reflection on problem solving

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Problem Solving through Reflective Practice

Reflective practice progresses through several steps. The practitioner first identifies a problem followed by the observation and analysis stage. Ostermann & Kottk amp (2004) identify this stage as “the most critical and complex of the four” (p. 28) stages. This stage entails the necessity of not only gathering information about the problem without tainting it with personal judgment but also analyzing the dilemma as it is compared from the current situation to the desired goal . The third stage, abstract re-conceptualization requires the practitioner to investigate new solutions and resources which address the root of the dilemma. Lastly, experimentation enters as the new strategies are utilized in changing behaviors. York-Barr et al. (2005) suggests that these steps are not linear, nor are they circular. Each step is interconnected

Using a learning journal aids in the learning process. Click on image.

with the others. 

This practice can be utilized through recording each step and later reviewing what was learned. It allows educators to provide the example for the students in a continuous learning environment of progression as they develop skills to be more proficient at teaching and more skilled at learning. It is simply the experiential model by which educators learn most effectively.

These are some of my favorite sources for a reflective practice and problem solving using reflective practice.

Click on image.

Osterman, K. & Kottkamp, R. (2004). Reflective practice for educators: Professional development to improve student learning. Thousand Oaks, CA: Sage.

York-Barr, J., Sommers, W., Ghere, G. & Monthie, J. (2005). Reflective practice to improve schools: An action guide for educators.  Thousand Oaks, CA: Sage.

By Tracy Harrington-Atkinson

Tracy Harrington-Atkinson, mother of six, lives in the Midwest with her husband. She is a teacher, having taught elementary school to higher education, holding degrees in elementary education, a master’s in higher education and continued on to a PhD in curriculum design. She has published several titles, including Calais: The Annals of the Hidden , Lemosa: The Annals of the Hidden, Book Two, Rachel’s 8 and Securing Your Tent . She is currently working on a non-fiction text exploring the attributes of self-directed learners: The Five Characteristics of Self-directed Learners.

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How to Practice Reflective Thinking

Understanding your present is critical to planning your future.

Sitting in silence and self-reflecting activates multiple parts of our brain and helps us increase awareness of what matters most to us. However, in the busyness of our everyday lives, it can be hard to find the time to stop and reflect. All self-reflection takes is a little bit of MAGIC: mirror, aspirations, goals, ideas, and commitments. The author created this method, based on their experience and coaching practice, to help people unlock the power of silence and reflective thought.

• Mirror: Start by imagining yourself looking into a metaphorical mirror, and reflect on your current situation. How did you get to where you are today, and how do you feel about your present circumstances? Start positively by recognizing everything that is going well. Then, identify ways in which you could improve.
• Aspirations: After reflecting on the present, it’s time to focus on the future. Visualize the person you want to see in your metaphorical mirror. What does success look like for you? If you could wave a magic wand, what would you really like to achieve in the next year?
• Goals: Once you have clarified your aspirations for the future, turn them into specific and tangible goals, with milestones and timescales to benchmark your progress. To do that, start with an action verb (increase, achieve, gain, sell). Then clearly specify what success looks like (becoming a manager, work on 2 high profile projects, reduce client complaints). Lastly, add a target date or deadline to aim for, chunked up into shorter milestones if necessary (over two months, in the next year, every week).
• Ideas: Once you have a set of clear goals which outline exactly what you want to achieve, you can then explore how these goals could be achieved, and start to create an action plan.Think about what you’ll have to give and what you’ll gain if you action a particular idea.
• Commitments: Finally, incorporate your ideas into a clear plan. A good plan contains specific step-by-step actions, with dates, deadlines and resources, and contingency plans for how you might overcome obstacles.

“I’m so pressed for time that I barely get the chance to think about what I want to do next.”

• RN Rosie Nice is the founder of MAGIC Coaching .  She runs coach training programs and helps organisations build a coaching culture, sharing the transformational results which coaching can bring. She is also the author of the book , The MAGIC Happens in the Silence , whihc is a guide to the art of reflective coaching.

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5 Activities That Promote Reflection in the Classroom

The metacognitive work of reflecting on learning boosts engagement and encourages the development of critical thinking skills.

Reflection is a powerful tool for enhancing learning and knowledge acquisition and is essential for teachers and students. When students engage in reflective thinking, they are better able to analyze and evaluate their experiences, which enables them to extract meaning and actively process what they have learned and to make sense of it. By taking the time to engage in the metacognitive practice of thinking and reflecting on learning, students can make more meaningful connections and gain a deeper understanding of the material, leading to greater long-term retention and application of knowledge.

Reflection also helps students develop metacognitive and social and emotional skills, such as self-awareness and self-regulation, by identifying areas for improvement and setting new goals. These are all important skills for lifelong learning.

5 Learning Activities that Can Foster reflection

To promote reflection, there are many options available that provide students with choices in how to share what they have learned and to engage in reflective practice. 

1. Blogging. For students who enjoy writing or jotting down ideas, blogging or journaling can be a great choice. Whether students contribute to a class blog or share it only with their teacher, it enables students to practice their writing skills, reflect on their learning, and potentially receive feedback from their peers. The blog can be on a topic related to their coursework, such as a book review, a reflection on a field trip, or a summary of a research project and what they learned and how the experience was for them.

WeVideo is a neat way for students to compile a series of video reflections and have an artifact of their learning to look back on throughout the year. It also promotes student choice and building digital skills with its editing tools and features. Students can even collaborate with classmates as they reflect. 

2. Digital storytelling. Digital storytelling is a popular and engaging option for students who are looking to showcase their knowledge through multimedia. With digital storytelling, students are empowered with choices in how to create a visual representation of their learning in a fun, engaging, and meaningful way. Depending on the tool used, students can include images, video, and audio to share thoughts and reflections of learning. 

StoryJumper is a digital storytelling platform that promotes student choice and voice in learning. Students can choose different background scenes, characters, and props and record audio for their books. Books can easily be shared with a QR code. 

3. Making mind maps. Creating graphic organizers or mind maps can be another way to boost visualization of learning and for students to present their thought processes, ideas, and connections between different concepts they have learned. Mind maps can promote critical thinking and creativity skills, as well as helping students evaluate how well they understand complex topics and develop a deeper understanding of the material.

Ideamapper is a tool that can be used by students and teachers for creating a mind map. There are many templates available to start with that make it easy to process learning, creating visualizations that help students reflect on concepts learned and make connections, leading to better content retention. 

4. Podcasting. For students who prefer speaking rather than writing to communicate their thoughts and ideas, podcasts are a great option. I started my own podcast as a way to reflect on my teaching practices and also to share what I was learning and how it impacted my classroom. By creating a podcast, students can explore their communication skills, delve deeper into a topic, and have a thoughtful discussion with classmates or simply a conversation with themselves that they can listen to and process for further reflection.

Students can create an episode to talk about a current event or a specific area of study, or to self-assess their learning experiences. Students can provide their unique perspective and insights on a topic while refining their speaking and communication skills. They will articulate their ideas more clearly, structure their thoughts, and engage in conversation, all of which also benefit their SEL skills.

Soundtrap for Education offers students and teachers many resources for getting started with podcasting in the classroom. Soundtrap also has lesson plans on a variety of topics and content areas for educators to explore and start podcasting with students right away.

5. Building digital portfolios. Digital portfolios are a great way to have students track their progress. Through a portfolio, they can build a narrative of their work and have a space to reflect on their progress and set goals.

Spaces EDU is a digital portfolio platform that helps teachers gain a deeper understanding of students’ interests, needs, and learning styles. Students can track their growth over time, identifying strengths and areas where they can set new goals. This information is critical in supporting reflective practice, allowing teachers to adjust their teaching strategies to better serve each student’s unique needs. 

Wakelet offers many possibilities for classroom use. Students can have their own Wakelet to add artifacts of work and create a digital portfolio, as well as record Flip videos to reflect on their learning. Flip has been a very beneficial tool in my classroom for several years. Whether students record videos to share their ideas or respond to prompts, it offers many choices that provide authentic and engaging learning and reflection opportunities for students. 

Benefits of reflection

Reflection promotes self-awareness and self-improvement and helps students identify strengths and weaknesses, set goals, and develop strategies to improve their learning outcomes. We want students to take ownership of their learning and become more active and engaged learners.

Reflective practices also enhance critical thinking and problem-solving skills. When we engage in the metacognitive process of thinking about thinking, we develop greater awareness of our learning experiences. Students will develop a habit of self-reflection that will enable them to better adapt to new challenges, learn from experiences, and continue to grow and develop as they prepare for the future.

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A 6-step reflection can improve your team's problem-solving

There’s no better time for reflection than at the beginning of a year. Designating time and space for retrospectives allows team members to identify problems and propose different solutions. Doing this habitually builds psychological safety, one of the key attributes of high-performing teams.

At Atlassian, we use the 4Ls Retrospective technique to facilitate team reflection. During this activity, team members identify what they Loved, Loathed, Learned, and Longed for in a project or sprint of work. Reflecting back on work helps the team use what they’ve learned to improve.

It only takes 60 minutes to run, and I have step-by-step instructions and templates for your team to try it, too. Let’s dive in!

Step 1: Prep

Before the session, agree as a team on the time period you’d like to look back on. For remote teams, create a collaboration document: you can check out these templates in Trello , Confluence , and Miro . For in-person teams, find a whiteboard and set out sticky notes and markers. Create six columns labeled Milestones, LOVED, LOATHED, LONGED FOR, LEARNED, and Actions.

If your team is distributed—meaning you have a few members who sit together, in-person, while others dial in virtually—we recommend running this play in an entirely virtual fashion by asking in-person team members to participate via Zoom.

Step 2: Set the stage

To build psychological safety, where team members feel they can speak freely without fear of repercussions, reiterate these points at the start of the session:

• We’re talking about how we have worked to see how we can make improvements.
• We understand everyone did the best they could given their knowledge and tools.
• This meeting is a safe space. Nothing that is shared will be used against anyone.
• We’re here to explore, not to blame.

Step 3: Identify key moments

Have the team think back over a specific time period and identify key events that occurred. Provide a few examples, such as results achieved, team celebrations, team members joining, or company events. Anchoring the team in key milestones jogs the team’s memory of events that occurred and how they felt about them. Then set a timer for five minutes for people to add their own key events to the Milestone column.

