Developing students ideas about lens imaging: teaching experiments with an image-based approach

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1 Physics Education PAPER Developing students ideas about lens imaging: teaching experiments with an image-based approach To cite this article: Sascha Grusche 2017 Phys. Educ Related content - Seeing lens imaging as a superposition of multiple views Sascha Grusche - Identifying pre-service physics teachers misconceptions and conceptual difficulties about geometrical optics Derya Kaltakci-Gurel, Ali Eryilmaz and Lillian C McDermott - Optical transfer function analysis of single pinhole glasses Mohammad Abolhassani and Abolfazl Akbari View the article online for updates and enhancements. This content was downloaded from IP address on 11/04/2018 at 18:00

2 (9pp) P a p e r iopscience.org/ped Developing students ideas about lens imaging: teaching experiments with an image-based approach Sascha Grusche University of Education Weingarten, Physics Education, Kirchplatz 2, Weingarten, Germany saschagrusche@gmail.com Abstract Lens imaging is a classic topic in physics education. To guide students from their holistic viewpoint to the scientists analytic viewpoint, an image-based approach to lens imaging has recently been proposed. To study the effect of the image-based approach on undergraduate students ideas, teaching experiments are performed and evaluated using qualitative content analysis. Some of the students ideas have not been reported before, namely those related to blurry lens images, and those developed by the proposed teaching approach. To describe learning pathways systematically, a conception-versustime coordinate system is introduced, specifying how teaching actions help students advance toward a scientific understanding. S Supplementary material for this article is available online 1. Introduction We experience lens images daily: They appear on our retinas, camera sensors, and projection screens. Hence, lens imaging is a standard topic in the physics classroom, and students bring many ideas about lenses to it [1 7]. The traditional teaching approach to lens imaging is incompatible with students everyday understanding [2, 5]. Before instruction, students typically use a holistic image conceptualization: a whole image travels from the object through the lens to the screen [2]. During instruction, students practice a point-to-point conceptualization: the lens makes light from each object point converge to an image point [2]. After instruction, students typically use a hybrid conceptualization, called image projection : a single ray from each object point transfers an image point [2]. Many students misinterpret the geometric rays as particles or streams of light [2, 7], and struggle using lens ray diagrams [2, 5, 6]. To guide students from their holistic viewpoint to the scientists analytic viewpoint, an image-based approach has recently been proposed [8]. It is based on whole images projected by individual lens-points. First, students experience with their naked eyes that they cannot see background and foreground objects sharp at once. Then, they put a pinhole onto the eye to see everything sharp at once. Moving the pinhole across the eye, they see the foreground shift against the background. Next, the eye is modeled by a lens and screen (figure 1). An array of pinholes is placed onto the lens, producing an array /17/ $ IOP Publishing Ltd

3 S Grusche Figure 1. First stage of the main experiment. A matchbox in the background and toy car in the foreground are projected by a convex lens onto a translucent screen. (a) Setup. (b) At a particular screen distance, the lens image is sharp for the matchbox, but blurry for the toy car. (c) At some larger screen distance, the lens image is sharp for the toy car, but blurry for the matchbox. Figure 2. Second stage of the main experiment. The lens is covered with three pinholes, producing three sharp images from different viewpoints, so-called elemental images. (a) Elemental images on a screen near the lens. (b) Further from the lens, the elemental images coincide for the matchbox, but are mutually shifted for the toy car. (c) Even further from the lens, the elemental images coincide for the toy car, but are mutually shifted for the matchbox. of sharp images from different viewpoints (figure 2(a)). Moving the screen back and forth, students observe the superposition of these elemental images (figures 2(b) and (c)). Unless the elemental images coincide, the lens image is blurry. The superposition is modeled with transparencies or projectors. Rays are introduced as lines connecting the object and its elemental images with each pinhole at the lens. Finally, students construct ray diagrams based on elemental images [8]. This approach has been designed according to students well-known ideas, but might need to be adapted to students unknown ideas about blurry images. Thus, it was our goal to trace students ideas about blurry versus sharp lens images before, during, and after image-based experiments. We have recently done so with 7th graders [7]. In the present study, we explored undergraduate students ideas. 2. Theoretical framework and research questions 2.1. The Model of Educational Reconstruction According to the Model of Educational Reconstruction, the design of instruction requires a comparison between students and scientists ideas [9, 10]. To enable this comparison, ideas are described at corresponding levels of complexity. From low to high complexity, ideas are called concepts (elementary thought processes), conceptions (combinations of elementary thought processes), and conceptualizations (thinking patterns) [10]. 2

