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Citation: Sebald, J.; Fliegauf, K.;
Veith, J.M.; Spiecker, H.;
Bitzenbauer, P. The World through
My Eyes: Fostering Students’
Understanding of Basic Optics
Concepts Related to Vision and
Image Formation. Physics 2022,4,
1117–1134. https://doi.org/
10.3390/physics4040073
Received: 9 August 2022
Accepted: 7 September 2022
Published: 22 September 2022
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Article
The World through My Eyes: Fostering Students’ Understanding
of Basic Optics Concepts Related to Vision and Image Formation
Janika Sebald 1,* , Kai Fliegauf 1, Joaquin M. Veith 2, Henrike Spiecker 1and Philipp Bitzenbauer 1
1Didaktik der Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7,
91058 Erlangen, Germany
2Institut für Mathematik und Angewandte Informatik, Stiftungsuniversität Hildesheim, Samelsonplatz 1,
31141 Hildesheim, Germany
*Correspondence: janika.sebald@fau.de
Abstract:
Prior research has shown that many secondary school students have a insufficient con-
ceptual understanding of basic optics concepts even after formal instruction. In this paper, we
empirically investigate whether a phenomenological approach might be a sensible alternative to
traditional model-based instruction of introductory optics in early physics education. We report
the results of a quasi-experimental field study to examine the effect of a phenomenological ap-
proach following the Erlangen teaching–learning sequence of introductory optics on
N=
42 eight
graders’ acquisition of conceptual understanding related to (1) the process of vision, (2) refraction,
and
(3) image
formation by converging lenses. We contrast the learning outcomes with those of
N=
55 control group students who participated in traditional model-based instruction. The results
of this study indicate that the phenomenological approach is superior to traditional (model-based)
instruction in promoting students’ conceptual understanding of basic optics concepts, in particular
with regard to circumventing widespread learning difficulties related to image formation. Our results
are further substantiated by a comparison of students’ situational interest in optics between both
groups. This adds further arguments in favor of the use of phenomenological approaches when it
comes to teaching basic optics concepts in classroom practice.
Keywords: optics; vision; image formation; secondary school; phenomenology
1. Introduction
Optics is a key element of physics education at the secondary school level. Topics
in early secondary school education range from the observation of shadow phenomena
and refraction to image formation by converging lenses. In traditional classroom teaching,
it is common practice to introduce students to optics topics based on the ray model of
light, e.g., in order to construct the image of an object (see Section 2.1). This model-based
approach poses some well-researched learning difficulties that impede students’ learning of
introductory optics topics (see Section 2.2), e.g., because light rays are erroneously assigned
a haptic ontology [
1
,
2
]. Phenomenological approaches provide a promising alternative to
model-based instruction of introductory optics (see Section 2.3) since many authors regard
these fruitful to (a) circumvent widespread learning difficulties and (b) foster students’
interest in science topics (see Section 2.5). In this paper, we introduce a teaching–learning
sequence that allows for a phenomenological approach to optics topics in early secondary
school physics education (see Section 2.4). From Section 3onward, we report and discuss
the results of a quasi-experimental study comparing the effect of this phenomenological ap-
proach on students’ conceptual understanding of introductory optics topics with traditional
model-based instruction.
Physics 2022,4, 1117–1134. https://doi.org/10.3390/physics4040073 https://www.mdpi.com/journal/physics
Physics 2022,41118
2. Research Background
2.1. Optics in Early Physics Education
The teaching of optics in early secondary school is confined chiefly to the field of
geometrical optics [
3
]. The key tool for describing and explaining a wide variety of optical
phenomena is the ray model of light, which enables geometric constructions, e.g., in the
context of image formation: students learn about ray constructions, for example, in order
to predict experimental results or to explain optical phenomena (see [4]).
In many school textbooks, a distinction is made between artificial and natural light
sources, which “does not contribute to the understanding of the process of vision and [
. . .
]
creates additional cognitive complexity" ([
5
], p. 12). However, traditional introductory
optics instruction does not place sufficient emphasis on the process of vision [
5
], which
is a crucial aspect of learning optics: for example, previous research has shown that an
understanding of the process of vision can be considered a necessary prerequisite for
developing a conceptual understanding of further optics topics [3,6].
In the course of traditional optics lessons, aspects such as reflection or refraction and
image formation are treated based on the ray model of light (see [
5
]). Abstract representa-
tions are often complemented by formalization: for example, students are introduced to the
lens equation. Prior research has questioned this tradition of introducing students to optics:
for example, traditional optics instruction has been referred to as optics “for the blindman”
(translated from [7], p. 2).
2.2. Widespread Learning Difficulties in Introductory Optics: A Brief Overview
Optical phenomena are omnipresent in students’ everyday lives. Hence, teachers are
confronted with a multitude of misconceptions about
• the process of vision (see [8–10]),
• the properties of light (see [4,11,12]),
• light propagation (see [13]),
• refraction (see [14,15]),
• image formation (see [4,13,15–19]),
even after formal instruction [
4
]. In the following, we provide more detailed insights into
widespread learning difficulties regarding the process of vision (see Section 2.2.1) and
image formation by converging lenses (see Section 2.2.2).