Step 4: Reflect

Explain the four lists to the team: “LOVED,” “LONGED FOR,” “LOATHED” and “LEARNED.”

• LOVED : what you loved about your work over the time period. This is what you want to keep doing, or do more of, in the future.
• LONGED FOR : what you wish you’d had. It could be more people, more time, more coffee. Nothing is off the table.
• LOATHED : what made life worse back then. What do you hope will never happen again?
• LEARNED : what you learned from your successes and your mistakes.

Set a timer for 10 minutes for everyone to place activities in each list. Don’t rush it. Giving time to write allows for processing and reflection while also giving quieter team members space for sharing their ideas.

Step 5: Create an action plan

For 10 minutes, either as a team or in breakout groups, discuss:

• One action you’ll take to remove something from the LOATHED list.
• One action you’ll take to amplify something from the LOVED list.
• Use the LONGED FOR and LEARNED lists to help shape your ideas for what actions to take.

Come back together and give each person or group a few minutes to share their plan. Use the actions list to capture each action. Make sure to include who will do it, what they are doing, and by when . Commit to when you’ll track progress on actions on a regular basis, such as at team meetings or at the next 4Ls.

Step 6: Follow up

Before you break, schedule your next 4Ls session. Once a quarter is a good start. I also like running this play at the end of a big project or moment, like a product launch or annual meeting.

I’ve run this play with dozens of teams, and it’s amazing to see the dynamic shift during the session. Giving team members an opportunity to reflect together and contribute to a better path forward can be transformational. What are you waiting for? Carve out an hour in the next month and see how it goes.

Mark Cruth is Atlassian’s resident Modern Work Expert. Focused on practice over theory, Mark spends his days coaching both Atlassian and customer teams on new ways of working, then sharing what he’s learned at events around the world.

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When Reflection Hinders Creative Problem-Solving: a Test of Alternative Reflection Strategies

• Original Paper
• Published: 15 April 2021
• Volume 37 , pages 429–441, ( 2022 )

Cite this article

• Julie Rosseel 1 &
• Frederik Anseel   ORCID: orcid.org/0000-0002-4697-7293 2  

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A growing body of evidence suggests that reflecting on performance is an important source of individual learning. Given the importance of creativity in contemporary business settings, reflection has also been cast as a useful strategy to facilitate creative problem-solving. Challenging this idea, we conducted a series of lab experiments to examine the effects of reflection on creative problem-solving. Drawing from theory in cognitive psychology on knowledge structures, we argue that reflection may sometimes debilitate rather than improve creative problem-solving, due to the reinforcement of existing cognitive schemas and the resulting cognitive entrenchment. To test our theoretical arguments, we developed two alternative reflection strategies, imaginative reflection and vicarious elaboration. In Study 1 ( N = 101), we observed a detrimental effect of task reflection on creative problem-solving, which was offset by having participants engage in imaginative reflection. In Study 2 ( N = 191), vicarious elaboration, elaborating on another’s creative experiences instead of reflecting on one’s own creative experiences, was introduced as a second strategy to counter cognitive entrenchment. In Study 3 ( N = 235), we combined the reflection strategies, demonstrating that imaginative thinking was more effective when focused on one’s own experiences rather than on others’ experiences (i.e., vicarious imaginative elaboration). Together, these findings increase our understanding of the effects of different reflection strategies, but also call for further research to address an intriguing observation: none of the reflection strategies led to better outcomes as compared to a control condition without reflection, suggesting that individual reflection might not help creative problem-solving at all.

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Acknowledgment

We would like to thank Ronald Bledow, Ute Hulsheger, Jonas Lang, and Hannes Leroy for the comments on the previous versions of our paper.

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Toilet paper scenario: A production manager of a multinational, which produces toilet paper, is confronted with a new package problem of toilet paper. Based on market research, it seems that consumers would like to have more compact packages of toilet paper without reduction of the amount and quality of toilet paper.

Shampoo bottle scenario: A production manager of a multinational, which produces shampoo bottles, is confronted with a complaint of consumers. Based on market research, it seems that consumers are being irritated if they are unable to use the last remnant due to the stickiness of shampoo.

Shampoo Design Coding Rules

General rule is ‘Count all specific design options for the shampoo bottle problem.’ The problem is stickiness of shampoo. Considering this problem: ‘Is the proposed design a concrete solution for the problem?’

One bullet point with different ideas separated by comma = count as different ideas.

A different idea written between brackets next to another idea = count as two ideas.

One idea combined with an arrow and followed by a consequence = count as one idea.

One idea combined with an arrow and followed by a new idea = count as two ideas.

Synonym and Rehearsal

Synonyms = count as one idea.

Writing down the same idea twice in different bullet points = count as one idea.

Conjunctions

One bullet point with different ideas separated by & or and or or = count as different ideas. Beware, if the different ideas belong to one idea = count as one idea.

If ideas are written as an essay instead of bullet points = count each different idea .

An idea combined with an example = count as one idea .

Different questions = count as different ideas.

If a drawing is a visualization of an idea = count as one idea.

If drawings represent different new ideas = count as different ideas.

Do not count the word ‘other’. If ‘other’ is written without suggestion, do not count it as an idea.

Do not count incomplete sentences.

Reflection Exercise Coding Rules

1. Did the participant continue writing additional creative applications?

2. Did the participant write a ‘?’, ‘/’, or absolutely nothing?

3. Did the participant write random words that had nothing to do with the creativity task?

4. Did the participant indicate that it is abstract or too complex?

5. Did the participant think imaginatively?

6. Did the participant think factually?

7. Did the participant think imaginatively and factually?

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Rosseel, J., Anseel, F. When Reflection Hinders Creative Problem-Solving: a Test of Alternative Reflection Strategies. J Bus Psychol 37 , 429–441 (2022). https://doi.org/10.1007/s10869-021-09741-8

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Factors influencing the complex problem-solving skills in reflective learning: results from partial least square structural equation modeling and fuzzy set qualitative comparative analysis

• Ying Wang 1   na1 ,
• Ze-Ling Xu 1   na1 ,
• Jia-Yao Lou 1   na1 &
• Ke-Da Chen 1  

BMC Medical Education volume  23 , Article number:  382 ( 2023 ) Cite this article

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The Organization for Economic Cooperation and Development emphasizes the importance of complex problem-solving (CPS) skills in the 21st century. CPS skills have been linked to academic performance, career development, and job competency training. Reflective learning, which includes journal writing, peer reflection, selfreflection, and group discussion, has been explored to improve critical thinking and problem-solving abilities. The development of various thinking modes and abilities, such as algorithmic thinking, creativity, and empathic concern, all affect problem-solving skills. However, there is a lack of an overall theory to relate variables to each other, which means that different theories need to be integrated to focus on how CPS skills can be effectively trained and improved.

Data from 136 medical students were analyzed using partial least square structural equation modeling (PLSSEM) and fuzzy set qualitative comparative analysis (fsQCA). A hypothesized model examining the associations between the CPS skills and influence factors was constructed.

The evaluation of the structural model showed that some variables had significant influences on CPS skills, while others did not. After deleting the insignificant pathways, a structural model was built, which showed that mediating effects of empathic concern and critical thinking were observed, while personal distress only had a direct effect on CPS skills. The results of necessity showed that only cooperativity and creativity are necessary conditions for critical thinking. The fsQCA analysis provided clues for each different pathway to the result, with all consistency values being higher than 0.8, and most coverage values being between 0.240 and 0.839. The fsQCA confirmed the validity of the model and provided configurations that enhanced the CPS skills.

Conclusions

This study provides evidence that reflective learning based on multi-dimensional empathy theory and 21 stcentury skills theory can improve CPS skills in medical students. These results have practical implications for learning and suggest that educators should consider incorporating reflective learning strategies that focus on empathy and 21 stcentury skills to enhance CPS skills in their curricula.

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Introduction

When putting forward the theoretical framework of skills and competencies in the 21st century, the Organization for Economic Cooperation and Development takes complex problem-solving (CPS) skills as an important component and brings them into the evaluation system of the Program for International Student Assessment [ 1 ]. Previous research results have proved that there is a significant positive correlation between CPS skills and academic performance [ 2 ], that is, the stronger the problem-solving skill, the better the academic performance. Similarly, it is also considered to have a great influence on career selection [ 3 ], career development [ 4 ], and job competency training [ 5 ]. Therefore, the improvement of the above-mentioned comprehensive qualities, such as learning ability and post competence, and the cultivation of CPS skills, has been emphasized by a variety of teaching strategies, such as problem-based learning (PBL) [ 6 ], context-based learning (CBL) [ 7 ], situational simulation [ 8 ], and reflective learning [ 9 ].

As an important process of metacognition, reflective learning is closely related to CPS skills. Gadbury-Amyot et al. claimed that the use of reflection and writing as educational strategies to promote critical thinking and problem-solving is one of the best ways for students to express their thought processes [ 10 ]. Exploration to improve CPS skills based on reflective learning and training can be seen in medicine, computer science, mathematics, and other industries. According to Bernack, establishing problem-solving training courses could feasibly enhance the abilities of pre-service teachers [ 11 ]. Kellogg suggested that reflection and writing, as educational strategies to promote critical thinking and problem-solving skill, is one of the best ways to improve students’ expression ability and logical thinking [ 12 ]. “Reflective learning” is a common way of exploring problems and solutions in the deliberative environment, a process of learning through experience, and is a necessary learning tool in professional education [ 13 ]. Reflective learning includes journal writing, peer reflection, self-reflection, and group discussion under the guidance of teachers [ 14 ]. Illeris suggested that the result of reflective learning spans cognitive, psychodynamic, and social-societal dimensions [ 15 ]. Through its influence on students’ behavior, thoughts, and emotions, it realizes the training and improvement of students’ various abilities. It has gradually developed into a more efficient and autonomous learning model and has become an indispensable educational and learning tool for many professionals [ 16 ]. Many experts suggest that the implementation of reflective learning can improve students’ critical thinking [ 17 ], insight [ 18 ], empathic concern [ 19 ], computational thinking [ 20 ], and other skills, and this improvement of a variety of thinking modes and abilities will eventually lead to improvement of their CPS skills [ 21 ]. Our research on the factors affecting the CPS skills is based on reflective learning.