4 Developing students ideas about lens imaging 2.2. Research questions Using the Model of Educational Reconstruction, we can specify our research questions: 1. What kinds of ideas do German undergraduate students of physics education use to understand blurry versus sharp lens imaging? 1.1. Which conceptualizations do students use (before, during, or after image-based lens experiments)? 1.2. Which conceptions do students use to relate images to one another, or to rays (before, during, or after image-based lens experiments)? 1.3. What are students concepts regarding the key words ray and focal point (without specific intervention)? 2. What is the chronological sequence of the students ideas in relation to image-based lens experiments? In other words: Which learning pathways emerge? 3. Methods 3.1. Teaching experiment methodology To uncover students ideas about lens imaging, and to study the effect of an image-based approach, the teaching experiment methodology [11] was used. Here, the researcher acts both as an interviewer, and as a teacher. Thus, the researcher can learn about students ideas, and try planned or improvised teaching actions. Seven students (Anna; Ben; Chris; David and Edgar; Fabian and Gerd) took part in five teaching experiments. They talked about their knowledge on lenses, and discussed lens experiments. The main experiment was performed in two stages, see figures 1 and 2. At each stage, students were asked to predict, describe, and explain the phenomena. Afterwards, they were asked to indicate the rays. Around the main experiment, the teacher adapted to the students ideas. He explained as little as possible so the students could think for themselves. Each session (ca min) was video-recorded Qualitative content analysis To evaluate the teaching experiments, the education-oriented version of qualitative content analysis [9, 10] was used: Transcribing Selecting relevant utterances Writing down the spoken words Mentioning non-verbal acts in parentheses Editing Selecting meaningful passages Deleting redundant words Formulating autonomous student statements Removing grammatical errors Summarizing Grouping statements thematically Identifying inconsistencies Condensing equivalent propositions Ordering the statements Explicating Describing the student s understanding Interpreting word use Finding sources of ideas Identifying problems and interests Structuring meant distilling a student s concepts, conceptions, and conceptualizations. Finally, the individual students ideas were generalized by categorizing, looking for similarities and differences across students ideas. It was helpful to sketch the individual ideas, and to group similar sketches together. Several measures ensured validity. For selection validity [10], only regular undergraduate students of physics education were interviewed. For correlative validity [10], students ideas were matched, as far as possible, with those reported previously, and with the key ideas of the teaching approach. For procedural validity [10], a trustworthy atmosphere was created in the teaching experiments, the analysis was performed and documented stepwise, interpretations were based on multiple kinds of evidence and supported by 3

5 S Grusche (a) (b) (c) (d) Figure 3. Conceptions within the holistic image conceptualization. (a) Image change (). (b) Receiving eye (). (c) Vignetted image (). (d) Gathered images (). arguments, and the categorization was independently applied by, and discussed with, a colleague Describing learning pathways A useful method of describing learning pathways is to plot the level of sophistication versus time [12]. Unfortunately, descriptions are sometimes arbitrary regarding the level of sophistication (as in [13]), and often do not report on ( ) important instructional interventions [12]. For a more systematic description, a conception-versus-time diagram was developed for this study. To define levels of sophistication, the generalized conceptions were arranged according to a hypothetical learning progression from novice to expert conceptualizations, and in line with the empirical trend. To describe crucial teaching actions, these were generalized and marked along the time axis. Individual conceptions were represented by points in this coordinate system. 4. Results 4.1. Students conceptualizations Overall, students used four conceptualizations: Holistic image. A whole image travels from an object through the lens. Lens image projection. A single ray from each object point goes through the lens to the lens image. Elemental image projection. A single ray from each object point goes through a given lens-point to the corresponding elemental image point. Point-to-point. Light diverging from an object point is made to converge to an image point. Additionally, some students considered a wave interference conceptualization, whereby waves interfere to produce a sequence of sharp and blurry images. We will neglect this conceptualization because our approach is about rays, not waves Students conceptions Within the four conceptualizations, students used the following key conceptions: Conceptions within the holistic image conceptualization Image change (). The lens changes the size or orientation of an image coming from the object (figure 3(a)). Receiving eye (). The image on the screen corresponds to the view from the screen (figure 3(b)). Vignetted image (). Partly covering the lens removes the image partly (figure 3(c)). Gathered images (). The lens collects images sent out by the object (figure 3(d)). Conceptions within the lens image projection conceptualization Image spots (). A blurry image comprises image spots (figure 4(a)). Crossing rays (). Rays from the edges of object and lens are made to cross behind the lens so the image is inverted (figure 4(b)). Eye analogy (). The lens and screen correspond to the eye lens and retina (figure 4(c)). Pinhole model (). Rays from the object pass straight through a lens-point toward the image (figure 4(d)). Focused rays (). The image is blurry unless rays behind the lens are brought to a point (figure 4(e)). 4

