comprehensive set of 82
rating scale items, encompassing the five thematic domains (i.e., sub-scales)
mentioned above, to be subjected to thorough evaluation (see next Subsection
IV.2). These 82 items were partly developed newly, and additionally, we also
drew upon earlier instruments and empirical findings gained from prior
research.

###  IV.2 Evaluation of the instrument

#### Expert survey

To ensure the content validity of the instrument we conducted an expert survey
involving a panel of three esteemed faculty members with extensive expertise
in astronomy research and teaching. The expert survey encompassed two key
aspects: content evaluation and linguistic refinement.

Regarding content evaluation, the experts provided valuable insights on the
scientific accuracy of the items and their alignment with the five content
domains covered in Section IV.1. Their comments helped identify any necessary
adjustments or reallocations. Simultaneously, the experts scrutinized the
language employed in the items, offering recommendations for rephrasing where
deemed essential.

Based on the invaluable feedback obtained from the expert survey, we refined
the item set, resulting in a total of 65 revised items. These revised items
were then subjected to further piloting.

#### Psychometric characterization

Finally, we conducted a psychometric evaluation of the remaining items.
Therefore, the items were administered to a sample of $N=390$ secondary school
and college students. The psychometric characterization of the items based on
classical test theory was carried out to select the final item set for the
five sub-scales. This involved examining the items’ difficulties, with an
accepted range of $0.2$ to $0.8$ according to [89], as well as their
discriminatory powers, with accepted values $\geq 0.2$ according to [90].
Additionally, Cronbach’s Alpha was calculated as an estimator of the internal
consistency of all five sub-scales [91].

During the assessment, a total of 10 items were identified and subsequently
excluded due to their inadequate psychometric characteristics. Consequently,
the final instrument comprises 55 items, distributed among the five sub-
scales. A comprehensive overview of the item distribution per sub-scale, along
with the internal consistencies of each sub-scale, the average item
difficulties and discriminatory powers, is given in Table 1. Furthermore, to
enhance clarity, we have included a sample item for each sub-scale. The final
version of the instrument, with items arranged by sub-scales and alongside
potential references, can be found in the appendix of this paper.

Taken together, the rigorous process of development and evaluation culminated
in a final version of the instrument that exhibits robust psychometric
properties and enables a reliable assessment of secondary school students’
views of various aspects of stars. Subsequently, this refined instrument was
employed in our main study, which focuses on addressing the research questions
outlined in Section III. In the following section, we provide a detailed
account of the methodology employed in our cross-age study, followed by the
presentation of our findings in Section VI.

Table 1:  Overview of the five sub-scales D1 to D5 (including the number $N$ of items comprised and the Cronbach’s $\alpha$ values) of the final version of the instrument used in this study to approach a clarification of the research questions alongside the average item difficulties and the average discriminatory powers of the corresponding items. We refrain from reporting the item difficulties and discriminatory powers of the single items due to the large number of items. Sub-scale | N | $\alpha$ |  $\varnothing$ Item difficulty |  $\varnothing$ Discriminatory power |  Anchor example
---|---|---|---|---|---
D1: Stars and solar system | 9 | $0.69$ | $0.65$ | $0.36$ |  The Sun is the largest star in the universe.
D2: Formation and Evolution of Stars | 16 | $0.83$ | $0.56$ | $0.44$ |  Stars do not form and die, they only undergo changes over time.
D3: Properties of Stars | 15 | $0.78$ | $0.66$ | $0.39$ |  All stars have the same mass.
D4: (Sub-)Stellar objects | 8 | $0.79$ | $0.35$ | $0.50$ |  All stars end as white dwarfs.
D5: Spectral aspects | 7 | $0.73$ | $0.70$ | $0.46$ |  All stars are white.

##  V Methods

###  V.1 Study design, sample and instrument

A cross-age study design was chosen to approach a clarification of our
research questions as has been done in previous studies concerned with similar
research objectives (cf. [92, 93]). The sample comprised $N=366$ German
secondary school students, divided into three different cohorts, enabling a
deeper investigation of the temporal progression of students’ views of stars
throughout secondary education (for limitations of this approach see Section
VIII): We included participants from various grades, namely $N_{1}=148$ ($81$
female) students from grades 7-8 (aged 13-14 years), $N_{2}=151$ ($70$ female)
students from grades 9-10 (aged 15-16 years) and $N_{3}=67$ ($31$ female)
students from grades 11-12 (aged 17-18 years). In the following, we will refer
to these subsamples as Cohort 1 (lower secondary school), Cohort 2 (middle
secondary school) and Cohort 3 (upper secondary school), respectively. The
participants did not receive any instruction as part of this study prior to
test administration beyond their regular physics lessons and participation was
completely voluntary as well as uncompensated. It it is noteworthy that
current physics curricula in Germany deal with astronomy topics in a rather
superficial manner, in particular many of the topics assessed by our
instrument remain a fringe topic throughout the entirety of secondary
education. An overview of the sample is provided in Table 2.

Table 2:  Overview of the sample for the main study. Cohort | Description | Grades | Sample Size
---|---|---|---
1 | lower secondary school | 7-8 | 148
2 | middle secondary school | 9-10 | 151
3 | upper secondary school | 11-12 | 67

The data collection, took place at the end of the school year 2021/2022 when
the instrument presented in Section IV was administered as a paper-pencil-test
(for all items of the five sub-scales, see the appendix). The Cronbach Alpha
values for the five-sub-scales calculated from the main study data (cf. Table
3) were stable compared to the ones obtained in the pilot study (cf. Section
IV.2).

Table 3:  Internal consistencies of the sub-scales of the instrument based on the data of the main study sample. These compare well with the ones obtained in the pilot study (cf. Section IV.2). For the descriptions of the sub-scales see Section IV.1 and Table 1, respectively. |  | Cronbach’s Alpha |
---|---|---|---
Sub-scale | Cohort 1 | Cohort 2 | Cohort 3
1 | 0.67 | 0.70 | 0.74
2 | 0.86 | 0.87 | 0.79
3 | 0.74 | 0.79 | 0.79
4 | 0.86 | 0.80 | 0.84
5 | 0.71 | 0.73 | 0.71

###  V.2 Data analysis

#### Analysis carried out to answer research question 1

Analyses of variance (ANOVAs) were conducted to check for differences between
the three cohorts, with corresponding Tukey-Kramer post-hoc tests to check for
significant differences between the groups. As a measure of effect size for
the overall comparisons we used partial eta squared ($\eta_{p}^{2}$) where the
commonly used categorization of small ($\eta_{p}^{2}<0.06$), medium
($0.06\leq\eta_{p}^{2}<0.14$) and large ($0.14\leq\eta_{p}^{2}$) effects was
applied [94]. As a measure of effect size regarding the pairwise comparisons
we used Cohen’s $d$ alongside the established ranges of small ($d<0.5$),
medium ($0.5\leq d<0.8$) and large ($0.8\leq d$) effect sizes [94]. To ensure
the assumption of homogeneity underlying ANOVA, we employed Levene’s Test
[95]. Additionally, the normal distribution of the data was assessed using the
Shapiro-Wilk test [96].