The purpose of human problem solving is to promote the understanding of human thinking through a detailed investigation of the way people solve difficult problems, such as logic or chess. Unlike computer simulations, human problem solving is influenced by psychological factors that cannot be ignored [ 22 ]. Therefore, problem solving is dynamic and needs to consider the influence of speculation, social background, and culture, while CPS skills emphasize the process of successful interaction between the problem solver and the dynamic task environment [ 23 ]. CPS skills are collections of self-regulating psychological processes necessary in the face of complex and dynamic non-routine situations across different domains [ 24 ], and comprises a combination of skills, abilities, motivation, and other psychological structures [ 25 , 26 ]. The factors that impact CPS skills are complex and include cognitive and non-cognitive factors. Research shows that the development of a variety of thinking modes and abilities, such as algorithmic thinking, cooperativity, creativity, critical thinking, personal distress, fantasy, perspective-taking, and empathic concern, all affect the problem-solving skill in varying degrees [ 27 , 28 ]. Among them, empathetic concern and critical thinking have been proven to affect problem-solving skill by many studies. After comprehensively exploring the emerging research on the impact of the factors on the CPS skills, we found that previous studies mainly focused on a single causality in the improvement of problem-solving skill, while there is a lack of overall theory to relate variables to each other, which means that we need to integrate different theories to advance existing research and focuson how CPS skills can be effectively trained and improved.

Theoretical background

The literature analysis of CPS skills reveals the current research status. Based on the relevant theories of skills needed in the 21st century [ 1 ], individuals use analytical, reasoning, and cooperative skills to identify and solve problems consistent with their areas of interest [ 29 ]. Kocak proposes that problem-solving skills are shaped by algorithmic thinking, creativity, cooperativity, critical thinking, digital literacy, and effective communication, and develops a model with critical thinking as a mediating factor [ 21 ]. Developing solutions for complex problems is a complicated process, and individuals require critical thinking skills [ 21 , 30 ] to do so. Critical thinking often occurs at the same time as CPS skills and is one of the core objectives of general education in all subjects of higher education [ 29 ]. Critical thinking, closely related to reflective learning [ 17 ], which has been emphasized in many studies, especially in the implementation of learning strategies including reflective learning. In problem-based learning and case-based learning, instructors encourage learners to use critical reflection to engage with subject matter and to develop their own practice in closing any knowledge gaps that may exist [ 31 ]. Additionally, digital literacy involves the ability to assess the accuracy and value of online resources [ 32 ]. In this study, reflective learning was the primary learning strategy [ 33 ]; therefore, digital literacy skills were not observed in detail. Drawing on the above analysis, we developed a theoretical model that identifies algorithmic thinking, creativity, and cooperativity as antecedents, and critical thinking as an intermediary variable that influences CPS skills.

Another major area related to affecting CPS skills is empathic concern. The research suggests that students with a higher level of cognitive empathy show more positive attitudes and deal with problems more effectively [ 34 ]. In essence, empathetic concern fosters values, beliefs, attitudes, and assumptions, and affect the CPS skills from the perspective of execution [ 35 , 36 ]. Some studies suggest that reflective learning improves empathy [ 37 ]. Based on Davis’s Interpersonal Reactivity Index [ 38 ], empathy was divided into four dimensions mentioned: Empathic concern, fantasy, perspective-taking, and personal distress. Nevertheless, some scholars disagree that personal distress belongs to the category of empathy. Personal distress is defined as an over-arousal caused by the lack of boundaries between oneself and others [ 39 , 40 ]. Some studies show that personal distress leads to egoism and overwhelms altruistic activities mediated by empathetic concern [ 41 ]. And there is a statistically significant correlation between personal distress and empathetic concern [ 42 ]. Therefore, we still adhere to the view that the two cannot be regarded as mutually exclusive emotions, bringing personal distress into the scope of our research and exploring its role in CPS skills. Empathetic concern has been proved to associate with prosocial behavior [ 43 ]. In the relationship between empathic concern and prosocial concern, empathic concern elicits an approach orientation toward the target [ 44 ] and is used as a mediator variable in some models. For example, some studies consider empathic concern and personal distress are both mediators of perspective-taking to helping behavior [ 45 ]. Based on the above analysis, we built our theoretical model and assume that personal distress, perspective-taking, and fantasy as antecedents and empathetic concern as intermediary variables that affect the CPS skills.

Above all, the empathic concern and the critical thinking are two remarkable characteristics of the CPS skills, which can play a common role in the CPS skills [ 46 ], however, there is a lack of overall theory to connect them, which means that different theories need to be integrated to promote research. The comprehensive study of the combination of the two aspects can better understand how to improve CPS skills, which cannot be provided by any theory alone. Moreover, the results on the factors affecting the CPS skills also show some inconsistencies. For example, Batson believes that personal distress in empathy inhibits the development of problem-solving skills [ 41 ], whereas Mora disagrees [ 47 ]. A possible reasonable explanation for these contradictory results is that the previous studies on the factors influencing problem-solving skill mainly adopted traditional symmetric methods (such as regression and SEM), which did not fully capture the complexity of the factors that influence problem-solving skills, and the factors affecting the CPS skills are often based on multiple causalities rather than a single causal relationship. Simply evaluating symmetric relationships might lead to divergent results, thus masking the complexity of the problem-solving skill. Considering the complex nature of CPS skills under the condition of reflective learning, it is necessary to check the symmetric and asymmetric relationships between structures to fully understand the strategies and methods to improve CPS skills, therefore, PLS-SEM [ 48 ] and fsQCA [ 49 ] were used in our study comprehensively.

Research model and hypothesis development

Designing the pls-sem research model.

Critical thinking in the field of cognition and empathic concern in the field of emotion are representatives of two different thinking modes affecting the CPS skills. PLS-SEM assumes that fantasy, perspective-taking, personal distress, algorithmic thinking, creativity, and cooperativity have a direct impact on the CPS skills. Empathetic concern and critical thinking play an intermediary role between these relationships and the CPS skills (Fig.  1 A).

Partial least square structural equation modeling (PLS-SEM) conceptual model and fuzzy set qualitative comparative analysis (fsQCA) conceptual model: ( A ) The PLS-SEM conceptual model. ( B ) The fsQCA conceptual model

Personal distress and CPS skills

The definition of personal distress in this study pertains to the discomfort and anxiety that respondents experience when observing negative experiences of others, including fear, apprehension, and discomfort. Personal distress is an aspect of emotional empathy [ 38 ]. Some studies show that personal distress and empathy are complex and dynamic emotional experiences [ 50 ]. Personal distress, as an indicator of self-other differentiation and emotional regulation, is a kind of negative emotion. Excessive personal distress can lead to emotional regulation and interpersonal difficulties [ 51 ]. These studies advocate reducing personal distress to relieve stress [ 52 ]. The healthcare sector prioritizes a patient-centered healthcare model, which mandates that we respond to patients’ emotional distress with this principle in mind. However, in practice, health professionals tend to regard emotional health problems as “routine”; therefore, it is necessary to put patients’ emotional and identity issues in the dominant position of the marginal biomedical model used by health professionals [ 53 ]. However, empathic pain is crucial to Hoffman’s moral development framework. He believed that pain can cause significant effects that might lead to action [ 54 ]. Moitra’s research also supports the positive effect of personal distress on problem-solving skill [ 47 ]. Reflection encourages individuals to confront their own embarrassing and uncomfortable past experiences, learn from their errors, and enhance their CPS skills [ 55 ].

Fantasy and CPS skills

Fantasy acts on all aspects of reflective learning. First, to some extent, our brains process information and decisions in an irrational way, and reflection contributes to the cultivation of irrational thinking [ 56 ]. The improvement of subjects’ irrational thinking, including fantasy, can be promoted through reflective learning. Research indicates that individuals with higher fantasy and perspective-taking skills tend to have stronger social understanding [ 57 ]. Second, the development of imagination and fantasy is an important part of cultivating empathic concern [ 58 ]. This is because people understand the world through fantasy, and fantasy gives people hope that the world will become a better place [ 59 ]. For example, Melissa McInnis Brown’s research showed that children who play using fantasies are better at sharing emotions than their peers [ 60 ]. Many studies have proven the role of fantasy in problem-solving. For example, David Weibel pointed out that one can effectively use imagination in an environment, such as in artistic expression or problem-solving [ 61 ]. Fantasy is an imaginative way to find creative solutions that can help people predict the realization of creative structures [ 61 ]. From a sociological point of view, scholars usually regard fantasy as an important factor in cultivating children’s prosocial behaviour [ 57 , 62 ]. Empathic concern requires a person or the whole team to have an overall and largely unconscious “feeling” in terms of emotions, body language, previous experiences, and interpersonal relationships; therefore, this requires significant support from the fantasy system [ 63 ].

Perspective-taking and CPS skills

The effectiveness of group problem solving heavily depends on group member interactions and group composition. For perspective-taking, it provides the possibility for effective communication, which mainly affects the effective presentation of information, effective understanding of that information, conflict resolution, and cooperative interaction [ 64 , 65 ]. In management, perspective-taking has become an important factor in teamwork to solve problems [ 66 ]. During perspective-taking, the problem-solving process can be facilitated by promoting empathic concern, which is evident in the subjects’ cognitive dimension. For example, Falk found that perspective-taking leads to more creative solutions, and team members are more cooperative and facilitate more effective communication [ 64 ]. Bethune and Brown suggested that reflection affects the professional identity of patients by encouraging personal insights and providing different perspectives on patient interaction [ 67 ]. Reflection requires us to think about the past and sum up experiences and lessons from it. Thinking about problems from the standpoint of others can circumvent the limitations of our perspective of looking at problems only through ourselves and can promote the solution of complex problems.

Based on the points discussed above, we propose the following assumptions:

Personal distress is positively related to the CPS skills.

Fantasy is positively related to the CPS skills.

Perspective-taking is positively related to the CPS skills.