6 Developing students ideas about lens imaging (a) (b) (c) (d) (e) Figure 4. Conceptions within the lens image projection conceptualization. (a) Image spots (). (b) Crossing rays (). (c) Eye analogy (). (d) Pinhole model (). (e) Focused rays (). (a) (b) (c) (d) (e) Figure 5. Conceptions within the elemental image projection conceptualization. (a) Sharpened image (). (b) Mutual shift (). (c) Different arrangements (). (d) Lens-point as viewpoint (). (e) Rays through lens-point (). (a) (b) (c) Figure 6. Conceptions within the point-to-point conceptualization. (a) Darkened image (). (b) Aperture image (). (c) Diverging and converging (). Conceptions within the elemental image projection conceptualization Sharpened image (). Partly covering the lens sharpens the blurry lens image (figure 5(a)). Mutual shift (). The more the elemental images from different lens-points are separated, the blurrier the lens image (figure 5(b)). Different arrangements (). Elemental images from different lens-points differ in composition (figure 5(c)). Lens-point as viewpoint (). The elemental image on the screen represents the view through (or from) the corresponding lenspoint (figure 5(d)). Rays through lens-point (). Rays from various object points go through a given lenspoint to the corresponding elemental image points (figure 5(e)). Conceptions within the point-to-point conceptualization Darkened image (). Covering part of the lens makes the lens image darker (figure 6(a)). Aperture image (). Before or after converging to an image point, light from an object point forms an image of the lens aperture (figure 6(b)). 5

7 S Grusche Diverging and converging (). Rays diverging from an object point are made to converge to an image point (figure 6(c)) Students concepts Students used three ray concepts and two concepts of a focal point: Concepts of a ray Light particle. A ray is a traveling part of light. Light stream. A ray is a narrow bundle of traveling light. Light trajectory. A ray is a path of traveling light. Concepts of a focal point Intersection of parallel rays. The focal point is where formerly parallel rays are converging. Image point. The focal point is where rays from an object point are converging Students learning pathways Overall, students learning pathways were guided by the following teaching actions: Moments of prepared teaching actions Asking a student to explain blurriness (T B ) Having a student look through a pinhole on the eye (T O ) Having a student move a pinhole across the eye (T A ) Placing one or more pinholes onto the lens (T P ) Moving a pinhole across the lens (T M ) Asking a student to compare elemental images (T E ) Moving the screen with the elemental images (T S ) Asking a student to identify the viewpoint for an elemental image (T V ) Asking a student to explain the different sharpness for background and foreground (T D ) Prompting a student to think of images instead of rays (T T ) Asking a student to indicate rays, based on the main experiment (T R ) Moments of improvised teaching actions Analogizing the lens and screen with the eye (t a ) Asking whether only one ray goes to the lens from each object point (t r ) Moving a sheet of paper across the lens (t x ) Asking what will appear on a screen near the uncovered lens (t n ) Presenting a blurry lens image without comment (t b ) Encouraging a student to abandon a previous conception (t e ) Covering half of the lens (t h ) Correcting the position of an elemental image in a student s drawing (t d ) Lighting a candle near a projection screen (t l ) With these teaching actions, students developed scientifically adequate conceptions. The learning pathways were similar, leading from the holistic image conceptualization through lens image projection and elemental image projection to the point-to-point conceptualization, see figures 7(a) (g). For verbal descriptions of all learning pathways, see the supplementary data (stacks.iop.org/physed/52/044002/mmedia). 5. Discussion 5.1. Ideas uncovered and developed We found all of the well-known conceptualizations [2]: holistic image, image projection, and point-to-point. For image projection, we identified two versions: lens image projection and elemental image projection. Additionally, we found a wave interference conceptualization. Within each conceptualization, we discovered conceptions not reported before: gathered images, image spots, focused rays, sharpened image, mutual shift, different arrangements, lens-point as viewpoint, rays through lens-point, and aperture image. Given the small sample, additional conceptions should be found in future studies. Some students used key words differently than scientists. Students used the word ray for a trajectory of light (like modern scientists), for 6