2.2.1. Learning Difficulties Regarding the Process of Vision
Regarding the process of vision, the notion of an active eye scanning objects has been
repeatedly documented in previous research, see [
8
,
20
]. This conception is supported by
expressions such as “looking at” or “casting a glance at something”, which emphasize the
activity of the eye in human vision ([
4
], p. 59). In addition, it was found that some students
do not know that all objects are invisible in a completely darkened room. The reason
for such ideas resides in the students’ thinking that light had substance-like properties
and filled the space around light sources: consequently, many students who possess the
above-mentioned conception believe that objects appear bright because the light is incident
onto them and then “stays” on them, while disregarding the concept of light scattering. It
has further been shown that students believe that light of low intensity, in general, does
not reach the human eye at all [21].
2.2.2. Learning Difficulties Regarding Image Formation by Converging Lenses
The variety of learning obstacles related to the properties of light (see [
4
,
11
,
12
]),
light propagation (see [
13
]), and refraction (see [
14
,
15
]) consequently results in numerous
learning difficulties on the topic of image formation (see [
4
,
13
,
15
–
19
]). For example, many
students assume that the image of an object travels through the lens as a whole, while the
underlying principle of point-to-point-imagining remains unheeded [
4
]. As a consequence,
many students with the above difficulty postulate that
Physics 2022,41119
•
the image would be cropped at the edges if the diameter of a lens is smaller than the
object under investigation (see [22]),
• the diameter of the lens influences the image size (see [23]), or
• covering half of the lens would make half of the image disappear (see [24]).
Accordingly, the use of apertures is thought to decrease the size of the image [
25
].
Lastly, the left-right reversal of the image often remains unnoticed: many students only
are aware of a reversal of top and bottom when being asked ([
4
], p. 72) while not having
in mind that the image represents a point inversion of the object. Many of the above-
mentioned difficulties are probably caused by abstracting too early in introductory optics
classes since prior research has indicated that
•
the introduction of the ray model of light (and corresponding ray diagrams) from the
beginning, and
• the focus on a mathematical description at too early a stage of teaching
often results in students struggling with different optics concepts. For instance, refraction
and reflection become blurred for many students ([
20
], p. 280). As a result, reflection is
claimed to be the reason for image formation by converging lenses, rather than students
recognizing refraction as a possible cause [3].
A common difficulty for students is that the model character of light rays does not
become obvious. Thus, students often mistakenly assign haptic ontology to light rays [
1
].
The subsequent introduction of wave or particle models of light in physics classes is likely
to result in hybrid models among learners as a result [
26
]. Given the above, it hardly seems
surprising that students often have a poor conceptual understanding of optics topics despite
formal instruction. Therefore, alternative approaches to introducing optics to youngsters in
early secondary education taking into account the above-mentioned difficulties have been
published (see [
5
]). In particular, some authors have even proposed (mainly) model-free
approaches in which models of light “are almost entirely replacedby the precise observation
of images, the optical phenomena themselves” ([
27
], p. 2). A known representative of
such phenomenological teaching concepts on optics is An Optics of Visual Experience by
Maier [28,29].
2.3. Phenomenological Approaches in Science Education
The meaning of the term “phenomenological approach“ in teaching contexts is broad
and its use is heterogeneous. The description of open-ended, preconceptual, and phe-
nomenon - oriented science teaching unifies all ideas about this term [
30
]. Phenomeno-
logical approaches relate learning directly to the observation and analysis of phenomena:
“Phenomenology [. . . ] emphasises the attempt to get to the truth of matters, to describe
phenomena, in the broadest sense as whatever appears in the manner in which it appears,
that is as it manifests itself to consciousness, to the experiencer. As such, phenomenology’s
first step is to seek to avoid all misconstructions and impositions placed on experience in
advance, whether these are [.. . ] from everyday common sense, or, indeed, from science
itself. Explanations are not to be imposed before the phenomena have been understood
from within” ([31], p.4).
Phenomenological approaches have a long tradition and represent a possible response
to widespread problems in science education: proponents of phenomenological teaching
often demand more time for (1) observations, descriptions, or reflections on what students
have experienced and (2) subsequent discussions of students’ various interpretations [
30
].
It is criticized that traditional teaching in science subjects, especially in physics, often
mainly leads to reproduced technical language or formulas, conceptual misunderstandings
(especially with regard to models), or reduced sensitivity to natural phenomena [
30
]. In con-
trast, in phenomenological approaches, teaching is based on asking questions, considering
all possible answers formulated by the students, and carefully perceiving phenomena.
Phenomenological approaches have been pursued for a long time. For example, already
Wagenschein [
32
] (see English translation [
33
]) demanded phenomena to stand at the begin-
ning of learning science, unimpeded by technical language, mathematization, or models.
Physics 2022,41120
From the pedagogical point of view, a step-by-step abstraction only makes sense if the
preceding results are sufficiently well-founded [
32
,
33
]. In this context, it is noteworthy that
phenomenological and model-based instruction are not mutually exclusive: Instead, in the
course of teaching “the teacher can move along that continuum, guiding students from
exploratory to more theory-laden experiments, from inductive to deductive reasoning, from
descriptive to explanatory modeling, and from their everyday world to the world of physics.
Thus, physics instruction may be phenomenon-based and model-oriented” [34] (p. 8).