Algorithmic thinking and CPS skills

Algorithm thinking draws lessons from the algorithms of computers and artificial intelligence, which enables people to think and deal with things in parallel, process things in data, carry on data and logical reasoning to things, and finally achieve the goal of completing plans and tasks. As one of the core skills in the 21st century, algorithmic thinking abstractly and logically determines the elements used to solve problems through analysis [ 28 ]. One of the major applications of algorithmic thinking is jigsaw puzzle-based learning, which aims to make subjects think about how to build and solve problems, and improve their critical analysis and problem-solving skills [ 68 ]. Hasan Gürbüz leveraged straightforward visual and language templates to help individuals develop models and analyze information about events through games, resulting in improved problem-solving skills [ 69 ]. This mode of thinking, based on logic and steps, is very important for the development of critical thinking and computational thinking [ 28 ]. Many studies have shown that there is a positive correlation between algorithmic thinking and critical thinking [ 70 ]. In reflective learning, algorithmic thinking plays a significant role in computing, as evidenced in this study by recording a short video that necessitates organizing large amounts of data to develop suitable algorithms for analysis [ 71 ].

Creativity and CPS skills

Creativity affects our lives and is vital to the progress of society [ 72 ]. The definition of creativity highlights the integration of novel (original, unexpected) and appropriate (useful, adaptive concerning task constraint) ideas [ 73 ]. Since the 20th century, a large number of scholars in various fields have paid attention to creativity and CPS skills. Creativity is a valuable skill while designing solutions to new challenges that arise in developing societies [ 74 ]. For instance, Garrett noted that creativity plays a crucial role in problem-solving [ 75 ]. In many studies, creativity and critical thinking are interdependent, and creative tasks can improve people’s creativity [ 76 ]. In reflective learning, we utilize divergent thinking that frequently enhances our creativity.

Cooperativity and CPS skills

Many critics believe that cooperativity plays an important role in the cultivation of critical thinking [ 77 ]. Cooperativity receives considerable attention in the learning process due to its association with effective communication. For example, service-learning attaches great importance to cooperation, democratic citizenship, and moral responsibility in the learning process [ 78 ], and preschool educational institutions need to improve the experience through the collaborative exchange, to create favorable conditions for educators to re-examine educational activities, and determine the direction of new relationships through observation [ 79 ]. In reflective learning, subjects become aware of their contradictions and gain valid information, and critically assess peer opinions through active communication, which advances their ideas for program and CPS skills improvement.

Algorithmic thinking is positively related to the CPS skills.

Creativity is positively related to the CPS skills.

Cooperativity is positively related to the CPS skills.

Mediators and CPS skills

This study assumes that empathetic concern and critical thinking act as mediators between the CPS skills and their antecedents.

In Gibbs’s theory, the emotional dimension is a very important aspect of reflective learning [ 80 ]. Madeline Kelly’s research showed that reflection has a positive effect on the improvement of cognitive empathy [ 81 ]; however, there are few studies on the effect of reflective learning on empathy. Cognitive empathy includes fantasy and perspective-taking, while the emotional empathy includes personal distress and empathic concern [ 82 ]. Research shows that the concept of emotional empathy is state empathy, with the focus on altruism [ 83 , 84 ]. Emotional empathy plays an important role in patient-nurse communication [ 85 ]. Failure to deal with or understand emotions will make it difficult for nurses to think rationally and critically about issues that are important to nursing practice [ 86 ]. Therefore, we cannot ignore the influence of empathic concern on the CPS skills in reflective learning. We assumed that the ability of empathic concern can increase altruism and help to improve CPS skills. However, personal distress is usually considered to lead to egoism, which is not conducive to the formation of altruism [ 41 ]. In-depth investigation is necessary to understand its effect on CPS skills. As an important factor in prosocial behavior, the empathic concern serving as a mediator between cognitive behavior and prosocial behavior [ 87 ]. Based on the theories of O’Brien and Gülseven, we constructed a CPS skills model with empathic concern as the mediating variable [ 88 , 89 ].

Effective reflection is characterized by purposeful, focused, and questioning [ 90 ]. In the process of reflection, this mode of thinking requires us to think critically and center on the results. Reflective learning, also known as critical reflection [ 17 ], emphasizes the use of critical thinking. Many critics affirm the results of critical reflection [ 91 , 92 , 93 ]. Parrish and Crookes found that among nursing graduates, reflection helped them to solve problems through thoughtful reasoning and to develop strategies for self-monitoring of their professional competence [ 94 ]. Critical thinking is typically rational thinking, and through combining theory with practice, exploring the similarities and differences between theoretical knowledge and practical experience, and considering a variety of different viewpoints and opinions, the effect of reflective learning can be enhanced. Therefore, speculative reflection is designed to help us identify our shortcomings and think about how to correct and improve them. Critical thinking is widely recognized as an important skill in mediating CPS skills [ 10 ]. Based on the research of Kocak and Tee, we also view critical thinking as an intermediary variable, playing a mediating role in algorithmic thinking, creativity, and cooperativity within CPS skills [ 21 , 95 ].

Personal distress indirectly affects the CPS skills through empathic concern.

Fantasy indirectly affects the CPS skills through empathic concern.

Perspective-taking indirectly affects the CPS skills through empathic concern.

Empathic concern is positively related to the CPS skills.

Algorithmic thinking indirectly affects the CPS skills through critical thinking.

Creativity indirectly affects the CPS skills through critical thinking.

Cooperativity indirectly affects the CPS skills through critical thinking.

Critical thinking is positively related to the CPS skills.

Designing the fsQCA configuration model

In this study, a Venn diagram is used to design the fsQCA configuration model (Fig.  1 B), which was used to explore the causal model for improving CPS skills. In the diagram, arrow A represents a combination of perspective-taking, fantasy, and personal distress, and adds configurations that affect the CPS skills through, or including, empathetic concern. Arrow B represents a combination of algorithmic thinking, creativity, and cooperativity, and adds configurations that affect the CPS skills through, or including, critical thinking. Arrow C represents the combination of all the variables and represents the complex interaction of these factors to predict the resulting conditions.

Participants

Participants were 136 freshmen and medical majors from a university in southeastern China (‾Xage = 18.47, female = 82.35%, male = 17.65%). The inclusion criterion comprised students who had conducted reflective learning. The exclusion criteria comprised: (1) Students who did not make reflective videos, or (2) students suspected of plagiarizing reflective learning achievements. A total of 163 cases were included in the empirical study of reflective learning, and 136 effective samples were recovered, with an effective recovery rate of 83.44%.

Design and procedure

After receiving appropriate online training, classroom teachers implemented a reflective learning curriculum design among medical students in the autumn of 2021 (Fig.  2 ). Based on the Biochemistry and Molecular Biology Courses, the two rounds of teaching plan lasted a total of 14 weeks was design. In the first round of reflective learning, subjects were asked to read relevant literature, watch relevant video materials, etc., and carry out online learning. They were then asked to record learning videos on their own, and then upload the videos, followed by a double-blind mutual evaluation of learning videos between online students. In the second round of reflective learning, students adjusted their reflective learning according to the feedback from the previous round of mutual evaluation, implemented a second round of deeper material learning exploration, improved their reflective video, and summarized the main points of reflective learning. Teachers evaluated the reflective videos and learning points offline, and students learned and summarized according to the evaluation results. After the end of the entire process, we issued a competency assessment questionnaire to measure learners’ competency levels and the data was collected.

Reflective learning process

To measure the constructs under study, existing scales were used (see Table  1 for items associated with each construct and scale reliabilities).

A questionnaire was developed based on the existing mature scale, and the items were slightly adjusted according to the model. The relationship between the retained items and the dimensions was not complementary. Improvement of CPS skills is described as a structure composed of six antecedent variables and two mediating variables with different ways of thinking. The Davis Interpersonal Reactivity Index (IRI) was used for personal distress, fantasy, perspective-taking, and empathic concern [ 38 ], and the Computational Thinking Scale (CTS) was used for critical thinking, algorithmic thinking, creativity, problem solving, and cooperativity [ 74 , 96 , 97 ]. We structured it as personal distress (three items), fantasy (three items), and perspective-taking (two items) as ante-dependent variables, and the mediating effect of empathic concern (three items) on CPS skills (three items) was directly and through empathic concern (3 items). Similarly, algorithmic thinking (3 items), creativity (three items), and cooperativity (three items) acted as ante-variables, both directly and through the mediating effect of critical thinking (three items). All items were evaluated using a Likert 5-point scale, 5 = strongly agree, 4 = agree, 3 = neither agree nor disagree, 2 = disagree, 1 = strongly disagree, and the scores of items in reverse scoring were reversed. Entries for reverse scoring are marked with * in Table  1 . The questionnaire was translated into Chinese and distributed after discussion with experts.

Data analysis

We use multiple methods to analyze the data. First, PLS-SEM was carried out on the data through Smart-PLS 3.0 software to adapt the complex model analysis and explore the impact of various factors [ 48 ].

We measured the characteristics of the structure using internal consistency reliability, convergence validity, and discrimination validity. Internal consistency reliability was measured using the alpha and combinatorial reliability of Cronbach. And we checked the collinearity of the internal model and evaluated the deviation of the method using a variance inflation factor (VIF). According to the research objectives, we tested two models with different paths with significant correlations. The direct predictive effects of fantasy, personal distress, perspective-taking, creativity, cooperativity, and algorithmic thinking, as well as the mediating effects of empathic concern and critical thinking, on CPS skills were tested. A nonparametric, bias-corrected bootstrap with 5,000 subsamples and a 95% confidence interval was used. The structural model was evaluated by R² and by the significance of the estimated value of pathway relationships. The significance of pathway coefficients was evaluated using the bootstrap subsamples, and the structural model was evaluated using 5000 bootstrap subsamples [ 98 ]. R² values of 0.25, 0.50, or 0.75 are considered weak, moderate, and significant, respectively.