8 Developing students ideas about lens imaging Gerd s learning pathway Ben s learning pathway t a t r t x T M t n T E T M T O T A T R (a) t b T P T D T R (b) Edgar s learning pathway Chris s learning pathway T B t b T P T E T V T S T D T R t e t e t h T P T D T T T R (c) (d) Anna s learning pathway T B T P T D T T T R t d (e) David s learning pathway T P T E T V T S T D T R (f) Fabian s learning pathway t l T P T M T D T V T R (g) Figure 7. Learning pathways of (a) Gerd, (b) Ben, (c) Edgar, (d) Chris, (e) Anna, (f) David, and (g) Fabian. Abbreviations are listed in section 4. 7

9 S Grusche a particle of light (like Newton), or for a flux of light (which modern scientists represent by a bundle of rays), see [2]. All students used the word focal point for a point in a sharp image, but only some required the imaged object to be extremely distant, see [3]. Guided by image-based teaching actions, all students advanced to the scientifically adequate elemental image projection conceptualization. Some used it as a stepping stone [12] toward the point-to-point conceptualization; others would need more time to take that final step. They only need to realize that the elemental image projection and point-to-point conceptualization are two sides of the same coin Implications for teachers Teachers may use the list of teaching actions to expand their repertoire, and may refer to the learning pathways to plan lessons. Moreover, they may use the list of conceptions to track students progress. Using the eye analogy, students ignore the refractive media around the eye lens [4]. If teachers use a glass lens and screen as an analogous model of the eye [8], they should point out that the glass lens represents the functions of the cornea, aqueous humor, eye lens, and vitreous humor combined. Students will stick to inadequate ideas, even in the face of phenomena (see supplementary data), unless the teacher directs student attention, encourages free experimentation, calls for quantitative measurements, and engages in discussion. For example, Anna thought that rays go straight through each lens-point, knowing that light travels in straight lines. Only when the teacher pointed out the precise position of an elemental image, she realized that rays are refracted at the lens. For teachers of large classes, an effective way to guide students inquiry and interpretation is to provide observation sheets [14]. To work against a student s inadequate idea, teachers can work with it. For example, Gerd s conception gathered images is scientifically questionable, but the teacher used it to guide Gerd to the elemental image projection conceptualization. Moreover, Gerd thought that the separation between elemental images vanishes if the object distance approaches infinity. However, this is only true for a screen in the focal plane. Thus, the misconception can be turned into an imagebased definition of the focal point, see [8]. In lens imaging, the focal plane is defined as the image plane for an infinitely distant object plane. In a computational counterpart to lens imaging, called synthetic aperture imaging, the focal plane is defined as the image plane for any chosen object plane [15]. By comparing and contrasting lens imaging with synthetic aperture imaging, teachers can show how both involve a superposition of elemental images, and discuss the different uses of the word focal plane [8]. To negotiate the use of the word ray with students, teachers can introduce rays as lines connecting elemental images [8], and interpret these lines as paths of hypothetical particles or streams of light, see [2]. To address the diversity of students ideas, teachers may offer additional activities. For example, once students look from the screen toward the lens, they can question the conception receiving eye [1, 9, 10]: from the sharp image, the whole lens appears colored like the image point where the eye is [16]. Then, rays behind the lens can be introduced as connections between the image point and all lens-points. A complementary teaching sequence can be designed using the conception aperture image : A small light source illuminates a lens covered with an arbitrarily shaped aperture, and rays are introduced as connections between aperture images, see [17]. Teachers of physics education need to ensure that their undergraduate students develop scientifically adequate ideas: when those students become high-school teachers, their ideas will affect the high-school students understanding, in turn. The image-based approach seems to be a fruitful path. Our undergraduate students initial ideas are similar to high-school students ideas, especially the holistic image conceptualization, and the problematic concepts of rays and focal points, see [3, 7, 8]. Thus, the teaching implications may be useful not only for teachers of undergraduate students, but also for teachers of high-school students. To enable a consistent learning experience, teachers may apply an image-based approach not only to lens imaging, but also to other topics in optics, such as the law of refraction [18]. 8