#### Analysis carried out to answer research question 2

To analyse the students’ views in terms of scientific accuracy we employed the
categorization of responses described in Section IV, namely (a) “in line with
the scientific view”, (b) “opposing the scientific view” and (c) “abstained
form voting”. In a next step, the proportion of agreements with statements
opposing the current scientific views was analysed and an interpretation of
the corresponding students’ views was given.

##  VI Results

In the following, we report the results of our study, separated by domain. For
each of the five investigated domains we will first report ANOVA results to
evaluate the development of secondary school students’ views of stars. In a
second step, we will analyze all responses on the corresponding sub-scale of
our instrument to identify widespread ideas opposing scientific views among
secondary school learners. We refer to certain items of the instrument with
the abbreviation x-y, which stands for item y of sub-scale x (for an overview
of all items, see the appendix). To provide a concise overview, the ANOVA
results are gathered in Table 4 and will be explored more thoroughly in the
following subsections.

Table 4: Results of ANOVAs comparing the percentage of responses aligned with the scientific view on all items across the three cohorts (1 corresponding to lower secondary students, 2 to middle secondary students, and 3 to upper secondary students) and across all sub-scales (domains D1 to D5). The $p$ values reported in the last three columns belong to a Tukey-Kramer post-hoc test. Cohen’s $d$ coefficients as measures of effect size for the pairwise comparisons are provided in the corresponding Figures 1-5. |  |  |  |  Sum of squares of residual error | $F$ | $p$ | $\eta_{p}^{2}$ | Post-hoc test
---|---|---|---|---|---|---|---|---
Domain |  | Sum of squares | df |  |  |  |  | 1-2 | 1-3 | 2-3
D1 | between groups | 3.30 | 2 |  1.65 | 39.7 | $<0.001$ | 0.18 | $<0.01$ | $<0.01$ | $<0.05$
within group | 15.10 | 363 |  0.04 |  |  |  |  |  |
D2 | between groups | 2.48 | 2 |  1.24 | 28.0 | $<0.001$ | 0.13 | $<0.01$ | $<0.01$ | $<0.01$
within group | 16.06 | 363 |  0.04 |  |  |  |  |  |
D3 | between groups | 1.82 | 2 |  0.91 | 24.0 | $<0.01$ | 0.12 | $<0.01$ | $<0.01$ | $<0.01$
within group | 13.78 | 363 |  0.04 |  |  |  |  |  |
D4 | between groups | 0.65 | 2 |  0.32 | 4.46 | $<0.05$ | 0.02 | $0.94$ | $<0.05$ | $<0.05$
within group | 26.26 | 363 |  0.07 |  |  |  |  |  |
D5 | between groups | 1.89 | 2 |  0.94 | 13.2 | $<0.001$ | 0.07 | $<0.05$ | $<0.001$ | $<0.01$
within groups | 25.99 | 363 |  0.07 |  |  |  |  |  |

###  VI.1 Domain 1: Stars and solar system

Table 5 shows the descriptive statistics for all cohorts regarding items of
domain 1. While cohort 1 students averaged 48.4% scientifically accurate
answers, the proportion of responses aligning with scientific views for cohort
2 is 64.2% and further increases to 72.6% for cohort 3. A similar observation
can be made for the median.

Table 5:  Descriptive statistics for the percentage of responses on all items of domain 1 that are in line with the scientific views, separated by cohort. Cohort | Mean | SD | Median | Min | Max
---|---|---|---|---|---
1 | 48.4 | 22.9 | 55.6 | 0.0 | 88.9
2 | 64.2 | 18.6 | 66.7 | 11.1 | 100
3 | 72.6 | 18.3 | 77.8 | 22.2 | 100

#### ANOVA results for domain 1

The trend observed in Table 5 is statistically substantiated by the ANOVA
results (cf. Table 4). The difference between the three cohorts is
statistically significant [$F(2,363)=39.7,p<0.001;\eta_{p}^{2}=0.18$].
Comparing the three cohorts directly yields a statistically significant
difference between cohort 2 and cohort 3 $(p<0.05)$ with a effect size of
$d=0.42$. Cohort 1, on the other hand, differs highly significantly from both
cohort 2 ($p<0.01$) and cohort 3 ($p<0.01$) with medium to high effect sizes
of $d=0.52$ and $d=1.07$, respectively. These results are summarized in the
form of boxplots in Figure 1 – for the presentation of our boxplots the
whiskers indicate $1.5\times\operatorname{IQR}$ throughout this article, where
IQR is the interquartile range.

Figure 1: Boxplot for the percentage of responses on all items of domain 1
that are in line with the scientific views. Asterisks indicate the statistical
significance of Tukey-Kramer post hoc pairwise comparisons (*: $p<0.05$, **:
$p<0.01$, ***: $p\leavevmode\nobreak\ <\leavevmode\nobreak\ 0.001$), whereas
Cohen’s $d$ is reported as a measure of effect size.

#### Secondary school students’ views of stars and the solar system

A more in-depth view of the student’s responses on the items of domain 1 is
provided by Table 15. Here, we report the more fine-grained categorization of
answers into answers that are in line with scientific views ($+$), opposing
scientific views ($-$) and the ones abstained from voting ($\circ$). Across
all items and cohorts, there is generally a high percentage of students
providing scientifically sound answers. Nevertheless, the ANOVA results are
also reflected in the observation that the share of answers in line with the
scientific view increase from throughout grades 7 to 12. An item that stands
out due to a large share of $-$ is item 1-4, indicating that between 32.4%
(lower), 46.1% (middle) and 41.8% (upper) secondary school students believe
that “the planets and the Sun were formed at the time of the Big Bang”. An
even higher share of answers opposing the scientific view and the most evident
view held by all students is revealed by item 1-5 which states that “there are
hundreds of stars in our solar system.” Here, 75.0% (lower), 70.9% (middle)
and 62.7% (upper) of all participants agreed with the statement, indicating
trouble with grasping the magnitude of our solar system. Lastly, item 1-6
exhibits the greatest share of abstained votes, with 32.4% (lower), 25.8%
(middle) and 28.4% (upper), respectively. In other words, this item stating
that “metals have existed in the universe since the Big Bang” was met with the
highest uncertainty and, consequently, a low percentage of scientifically
sound responses.

###  VI.2 Domain 2: Formation and evolution of stars

Table 6 shows the descriptive statistics for all cohorts regarding items of
domain 2. While mean and median are, on average, slightly lower compared to
domain 1, we again observe an increase of all metrics with the exception of
standard deviation.