Although PLS-SEM can handle both external (measurement) and internal (structural) models [ 98 ], it is limited by symmetry. Therefore, we used fsQCA 3.1 software [ 49 ] to analyze asymmetry and obtain a sufficient causal combination configuration to study the complex relationship between variables more comprehensively and in detail. According to the fsQCA user guide, data calibration, truth table construction, and causal condition analysis are necessary steps in the process of data analysis [ 49 ]. In the first step, we converted the ordinary data into fuzzy sets by setting the original values from the Likert scale, which corresponded to full membership, cross-over anchors, and full non-membership based on Kallmuenzer’s analysis [ 99 ]. The second step is to construct the truth table and generate different combinations of causal conditions that are sufficient to affect the CPS skills by specifying a consistent cutoff value as the natural breakpoint in the consistency and the case number threshold as 1. The third, we analyzed the necessity of all the variables (critical thinking, creativity, algorithmic thinking, cooperativity, empathetic concern, perspective-taking, personal distress and fantasy) to the CPS skills, and the antecedent variables for mediate variables (critical thinking and empathic concern), and the necessity of mediating variables to the outcome variables. It is generally believed that a condition or combination of conditions is “necessary” or “almost always necessary” when the consistency score is higher than 0.9 [ 49 ]. Finally, we use standard analysis to obtain “intermediate solutions” (i.e., partial logical remainders are incorporated into the solution) to identify causal patterns that affect CPS skills.

The result of PLS-SEM

Evaluation of the reflection measurement model.

Except for the perspective-taking, the Cronbach’s alpha in the other dimensions was generally more than 0.7, reaching the standard recommended by Cohen (Table  1 ) [ 100 ]. After examining the external loads in the external model, we observed that most of the loads were more than 0.7, while the PD1 project was still less than 0.7. After checking the Cronbach’s alpha and average variance extracted (AVE), we confirmed that this factor had no negative effect on our research [ 98 ], and was thus retained the project. The sample size of the model is small (less than 300), and the items considered by perspective-taking are 2 (less than 3), so Cronbach’s alpha is easily less than 0.6. The alpha of perspective-taking is more than 0.5, which is still in a slightly plausible range. Therefore, we kept the item of perspective-taking. Secondly, the square root of AVE was greater than 0.5, which accords with the convergence validity [ 101 ]. In addition, we used the Fornell-Larker criteria to evaluate the discriminant validity (Table  2 ).

Evaluation of formative measurement models

The results showed that the VIF of all constructs was lower than the threshold of 3.3 (see Additional file. 1 ) [ 98 ]. In order to further analyze, this study evaluated the quality by blindfolding program (Q 2 ) and standardized root mean square residual (SRMR). The results showed that SRMR = 0.079, not exceeding 0.09 [ 102 ]. The blindfold program showed that Q 2 was greater than 0, which verified the predictive correlation of the research model [ 103 ].

Structural model evaluation

Evaluation of the structural model showed that the R² value was reasonable for exploratory research. Meanwhile, the direct pathway effect of fantasy, algorithmic thinking, creativity, and cooperativity on CPS skills was not significant ( p  > 0.05), and the pathway effect of personal distress on empathic concern was also not significant ( p  > 0.05). The other variables showed significant influences on CPS skills ( p  < 0.05) (Table  3 ). After deleting the insignificant pathways, we built a structural model between the CPS skills and the influencing factors (critical thinking, cooperativity, creativity, algorithmic thinking, empathic concern, fantasy, perspective-taking, and personal distress) (Fig.  3 ). Compared with the hypothetical model, mediating effects of empathic concern and critical thinking were observed; however, personal distress only had a direct effect on CPS skills, which was consistent with the previous view that empathic concern and personal distress should be discussed [ 51 ].

Path model and partial least square structural equation modeling (PLS-SEM) estimates

The result of fsQCA

The results of necessity showed that only cooperativity and creativity are necessary conditions for critical thinking (see Additional file. 2 , Additional file. 3 , and Additional file. 4 ).

FsQCA assessed the complex causal combination that led to improved CPS skills (Tables  4 , 5 , 6 and 7 ). The solution provided clues for each different pathway to the result, with all consistency values being higher than 0.8, and most coverage values being between 0.240 and 0.839 [ 104 ].

As shown in Table  4 , there are six approaches to the final model of complex conditions that lead to high CPS skills, among which the top three in terms of coverage are: (1) To achieve high CPS skills through high critical thinking, cooperativity, creativity, algorithmic thinking, empathic concern, personal distress, and perspective-taking (consistency = 0.974, coverage = 0.354). (2) Under conditions of high critical thinking, cooperativity, algorithmic thinking, and creativity, combined with high empathic concern, personal distress, and fantasy, the CPS skills can be improved (consistency = 0.950, coverage = 0.352). (3) A high level of critical thinking, cooperativity, algorithmic thinking, creativity, personal distress, perspective-taking, and fantasy (consistency = 0.950, coverage = 0.340) can promote the improvement of CPS skills.

To examine the mediating effect of empathic concern and critical thinking on the CPS skill, we analyzed the complex causality of fantasy, personal distress, perspective-taking, and empathic concern. The results showed in Table  5 indicated that the complex causal statement of fantasy, personal distress, perspective-taking, and empathic concern is one way, i.e., high perspective-taking and fantasy improves empathic concern skill (consistency = 0.821; coverage = 0.612), which supports the H7b and H7c assumptions in the SEM model. By contrast, the results of analyzing the complex causal relationship of creativity, cooperativity, and algorithmic thinking for critical thinking showed that there is a pathway for the complex causal statement of creativity, cooperativity, algorithmic thinking, and critical thinking (consistency = 0.867, coverage = 0.760), which will lead to improved critical thinking ability. This supported the hypotheses of H8a, H8b, and H8c in the SEM model.

The results of further analysis of the complex causal relationship between empathic concern and critical thinking for improved CPS skills (Table  7 ) showed that high empathic concern and critical thinking (consistency = 0.890, coverage = 0.550) will lead to improved CPS skills. This supported the H7d and H8d assumptions in the SEM model.

Discussion and conclusion

Theoretical implication.

To improve its ability to deal with complex practical problems, education has been committed to providing teaching measures that can stimulate subjects’ rational and irrational thinking. Healthcare professionals who utilize reflective learning must apply empathetic concern and critical thinking to confront challenges with high-quality solutions. Although previous studies confirmed the positive effects of empathic concern [ 19 ], and critical thinking [ 17 ] on CPS skills through symmetrical analysis, few studies have tested empathic concern and critical thinking at the same time. There is a dearth of studies that specifically investigate the factors that affect CPS skills in the context of reflective learning. And the previous studies on the factors influencing CPS skills mainly adopted traditional symmetric methods (such as regression and SEM), which did not fully capture the complexity behind the factors of influencing CPS skills. For instance, Hwang discovered that collaboration plays a crucial role in problem-solving, whereas communication may not be essential. In contrast, Kocak holds a contrasting perspective [ 21 , 105 ]. The factors affecting the CPS skills are often based on multiple causalities rather than a single causal relationship. Therefore, based on the theory of multi-dimensional empathy [ 38 ] and 21st-century skills [ 21 ], we analyzed the data of 136 medical students undergoing reflective learning using PLS-SEM and fsQCA, and constructed a hypothetical model to examine the relationships between the CPS skills and influence factors (critical thinking, cooperativity, creativity, algorithmic thinking, empathic concern, fantasy, perspective-taking, personal distress).

The PLS-SEM results (Table  3 ) showed that a variety of attributes can affect the CPS skills, among which critical thinking and empathic concern play an intermediary role between most antecedents and CPS skills. The fsQCA results partly verified the mediating effect of critical thinking and empathetic concern (Tables  5 and 6 ). In the PLS-SEM results (Table  3 ), personal distress was identified to directly affect the CPS skills; and the effect of personal distress on empathic concern was not shown in the fsQCA solution (Table  5 ), which proved that personal distress directly affects the CPS skills without the intermediary of empathetic concern. This result is similar to that of Jeon [ 106 ]; however, he believed that there is a negative correlation between personal distress and problem solving, which might be related to the different learning patterns (reflective learning) used in this study. Personal distress is a necessary process in reflective learning because the motivation of prosocial behavior eases our uncomfortable state of mind by reducing the disgusting and awakening cues sent out by others [ 107 ]. Reflection urges us to face these emotions and draw lessons from them. Hoffman noted that excessive personal distress can turn others-oriented motivation into self-directed motivation, thus reducing the occurrence of prosocial behavior [ 54 ], which emphasizes the differential treatment of personal distress in different learning modes. In addition, perspective-taking was identified to affect the CPS skills directly (Table  3 ; C1 in Table  4 ) and indirectly (Table  3 ; C1 in Table  5 ). Therefore, some of the results obtained from fSQCA validated the conclusions of PLS-SEM to some extent (Table  8 ).

The fsQCA results provided more configuration solutions of complex causality, which extended the results of PLS-SEM and further revealed the complexity of affecting the CPS skills. For example, the fsQCA results in Table  7 not only proved the mediating effect of empathetic concern and critical thinking, but also suggest that they work together to affect the CPS skills. This demonstrates that CPS skills are impacted by both rational and irrational thinking, and positive emotions play a critical role in fostering CPS skills [ 108 ]. In Table  4 cooperativity, creativity, algorithmic thinking, critical thinking, and personal distress all appear in forward solutions with high coverage (C1, C2, C3 in Table  4 ). This suggested that personal distress, cooperativity, creativity, algorithmic thinking, and critical thinking can be regarded as the core conditions to affect the CPS skills, and these conditions make an important contribution in the context of reflective learning. Researches by Chen [ 77 ], Garrett [ 75 ], Geisinger [ 70 ] and Ellis [ 17 ] respectively believed that collaboration, creativity, algorithmic thinking and critical thinking play an important role in CPS skills, and Sze [ 109 ] believed that personal distress could have a positive impact on prosocial behavior and altruism. The studies above provide are similar to our perspective.