In the context of teaching and learning optics, prime examples for the use of phe-
nomenological ideas can be found and the essentials of phenomenological teaching ap-
proaches can easily be understood considering optics teaching (see [
27
–
29
,
35
]). Grebe-
Ellis, an author of key contributions to this field [
7
,
36
], sees a break in the explanation
of phenomena in traditional classroom instruction, e.g., by means of light rays that are
deflected, reflected, or scattered. The students see “no refraction of rays, but bending
shadow edges” (translated from [
36
], p. 155). Phenomenological optics, in contrast, is
guided by questions such as “what do we see?” and “what are the conditions for what we
see?”. Hence, despite the phenomenon being at the center of the lesson, phenomenological
approaches also enable us to link theory and practice in science education [
37
]. In particu-
lar, it has been shown that “phenomenology and science education meet most fruitfully
when phenomenology is done, when it is turned into actual efforts for understanding and
promoting learning” ([30], p. 115).
The use of phenomenology in teaching practice seems particularly natural in the
context of optics. In Section 2.4, we present a phenomenological teaching–learning sequence
for introductory optics in which learners explore phenomena in optics in a hands-on way,
and which aims to circumvent learning difficulties that are widespread among students
who have participated in (model-based) traditional teaching (see Section 2.2).
2.4. A Phenomenological Approach to Introductory Optics: The Erlangen Teaching–Learning Sequence
The “Erlangen teaching–learning sequence of introductory optics” [
27
] is a phenomeno-
logical teaching concept developed for introductory optics education in secondary school
(grade 7/8, depending on national curricula). The teaching concept can be taught in at
least ten school lessons of 45 min or five lessons of 90 min and is divided into four chapters:
(i) Vision and brightness, (ii) Refraction and apparent depth, (iii) The look through a prism,
and (iv) The images of a converging lens. A detailed overview of the teaching–learning
sequence is provided in [27]. Hence, we only sketch the key ideas in the following.
2.4.1. Vision and Brightness
The pupils are introduced to optics by the distinction between optical and haptic
perceptions of the human senses. They become aware that the visual and the tactile sense
do not always coincide. The transmitter–emitter–receiver concept is established to explain
the visual process [
5
] based on this: on the one hand, the students learn to distinguish
two different sources of light (emitting sender and re-emitting sender). On the other
hand, “vary the visual contact between each other and conclude that light always travels
in a straight direction—at least, this turns out to be the case for only one surrounding
medium” ([27], p. 6)
. In addition, the students realize “that brightness varies as they move
through the
room” ([27], p. 5)
and “the conditions that make a surface appear bright and
in a certain colour to us are discussed” ([27], p. 6).
2.4.2. Refraction and Apparent Depth
The second chapter focuses on the principle of light refraction. The students approach
this topic by performing experiments on apparent depth: they observe a coin in a basin
of water by means of a straw, which they place obliquely on the edge. Pushing a skewer
through the straw the coin is not hit. In this way, the pupils derive further evidence of the
discrepancy between visual and tactile space. The explanation for what has been observed
can be summarized using the principle of light refraction: for this purpose, the students
Physics 2022,41121
observe the kink shadow on the boundary surface of an aquarium. Finally, they formulate
preconditions for the occurrence of the optical phenomenon of light refraction.
The explanation for what is seen is summarized in the principle of light refraction.
For this purpose, the pupils observe the bending shadow at the boundary surface of
an aquarium. Finally, they formulate requirements for the optical phenomenon of light
refraction to occur.
2.4.3. The Look Through a Prism
In this chapter, the students build water prisms themselves using overhead film and
a glass slide. A description of how to build these water prisms can be found in [
27
].
Looking through the water prisms held at different distances and different observation
angles from an object, the pupils recognize a shift in the image of varying magnitude.
In partner work, two oppositely oriented prisms are put together—this constellation
paves the way towards the introduction of the converging lens in the last chapter of
the teaching–learning sequence.
2.4.4. The Images of Converging Lens
At the beginning of this last chapter, the students produce their own self-made optics
inventory according to craft instructions provided by [
27
]—hands-on from low-cost every-
day materials. Among others, they fabricate self-made liquid lenses, apertures, and optical
benches made from a cable duct [27,38].
In a first exploration, the students take a look through their self-made lenses slowly
varying object distance. In this way, the students anticipate principles underlying image
formation by the converging lens. As is common in phenomenological teaching concepts,
the transition from the experimenter’s being part of the experiment (students’ view through
the lens) to the experiment being detached from the experimenter is made subsequently:
“the students are asked to map a sharp image of the sender that is (a) in original size,
(b) enlarged and, lastly, (c) downsized” ([
27
], p. 9) and the experimental results may be
used to derive that “an object width
g
is always coupled with a certain image width
b
in order to get a sharp image” ([
27
], p. 9). In the following, the students produce and
use different apertures to investigate the relations between object, lens, and image and to
further elaborate on the conditions, under which sharp and bright images can be observed
on the screen. Finally, the connection is made to the introduction of the process of vision
discussed in chapter one: using a self-made lens with variable curvature according to the
proposal of [
39
], the eye’s accommodation is explored. This brings us full circle to the
introduction of the Erlangen teaching–learning sequence of introductory optics.
