1. Introduction
Enhancing the understanding of some of the fundamentals of the refraction of light is the topic of this article. Such understanding involves realizing that the speed of light is finite, that it changes when light passes through different transparent materials, and that the denser the material, the slower the speed of light in it. This change in speed results in the changing of the direction of the progression of light. As light moves from air to water and back, objects appear to be “bent”.
High school students’ understanding of the refraction of light can be tainted by alternative conceptions not only in this specific area but in other domains as well. For example, students may wrongly believe that light emanates from the eyes (
Kaewkhong et al., 2010), that emitting and re-emitting light are the same (
Fliegauf et al., 2022), and that light does not travel (
Favale & Bondani, 2013) or does not change directions (
Kaewkhong et al., 2010). Such alternative conceptions seem to persist despite having learned these subjects in school (
Fliegauf et al., 2022;
Kaewkhong et al., 2010;
Putri et al., 2023), and even among qualified optometrists (
Nourrit, 2023), perhaps because formal explanations seem to contradict everyday experiences. For instance, the bodily sensations involved in looking may strengthen the belief that light emanates from the eyes, even though it is impossible to see objects in a dark room (
Fliegauf et al., 2022). After being exposed to formal teaching, students often form multiple interim and unstable concepts that lie between their initial intuitive ones and the scientific concepts they were taught (
diSessa, 2017;
Fyttas et al., 2023;
Sherin, 2017;
Vosniadou, 2017). Connecting formal explanations to concrete experiences (
Fliegauf et al., 2022;
Kroothkaew & Srisawasdi, 2013) and holding group discussions that expose the inconsistent nature of alternative conceptions (
Wangchuk & Penjor, 2020) yielded promising yet not entirely successful results. In view of the individualistic and transient nature of students’ alternative conceptions, it is possible that teachers’ ability to address them would improve if they could identify a student’s alternative conceptions during the lesson itself and intervene on the spot, relating to each student’s specific ideas.
In this study, we would like to present a means to identify these emerging alternative conceptions. The goal of this study is to suggest such means. It follows students’ understanding of the concept of the refraction of light and the processes of conceptual change they undergo in response to Attentive Teaching. The theory of Attentive Teaching is presented below and is followed by a description of the multiple case studies we conducted to follow students’ conceptual and emotional changes as they studied the refraction of light.
2. Attentive Teaching
Overview. Attentive Teaching is a dialogic teaching approach based on social constructivism. Social constructivism views learning as an active process in which learners change their previous conceptualizations to fit those that are accepted within their culture, with the help of other individuals, such as teachers and peers (
Bruner, 1966;
Vygotsky, 1978). During Attentive Teaching lessons, students represent their conceptualizations visually, mainly in drawings, and explain them in writing and orally to their peers. The teacher attentively responds to students’ individual presentations (drawings) and the class discussions and together, their understanding is improved and enriched. Teachers and students, in unison, challenge students’ previous conceptualizations and at the same time build bridges between these conceptualizations and scientific ones, thus utilizing two efficient ways of inducing conceptual change (
Pacaci et al., 2024). Because drawings and their explanations represent how each student interprets what they learn, they provide teachers with a formative assessment tool they can embed in “standard teaching”, as
Métioui (
2023) suggested. Reviewed over time, the drawings become an ongoing documentation of individual students’ conceptual change processes and evolving understanding. In the following, we focus on specific aspects of Attentive Teaching and explain technical terminology.