Table 6:  Descriptive statistics for the percentage of responses on all items of domain 2 that are in line with the scientific views, separated by cohort. Cohort | Mean | SD | Median | Min | Max
---|---|---|---|---|---
1 | 42.9 | 21.4 | 43.8 | 0.0 | 75.0
2 | 53.8 | 20.8 | 50.0 | 6.3 | 100
3 | 65.4 | 20.9 | 68.8 | 6.3 | 100

#### ANOVA results for domain 2

The trend observed for domain 1 also holds for domain 2 (cf. Table 4): The
difference between the cohorts is very highly significant
[$F(2,363)=28.0,p<0.001;\eta_{p}^{2}=0.13$]. Likewise, all between group
comparisons show highly statistical significance ($p<0.01$) with effect sizes
ranging from $d=0.52$ between cohort 1 and 2, $d=0.55$ between cohort 2 and 3
as well as $d=1.07$ between cohort 1 and 3. Hence, not only do the groups
differ highly significantly, but medium to high effect sizes can be associated
with each of the pairwise comparisons, indicating a steady increase of
scientifically accurate views across secondary education. These results are
summarized in the form of boxplots in Figure 2.

Figure 2: Boxplot for the percentage of responses on all items of domain 2
that are in line with the scientific views. Asterisks indicate the statistical
significance of Tukey-Kramer post hoc pairwise comparisons (*: $p<0.05$, **:
$p<0.01$, ***: $p\leavevmode\nobreak\ <\leavevmode\nobreak\ 0.001$), whereas
Cohen’s $d$ is reported as a measure of effect size.

#### Secondary school students’ views of the formation and evolution of stars

A more fine-grained overview of responses is provided in Table 16. Again, we
observe a general tendency towards answers in line with the scientific view
compared to answers opposing it. Additionally, the pattern of upper secondary
school students outperforming their middle and lower peers repeats. An item
with a notable percentage of scientifically inaccurate views is item 2-10
which deals with the color of stars. Here, 50.7% of lower, 49.0% of middle and
38.8% of upper secondary school students hold the opinion that stars do not
change their color throughout their life, neglecting their evolutionary stages
that impact the perceived color. This lack of awareness regarding the
evolutionary stages is substantiated by item 2-13 which states that “stars
fade and disappear over time”. An almost equal share of 63.5% (lower), 58.3%
(middle) and 53.7% (upper) disagreed with this statement and, thus, perceive
stars as permanent objects. Lastly, item 2-16 reveals another view that falls
in line with the responses on item 1-5: Almost half of each cohort responded
that “a supernova immediately destroys a large part of the galaxy”, indicating
yet again a skewed perception of astronomic scales.

###  VI.3 Domain 3: Properties of Stars

The descriptive statistics for all cohorts regarding items of domain 3 are
provided in Table 7. The values overall compare very well to the ones from
domain 1 and 2 (cf. Table 5 and Table 6).

Table 7:  Descriptive statistics for the percentage of responses on all items of domain 3 that are in line with the scientific views, separated by cohort. Cohort | Mean | SD | Median | Min | Max
---|---|---|---|---|---
1 | 55.7 | 22.2 | 60.0 | 0.0 | 93.3
2 | 64.2 | 17.5 | 66.7 | 13.3 | 100
3 | 75.3 | 17.2 | 80.0 | 20.0 | 100

#### ANOVA results for domain 3

The ANOVA results for domain 3 show almost identical values with those of
domain 2 (cf. Table 4). The cohorts differ highly statistically significantly
[$F(2,363)=24.0,p<0.01;\eta_{p}^{2}=0.12$] and the same is true for all
pairwise cohort comparisons ($p<0.01$ each). The corresponding effect sizes
are all high with $d=0.44$ between Cohort 1 and 2, $d=0.57$ between Cohort 2
and 3 as well as $d=1.01$ between Cohort 1 and 3. Hence, as before, a
continuous improvement in scientifically accurate views held by students can
be observed from lower to middle and, lastly, higher secondary education. A
summary of these results in terms of Boxplots is provided in Figure 3.

Figure 3: Boxplot for the percentage of responses on all items of domain 3
that are in line with the scientific views. Asterisks indicate the statistical
significance of Tukey-Kramer post hoc pairwise comparisons (*: $p<0.05$, **:
$p<0.01$, ***: $p\leavevmode\nobreak\ <\leavevmode\nobreak\ 0.001$), whereas
Cohen’s $d$ is reported as a measure of effect size.

#### Secondary school students’ views of properties of stars

Table 17 provides an overview of the responses on all items of domain 3,
exhibiting similar answer patterns as before (cf. Table 15 and Table 16).
Here, item 3-4 stands out as it extends an idea observed in domain 2: 43.9% of
lower, 29.1% of middle and 37.3% of upper secondary school students held the
misguided view that stars do not underlie gravitational pull, viewing stars as
stationary celestial objects that do not interact with their surroundings. The
share of scientifically accurate responses on this item being the same for
cohorts 2 and 3 suggests that this view is somewhat persistent throughout
higher secondary education. This is further substantiated by the response
pattern of item 3-13 which states that “stars seem to rise and set”. Again,
with 35.8%, 43% and 34.3%, respectively, a substantial share of participants
disagreed with that statement, expressing yet another view of rigid stars. On
a different note, item 3-7 reveals that 39.9% of lower, 42.4% of middle and
28.4% of higher secondary school students relate a star’s distance to its
apparent brightness in the sky, stating that “the brightest stars are closest
to Earth”.

###  VI.4 Domain 4: (Sub-)Stellar objects

Table 8 provides an overview of descriptive statistics for all items of domain
4. This domain holds the overall lowest descriptive statistics. While cohort 1
students averaged 32.9% scientifically accurate answers, the proportion of
responses aligning with scientific views for cohort 2 is 31.8% and 43.1% for
cohort 3. The median reflects this performance and, for the first and only
time, there are participants with no responses that are in line with the
scientific view. Thus, on average secondary school students’ views differed
the most from the current scientific view regarding (sub-)stellar objects. We
will elaborate on this observation in the discussion section (cf. Section
VII).

Table 8:  Descriptive statistics for the percentage of responses on all items of domain 4 that are in line with the scientific views, separated by cohort. Cohort | Mean | SD | Median | Min | Max
---|---|---|---|---|---
1 | 32.9 | 27.9 | 37.5 | 0.0 | 87.5
2 | 31.8 | 26.4 | 25.0 | 0.0 | 100
3 | 43.1 | 25.7 | 37.5 | 0.0 | 100

#### ANOVA results for domain 4

With the scores being relatively low in each cohort, the variance in
performance did not differ as much compared to the other domains. While
overall group comparison still results in a statistically significant
difference [$F(2,363)=4.46,p<0.05;\eta_{p}^{2}=0.02$], no statistically
significant difference was found between cohorts 1 and 2 ($p=0.94$). The
differences between cohort 1 and 3 as well as cohort 2 and 3 were found to be
statistically significant by Tukey-Kramer post-hoc tests ($p<0.05$ each) but
the corresponding effect sizes were low with $d=0.38$ and $d=0.42$,
respectively. Thus, for the domain of (sub-)stellar objects we record the
overall least distinguishable progress throughout secondary education, with
only the later grades (11 and 12) meaningfully separating themselves from the
rest. The boxplots reflecting this observation are presented in Figure 4.