In summary, the Erlangen teaching–learning sequence of introductory optics is a
hands-on phenomenological approach aimed at introductory physics education in sec-
ondary schools. As such, it meets the condition formulated in [
30
] according to which
doing phenomenology is likely to be conducive to learning. The extent to which this
(model-free) phenomenological teaching concept to optics actually implies stronger learn-
ing efficacy than traditional (model-based) instruction is empirically investigated in this
paper (
see Section 3
onward). However, despite fostering students’ understanding of intro-
ductory optics the hands-on approach also seems promising in terms of fostering students’
situational interest in science in general, and in optics in particular. We elaborate more on
this in Section 2.5 just below.
2.5. Situational Interest
For the situational interest, we follow Ref. [
40
] and conceive it as a “short term
preference which can be generated by particular conditions such as a demonstration of
a discrepant event or a novel hands-on experiment”([
40
], p. 2153). Situational interest
has already been researched extensively and three key statements have emerged from this
research: first, situational interest shows a positive correlation with students’ attention.
Second, it is positively correlated with learning outcomes in general, and third, students’
Physics 2022,41122
situational interest is influenced by a variety of different factors, e.g., students’ prior
knowledge in a given domain, see [41].
A number of authors have already observed high situational interest in a given topic
among students who have learned within learning environments that foster students’
experience of autonomy, e.g., by providing students with choices and control over their
work [42]
. Palmer [
43
] showed that students’ situational interest was higher when they
were involved in the observation, performance, and explanation phases of experimenta-
tion. Furthermore, hands-on experiments have been found likely to lead to a high situa-
tional interest in a topic under investigation among students [
40
,
43
]. The findings from
Blankenburg [44]
and Swarat [
45
] further support these results, since both authors have
found higher situational interest among students who worked on hands-on experiments.
The question remains as to whether or not a phenomenological approach to introduc-
tory optics according to the Erlangen teaching–learning sequence may lead to a higher
situational interest in optics among students than traditional instruction (see Section 3).
3. Research Questions
The purpose of this study is to examine the extent, to which a phenomenological
(model-free) approach to introductory optics in early secondary school physics following
the Erlangen teaching–learning sequence, can help (1) improve students’ conceptual under-
standing of introductory optics topics and (2) lead to a higher situational interest in optics
compared to traditional (model-based) instruction. Hence, in this study, we approach a
clarification of the following research questions (RQs):
RQ1:
How does the phenomenological teaching approach to introductory optics affect
students’ situational interest in optics compared to traditional instruction?
RQ2:
Which differences appear in students’ learning gains regarding the conceptual under-
standing of introductory optics topics, namely:
(a) the process of vision,
(b) refraction and apparent depth, and
(c) image formation,
when comparing the phenomenological teaching approach and traditional instruction
in German secondary schools?
4. Methods
4.1. Study Design and Sample
We conducted a field study aimed at contrasting the effect of the phenomenological
approach via the Erlangen teaching–learning sequence (intervention group, IG) on student
learning of introductory optics in early physics education in secondary schools in Germany
with that of the model-based traditional instruction (control group, CG). A detailed de-
scription and comparison of the intervention in both groups is provided in Section 4.2. The
study took place in the natural school setting to optimize the transferability of the empirical
findings to classroom practice. Therefore, we opted for cluster randomization [
46
], mean-
ing that whole school classes were randomly assigned to either the intervention group
(phenomenological approach) or the control group (traditional instruction). The classes
were taught by their regular teachers. The teachers were briefed prior to the study to ensure
a standardized approach. The study followed a pre–post test design to
analyze learners’
(a) situational interest (for the scale used in this study see Section 4.3.1), and (b) conceptual
understanding of optics (for the instrument see Section 4.3.2), in IG and CG at pre-test, and
post-test points in time (see Figure 1).
Physics 2022,41123
Intervention Group (IG)
N=42
Control Group (CG)
N=55
Pre-test
• Demographics
• Inventory on
introductory
optics
phenomenological
approach of
introductory optics
traditional
instruction on
introductory optics
Post-test
• Situational
Interest in optics
• Inventory on
introductory
optics
Figure 1. Overview of the study design. For a detailed description of all scales, see Section 4.2.
The sample comprised a total of
N=
97 eight graders from four classes of German
secondary schools. A detailed overview of the study sample in terms of IG and CG is given
in Table 1.
Table 1. Overview of the study sample. See text for detils.
Total Sample Intervention Group (IG) Control Group (CG)
(Phenomenological Approach) (Traditional Instruction)
Students 97 42 55
Teachers 3 2 1
Classes 4 2 2
Gender
males 51 19 32
females 40 22 18
not specified 6 1 5
Students’ and teachers’ participation in our study was voluntary and not financially
recompensed. The students were also informed about the anonymity and the processing of
their data and asked for their consent to participate.
4.2. Interventions
The interventions in both IG (phenomenological approach according to Erlangen
teaching–learning sequence; for a description, see Section 2.2) and CG (model-based tra-
ditional instruction) comprised a total of ten school lessons (45 min each). In both inter-
ventions, the same introductory optics topics were covered: vision, refraction, apparent
depth, and image formation by the converging lens—hence, the interventions did not differ
in terms of content. In addition, design features such as the use of media and the way
tasks are formulated were kept constant in order to highlight the difference between the
model-based and phenomenological approaches.