The significance of drawings. Ainsworth et al. (
2011) and
Quillin and Thomas (
2015) list the many advantages of using drawings to present students’ knowledge and conceptualizations. Drawings are a useful tool for presenting conceptualizations, as they bring together multiple pieces of information and arrange them clearly and concisely on paper, thus emphasizing the relationships between the components and their overall organization. When students represent their ideas in drawings, they cannot rely on rote-learned phrases they do not understand. Therefore, presenting conceptualizations through drawings is an “open-ended” task that requires demonstration of understanding (
Perkins & Unger, 1999). Furthermore, while drawing, all students must be active and involved. Another advantage is that drawings are a means of communication. The fact that concepts can be explicitly represented makes drawings a comfortable platform for discourse and critical examination of their contents. Drawings can function as learning tools. The critical scrutiny of drawings encourages asking questions and developing conclusions and drives conceptual change. Finally, drawings can document students’ individual conceptualizations and the changes they underwent over time. Observed changes in students’ conceptualizations over time are described as Dynamic Learning (
Schur, 2015,
in press). However, drawings may be unclear to the viewers, which is why graphic images are combined with oral and written explanations (
Kress, 2015).
Mediation. Mediation is a significant interaction that improves students’ abilities to understand and act upon their environment (
Feuerstein, 1990;
Vygotsky, 1978). In Attentive Teaching, the activities that take place during the lessons are mediating interactions.
Bruner (
1966) suggested three types of representation that are connected with three modes of learning: (1) enactive learning—through physical experience that is mediated through objects, gestures, and facial expressions; (2) iconic learning—through drawings; and (3) symbolic learning—through language. Using a combination of these three modes—physical experience, images, and language—experiences become knowledge. This combination is also vital in formal learning. It undergirds Attentive Teaching, where students and teachers employ all three types of representation in their intensive classroom discourse (
Cazden, 2001), over students’ successive drawings of the concept under study. During this discourse, individual students represent their conceptualizations, alternative conceptions, associations, and perplexities, and the teacher can provide attentive mediation, specifically adapted to students’ needs.
Thinking Journeys are carefully crafted lessons that are designed to appeal to the imagination. They are intended to invite students to engage in seeing a problem or concept from an unfamiliar perspective and thus create a “Space of Learning” (
Marton et al., 2004) that can help to deepen the understanding of the concept being learned (
Carey, 2009). In this study, the Thinking Journey’s task was imagining how the world looks from within a drop of water. Furthermore, Thinking Journeys connect the learned subject (in this case, the refraction of light) to students’ embodied cognition and personal lives, thus raising their interest, curiosity, and motivation to learn (
Doğru & Kurnaz, 2023).
Attentive Teaching was developed for science education. It was used to help students understand scientific concepts through Thinking Journeys that enabled them to compare instances of the learned concepts across environments (
Marton et al., 2004). For example, going on a Thinking Journey to the moon and comparing the moon’s gravity to Earth’s. The students learned that astronauts walked on the moon and did not float as they did in space. They also learned that in order to watch Earth from the moon, they would have to look “up,” thus correcting two alternative conceptions that are common to most seventh- and eighth-grade students (
Schur & Galili, 2009). A recent study (
Gal et al., 2023) followed college students’ evolving understanding of social-ecological systems through their drawings from an initial state in which they did not represent any specific location to a mature state in which complex systems were represented, and students’ realizations were generalized to additional social–ecological systems. Although most of the participants did not reach the mature state, they did show progress by representing the connections between the systems’ components.
Emotional aspects. Emotions are an inseparable part of thinking and learning (
Schur, 2015). Although emotions are situational, awareness and understanding of their presence are essential in the mediation of meaning (
Feuerstein, 1990). Optimal learning occurs when students are not too worried or anxious, and alternately, not too bored (
Pekrun & Garcia-Linnenbrink, 2012), and when they are equipped with the appropriate level of uncertainty to enable learning for understanding (
Schur, 2015). When asked to present assignments that require deep thinking (
Kahneman, 2011) and understanding performances (
Perkins & Salomon, 1992), students may feel negative emotions such as uncertainty, a lack of confidence in their ability to complete the assignment (
Shulman, 2005), confusion, and a sense of shame about exposing their lack of knowledge in front of other students and the teacher. However, having completed the learning assignments successfully and having undergone conceptual changes, the students may gain a feeling of self-competence, which increases intrinsic motivation to further learning (
Deci et al., 1996). The challenging content the teacher presents can evoke students’ curiosity, surprise, and unconventional thinking about ways of completing the assignment (
Schur, 2015). When students share their work with their peers and the teacher and obtain supportive feedback, feelings of relatedness emerge (
Deci et al., 1996). Teachers using the principles of Attentive Teaching should be aware of these complex aspects and work to foster a supportive class atmosphere that enables all students to express themselves freely without missing out on critical examinations of the arguments and the evidence students present.