Figure 4: Boxplot for the percentage of responses on all items of domain 4
that are in line with the scientific views. Asterisks indicate the statistical
significance of Tukey-Kramer post hoc pairwise comparisons (*: $p<0.05$, **:
$p<0.01$, ***: $p\leavevmode\nobreak\ <\leavevmode\nobreak\ 0.001$), whereas
Cohen’s $d$ is reported as a measure of effect size.

#### Secondary school students’ views of (sub-)stellar objects

A deeper look into this evidently more elusive domain is enabled by the
response pattern on all items, provided in Table 18. It becomes clear that
students on average did not hold inaccurate views but rather abstained from
voting, perhaps due to the (currently) marginal nature of the corresponding
contents in secondary curricula. Items 4-3, 4-5 as well as 4-7 all address
brown and white dwarfs and have in common that students across all cohorts
held similar views. With on average one third of all participants expressing
views opposing the scientific view across these items, it is suggested that
(sub-)stellar objects constitute a fringe topic for which little progress is
recorded throughout the grades 7 to 12.

###  VI.5 Domain 5: Spectral aspects

Table 9 shows the descriptive statistics for all cohorts regarding items of
domain 5. In contrast to domain 4, domain 5 records the overall highest mean
percentages of responses in accordance with the scientific views with 58.9%
for lower, 67.3% for middle and 78.9% for higher secondary school students.
The minimum and maximum in each cohort are 0.0% and 100.0%, respectively.

Table 9:  Descriptive statistics for the percentage of responses on all items of domain 5 that are in line with the scientific views, separated by cohort. Cohort | Mean | SD | Median | Min | Max
---|---|---|---|---|---
1 | 58.9 | 29.5 | 71.4 | 0.0 | 100
2 | 67.3 | 24.9 | 71.4 | 0.0 | 100
3 | 78.9 | 24.3 | 85.7 | 0.0 | 100

#### ANOVA results for domain 5

The ANOVA results for domain 5 demonstrate a much pronounced improvement along
the trajectory of secondary education (cf. Table 4). The overall difference
between the three cohorts is highly statistically significant
[$F(2,363)=13.2,p<0.001;\eta_{p}^{2}=0.07$]. A Tukey-Kramer post-hoc test
indicates that the advancement from grades 7-8 to grades 9-10 is statistically
significant ($p<0.05$) with an effect size of $d=0.31$, whereas the difference
between grades 9-10 and 11-12 is highly statistically significant ($p<0.01$)
with an effect size $d=0.48$. Lastly, the difference between cohorts 1 and 3
is very highly statistically significant ($p<0.001$) with a medium effect size
of $d=0.75$. The boxplots reflecting this continuous increase in accurate
scientific views are illustrated in Figure 5.

Figure 5: Boxplot for the percentage of responses on all items of domain 5
that are in line with the scientific views. Asterisks indicate the statistical
significance of Tukey-Kramer post hoc pairwise comparisons (*: $p<0.05$, **:
$p<0.01$, ***: $p\leavevmode\nobreak\ <\leavevmode\nobreak\ 0.001$), whereas
Cohen’s $d$ is reported as a measure of effect size.

#### Secondary school students’ views of Spectral aspects

The fine-grained overview of responses to items of the final sub-scale is
presented in Table 19. Here, the item that stands out the most is item 5-7
which states that “it is said that stars twinkle because they change their
brightness” – 45.9% of lower, 39.1% of middle and 25.4% of higher secondary
school students agreed with this statement. In congruence to the response
pattern on items 2-10 and 3-7 singled out earlier, the brightness of stars
seems to constitute a recurring theme where students’ views are inaccurate to
a greater extent than usual. We will discuss this observation more thoroughly
in Section VII.

##  VII Discussion

In this section, we contextualize our findings against the backdrop of prior
astronomy education research. In particular, we shed light on the extent to
which our findings are consistent with prior research, identify areas where
differences have emerged, and highlight new contributions to the understanding
of secondary school students’ views of stars. Moreover, we discuss
implications of our findings for both astronomy education research and
practice.

In general, our cross-age analysis reveals a progressive development of
students’ perspectives on star-related topics throughout their secondary
school education. The statistically significant increase in the percentage of
responses aligned with current scientific views from lower to upper secondary
school applies to all aspects of stars examined in this study, as demonstrated
through ANOVAs and post-hoc pairwise comparisons (see Section VI).
Furthermore, our study expands upon existing literature, which primarily
focuses on students’ views of the nature, apparent motion, and properties of
stars [26, 76, 65].

###  VII.1 Discussion of findings regarding domain 1

The percentage of responses aligning with scientific views in domain 1 (stars
and solar systems) shows an increase from 48.4% among lower, and 64.2% among
middle to 72.6% among upper level secondary school students (see Table 5). An
item with a very big gain of alignment towards scientific views was for
example item 1-9, where progressively more students disagreed with the
statement that the Sun is the largest star in the universe (75.0% of the
lower, 43.7% of the middle and 34.3% of the upper secondary students). On the
single-item level we also found, that a majority of the study participants
(75.0% of the lower, 70.9% of the middle and 62.7% of the upper secondary
students) agreed that there are hundreds of stars in our solar system (item
1-5, see Table 15). This idea opposes the scientific view and has already been
reported in Ref. [97]. This student view can possibly be explained by the
confusion of the terms solar system and stellar system as indicated by Rajpaul
et al. [1]. Another widespread perspective among our study participants is
that metals have existed since the Big Bang (item 1-6, see Table 15): 46.6% of
the lower, 40.4% of the middle, and 29.9% of the upper secondary students were
of that opinion, while in addition, around a third of the students at all
grade levels were undecided (32.4%, 25.8% and 28.4%, respectively). This
finding supports the study by Slater et al. [70], in which around a third of
the students have been reported to hold the view that heavy atoms have existed
since the Big Bang.

In contrast to previous research by Dunlop [75], Philips [98] or Comins [97],
in our study, we did not find evidence of students misconceiving that the Sun
is not a star: Only approximately 10% of lower and middle secondary school
students, and merely 3% of upper secondary school students, subscribed to this
view (see see item 1-8 Table 15). It is noteworthy, that it remains unclear
which research methods Philips [98] and Comins [97] employed to uncover this
confusion to be widespread among learners. Additionally, Comins [97] stated
that many students would believe that the sun is bigger than other stars. In
our study, we identified this view to be widespread among the lower secondary
school students (60.1%, see Table 15), while only 37.7% of the middle and
29.9% of the upper secondary students agreed with item 1-9 (“The sun is the
largest star in the universe.”).