However, of course, the two interventions examined in our study differ with regards
to the approach taken to introduce students to the topics covered: the Erlangen teaching–
learning sequence of introductory optics used in the IG follows a (mainly model-free)
phenomenological approach. In contrast, traditional instruction is based on an early use of
the ray model of light and corresponding geometrical and mathematical abstractions, e.g.,
based on students completing hands-on experiments using ray boxes and lenses.
While the visual process in traditional teaching is usually only used as an introduction,
in the phenomenological teaching concept it is at the core of teaching optics. Still, the
transmitter–receiver concept for explaining human vision may be regarded as the concep-
tual interface between the two approaches. Table 2provides a summary of the differences
between and similarities of the two interventions used in IG and CG.
Physics 2022,41124
Table 2.
Conceptual differences between and similarities of the two interventions used in this study.
Phenomenological Approach to Optical Concepts, IG Traditional Optics Teaching, CG
Consistent treatment of the process of vision along the entire
sequence.
The process of vision as an introductory topic.
Transmitter–receiver concept of vision. Transmitter–receiver concept of vision.
Model-free treatment of apparent depth, refraction, and image
formation.
Use of the ray model of light for the explanation of light re-
fraction and for geometrical construction of image positions.
Experimental determination of dependencies between object
width, image width, and focal length of a converging lens
Mathematical description of image formation using the thin
lens formula.
4.3. Instrument
The questionnaire completed by the students consisted of two parts, P1 and P2:
P1:
Scale to assess students’ situational interest in optics (only post-test); for details, see
Section 4.3.1.
P2:
Concept inventory to assess students’ conceptual understanding of introductory
optics topics (pre-test and post-test); for details, see Section 4.3.2.
4.3.1. Assessment of Students’ Situational Interest
We adopted a 5-point rating scale (1 denotes the lowest trait level, 5 denotes the highest
trait level) comprising nine items to assess students’ situational (optics) interest from [
47
].
A sample item of the scale reads: “I would like to learn more about optics”. Cronbach’s
alpha [
48
] serves as a measure for the scale’s internal consistency and was found to be
α=0.90 in this study, where values above 0.7 are considered acceptable (cf. [49]).
4.3.2. Assessment of Students’ Conceptual Understanding of Introductory Optics
We used a concept inventory consisting of a total of 15 two-tier single-choice items to
assess students’ conceptual understanding of introductory optics topics. The items used in
this study have been adapted from the literature [
47
,
50
,
51
] and have already been used in
prior empirical research into teaching and learning introductory optics.
For each item, the students are asked to choose exactly one out of four answer options
in tier one. Furthermore, the students are asked to rate their confidence in the given answer
on a 5-point rating scale (1 reserved for “guessed”,
. . .
, 5 for “very confident”). A point
is awarded to the respondent for a specific test item if and only if (a) the correct answer
option was chosen in tier one and (b) the answer was given with confidence, meaning
that 4 or 5 had
to be marked on the rating scale in tier two. This coding scheme ensures
to minimize the effect of guessing [
52
–
55
], and hence, is “useful for gauging the quality
of students’ understanding” ([
55
], p. 3). Cronbach’s alpha as a measure for internal
consistency has been found to be satisfactory (α=0.71).
In terms of content, the items of the concept inventory are arranged in three content
domains as shown in Table 3.
Physics 2022,41125
Table 3.
Description of content domains covered in the concept inventory used in this study and the
corresponding items. See text for details.
Domain Descriptors Items
Process of vision
Light propagation, visibility of objects, sender-emission-
receiver-concept, shadow. 1, 2, 3, 4, 14, 15
Refraction and apparent depth
Apparent depth, definition of light refraction, distinction
between refraction and reflection. 5, 6, 7, 8, 9
Image formation by a converging lens
Real images of the converging lens, image size, brightness of
images. 10, 11, 12, 13
The items corresponding to the content of domain 1 (Process of vision) address the
visual process and focus on light propagation. In addition, different light sources are dealt
with, especially with respect to a distinction between emitting and re-emitting senders. The
last item of this domain covers shadow formation. A sample item for content domain 1 is
shown in Table 4.
Table 4. Item 2 of the test covering the visual process (see Table 3).
Item 2: Which of the following objects/animals can you see in a completely
darkened room?
A glowing firefly.
A white sheet of paper.
A bicycle reflector.
The eyes of a cat.
Very sure
Sure
Undecided
Unsure
Guessed
The items corresponding to content domain 2 (Refraction and apparent depth) deal
with the topic of light refraction. The main focus of the items is on the change of light
propagation at an interface. Moreover, the distinction between refraction and reflection is
addressed. A sample item for content domain 2 is shown in Table 5.
Table 5. Item 9 of the test covering straight light paths, refraction, and reflection (see Table 3).
Item 9: Comment on the following statement of a classmate: I do not
believe that light propagates in a straight line. If light falls obliquely on a
water surface, its direction of propagation changes.
I agree with the classmate. Light does not propagate in a straight line.
I do not agree with the classmate. When light hits a water surface, it is reflected.
I agree with the classmate. When light hits a water surface, it always passes
through in a straight line.
I do not agree with the student. The light is refracted at the water surface, but
then it propagates in a straight line again.
Very sure
Sure
Undecided
Unsure
Guessed
The items corresponding to content domain 3 (Image formation by a converging lens)
are used to examine students’ understanding of image formation using converging lenses.