5. Findings
5.1. Students’ Understanding of the Refraction of Light at the Beginning of the Study Unit
Hanna (
Figure 1) drew a leaf of grass. The leaf takes up the entire page. In her interview, she revealed that she had been occupied with objects’ size. “At first, I thought that maybe I would see small molecules because I am small … then I said to myself, ok, maybe what I’m seeing is actually bigger”. As she continued, an alternative conception concerning light emerged. It seems she believed that the source of light was in the water. “How do we see the world being immersed in water? Like how the light exits the water and then reaches the outside?” She understood that the transition into water changes the visual image that is formed, but was not sure how. “Then I thought, if it’s [seen] from the drop of water, so what is the connection to what is outside? … A drop of water somehow always changes reality”. Because she was uncertain, Hanna drew a leaf of grass without relating to the effects of its being seen from within a drop of water. Her oral explanations revealed her perplexity and alternative conception concerning the origin of light.
Sophie (
Figure 2) was also concerned with size. “I was always interested in shrinking.... Here it was to shrink even more.... You don’t see our world as being small, you see a world that is deeper.” Sophie described the molecular structure of water and molecules of air around it. “I know that in water, the particles are not scattered like they are in the air, but neither are they compressed like in a solid material”. Her drawing and explanations reveal an alternative conception concerning the differences in scale between a drop of water and molecules. Furthermore, her drawing does not represent the refraction of light.
Ben (
Figure 3) drew leaf cells, bacteria, germs, and dust. “So, you will be like… see the cells… and around it will be all kinds of groups of germs or bacteria and dust and all kinds of small things that are difficult to see normally”. His drawing also reveals his alternative conceptions concerning differences in scale—the germs and bacteria are large, relative to the cells, whereas in reality, bacteria are one-cell organisms. Ben was aware that the light would be refracted because of the drop of water, but he was not sure how to represent it. “I had a thought that maybe I’ll see… that the light would refract slightly because of the water. But in the end, I didn’t draw it like that”. Nonetheless, the convex shape of the grass cells in his drawing shows the effect of the convex shape of the drop.
Gillian (
Figure 4) drew the refraction of light and was interested in the vision process of the person within the drop of water. Her drawing shows light rays that are broken in the drop and reach the eye which sees an enlarged view of the surroundings. Gillian emphasized that her thinking that the world would appear to be larger does not stem from an intuitive perception. “Let’s say that if I were an ordinary person, I could have thought that... because I am in the drop, or I am smaller, then everything would appear to me to be larger… I think everything is based on science.” In the drawing, the source of light is external, and light rays reach the eye. Although the convex shape of the drop was not presented in the drawing, it appears in the verbal text. “In my opinion, I would compare it to a lens. Let’s say, it’s kind of rounded.” Gillian added a key to the drawing (lower right side). She portrayed an eye (on the lower left side) without the rest of the body, as is the norm in scientific illustrations. Gillian’s multi-modal text (drawing and written explanations) suggests some understanding of the effects a drop of water would have on vision. The rays move from the outside, are reflected off the trees and the house, change direction as they enter the drop, reach the eye, and form an enlarged image. However, the effect of the convex form of the drop is missing from the description, as is the sun as the source of light. The refraction of light was not mentioned in her interview.
To summarize, all four students seemed to lack explicit scientific knowledge about the refraction of light. Such knowledge could enable them to make the connection between it and the ability to understand what they would see from within a drop of water, although Gillian had some implicit knowledge that was presented in her drawing. The other three students were occupied with differences in size and expressed several alternative conceptions. Some of these alternative conceptions (differences in scale) were unrelated to the refraction of light, whereas others (the origin of light) could impede further learning in this area.