###  VII.2 Discussion of findings regarding domain 2

Similar to domain 1, the percentage of responses aligning with scientific
views in domain 2 (formation and evolution of stars) shows an increase from
42.9% among lower secondary school students to 53.8% among middle secondary
school students and 65.4% among upper secondary school students (see Table 6).
An item with a very big gain of alignment towards scientific views was, for
example, item 2-10, where progressively more students agreed that stars can
change in color (16.9% of the lower, 35.8% of the middle and 79.1% of the
upper secondary students). But on the single-item level, we also found that –
in line with earlier research conducted by Agan [67] – more than half of our
participating students agreed with item 2-13 stating that stars would fade and
disappear over time (63.5% of the lower, 58.3% of the middle, and 53.7% of the
upper secondary students).

###  VII.3 Discussion of the findings regarding domain 3

A study similar to the one presented in this paper, focusing on star-related
aspects, was conducted by Plummer [76]. In her cross-age study, Plummer aimed
to assess students’ views of celestial motion and identify any misconceptions
held at different grade levels (1st, 3rd, and 8th grade students). One part of
her study specifically focused on students’ views of the apparent motion of
stars. Among the sample students, two main perspectives emerged: those who
could provide a general description of stars moving slowly across the night
sky (40% of 8th graders, 50% of 3rd graders, and 35% of 1st graders), and
those who believed that stars never move (40%, 40%, and 25%, respectively).
The remaining students held various perspectives, including the idea that
stars only move at the end of the night. Our study complements Plummer’s
findings by providing insights into the views of older students regarding the
apparent motion of stars. Among our cohort 1 students (grades 7 and 8), only
18.2% believed that stars are stationary and fixed in the sky (item 3-11, see
Table 17). This percentage was even lower among cohort 3 students (grades 11
and 12) at 14.9%. In addition, our findings align with the research conducted
by Agan [67], revealing a comparable proportion of students (approximately
14%) who share the view that stars are stationary. This stands in contrast to
studies published in Refs. [33, 70, 48], which reported a higher prevalence of
this view among approximately 40% of students. On a further note, our findings
are supported by Plummer’s study, according to which more than “one-half of
the students in the first, third, and eight grades do not think that we see
different stars in the sky during the night (65%, 60%, and 65%), respectively”
([76], p. 1598). In our study, 60.8% of lower secondary school students, 75.5%
of middle secondary school students, and 82.1% of upper secondary school
students agreed with item 3-12, which states that we see different stars over
the course of a night (see Table 17). In summary, our findings suggest a
continued evolution of students’ views on the apparent motion of stars
throughout secondary education.

Another cross-age study on basic astronomy concepts was conducted by Trumper,
which included both junior (grades 7-9) [99] and senior (grades 10-12) [100]
high school students. In Trumper’s study, only 36% of junior high school
students were aware that stars are the farthest objects from the Earth ([99],
p. 1117), while this percentage increased to 49% among senior high school
students ([100], p. 103). In our study, the percentages of students agreeing
with the scientific views on this matter were slightly higher in the sample
cohorts. Among lower secondary school students, 43.9% agreed that stars are
farther away from the Earth than the Sun (item 3-9, see Table 17). This
percentage increased to 51.7% among middle secondary school students and 53.7%
among upper secondary school students. Therefore, it appears that students’
views regarding distances develop throughout their school careers. This
observation is further supported by the decreasing agreement with item 3-10,
which states that the distance between stars is about the same as the distance
between planets. While half of the lower secondary school students disagreed
with this item, the disagreement percentage increased to 62.9% among middle
secondary school students and 74.6% among upper secondary school students (see
Table 17). Our findings align with earlier research on learners’ views of
astronomical object distances from the Earth’s surface (e.g., see [1, 20,
48]).

###  VII.4 Discussion of findings regarding domains 4 & 5

While the percentage of responses aligning with scientific views in domain 4
remains below 50% for students across all grade levels (see Section 8), we
found a majority of students demonstrating views in line with current
scientific understandings of the spectral aspects of stars in domain 5 (see
Section 9). No statistically significant difference can be observed in the
percentage of responses aligning with scientific views for items in domain 4
between lower (32.9%) and middle secondary school students (31.8%), see Table
8. This finding can likely be attributed to the omission of (sub-)stellar
objects from the German astronomy curricula at both lower and middle school
levels. Insights into current curriculum developments regarding astronomy in
German secondary schools can be found in Ref. [20]. The topic of spectral
aspects shows a similar pattern: Surprisingly, a small but statistically
significant difference exists in the percentage of responses aligning with
scientific views for items in domain 5 between lower (58.9%) and middle
secondary school students (67.3%). This discrepancy can possibly be attributed
to either implicit learning, which occurs unconsciously as students engage
with different topics, such as atomic physics (for more details on implicit
learning, see Reber [101]), or the influence of informal learning environments
[102], such as planetariums [75]. There were items like 4-6 (see Table 18) and
5-6 (see Table 19), where a bigger shift towards a perspective aligned with
scientific views was observed (38.5% to 70.1% and 39.2% to 86.6%
respectively), though for most, the shifts remained smaller. In future
research, it would be valuable to explore (a) which topics in the secondary
school curriculum facilitate implicit learning of astronomy and (b) the
sources from which students gain insights into astronomy topics in informal
settings.

###  VII.5 Implications for Educational Research

The results of this study imply that, in general, students’ ideas about stars
show a progressive alignment with the current scientific views. This quite
positive development, however, lacks a clear explanation at this point,
meaning that further extensive research is advised to clear up the various
causes for the developments presented in this study: While teaching in the
classroom appears to play a role, it is important to consider the potential
influence of informal learning environments such as out-of-school visits [103,
104] or explanatory videos [105]. These supplementary resources may contribute
to the positive evolution of students’ understanding. Additionally, no data
about the traits of the students have been gathered. As previous research has
shown, astronomical topics tend to rank highly in studies on interesting
topics for students [17]. A thorough investigation into how and what affective
traits facilitate the increase in alignment with scientific topics during the
secondary school years could give new and more detailed insights into the role
of interests in learning processes. Furthermore, the instrument utilized in
this study has the potential to be employed in future research to identify the
specific factors and properties of learning materials and methodologies that
facilitate these favorable learning outcomes. By using this instrument,
researchers can gain insights into the effective strategies and approaches
that support students’ development of ideas in the domain of stars and related
astronomical concepts, complementing previous instruments devised for this
purpose (e.g., see [106, 57]). Further investigation is warranted to delve
deeper into the mechanisms driving this positive learning trajectory.
Additionally, exploring the comparative impact of various educational
interventions and materials could shed light on the most effective approaches
for promoting accurate scientific understanding of stars among students.

###  VII.6 Implications for Educational Practice

From the findings presented in this study, we surmise that current educational
practices available between the lower and upper secondary school level likely
facilitate a basic development of ideas about stars that in general align
progressively more with scientific views during these years. However, some
persistent ideas have also been isolated that have also been found in
corresponding literature (e.g., see [76, 67, 107]). Mainly, static ideas have
been found especially in the lower high school classes and confusions of
central ideas like stellar system and solar system have also been documented.
Ideas of change and dynamics (stars changing brightness or stars changing
color) might be better facilitated by incorporating learning materials that
depict these dynamic properties (such as videos or comics, cf. [105, 108]) or
even enable learners to interact with the material (such as simulations, cf.
[109]).