In particular, students are asked to what extent the image of an object changes when the
Physics 2022,41126
lens aperture changes or part of the lens is occluded. A sample item for content domain 3
is shown in Table 6.
Table 6. Item 10 of the test covering the real image of a converging lens (see Table 3).
Item 10: What can you say about the image of an object produced by a
converging lens on a screen?
The image is upside down and side-inverted.
The image is upright and real.
The image is upside down and black and white.
The image is upright and in color.
Very sure
Sure
Undecided
Unsure
Guessed
4.4. Data Analysis
We provide an overview of IG and CG students’ situational interest and conceptual
understanding of introductory optics topics for both pre- and post-test points in time,
using descriptive statistics such as median, mean value
µ
, and standard deviation (SD).
We calculate non-parametric Mann–Whitney
U
-tests to test differences between IG and
CG students for statistical significance (for our research questions, see Section 3) due to
deviations of our data from a normal distribution. These nonparametric tests perform at up
to 95% of the test power of their parametric equivalents [
56
]. We report the Mann–Whitney
U-test statistics according to the APA (American Psychological Association) standards as
U(N) = (U,z,p),
where
U
is the test-statistic,
N
is the number of observations,
z
is the
z
-score, and
p
is the
p
-value; for details, see Ref. [
57
]. Each effect is considered statistically significant when
the p-value was below the 5% threshold, while
p
-values below the 10% threshold indicate
statistical significance by trend. We also report the effect of size measure in terms of the
biserial rank correlation,
r
, to judge the magnitude of statistically significant effects. Note
that for all statistics applied to our data, we only used data from those students who
completed all items of the corresponding instrument or scale, respectively.
In addition, we use Hake’s g[58] calculated as
g=postscore% −prescore%
1−prescore% , (1)
to compare IG and CG students’ pre-test and post-test results [
59
] in the optics concept
inventory. While the difference between post-test and pre-test scores does not provide a
reliable measure for students’ learning achievement at both ends of the scale, i.e., for high
and low performers [
60
], Hake’s normalized gain
g
is not biased by students’ pre-test results,
see [
59
]. The normalized gain
g
takes values below 1, while values of 0.30
≤g≤
0.70 may
be associated with a medium learning gain ([58], p. 65).
It is noteworthy that our study design, by including a cluster-randomized controlled
trial, implies that students’ learning process may be influenced by the social groups the
students belong to. We calculated the intraclass correlation coefficient (ICC) to quantify the
influence of students’ aggregation in classes by the proportion of variance explained at the
class level and found that only a small proportion of the variance is localized at the class
level (ICC
=
0.05). Since (1) the ICC lays well below the threshold of
0.10 ([61], p. 544)
and
(2) our sample only comprises two classes for intervention and control group, respectively,
we have refrained from multilevel analysis for our study.
Physics 2022,41127
5. Results
5.1. Results regarding RQ1
The situational interest averaged
µ=
3.58 (SD
=
0.84) with a median of 3.56 for the
IG and
µ=
2.82 (SD
=
0.90) with a median of 2.89 for the CG. A boxplot of the data is
provided in Figure 2. The difference in both groups was further verified to be statistically
highly significant by means of a Mann–Whitney
U
-test (
U(
76
) =
379,
z=
4.10,
p<
0.001).
The effect size r=0.47 is regarded medium according to [62].
1
2
3
4
5
Control Group Intervention Group
Sit. interest
Figure 2.
Boxplot of the situational interest for the intervention and control group (1 denotes the
lowest trait level, 5 the highest trait level). The two minima indicate the lowest data points in the set
and the maxima the highest. The boxes range from the 25th percentile to the 75th percentile while the
horizontal line indicates the median.
5.2. Results regarding RQ2
The pre-test score averaged
µ=
4.73 for CG and
µ=
4.24 for IG, while the post-test
score averaged
µ=
6.62 for CG and
µ=
7.93 for IG. A visualization of the change in
µ
for
both groups is provided in Figure 3. The median pre-test and post-test scores are provided
in Table 7alongside the statistics of two Mann–Whitney
U
-tests confirming that (a) the
groups’ pre-test scores did not differ statistically significant (
p=
0.47) and (b) there is a
significant difference by trend between the groups’ post-test scores.
Here, it is noteworthy to reiterate that a point was awarded in the post-test if and only
if the correct answer option was selected and additionally confident (rating scale 4) or very
confident (rating scale 5) was selected on the certainty scale. If uncertain (rating scale 3)
but correct answers are awarded a point as well, the difference in the groups’ average
scores becomes even more pronounced with
µ=
10.24 (SD
=
2.96) for IG and
µ=
8.12
(SD =2.70) for CG (U(55) = 210, z=3.29, p<0.01; r=0.44).
Table 7.
Descriptive statistics on pre-test and post-test scores for the intervention group (IG) and the
control group (CG). The maximum achievable score in the test was 15 points. See text for deatails.
Group Median SD Mann–Whitney-U p r
Pre-test CG 5.00 2.54 U(55) = 334, 0.47 -
IG 4.00 2.49 z=0.85
Post-test CG 7.00 3.02 U(55) = 276, <0.1 0.27
IG 8.00 3.24 z=2.00
Physics 2022,41128
µ
4
5
6
7
8
9
Pre-test post-test
CG
IG
Figure 3.
Change in average test score,
µ
, for the intervention group (IG) and the control group
CG). The error bars indicate three times standard error.