5.2. The Effects of Mediation on Students’ Understanding of the Refraction of Light
Recognizing that her students had very little knowledge of the refraction of light, the teacher determined to engage her students with the concept in an imaginative, structured, and supportive way. Using
Hewitt’s (
1993) text, she crafted two Thinking Journey scenarios as mediations to support their learning. As with all Attentive Teaching practices, these involved students’ drawings and explanations in response to the information with which they were interacting.
5.2.1. Thinking Journey 1: Saving the Drowning Princess
The first interaction was a variation of Fermat’s thinking exercise in 1661 (
Hewitt, 1993, p. 28). The students were asked to imagine light as Superman standing on the coastline, having to save a drowning princess (
Figure 5). Assuming that he moves faster on land than in water, the students were asked to draw the fastest path he can take to reach the drowning princess.
Figure 5 shows the fastest path as two arrows and the suggestions presented in class. A number of students asked the teacher to define the proportion between Superman’s speed on land and in water. Instead of obtaining an answer from her, they decided to try different proportions. This move enabled a transition from a qualitative, informal description to an algebraic presentation of the refractive index concept.
5.2.2. Thinking Journey 2
The second task, which was also based on
Hewitt (
1993), began by asking the students to look at two photographs of a man in a pool with a transparent wall (
Figure 6a,b). Both photos were taken with a side view. In one of them, it appears as if the man’s head is disconnected from his body. The students had to determine which of the two photographs was fake.
After engaging in Thinking Journey 2, all the students correctly concluded that the figure that appears to have a complete and unbroken body is not possible. They used different ways to reach their conclusion. Sophie made direct reference to a spoon in a cup of water which appeared to be broken and concluded that the man’s body would also appear broken (
Figure 7a). The other three students whose work we analyzed (Hanna, Ben, and Gillian) referred to the classic statement of “apparent depth” which states that if one looks at a long object that is submerged in water, it will seem broken. They implemented this principle to relate to the man in the water and concluded that he would also not appear whole. Using negation, they concluded that it is not possible that the photographed body would appear to be whole, and, therefore, the head will seem to be separated from the body (
Figure 7b).
The first mediated assignment relied on students’ everyday life experience that moving on land is faster than moving in water. This experiential knowledge led them to understand the itinerary of light moving from one transparent material to another. The second mediated task helped students accept the counter-intuitive fact that observing refraction would result in a different image than that they would normally see when light travels through air. In contrast to a spoon, the use of a human body was surprising and engaging and, therefore, could have more impact on the learning process.
5.3. Students’ Conceptualizations After the Mediating Interactions
After learning, Hanna (
Figure 8) drew lines that she described as representing light rays. The vertical lines come down from the sky (not from the sun, although she drew it). She drew horizontal lines in the background, perhaps representing the side of the drop. Thus, the figure shows the distribution of light rays and a change in direction. The leaves tend to bend to the right, seemingly representing the effect of the convex structure of the drop on the image of the leaves. In her oral explanation, she specifically referred to the refraction of light and included the enlarged image. “After we learned about optics, I know that when light passes through different materials, it changes direction. When light passes through water, then the light rays are distributed and increase the size of the object”. None of that appeared in her first drawing.
Sophie (
Figure 9) showed parallel light rays that are broken into different colored light waves on the surface of a drop. Sophie’s drawing is a good description of dispersion. When compared to her initial drawing, she shows progress in understanding the interaction between light and a drop of water. However, she did not present the world as seen from within a drop.
Ben’s drawing (
Figure 10) presents the change in sharpness and color that will occur as light travels through water as well as the enlarged image. Nonetheless, he did not provide an explanation as to how the process occurs.