Critical thinking is not only one of the basic skills in the 21st Century but also a key ability in reflective learning [ 110 , 111 ]. The process of questioning and reorganizing critical thinking is key to reflective learning. The complex structure of the problem-solving process requires critical thinking skills to find different solutions [ 30 , 112 , 113 , 114 ]. Table  4 higher coverage solutions (C1, C2, C3, NC1, NC2, NC3 in Table  4 ) and Table  7 higher coverage solutions (C1, NC1 in Table  7 ) showed that critical thinking ability training is helpful to improve a subject’s CPS skills. By contrast, a lack of critical thinking training is not conducive to improving CPS skills (NC1, NC2, NC3 in Table  4 ; NC1 in Table  7 ). Critical thinking is widely considered to be a competency closely linked to CPS skills [ 29 ], and our study approves this perspective. Moreover, cooperativity, creativity, and algorithmic thinking also appear in the forward solutions with high coverage (C1, C2, C3 in Table  4 ), combined with the mediating effect of critical thinking on cooperativity, creativity, algorithmic thinking, and the CPS skills. It is logical that the antecedents of critical thinking, such as cooperativity, creativity and algorithmic thinking, also play a positive role in the CPS skills. The result is similar to the findings of Özgenel [ 115 ], who believed that critical thinking and creative thinking affected problem-solving skill through decision-making style. These results suggested that we should pay attention to the cultivation of a critical thinking ability, especially through the cultivation of cooperativity, creativity, and algorithmic thinking, which positively and significantly improve a subject’s ability to solve complex problems.

Empathetic concern relationship with the complex configuration between its antecedent variables provides new ideas and insights to improve our ability to solve complex problems. Empathic concern, as a key factor of prosocial behavior [ 43 ], is also of positive significance to CPS skills in this study. The higher coverage solutions (C1, C2, C3 in Table  4 ; NC1, NC2, NC3 in Table  4 ; C1 in Table  7 ; NC1 in Table  7 ) showed that training in empathic concern is beneficial to improve a subject’s CPS skills, while a lack of empathic concern training is not conducive to improving CPS skills (NC1, NC2 in Table  4 ; NC1 in Table  7 ). By contrast, fantasy (C2, C3 in Table  4 ) and perspective-taking (C1, C3 in Table  4 ) appeared among the forward solutions with higher coverage in Table  4 . Combined with the mediating effect among empathic concern, fantasy, perspective-taking, and the CPS skills, it is not difficult for us to understand that the empathic concern antecedent variable: fantasy, and perspective-taking, also have positive significance for the CPS skills. This result aligns with the research findings of Hashmi [ 57 ] and Davenport [ 66 ]. Moreover, in the absence of empathetic concern, the pathway support of the combination of fantasy, perspective-taking, and personal distress for CPS skills also verified this positive significance from the other side (C3 in Table  4 ). However, personal distress (C1, C2, C3 in Table  4 ) appears independently in the forward solution, with high coverage in Table  4 , which verifies the direct effect of personal distress on the CPS skills, which was consistent with the results of PLSSEM. These further confirmed the theory of Dorner and Funke, who suggested that complex and dynamic non-routine situations across different domains require a collection of self-regulating psychological processes and a creative combination of knowledge and strategies, and is influenced by motivation and emotion, especially in a high-stakes environment[24]. In addition, according to the observation of the reverse solution of Table  4 , the combination of negative perspectivetaking and negative personal distress will be conducive to the low-level CPS skills (NC1, NC2, NC3, NC5 in Table  4 ). Interestingly, fantasy appeared not only in the forward solution with high coverage (C2, C3 in Table  4 ), but also in the inverse solution with high coverage (NC2, NC3 in Table  4 ), which seemed to suggest that the contribution of fantasy to improving CPS skills is neutral, which requires further research.

Consistent with the principle of causal asymmetry, fsQCA suggested that solutions generated by the same attributes in different areas might have the opposite impact on CPS skills, depending on how they combine or interact with other attributes. The lack or negation of some positive factors will lead to improved CPS skills, while the existence of some negative factors might also lead to similar results, depending on how they are configured with the other factors. For example, solution 4 in Table  4 shows that in the absence of critical thinking, cooperativity, algorithmic thinking, creativity, and fantasy, a combination of empathetic concern, personal distress, and perspective-taking could also have a positive effect on the improvement of CPS skills. There is a paucity of literature exploring the effects of empathetic concern, personal distress, and perspective-taking on CPS skills under conditions of low levels of critical thinking, cooperativity, algorithmic thinking, creativity, and fantasy. These insights provide new ideas for exploring improvements in CPS skills. Although PLS-SEM can verify the predetermined relationship between previous factors and the results of interest, it cannot provide these insights.

In addition, considering the complex nature of problem-solving skill under the condition of reflective learning, it is necessary to check the linear and nonlinear relationships between structures to fully understand the strategies and methods to improve CPS skills. In this study, as an ideal approach, PLS-SEM was used to identify the linear (symmetric) causal relationship between the improvement of CPS skills and influence factors. The fSQCA was used to identify the nonlinear (asymmetric), heterogeneous, and dynamic interactions between antecedents and behavioral results. The fSQCA improved identifying sufficient causal conditions for outcomes. The comprehensive application of PLS-SEM and fsQCA helped capture complex multiple causalities in the improvement of CPS skills, which makes theoretical contributions in terms of analytical techniques.

Practical implications

Aquino believes that the implementation of reflective learning strategies is conducive to the improvement of CPS skills [ 116 ], which is of practical significance for the design of learning strategies and training tools, including reflective learning. The PLS-SEM results showed that perspective-taking, as an important condition for affected CPS skills, not only plays a role through the intermediary effect of empathetic concern, but also directly affects the CPS skills. The researchers and learners can train subjects to think for others in the form of team communication and exchange of views. For the sake of others, it is necessary to think about CPS skills solutions from multiple angles and more comprehensively, by thinking about problems from the standpoint and perspective of others. Therefore, it is necessary to adopt evidence-based strategies for training to improve the CPS skills.

While the fsQCA results confirmed the PLS-SEM results, in turn its complex configuration helps researchers and learners to make more informed decisions about learning methods to improve CPS skills. The derived pathways indicated that there is more than one causal configuration that can improve CPS skills, and how to improve depends on a combination of attributes. For example, our results showed that the high level of critical thinking and its antecedent attributes, combined with the high level of empathic concern, personal distress, and perspective-taking, will lead to improvement of the CPS skills. The lack of critical thinking, cooperativity, algorithmic thinking, creativity, and fantasy, which to some extent emphasizes the utility of empathic concern, personal distress, and perspective-taking (Table  4 solution 4), make it necessary to pay attention to training medical students in empathic concern, personal distress, and perspective-taking using reflective learning. Aligned with our own research, it was acknowledged reflective learning as a potent method to enhance empathy [ 37 ]. Medical reflection should focus on cultivating the ability to speculate on materials and self-views, and at the same time, understand decision-making from the situation of others and feel the emotions of others to trigger empathy. Improvement of CPS skills should not only emphasize the reduction of personal distress, but also should look at the role of personal distress critically. At the same time, it also reminds us that we should fully consider the training situation of the subjects in the design of learning strategies. Critical thinking and its antecedents are regarded as the key solutions in fsQCA, which suggests that we can focus on the reflective learning mode when we train subjects for critical thinking, creativity, cooperativity, and algorithmic thinking. We should also consciously use this kind of thinking to solve problems in the process of reflective learning. In the design of other learning strategies, training in critical thinking ability and its antecedent variables, cooperativity, creativity, and algorithmic thinking, can effectively help subjects to improve their CPS skills.

Based on our understanding of how empathic concern and critical thinking work together to improve the CPS skills, we suggest that real and complex problems in life be taken as examples in the choice of reflective teaching strategies, to involve a series of related skills and characteristics, and fully exercise the two modes of thinking. This is because, in reflective learning, subjects internalize the thinking skills taught by others into their own thinking skills, cultivating the ability to monitor and reflect on the whole problem-solving process, and helping subjects to extract useful strategies, experiences, and patterns into their cognitive structure, thereby improving their CPS skills and accumulating more experience for possible intuitive thinking. This is more suitable for problems based on real-life, which is in line with the medical learning problem-based learning and case-based learning models.

In this study, a hypothetical model of the relationship between the CPS skills and influencing factors (critical thinking, cooperation, creativity, algorithmic thinking, empathic concern, fantasy, perspective-taking, and personal distress) was constructed and validated. The model confirmed the mediating effect of critical thinking and empathic concern on the CPS skills, the direct effect of personal distress, and the direct and indirect effect of perspective-taking on the CPS skills. Besides, fsQCA results provided a variety of configurations that enhanced the improvement of CPS skills. The findings not only enriched the theoretical system of affecting CPS skills, but also provided practical guidance for the development of learning strategies and assessment tools aimed at improving CPS skills.

Limitations and future research

Although this study enriches the theoretical and practical knowledge concerning the relationship between CPS skills and critical thinking, empathic concern, and other variables, it also has some limitations. First, the subjects were beginners in terms of reflective learning under the guidance of teachers, and lack experience in reflective learning, which might affect the accuracy and applicability of variables to some extent. In future research, we will improve these shortcomings, practice reflective learning practices in more subjects, and validate the model in a broader learning strategy, which would be very meaningful. Second, based on the model of this study, it is necessary to enrich the paths and develop a variety of learning and training tools to improve the CPS skills in the future research. The development of assessment tools for factors related to the measurement of CPS skills will facilitate targeted training and realize personalized learning practice guidance.

Data Availability

The data sets used and / or analyzed in this study have not been made public. If there is a reasonable need, they can be obtained from and provided by the corresponding author of this article.

Abbreviations

Complex problem-solving

Organisation for Economic Co-operation and Development

Partial least square structural equation modeling

• Fuzzy set qualitative comparative analysis

Average variance extracted

Variance inflation factor

Interpersonal Reactivity Index

Computational Thinking Scale

Structural equation modeling.

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Acknowledgements

The authors would like to thank the teachers and students who participated (including the teachers and students of Shulan International Medical College, Zhejiang Shuren University, China), and SmartPLS 3.0 and fsQCA 3.1 for their assistance in analysis of data of this process.

This study was funded by the Provincial Industry-University Cooperation Collaborative Education Project (NO.318 [2022] of the Zhejiang Development Reform Society), the Scientific and technological Innovation activity Plan and New Seedling Talent Plan for College students in Zhejiang Province in 2023, the First-class curriculum project of Zhejiang Province of China (NO.195 [2022] of the Zhejiang Education Office Letter, NO.352 [2022] of the Zhejiang Education Office Letter), the First batch of ideological and political demonstration courses of Zhejiang Province of China (NO.47 [2021] of the Zhejiang Education Letter), and the High-level pre-level program of Zhejiang Shuren University in 2019.