Figure 4shows the students’ score distribution in the post-test for IG as well as CG.
Score
012345678910 11 12 13 14 15
Percentage
4%
8%
12%
16%
20%
24%
CG
IG
Figure 4.
The students’ score distribution in the post-test for the intervention group (IG) and the
control group (CG).
The students’ learning gains for each of the three domains (see Table 3) as well as
the total learning gain expressed by Hake’s
g
are provided in Table 8. A Mann–Whitney
U
-test further verifies that the groups statistically differ regarding
gtotal
and
gimage
while
the difference is not statistically significant in the first two domains (see Table 8).
Physics 2022,41129
Table 8.
Normalized learning gains
gvision
,
grefraction
and
gimage
regarding the different domains such
as process of vision (domain 1), refraction and apparent depth (domain 2), and image formation by a
converging lens (domain 3), respectively. See Table 3and text for details.
gvision grefraction gimage gtotal
µ(CG) 0.08 0.21 0.11 0.17
µ(IG) 0.27 0.30 0.47 0.36
Median (CG) 0.20 0.25 0.00 0.24
Median (IG) 0.25 0.29 0.50 0.39
Mann–Whitney UU(
56
) =
320,
z=
1.30,
p=0.27
U(
61
) =
432,
z=
0.55,
p=0.64
U(
61
) =
182,
z=
4.73,
p<0.001
U(
55
) =
229,
z=
2.91,
p<0.05
r- - 0.61 0.39
In Figure 5, the difference in the groups’ learning gains is illustrated by a boxplot for
each domain.
g
−0.5
0
0.5
1
Domain 1 Domain 2 Domain 3 Total
CG
IG
Figure 5.
Boxplots of the learning gain (Equation (1)) for each of the three domains (see Table 3) as
well as the total learning gain for the intervention group (IG) and the control group (CG).
6. Discussion
6.1. Discussion of RQ1
We observed a statistically significant difference in students’ situational interest in op-
tics between IG and CG (
U(
74
) =
276,
z=
4.10,
p<
0.001;
r=
0.47). In both interventions,
the same topics have been covered, and hence, this result is not an artifact of different top-
ics. However, it seems that the (model-free) phenomenological approach using hands-on
experiments in the intervention group (following the Erlangen teaching–learning sequence
of introductory optics [
27
]) indeed led to higher situational interest among students than
traditional model-based instruction. In this respect, the findings presented in this study
add further evidence according to which students’ situational interest may be increased
by hands-on experiments [
44
,
45
,
63
]. This is of particular interest for science introduction
since “regular experiences of situational interest in a subject may eventually lead to the
development of individual interest in that subject” ([64], p. 731).
6.2. Discussion of RQ2
No significant difference between the pre-test results of the IG and CG students was
found (
p=
0.47). After instruction, an increase in students’ conceptual understanding of
Physics 2022,41130
basic optics topics was observed in both groups. However, the IG students (
median =8.00
,
µ=7.93
,
SD =3.24
) outperform the CG students (median
=
7.00,
µ=
6.62, SD
=
3.02).
This difference is statistically significant by trend (
U(
55
) =
276,
z=
2.00,
p<
0.1;
r=
0.27).
This result has been obtained by only awarding points in the concept test if and only if the
correct answer option was selected with (high) confidence. By loosening up this coding
scheme, this finding can become even more prominent: the difference in post-test scores
between IG and CG students is found to be highly significant if points are also awarded for
correct answers where the students state to be undecided (
U(
55
) =
210,
z=
3.26,
p<
0.01;
r=0.44).
The total normalized gain among the IG students was
gTotal =
0.36
(SD =0.24)
.
Specifically, the difference to the one in the CG at
gTotal =
0.17 (SD
=
0.31) is statistically
significant (
U(
55
) =
229,
z=
2.91,
p<
0.05;
r=
0.39). The normalized learning gain in
the IG can be regarded medium and comparable to the ones found in prior projects using
similar research designs in different contexts (cf. 0.40
±
0.21 in [
60
] (p. 8), 0.48
±
0.14 in [
58
]
(p. 66)). Hence, our study reveals a positive impact of the phenomenological (model-free)
approach to introductory optics (following the Erlangen teaching–learning sequence) on
students’ conceptual understanding of basic optics concepts—in particular, in comparison
to traditional (model-based) instruction.
Analyzing the normalized learning gains for the three content domains, namely pro-
cess of vision (domain 1), refraction and apparent depth (domain 2), and image formation
(domain 3), we found the following: no statistically significant difference could be found for
the first two. In contrast, the average normalized learning gain regarding image formation
by converging lenses among the IG students (
gImage =
0.47, SD
=
0.30) was higher than
among the CG students (
gImage =
0.11, SD
=
0.31). This difference has been found to be
highly statistically significant (
U(
61
) =
182,
z=
4.73,
p<
0.001;
r=
0.61) with a large
effect size according to [62].
To substantiate this finding qualitatively, it is worth analyzing students’ answers to
the corresponding items in more detail. For example, in item 12 (see Table 3) of the concept
inventory, the students were asked what happens with the image if the lower half of the
converging lens is covered. While no significant differences in the IG and CG students
have been revealed at the pre-test point in time, in the post-test, we observe the following:
among the CG students, 15.38% were certain that the upper half of the image will be cut
off. In the IG that was the case for only 12.12% of the students. Another 20.51% of the
CG students were certain that the lower half of the image will be cut off—none of the IG
students voiced this opinion. However, 39.39% of the IG students gave the correct answer
with certainty: the image becomes darker. Only 10.26% of the CG students were certain
that this would be the correct answer option.