Gillian’s drawing (
Figure 11) shows light rays emitted from the sun hitting houses, being reflected back to the external surface of a drop of water, and then being refracted to the observer’s eye on the left. The eye is enlarged beneath the seeing figure, within which a diminutive image of the objects is formed. This interpretation of the drawing is strengthened by the interview. “The light rays that hit the objects afterward are in the drop of water, and the rays reach my eyes through the drop and are distorted when traveling from the drop to my eyes.” However, she seems unsure about the size of the figure. On the one hand, she says “The figure is enlarged and is situated in a different location from the real place … the distances are different”. On the other hand, she writes “Small” in English on the drawing, implying that there will be a reduction in size.
Looking back at the eight drawings, it seems that although each of the students had a different way of representing the world as seen from within a drop of water, they all acquired scientific knowledge. Hanna and Gillian represented the refraction of light, and Sophie represented dispersion. Ben represented some of the effects that would be seen, although he could not describe the process. Alternative conceptions concerning differences in scale were eliminated from Hanna, Ben, and Sophies’ drawings and explanations. Gillian learned that the origin of light is the sun, whereas this still seems unclear to Hanna. Thus, the drawings can inform the teacher about her students’ achievements—visible personal conceptual changes—as well as specific areas where her support is still needed.
5.4. Uncertainty as Part of Learning Physics
Learning involves emotions. Attentive Teaching addresses emotions associated with learning by encouraging teachers to invite students to express their feelings through drawings and explain them in writing and orally.
Hanna’s drawing (
Figure 12), performed at the end of the unit, shows clouds in a dark sky and a large yellow sun with pink rays emerging above the clouds. Hanna explained that her thoughts are usually confused and heavy, but when she feels that she has understood something new, her heart lights up.
Ben (
Figure 13) felt that he was not completely clear about the subject. He drew a path that became blurred in the middle. In addition to the drawing, he wrote “I think that only in the middle the material is unclear”. In the interview, he said he feels that he is in the middle of the journey and that the end is not clearly visible. However, he hopes that at the end of the process, he will reach an understanding.
Gillian also drew mixed emotions (
Figure 14). Thinking about physics, she wrote (in Hebrew) within the thought bubbles “It will help a lot in life”. “It was fun”. “Equations are my favorite thing”. “I succeeded, it was easy”. Other thought bubbles expressed self-doubt: “I will not succeed”, “????”, “I don’t understand a thing”. Concerning learning, she wrote “I learnt a lot, and I’m continuing to learn”. Gillian probably felt a certain sense of social isolation, as she wrote “I am the only one of the group and of my friends who studies physics”. Yet, she also wrote, “I am special”.
In the interview she said that being asked to enter a drop of water made her feel unconfident. “Why am I doing this? What do I need it for?”, and “Why are we not given a regular math exercise? … It’s easier for me... I prefer when it is organized… That I know that I have a solution in the end. It’s OK that I don’t know it [the solution] but I know there is a solution. That makes me calmer”. Nonetheless, she could overcome those feelings and even withstand social pressure. “I was under pressure, but I understood that I am correct, and although the entire class said ‘No, no you are making a mistake…’, I thought, ‘What!? Did I make a mistake?’ and then I understood that I had not [made a mistake], and I wanted to explain this to the class”.
To summarize, all the students expressed mixed feelings about learning. On the one hand, they felt uncertainty and self-doubt concerning their understanding. Ben focused on the refraction of light. For Hanna, this was only an example of the difficulties she encountered. Gillian referred to her social world, such as the difficulty of being assertive and withstanding group pressure when she expressed her views and her identity as the only girl among her friends who chose to study physics. On the other hand, when they felt they were learning and making progress, the bright side prevailed.
6. Discussion
The goal of the current study was to follow students’ developing an understanding of the refraction of light. We found that at the beginning of the study unit, none of the students had explicit knowledge and only one student had implicit knowledge in this area. Students’ drawings expressed alternative conceptions concerning differences in scale, the shape and size of images, and the origin of light. Using drawings, the teacher could see what each of her students was thinking and respond accordingly. At the end of the unit, they had all acquired explicit knowledge about light and could clearly represent their knowledge, and most of the initial alternative conceptions that were present in their initial drawings and explanations were eliminated. Although initially, the students felt unconfident addressing the refraction of light, they were eventually satisfied with their progress and optimistic about the future.