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Ying Wang, Ze-Ling Xu, Jia-Yao Lou & Ke-Da Chen

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ZLX and JYL conceived the project with the input of YW and KDC. YW, ZLX, and JYL collected and analyzed the relevant data for this study. YW and ZLX are the main authors of this study. All the authors read and approved the manuscript.

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Wang, Y., Xu, ZL., Lou, JY. et al. Factors influencing the complex problem-solving skills in reflective learning: results from partial least square structural equation modeling and fuzzy set qualitative comparative analysis. BMC Med Educ 23 , 382 (2023). https://doi.org/10.1186/s12909-023-04326-w

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Conceptualizing the complexity of reflective practice in education

Misrah mohamed.

1 Centre for Enhancement of Learning and Teaching, University of West London, London, United Kingdom

Radzuwan Ab Rashid

2 Faculty of Languages and Communication, Universiti Sultan Zainal Abidin, Terengganu, Malaysia

Marwan Harb Alqaryouti

3 Department of English Language, Literature and Translation, Zarqa University, Zarqa, Jordan

In higher education, reflective practice has become a dynamic, participatory, and cyclical process that contributes to educators’ professional development and personal growth. While it is now a prominent part of educators, many still find it challenging to apply the concept for it carries diverse meaning for different people in different contexts. This article attempts to (re)conceptualize the complexity of reflective practice in an educational context. Scholars in this field have taken different approaches to reflective practice, but all these approaches consist of four main components in common: (i) reflecting; (ii) planning for future action; (iii) acting; and (iv) evaluating the outcomes. We extend the existing literature by proposing a model which integrates these four components with three key aspects of reflection: problem-solving, action orientation, and criticality. The novelty of this model lies within its alignment of the three key aspects with different levels of criticality in a comprehensive framework with detailed descriptors provided. The model and its descriptors are useful in guiding individuals who directly or indirectly involve in critical reflection, especially educators, in appraising their levels of criticality and consequently engage in a meaningful reflection.

Introduction

In the field of education, reflective practice has been recognized as an important aspect in continuing professional development. Through reflective practice, we can identify the factors, the consequences of and the assumptions that underlie our actions. In higher education, reflective practice has become a dynamic, participatory, and cyclical process ( Ai et al., 2017 ) that contributes to educators’ professional development and personal growth ( McAlpine et al., 2004 ; De Geest et al., 2011 ; Davies, 2012 ; Marshall, 2019 ). It enables professional judgment ( Day, 1999 ) and fosters professional competence through planning, implementing and improving performance by rethinking about strengths, weaknesses and specific learning needs ( Huda and Teh, 2018 ; Cirocki and Widodo, 2019 ; Zahid and Khanam, 2019 ; Seyed Abolghasem et al., 2020 ; Huynh, 2022 ). Without routinely engaging in reflective practice, it is unlikely that educators will comprehend the effects of their motivations, expectations and experiences upon their practice ( Lubbe and Botha, 2020 ). Thus, reflective practice becomes an important tool that helps educators to explore and articulate lived experiences, current experience, and newly created knowledge ( Osterman and Kottkamp, 2004 ). Educators are continually recommended to apply reflective practice in getting a better understanding of what they know and do as they develop their knowledge of practice ( Loughran, 2002 ; Lubbe and Botha, 2020 ). In fact, reflective practice is now a prominent part of training for trainee teachers (e.g., Shek et al., 2021 ; Childs and Hillier, 2022 ; Ruffinelli et al., 2022 ) because it can help future teachers review their own practices and develop relevant skills where necessary.

Despite the wide acceptance of the concept of reflective practice, the notion of ‘reflection’ in itself is still broad. Our review of literature reveals that reflection is a term that carries diverse meaning. For some, “it simply means thinking about something” or “just thinking” (e.g., Loughran, 2002 , p. 33), whereas for others, it is a well-defined practice with very specific purpose, meaning and action (e.g., Dewey, 1933 ; Schön, 1983 ; Grimmett and Erickson, 1988 ; Richardson, 1990 ; Loughran, 2002 ; Spalding et al., 2002 ; Paterson and Chapman, 2013 ). We found many interesting interpretations made along this continuum, but we believe the most appealing that rings true for most people is that reflection is useful and informing in the development and understanding of teaching and learning (e.g., Seitova, 2019 ; McGarr, 2021 ; Huynh, 2022 ). This, however, is not enough to signify the characteristics of reflection. Consequently, many teachers find it hard to understand the concept and engage in reflective practice for their professional development ( Bennett-Levy and Lee, 2014 ; Burt and Morgan, 2014 ; Haarhoff et al., 2015 ; Marshall, 2019 ; Huynh, 2022 ; Knassmüller, 2022 ; Kovacs and Corrie, 2022 ). For example, some teachers from higher arts education have considered reflective practice as antithetical to practical learning ( Guillaumier, 2016 ; Georgii-Hemming et al., 2020 ) as they often frame explicit reflection as assessed reflective writing, which is “disconnected from the embodied and non-verbal dimensions of making and reflecting on art” ( Treacy & Gaunt, 2021 , p. 488). The lack of understanding of the concept has created disengagement in reflection and reflective practice ( Aliakbari and Adibpour, 2018 ; Huynh, 2022 ; Knassmüller, 2022 ) which resulted in poor insight and performance in practice ( Davies, 2012 ). To overcome this, educators should foster their understanding of the reflective practice, so they not only can reap its benefits for their own learning, but also facilitate and maximize reflective skills within their students.

In this paper, we aim to provide an overview of the concepts of effective reflective practice and present the value of reflective practice that can help teachers to professionally develop. First, we situate our conceptual understanding of reflective practice by discussing key issues surrounding reflection and reflective practice. Second, we present the key aspects of effective reflective practice. Finally, based on our discussion of key aspects of effective reflective practice, we introduce a revised model of reflective practice that may serve as a guide for educators to professionally develop. Although the model is but one approach, we believe it holds promise for others grappling as we are with efforts to encourage reflective practices among educators who find reflection in and on their practices a complex concept.

Key issues in reflective practice

The concepts of “reflection,” “reflective thought,” and “reflective thinking” have been discussed since 1904, when John Dewey claimed that an individual with good ethical values would treat professional actions as experimental and reflect upon their actions and consequences. Dewey defined reflection as the “active, persistent, and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” ( Dewey, 1904 , p. 10). His basic notion is that reflection is an active, deliberative cognitive process involving a sequence of interconnected ideas that include the underlying beliefs and knowledge of an individual.

Following Dewey’s original work and its subsequent interpretation, four key thought-provoking issues are worthy of discussion: reflective thinking versus reflective action; time of reflection; reflection and problem solving; and critical reflection. The first concern is whether reflection is a process limited to thinking about action or also bound up in action ( Grant and Zeichner, 1984 ; Noffke and Brennan, 1988 ; Hatton and Smith, 1995 ). There seems to be broad agreement that reflection is a form of thought process ( Ross, 1989 ; McNamara, 1990 ; Sparks-Langer et al., 1991 ; Hatton and Smith, 1995 ) even though some do not lead to action. However, Dewey’s first mention of “reflective action” suggests he was concerned with the implementation of solutions after thinking through problems. Therefore, reflective practice, in our view, is bound up with the constant, careful consideration of practice in the light of knowledge and beliefs. The complete cycle of reflection should then lead to clear, modified action and this needs to be distinguished from routine action derived from impulse, tradition, or authority ( Noffke and Brennan, 1988 ; Gore and Zeichner, 1991 ; Hatton and Smith, 1995 ).

The time frames within which reflection takes place, needs to be addressed—relatively immediate and short term, or rather more extended and systematic. Schön (1983) holds that professionals should learn to frame and reframe the problems they often face and after trying out various interpretations, modify their actions as a result. He proposes “reflection-in-action,” which requires conscious thinking and modification, simultaneously reflecting and doing almost immediately. Similar to this concept is “technical reflection,” involving thinking about competencies or skills and their effectiveness and occurs almost immediately after an implementation and can then lead to changes in subsequent action ( Cruickshank, 1985 ; Killen, 1989 ). While the notion of immediacy in reflective practice seems appropriate, some argue that the process should involve conscious detachment from an activity after a distinct period of contemplation ( Boud et al., 1985 ; Buchmann, 1990 ). This is because reflection demands contemplating rational and moral practices in order to make reasoned judgments about better ways to act. Reflective practice often involves looking back at actions from a distance, after they have taken place ( Schön, 1983 ; Gore and Zeichner, 1991 ; Smith and Lovat, 1991 ). While immediate and extended “versions” of reflections are both recognized, we suppose no one is better than another. However, we believe that being able to think consciously about what is happening and respond instantaneously makes for a higher level of reflective competence.

The third issue identified from our literature review is whether reflection by its very nature is problem orientated ( Calderhead, 1989 ; Adler, 1991 ). Reflection is widely agreed to be a thought process concerned with finding solutions to real problems ( Calderhead, 1989 ; Adler, 1991 ; Hatton and Smith, 1995 ; Loughran, 2002 ; Choy and Oo, 2012 ). However, it is unclear whether solving problems is an inherent characteristic of reflection. For example, Schön’s (1983) reflection-in-action involves thought processing simultaneously with a group event taking place, and reflection-on-action refers to a debriefing process after an event. Both aims to develop insights into what took place—the aims, the difficulties during the event or experience and better ways to act. While focusing on reacting to practical events, these practices do not often intend to find solutions to specific practical problems. Instead, reflective practitioners are invited to think about a new set of actions from if not wider, at least different perspectives.

The fourth issue in the literature revolves around “critical reflection.” Very often critical reflection is concerned with how individuals consciously consider their actions from within wider historical, cultural and political beliefs when framing practical problems for which to seek solutions ( Gore and Zeichner, 1991 ; Hatton and Smith, 1995 ; Choy and Oo, 2012 ). It is a measure of a person’s acceptance of a particular ideology, its assumptions and epistemology, when critical reflection is developed within reflective practice ( McNamara, 1990 ; Hatton and Smith, 1995 ). It implies the individual locates any analysis of personal action within her/his wider socio-historical and political-cultural contexts ( Noffke and Brennan, 1988 ; Smith and Lovat, 1991 ; Hatton and Smith, 1995 ). While this makes sense, critical reflection in the literature appears to loosely refer to an individual’s constructive self-criticism of their actions to improve in future ( Calderhead, 1989 ), not a consideration of personal actions with both moral and ethical criteria ( Senge, 1990 ; Adler, 1991 ; Gore and Zeichner, 1991 ). Thus, we see a need to define critical reflection in line with the key characteristics of reflective practice.