Similar observations are made when analyzing students’ answers regarding item 13
(see Table 3). In this item of the concept inventory, the students were asked what happens
with the image if an aperture with a very small diameter is placed in front of the lens. While
again no significant differences in IG and CG students have been revealed at the pre-test
point in time, in the post-test, we observe the following: among the CG students, 12.50%
were certain that the image becomes smaller. In the intervention group, that was the case
for none of the students. Another 25.00% of the CG students were certain that the edges
of the image would be cut off circularly, while only 3.03% of the IG students were of that
opinion. In contrast, 75.76% of the IG students gave the correct answer with certainty: also,
in this case, the image becomes darker. Only 5.00% of the CG students were certain that
this would be the correct answer option.
It is noteworthy that the above-given differences in students’ answers may not be
drawn back to differences in the interventions in both groups, since they did not differ
in terms of content, tasks, or media used. However, our results support the implication
that a phenomenological (model-free) approach is superior to traditional (model-based)
instruction in circumventing widespread learning difficulties related to image formation by
a converging lens among learners (see [4,13,15–19]).
Physics 2022,41131
7. Conclusion
7.1. Limitations
The study presented in this paper has some limitations that need to be tackled in
follow-up projects. First, our study was conducted in the field and we used a quasi-
experimental design. It is widely accepted that field studies lead to high external validity
and low internal validity compared to a experimental lab study, which is characterized by a
randomized distribution of the study participants between intervention and control groups.
Thus, in the case of experimental studies, it can be assumed that there is a neutralization of
person-specific confounding variables, such as self-concept, motivation, or interest [
65
]. In
contrast, in the case of quasi-experimental studies, there is a risk that such confounding
variables do not balance out between the comparison groups. As a result, the different
study groups may differ systematically. The (significant) differences found in a study
with regard to the dependent variables can then no longer be conclusively attributed to
differences in the independent variables. As a result, a quasi-experimental study has a
lower internal validity compared to an experimental study.
Second, to get in-depth insights into the success of the Erlangen teaching–learning
sequence of introductory optics, the analysis of more covariates from the participating
students, classes, and teachers seems valuable. Specifically, we believe that taking into
account interactions of student learning and students’ affective characteristics, so-called
aptitude–treatment interactions [
66
], might influence the learning effectiveness of the inter-
vention. Furthermore, in our study the gender distribution among the study participants
was unbalanced. Hence, we believe that future research should take particular attention to
the gender sensibility of our proposed teaching approach.
Third, in this study, we explored the advantages of the phenomenological approach
for teaching introductory optics in early physics education exclusively with respect to
students’ learning gain and students’ situational interest. Although we found evidence that
this new approach is superior to traditional model-based instruction in this respect, further
research is needed with respect to the students’ conceptions acquired about introductory
optics topics. Therefore, we believe qualitative methods will enable comprehensive insights
into student thinking. In particular, we are interested as to whether our phenomenological
approach will help circumvent learning difficulties documented in the literature that are
widespread in traditional model-based instruction (see Section 2.2).
7.2. Outlook
In this study, we found empirical evidence for a phenomenological approach in teach-
ing introductory optics being superior to traditional model-based instruction with regards
to fostering (a) students’ conceptual understanding and (b) students’ (situational) interest.
Despite being restricted to the context of optics, i.e., not being generalizable to other sub-
jects, the study results presented in this paper support previous research results according
to which phenomenological (hands-on) teaching might serve as a fruitful endeavor for
science education in general (see Section 2.5). In future research, we aim at delving deeper
into the conceptions acquired by students’ introduced to introductory optics in the course
of the phenomenological approach proposed in this article, in particular, compared to the
ones acquired by students participating in traditional model-based instruction.
Author Contributions:
Conceptualization, J.S., K.F. and P.B.; methodology, J.S. and P.B.; formal analy-
sis, J.S.; investigation, J.S. and K.F.; writing—original draft preparation, J.S. and P.B.;
writing—review
and editing, J.S., K.F., J.M.V., H.S. and P.B.; visualization, J.M.V.; supervision, P.B. All authors have
read and agreed to the published version of the manuscript.
Funding:
We acknowledge financial support by Deutsche Forschungsgemeinschaft and Friedrich-
Alexander-Universität Erlangen-Nürnberg within the funding programme “Open Access Publica-
tion Funding”.
Physics 2022,41132
Institutional Review Board Statement:
Ethical review and approval were waived for this study due
to the fact that the study was in accordance with the Local Legislation and Institutional Requirements:
Research Funding Principles (https://www.dfg.de/en/research_funding/principles_dfg_funding/re
search_data/index.html) and General Data Protection Regulation (https://www.datenschutz-grun
dverordnung.eu/wp-content/uploads/2016/04/CONSIL_ST_5419_2016_INIT_EN_TXT.pdf). Both
links accessed on 18 September 2022.
Informed Consent Statement:
Informed consent was obtained from all subjects involved in the
study to publish this paper.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.
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