##  VIII Limitations

While our study on students’ views of stars throughout their secondary school
careers provides valuable insights, it is important to acknowledge several
limitations. Firstly, it is crucial to note that our research adopted a cross-
age study design rather than a conventional longitudinal approach: Instead of
longitudinally tracking the views of a specific group of students, we assessed
students from different grade levels at a single time point. Our approach
offers valuable cross-sectional data but (a) limits our ability to capture
individual students’ developmental trajectories and the specific changes in
their views of stars over time and (b) may be subject to cohort bias [110].
Secondly, it is important to acknowledge the limited emphasis on astronomy
within the secondary school curriculum in Germany where this study was
conducted (e.g., see [111]). The lack of continued instruction in astronomy
raises the question of how students’ views of stars might be influenced if
they had participated in continued astronomy instruction throughout their
secondary school careers. Thirdly, the subsamples of lower and middle
secondary school students consisted of approximately 150 participants each,
whereas the number of participants in the upper secondary school group was
only about half that size. This discrepancy arises from the fact that in
Germany, students make a decision after completing grade 10 regarding whether
to pursue a physics course in upper secondary school. Consequently, the total
cohort of possible study participants becomes significantly smaller at this
grade level. Furthermore, teachers are often less inclined to participate in
research studies during the twelfth grade due to the impending final exams.
These factors imposed limitations on our sampling approach, resulting in an
asymmetric distribution of participants among the three subsamples.

Another limitation stems from the question format used in our instrument,
which consisted of closed-ended rating-scale items. While this format
facilitated efficient data collection on students’ views of stars on a large
scale, it is important to recognize that the predetermined statements may have
influenced participants’ responses, potentially leading to the generation of
ad hoc conceptions. To mitigate this limitation, future research should
incorporate qualitative data collection methods, such as mind mapping or
concept mapping [112, 113, 114, 115], to gather in-depth insights that
validate and expand upon our findings. Furthermore, it is crucial to
acknowledge that our study primarily focused on assessing students’ ideas and
views of stars, rather than their conceptual understanding of relevant aspects
related to stars. While our study provides valuable perspectives, it is
essential to complement these findings with investigations into students’
conceptual understanding. Developing a concept inventory should therefore be a
priority for future research, enabling the assessment of students’ conceptual
understanding of the topic under investigation (cf. [66]).

##  IX Conclusion

From the data collected and analyzed, our findings about students’ ideas about
stars compared to scientific views have shown that progressing from lower to
upper secondary school, ideas start to align more with the current scientific
views. This development in itself is positive, though the exact factors for it
still need to be further determined. From the data gathered, some of the ideas
are already being developed rather effectively, such as ideas about Sun’s size
when compared to other stars (see items 1-9 in Table 15 and 3-2 in Table 17)
or that stars can change both color and brightness (see items 2-10 in Table 16
and 5-6 in Table 19) while others seem more robust, such as the idea that
there are hundreds of stars in the solar system (item 1-5, see Table 15) or
that white dwarfs are suns (item 4-5, see Table 18). In summary, our analysis
indicates a positive trend of students’ ideas aligning more closely with
scientific views regarding stars as they progress through secondary school,
although the specific contributing factors remain to be determined.

## Data availability

Anonymized data from the study is available on request from the authors.

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## Appendix: The instrument used in this study

In this appendix, we provide all items of the instrument used in this study,
sorted by the five sub-scales included.

###  .1 Sub-scale on domain 1: Stars and solar system

Table 10:  Overview of the rating scale items related to the sub-scale on
domain 1. The table includes the item numbers (No.), the statements
themselves, indications of whether the statements align with the scientific
view or oppose it, and any references or sources of inspiration.

No. |  Item |  In line with scientific view |  Opposing scientific view |  Reference / Inspired by
---|---|---|---|---
1-1 |  The Earth orbits the Sun and the Moon. |  |  x |
1-2 |  Sun and Moon orbit the Earth. |  |  x |
1-3 |  Earth and Moon orbit the Sun. |  x |  |
1-4 |  The planets and the Sun were formed at the time of the Big Bang. |  |  x |  [43]
1-5 |  There are hundreds of stars in our solar system. |  |  x |  [87, 67]
1-6 |  Metals have existed in the universe since the Big Bang. |  |  x |
1-7 |  The Moon is a star. |  |  x |  [88]
1-8 |  The Sun is a star. |  x |  |  [75]
1-9 |  The Sun is the largest star in the universe. |  |  x |  [67]

###  .2 Sub-scale on domain 2: Formation and Evolution of Stars

Table 11:  Overview of the rating scale items related to the sub-scale on
domain 2. The table includes the item numbers (No.), the statements
themselves, indications of whether the statements align with the scientific
view or oppose it, and any references or sources of inspiration.

No. |  Item |  In line with scientific view |  Opposing scientific view |  Reference / Inspired by
---|---|---|---|---
2-1 |  Stars already existed before the Big Bang. |  |  x |  [43, 87]
2-2 |  Stars don’t form and die, they just change over time. |  |  x |
2-3 |  All stars are orbited by planets. |  |  x |
2-4 |  Stars have spikes. |  |  x |
2-5 |  The surface of stars is almost completely covered by volcanoes. |  |  x |  [67]
2-6 |  All stars are the same age. |  |  x |
2-7 |  We see the stars exactly as they are in this moment. |  |  x |
2-8 |  Stars undergo changes. |  x |  |
2-9 |  Stars change their size. |  x |  |
2-10 |  Stars change their color. |  x |  |
2-11 |  Massive stars can evolve into neutron stars. |  x |  |
2-12 |  Massive stars can evolve into black holes. |  x |  |
2-13 |  Stars fade and disappear over time. |  |  x |  [67]
2-14 |  Supernova eruptions occur only in our galaxy. |  |  x |
2-15 |  All stars end up in a supernova. |  |  x |
2-16 |  A supernova immediately destroys a large part of the galaxy. |  |  x |

###  .3 Sub-scale on domain 3: Properties of Stars

Table 12:  Overview of the rating scale items related to the sub-scale on
domain 3. The table includes the item numbers (No.), the statements
themselves, indications of whether the statements align with the scientific
view or oppose it, and any references or sources of inspiration.