10 Developing students ideas about lens imaging 6. Conclusion In teaching experiments, we uncovered undergraduate students ideas about lens imaging, and studied the effect of an image-based approach. We found previously unknown conceptions about blurry images. Besides the well-known holistic image conceptualization and the point-to-point conceptualization, we identified two versions of the image projection conceptualization: lens image projection and elemental image projection. Initially, students used the lens image projection conceptualization, which is only partly adequate. Using the image-based approach, they progressed to the elemental image projection conceptualization, an adequate precursor of the point-to-point conceptualization. Although the proposed teaching approach was effective, teachers may want to enrich it with additional activities to address the full range of students ideas. Acknowledgments Professor Dr Florian Theilmann checked the coding. I thank all interviewees. Received 17 January 2017, in final form 13 March 2017 Accepted for publication 13 April References [1] Goldberg F M and McDermott L C 1987 An investigation of student understanding of the real image formed by a converging lens or concave mirror Am. J. Phys [2] Galili I and Hazan A 2000 Learners knowledge in optics: interpretation, structure and analysis Int. J. Sci. Educ [3] Pompea S M, Dokter E F, Walker C E and Sparks R T 2007 Using misconceptions research in the design of optics instructional materials and teacher professional development programs Education and Training in Optics and Photonics OSA Technical Digest Series (Washington, : Optical Society of America) paper EMC2 ( [4] Kaltakci D and Eryilmaz A 2010 Sources of optics misconceptions Contemporary Science Education Research: Learning and Assessment ed G Cakmakci and M F Tasar (Ankara: Pegem Akademi) pp 13 6 [5] Tural G 2015 Cross-grade comparison of students conceptual understanding with lenses in geometric optics Sci. Educ. Int [6] Kaltakci-Gurel D, Eryilmaz A and McDermott L C 2016 Identifying preservice physics teachers misconceptions and conceptual difficulties about geometrical optics Eur. J. Phys [7] Grusche S 2016 Präkonzepte zur Projektion eines unscharfen Bildes mit einer Linse PhyDid B DD [8] Grusche S 2016 Seeing lens imaging as a superposition of multiple views Phys. Educ [9] Kattmann U, Duit R, Gropengießer H and Komorek M 1996 Educational reconstruction-bringing together issues of scientific clarification and students conceptions Annual Meeting of NARST [10] Gropengießer H 2007 Didaktische Rekonstruktion des Sehens (Oldenburg: Didaktisches Zentrum) [11] Steffe L P and Thompson P W 2000 Teaching experiment methodology: Underlying principles and essential elements Research design in mathematics and science education ed R Lesh and A E Kelly pp (Hillsdale, NJ: Erlbaum) [12] Duschl R, Maeng S and Sezen A 2011 Learning progressions and teaching sequences: a review and analysis Stud. Sci. Educ [13] Riemeier T and Gropengießer H 2008 On the roots of difficulties in learning about cell division: process-based analysis of students conceptual development in teaching experiments Int. J. Sci. Educ [14] Oğuz-Ünver A and Yürümezoğlu K 2009 A teaching strategy for developing the power of observation in science Ondokuz Mayis Üniversitesi Eğitim Fakültesi Dergisi [15] Vaish V 2007 Synthetic aperture imaging using dense camera arrays PhD Thesis Stanford University [16] Maier G 2011 An Optics of Visual Experience (New York: Adonis Press) [17] Merklinger H M 1997 A technical view of bokeh Photo Tech [18] Grusche S and Wagner S 2016 Two different looks at Kepler s refraction experiment Phys. Educ Sascha Grusche, born in 1986, holds a master's degree in physics education. Since October 2013, he has been a research assistant at the University of Education in Weingarten, developing an image-based approach to lenses, prisms, and gratings. 9