The students were all in the same classroom, yet each began the learning process from his or her personal viewpoint. The opportunity to present their conceptualizations in drawings and explain them revealed a wide array of alternative conceptions. Some of these alternative conceptions were completely unrelated to the concept of the refraction of light, such as believing that molecules are as large as cells, whereas others could impede their learning of this specific subject, such as the belief that light rays are disconnected from the sun. Students’ alternative conceptions as seen in this study corroborate previous findings that people think about scientific situations in diverse individual manners and that their intuitive insights are not coherent (
diSessa, 2017;
Fyttas et al., 2023;
Sherin, 2017;
Vosniadou, 2017). Nonetheless, exposing these alternative conceptions provided the teacher with opportunities to address them and enhance the students’ scientific knowledge.
Listening to the students’ discussion enabled the teacher to suggest relevant explanations and provide appropriate experiences to enhance their understanding. The teacher used traditional teaching materials (
Hewitt, 1993), but their use was aligned with the Attentive Teaching approach. The teacher invited the students to observe and think about the refraction of light from a variety of perspectives and involved their active participation throughout the process. The students had to integrate their imagination, previous experiences, and logic (
Bruner, 1966) to form their own solutions to the challenging tasks. Drawing on the students’ physical experiences—movement on dry land and in water—the teacher supported her students’ developing conceptualizations about the changes in the speed of light in various transparent materials and the resultant change in its direction (
Fliegauf et al., 2022). In another lesson, the students had to decide which of two photographs was correct: a picture in which the body of a person in a transparent pool seemed to be disconnected from his head or a picture in which the body and head were connected. Together, the students arrived at the counter-intuitive conclusion that the “disconnected” picture was the correct one. By gaining this realization independently, the students were more willing to let go of other alternative conceptions concerning light.
Mortimer and Scott (
2003) described typical classroom discourse as a discourse sequence beginning with an interactive dialogic, which later becomes authoritarian interactive (teacher giving explanations), and ending with non-dialogic authoritarian (teacher summary). This was not so in this set of lessons. Throughout the Attentive Teaching process, an interactive dialogic discourse (
Cazden, 2001) took place in which the students presented their conceptualizations and shared their uncertainties. They received their peers’ positive feedback and were encouraged to deal with counterarguments, think more deeply, and foster their explanatory and justification skills (
Cazden, 2001;
Wangchuk & Penjor, 2020).
At the end of the study unit, the students learned that the speed of light changes as it moves from one transparent material to another and that that affects the direction of light and images’ shape and color. That knowledge was integrated with previous knowledge the students acquired about convex lenses and light dispersion. The students demonstrated their growth in understanding not as a repetition of what they had learned in class but through their individual drawings and verbal explanations. These were the outcomes of the students’ personal and collective processing of information and the construction of knowledge.
The teacher’s choice to shape her teaching as imaginative Thinking Journeys aroused emotions of uncertainty among the students. These emotions were limited to studying the refraction of light only for one of the students. For Hanna, the feelings revolved around her overcoming difficulties, whereas for Gillian, they aroused an inner discussion of what it meant to be a girl who leads the class in her understanding of physics and withstands group pressure. By asking about their emotions, the teacher could monitor these emotions and ensure they do not compromise students’ well-being. Furthermore, she showed interest in her students as whole persons and not just in their cognition, thus strengthening their relationships and enhancing their sense of relatedness (
Deci et al., 1996).
At the end of the study unit, the students were encouraged by gaining more understanding, not by learning everything there is to know about the refraction of light. Their newly found self-confidence seems to have come from their developing a feeling of competence about their ability to think about problems, share what they know, and theorize together (
Deci et al., 1996;
Cazden, 2001). The students seemed to develop patience with their sense making as they felt actively engaged in their learning (
Kozulin, 2003). The teacher enabled them to achieve this by posing challenging tasks instead of providing them with the right answer right away and moving on to the next problem.