No. |  Item |  In line with scientific view |  Opposing scientific view |  Reference / Inspired by
---|---|---|---|---
3-1 |  All stars are the same size. |  |  x |
3-2 |  There are stars that are larger than the Sun. |  x |  |  [67]
3-3 |  All stars have the same mass. |  |  x |
3-4 |  Stars underlie gravitational pull. |  x |  |
3-5 |  Stars exert attraction on things. |  x |  |
3-6 |  All stars have about the same distance from Earth as the Moon. |  |  x |
3-7 |  The brightest stars are closest to Earth. |  |  x |  [67]
3-8 |  All stars are the same distance from Earth. |  |  x |
3-9 |  Stars are farther away from Earth than the Sun. |  x |  |
3-10 |  The distance between stars is about the same as the distance between planets. |  |  x |
3-11 |  All stars are stationary – they are fixed in the sky and do not move. |  |  x |  [76, 116, 40]
3-12 |  During the course of a night we see different stars. |  x |  |  [76]
3-13 |  Stars seem to rise and set. |  x |  |  [97, 67]
3-14 |  The observable motion of the stars is a result of the Earth’s rotation around its own axis. |  x |  |  [25, 73]
3-15 |  Stars don’t rotate. |  |  x |  [97, 67]

###  .4 Sub-scale on domain 4: (Sub-)Stellar objects

Table 13:  Overview of the rating scale items related to the sub-scale on
domain 4. The table includes the item numbers (No.), the statements
themselves, indications of whether the statements align with the scientific
view or oppose it, and any references or sources of inspiration.

No. |  Item |  In line with scientific view |  Opposing scientific view |  Reference / Inspired by
---|---|---|---|---
4-1 |  Two orbiting stars (binary star system) would quickly collide. |  |  x |
4-2 |  There are long-standing binary star systems. |  x |  |
4-3 |  Brown dwarfs describe the final stage of a star. |  |  x |
4-4 |  White dwarfs are planets. |  |  x |
4-5 |  White dwarfs are suns. |  x |  |
4-6 |  White dwarfs are stars. |  x |  |
4-7 |  All stars end up as white dwarfs. |  |  x |
4-8 |  Pulsars are stars that alternately emit light of different intensities. |  |  x |

###  .5 Sub-scale on domain 5: Spectral aspects

Table 14:  Overview of the rating scale items related to the sub-scale on
domain 5. The table includes the item numbers (No.), the statements
themselves, indications of whether the statements align with the scientific
view or oppose it, and any references or sources of inspiration.

No. |  Item |  In line with scientific view |  Opposing scientific view |  Reference / Inspired by
---|---|---|---|---
5-1 |  All stars have the same color. |  |  x |
5-2 |  All stars are white. |  |  x |
5-3 |  All stars are yellow. |  |  x |  [97, 67]
5-4 |  There are blue stars. |  x |  |
5-5 |  Stars emit many colors of light. |  x |  |
5-6 |  The brightness of stars is constant. |  |  x |
5-7 |  It is said that stars twinkle because they change their brightness. |  |  x |  [97, 67]

###  .6 Distribution of students’ responses on all items

Table 15:  Share of responses to all items of domain 1 that are in line with
scientific views ($+$), opposing scientific views ($-$) or abstained form
voting ($\circ$), for all three cohorts.

Item | Cohort | $-$ | $\circ$ | $+$ | Item | Cohort | $-$ | $\circ$ | $+$
---|---|---|---|---|---|---|---|---|---
1-1 | 1 | 41.9 | 10.1 | 48.0 | 1-6 | 1 | 46.6 | 32.4 | 20.9
2 | 13.9 | 2.0 | 84.1 | 2 | 40.4 | 25.8 | 33.8
3 | 9.0 | 0.0 | 91.0 | 3 | 29.9 | 28.4 | 41.8
1-2 | 1 | 36.5 | 6.8 | 67.6 | 1-7 | 1 | 19.6 | 10.1 | 70.3
2 | 12.6 | 0.7 | 86.6 | 2 | 11.9 | 6.0 | 82.1
3 | 11.9 | 0.0 | 88.1 | 3 | 10.4 | 1.5 | 88.1
1-3 | 1 | 25.7 | 6.8 | 67.6 | 1-8 | 1 | 10.8 | 6.8 | 82.4
2 | 21.2 | 3.3 | 75.5 | 2 | 11.3 | 2.0 | 86.6
3 | 9.0 | 0.0 | 91.0 | 3 | 3.0 | 0.0 | 97.0
1-4 | 1 | 32.4 | 17.6 | 50.0 | 1-9 | 1 | 60.1 | 14.9 | 25.0
2 | 46.1 | 10.6 | 43.0 | 2 | 37.7 | 6.0 | 56.3
3 | 41.8 | 4.5 | 53.7 | 3 | 29.9 | 4.5 | 65.7
1-5 | 1 | 75.0 | 10.1 | 14.9 |  |  |  |  |
2 | 70.9 | 0.0 | 29.1 |  |  |  |  |
3 | 62.7 | 0.0 | 37.3 |  |  |  |  |

Table 16:  Share of responses to all items of domain 2 that are in line with scientific views ($+$), opposing scientific views ($-$) or abstained form voting ($\circ$), for all three cohorts. Item | Cohort | $-$ | $\circ$ | $+$ | Item | Cohort | $-$ | $\circ$ | $+$
---|---|---|---|---|---|---|---|---|---
2-1 | 1 | 52.0 | 18.2 | 29.7 | 2-9 | 1 | 14.2 | 20.9 | 64.9
2 | 37.7 | 18.5 | 43.7 | 2 | 24.5 | 13.2 | 62.3
3 | 23.9 | 11.9 | 64.2 | 3 | 11.9 | 9.0 | 79.1
2-2 | 1 | 71.6 | 10.1 | 18.2 | 2-10 | 1 | 50.7 | 32.4 | 16.9
2 | 41.7 | 9.3 | 49.0 | 2 | 49.0 | 15.2 | 35.8
3 | 25.4 | 3.0 | 71.6 | 3 | 38.8 | 9.0 | 79.1
2-3 | 1 | 50.0 | 18.2 | 31.8 | 2-11 | 1 | 7.4 | 50.7 | 41.9
2 | 24.5 | 15.2 | 60.3 | 2 | 12.6 | 56.3 | 31.1
3 | 11.9 | 9.0 | 79.1 | 3 | 10.4 | 44.8 | 44.8
2-4 | 1 | 7.4 | 24.3 | 68.2 | 2-12 | 1 | 37.2 | 35.1 | 27.7
2 | 11.3 | 9.9 | 78.8 | 2 | 22.5 | 27.8 | 49.7
3 | 4.5 | 9.0 | 86.6 | 3 | 16.4 | 22.4 | 61.2
2-5 | 1 | 33.1 | 27.0 | 39.9 | 2-13 | 1 | 63.5 | 10.8 | 25.7
2 | 29.1 | 24.5 | 46.4 | 2 | 58.3 | 11.3 | 30.5
3 | 13.4 | 20.9 | 65.7 | 3 | 53.7 | 10.4 | 35.8
2-6 | 1 | 18.2 | 11.5 | 70.3 | 2-14 | 1 | 27.7 | 29.7 | 42.6
2 | 9.9 | 6.0 | 84.1 | 2 | 11.9 | 25.2 | 62.9
3 | 9.0 | 1.5 | 89.6 | 3 | 13.4 | 14.9 | 71.6
2-7 | 1 | 14.9 | 20.9 | 64.2 | 2-15 | 1 | 38.5 | 25.0 | 36.5
2 | 19.2 | 5.3 | 75.5 | 2 | 38.4 | 30.5 | 31.1
3 | 16.4 | 6.0 | 77.6 | 3 | 34.3 | 17.9 | 47.8
2-8 | 1 | 3.4 | 17.6 | 79.1 | 2-16 | 1 | 50.0 | 21.6 | 28.4
2 | 5.3 | 2.6 | 92.1 | 2 | 35.1 | 36.4 | 28.5
3 | 6.0 | 4.5 | 89.6 | 3 | 47.8 | 22.4 | 29.9
Table 17:  Share of responses to all items of domain 3 that are in line with scientific views ($+$), opposing scientific views ($-$) or abstained form voting ($\circ$), for all three cohorts. Item | Cohort | $-$ | $\circ$ | $+$ | Item | Cohort | $-$ | $\circ$ | $+$
---|---|---|---|---|---|---|---|---|---
3-1 | 1 | 0.0 | 14.2 | 85.8 | 3-9 | 1 | 35.1 | 20.9 | 43.9
2 | 2.0 | 2.0 | 96.0 | 2 | 33.1 | 15.2 | 51.7
3 | 1.5 | 0.0 | 98.5 | 3 | 35.8 | 10.4 | 53.7
3-2 | 1 | 48.6 | 14.2 | 37.2 | 3-10 | 1 | 17.6 | 32.4 | 50.0
2 | 28.5 | 7.3 | 64.2 | 2 | 13.9 | 23.2 | 62.9
3 | 10.4 | 6.0 | 83.6 | 3 | 7.5 | 17.9 | 74.6
3-3 | 1 | 6.8 | 25.0 | 68.2 | 3-11 | 1 | 18.2 | 10.1 | 71.6
2 | 6.6 | 4.6 | 88.7 | 2 | 26.5 | 11.3 | 62.3
3 | 4.5 | 0.0 | 95.5 | 3 | 14.9 | 9.0 | 76.1
3-4 | 1 | 43.9 | 18.9 | 37.2 | 3-12 | 1 | 25.0 | 14.2 | 60.8
2 | 29.1 | 22.5 | 48.3 | 2 | 15.9 | 8.6 | 75.5
3 | 37.3 | 13.4 | 49.3 | 3 | 11.9 | 6.0 | 82.1
3-5 | 1 | 25.0 | 14.9 | 60.1 | 3-13 | 1 | 35.8 | 20.9 | 43.2
2 | 25.8 | 25.8 | 48.3 | 2 | 43.0 | 20.5 | 36.4
3 | 19.4 | 11.9 | 68.7 | 3 | 34.3 | 11.9 | 53.7
3-6 | 1 | 14.2 | 21.6 | 64.2 | 3-14 | 1 | 25.7 | 28.4 | 43.2
2 | 9.3 | 7.3 | 83.4 | 2 | 18.5 | 21.9 | 59.6
3 | 1.5 | 3.0 | 95.5 | 3 | 11.9 | 14.9 | 73.1
3-7 | 1 | 39.9 | 10.8 | 49.3 | 3-15 | 1 | 43.9 | 18.9 | 37.2
2 | 42.4 | 8.6 | 49.0 | 2 | 33.1 | 22.5 | 44.4
3 | 28.4 | 4.5 | 67.2 | 3 | 26.9 | 11.9 | 61.2
3-8 | 1 | 0.0 | 22.3 | 77.7 |  |  |  |  |
2 | 6.0 | 2.0 | 92.1 |  |  |  |
3 | 1.5 | 1.5 | 97.0 |  |  |  |
Table 18:  Share of responses to all items of domain 4 that are in line with scientific views ($+$), opposing scientific views ($-$) or abstained form voting ($\circ$), for all three cohorts. Item | Cohort | $-$ | $\circ$ | $+$ | Item | Cohort | $-$ | $\circ$ | $+$
---|---|---|---|---|---|---|---|---|---
4-1 | 1 | 29.7 | 31.8 | 38.5 | 4-5 | 1 | 38.5 | 48.0 | 13.5
2 | 30.5 | 37.1 | 32.5 | 2 | 28.5 | 45.0 | 26.5
3 | 25.4 | 29.9 | 44.8 | 3 | 47.8 | 26.9 | 25.4
4-2 | 1 | 21.6 | 21.6 | 56.8 | 4-6 | 1 | 17.6 | 43.9 | 38.5
2 | 13.9 | 43.0 | 43.0 | 2 | 16.6 | 44.4 | 39.1
3 | 13.4 | 29.9 | 56.7 | 3 | 9.0 | 20.9 | 70.1
4-3 | 1 | 39.2 | 36.5 | 24.3 | 4-7 | 1 | 20.9 | 47.3 | 31.8
2 | 30.5 | 48.3 | 21.2 | 2 | 20.5 | 48.3 | 31.1
3 | 37.3 | 34.3 | 28.4 | 3 | 26.9 | 32.8 | 40.3
4-4 | 1 | 10.8 | 51.4 | 37.8 | 4-8 | 1 | 36.5 | 41.9 | 21.6
2 | 5.3 | 45.7 | 49.0 | 2 | 36.5 | 55.0 | 11.9
3 | 10.4 | 26.9 | 25.4 | 3 | 41.8 | 44.8 | 13.4
Table 19:  Share of responses to all items of domain 5 that are in line with scientific views ($+$), opposing scientific views ($-$) or abstained form voting ($\circ$), for all three cohorts. Item | Cohort | $-$ | $\circ$ | $+$ | Item | Cohort | $-$ | $\circ$ | $+$
---|---|---|---|---|---|---|---|---|---
5-1 | 1 | 20.3 | 10.8 | 68.9 | 5-5 | 1 | 15.5 | 14.4 | 69.6
2 | 13.9 | 7.9 | 78.1 | 2 | 18.5 | 12.6 | 68.9
3 | 4.5 | 7.5 | 88.1 | 3 | 11.9 | 7.5 | 80.6
5-2 | 1 | 14.2 | 10.8 | 75.0 | 5-6 | 1 | 38.5 | 22.3 | 39.2
2 | 13.9 | 8.6 | 77.5 | 2 | 19.2 | 6.6 | 74.2
3 | 9.0 | 7.5 | 83.6 | 3 | 9.0 | 4.5 | 86.6
5-3 | 1 | 10.8 | 18.2 | 70.9 | 5-7 | 1 | 45.9 | 29.1 | 25.0
2 | 13.2 | 9.9 | 76.8 | 2 | 39.1 | 19.2 | 41.7
3 | 4.5 | 7.5 | 88.1 | 3 | 25.4 | 19.4 | 55.2
5-4 | 1 | 14.9 | 21.6 | 63.5 |  |  |  |  |
2 | 30.5 | 15.9 | 53.6 |  |  |  |
3 | 19.4 | 10.4 | 70.1 |  |  |  |