Effective reflective practice

Reflecting on the issues discussed above, we conclude that for reflective practice to be effective, it requires three key aspects: problem-solving, critical reflection and action-orientation. However, these aspects of reflective practice have different levels of complexity and meaning.

Problem-solving

A problem is unlikely to be acted upon if it is not viewed as a problem. Thus, it is crucial to problematize things during reflection, to see concerns that require improvement. This is not a simple process as people’s ability to perceive things as problems is related to their previous experiences. For example, a senior teacher with years of teaching experience and a rapport with the students s/he teaches will be immediately aware of students experiencing difficulties with current teaching strategies. However, a junior teacher whose experience is restricted to a three-month placement and who has met students only a few times will be less aware. The differences in experience also influence the way people interpret problems. For example, the senior teacher may believe his/her teaching strategy is at fault if half the students cannot complete the given tasks. A junior teacher with only 2 weeks teaching experience may deduce that the students were not interested in the topic, and that is why they cannot complete the tasks given. This example illustrates the range of ways a problem can be perceived and the advantages of developing the ability to frame and reframe a problem ( Schön, 1983 ). Problems can also be perceived differently depending on one’s moral and cultural beliefs, and social, ethical and/or political values ( Aliakbari and Adibpour, 2018 ; Karnieli-Miller, 2020 ). This could be extended to other factors such as institutional, educational and political system ( Aliakbari and Adibpour, 2018 ).

Framing and reframing a problem through reflection can influence the practice of subsequent actions ( Loughran, 2002 ; Arms Almengor, 2018 ; Treacy and Gaunt, 2021 ). In the example above, the junior teacher attributes the problem to the students’ attitude, which gives her/him little to no incentive to address the situation. This is an ineffective reflective practice because it has little impact on the problem. Thus, we believe it is crucial for individuals to not only recognize problems but to examine their practices ( Loughran, 2002 ; Arms Almengor, 2018 ; Zahid and Khanam, 2019 ) through a different lens to their existing perspectives so solutions can be developed and acted upon. This requires critical reflection.

Critical reflection

We believe it is the critical aspect of reflection that makes reflective practice effective and more complex, formulated by various scholars as different stages of reflection. Zeichner and Liston (1987) proposed three stages of reflection similar to those described by Van Manen (1977) . They suggested the first stage was “technical reflection” on how far the means to achieve certain end goals were effective, without criticism or modification. In the second stage, “practical reflection,” both the means and the ends are examined, with the assumptions compared to the actual outcomes. This level of reflection recognizes that meanings are embedded in and negotiated through language, hence are not absolute. The final stage, “critical reflection,” combined with the previous two, considers both the moral and ethical criteria of the judgments about professional activity ( Senge, 1990 ; Adler, 1991 ; Gore and Zeichner, 1991 ).

While the three stages above capture the complexity of reflection, individuals will only reach an effective level of reflection when they are able to be self-critical in their judgments and reasoning and can expand their thinking based on new evidence. This aligns with Ross’ (1989) five stages of reflection (see Table 1 ). In her five stages of reflection, individuals do not arrive at the level of critical reflection until they get to stages 4 and 5, which require them to contextualize their knowledge and integrate the new evidence before making any judgments or modification ( Van Gyn, 1996 ).

Five stages of reflections ( Ross, 1989 ).

Action-orientation

We believe it is important that any reflections should be acted upon. Looking at the types and stages of reflection discussed earlier, there is a clear indication that reflective practice is a cyclical process ( Kolb, 1984 ; Richards and Lockhart, 2005 ; Taggart and Wilson, 2005 ; Clarke, 2008 ; Pollard et al., 2014 ; Babaei and Abednia, 2016 ; Ratminingsih et al., 2018 ; Oo and Habók, 2020 ). Richards and Lockhart (2005) suggest this cyclical process comprises planning, acting, observing, and reflecting. This is further developed by Hulsman et al. (2009) who believe that the cyclical process not only involves action and observation, but also analysis, presentation and feedback. In the education field, reflective practice is also considered cyclical ( Clarke, 2008 ; Pollard et al., 2014 ; Kennedy-Clark et al., 2018 ) because educators plan, observe, evaluate, and revise their teaching practice continuously ( Pollard et al., 2014 ). This process can be done through a constant systematic self-evaluation cycle ( Ratminingsih et al., 2018 ) which involves a written analysis or an open discussion with colleagues.

From the descriptions above, it seems that cyclical reflective practice entails identifying a problem, exploring its root cause, modifying action plans based on reasoning and evidence, executing and evaluating the new action and its results. Within this cyclical process, we consider action as a deliberate change is the key to effective reflective practice, especially in the field of education. Reflection that is action-oriented is an ongoing process which refers to how educators prepare and teach and the methods they employ. Educators move from one teaching stage to the next while gaining the knowledge through experience of the importance/relevance of the chosen methods in the classroom situation ( Oo and Habók, 2020 ).

While reflection is an invisible cognitive process, it is not altogether intuitive ( Plessner et al., 2011 ). Individuals, especially those lacking experience, may lack adequate intuition ( Greenhalgh, 2002 ). To achieve a certain level of reflection, they need guidance and this can be done with others either in groups ( Gibbs, 1988 ; Grant et al., 2017 ) or through one-on-one feedback ( Karnieli-Miller, 2020 ). The others, who can be peers or mentors, can help provide different perspectives in exploring alternative interpretations and behaviors. Having said this, reflecting with others may not always feasible as it often requires investment of time and energy from others ( Karnieli-Miller, 2020 ). Therefore, teachers must learn how to scaffold their own underlying values, attitudes, thoughts, and emotions, and critically challenge and evaluate assumptions of everyday practice on their own. With this in mind, we have created a cyclical process of reflective practice which may help in individual reflections. It captures the three key aspects of reflective practice discussed above. This model may help teachers having a range of experience enhance their competence through different focus and levels of reflection (see Figure 1 ).

Cyclical reflective practice model capturing problem-solving, action-oriented critical reflection.

The model illustrates the cyclical process with three stages: reflection, modification and action. At the reflection stage, a problem and the root of the problem is explored so it can be framed as it is/was and then reframed to identify a possible solution. This is followed by a modification for change based on the reasoning and evidence explored during the reflection stage. Finally, the action stage involves executing action (an event), followed by the reflection stage to begin another cycle and continue the process.

As presented earlier, it is crucial for individuals to be able to frame and reframe problems through a different lens to their existing perspectives so solutions can be developed and acted upon. Thus, the model above expands Tsangaridou and O’Sullivan’s (1994) framework by adding together the element of problematizing. The current revised framework highlights the four focuses of reflection; technical addresses the management or procedural aspects of teaching practice; situational addresses the context of teaching; sensitizing involves reflecting upon the social, moral, ethical or political concerns of teaching; and problematizing concerns the framing and reframing of the problem identified within the teaching context. Considering the different levels of critical reflection, we extend the four focuses of reflection to three different levels of critical reflection: descriptive involves reflection of the four focuses without reasoning or criticism; descriptive with rationale involves reflection of the four focuses with reasoning; and descriptive with rationale and evaluation involves reflection of the four focuses with both reasoning and criticism (see Table 2 ). Each of these levels requires different degrees of critical analysis and competence to extract information from actions and experiences. Overall, level three best captures effective critical reflection for each focus.

A framework of reflection.

This revised model that we proposed encompasses different levels of critical reflection and is action-oriented. There is also a clear link to problem-solving which requires framing and reframing problems to accurately identify them, which may influence the value and effectiveness of the actions that follow ( Loughran, 2002 ). Thus, this model may help people, especially those with lack experience to recognize the different aspects of reflection so they can make better assessments of and modifications to their procedures ( Ross, 1989 ; Van Gyn, 1996 ).

The meaning of reflection and reflective practice is not clear cut. However, we believe a reflective educator should cultivate a set of responses to how their teaching operates in practice. As Dewey (1933) suggested, educators must find time to reflect on their activity, knowledge, and experience so that they can develop and more effectively serve their community, nurturing each student’s learning. However, this does not always happen. Some educators do not reflect on their own practice because they find the concept of reflective practice difficult to put into practice for their professional development ( Jay and Johnson, 2002 ; Bennett-Levy and Lee, 2014 ; Burt and Morgan, 2014 ; Haarhoff et al., 2015 ; Marshall, 2019 ; Huynh, 2022 ).

Our review of the literature indicates that reflective practice is a complex process and some scholars argue that it should involve active thinking that is more bound up with action ( Grant and Zeichner, 1984 ; Noffke and Brennan, 1988 ; Hatton and Smith, 1995 ). Thus, the complete cycle of reflective practice needs to be distinguished from routine action which may stem from impulse, tradition, or authority ( Noffke and Brennan, 1988 ; Gore and Zeichner, 1991 ; Hatton and Smith, 1995 ). In addition, some also argue that reflective practice involves the conscious detachment from an activity followed by deliberation ( Boud et al., 1985 ; Buchmann, 1990 ), and therefore reflective practice should not occur immediately after action. Although this is acceptable, we believe that instant reflection and modification for future action can be a good indicator of an individual’s level of reflective competence.

Reflective practice is an active process that requires individuals to make the tacit explicit. Thus, it is crucial to acknowledge that reflection is, by its very nature, problem-centered ( Calderhead, 1989 ; Adler, 1991 ; Hatton and Smith, 1995 ; Loughran, 2002 ; Choy and Oo, 2012 ). Only with this in mind can individuals frame and reframe their actions or experiences to discover specific solutions. Reflective practice is also complex, requiring critical appraisal and consideration of various aspects of thought processes. Individuals must play close attention to what they do, evaluate what works and what does not work on a personal, practical and professional level ( Gore and Zeichner, 1991 ; Hatton and Smith, 1995 ; Choy and Oo, 2012 ). However, some would consider critical reflection as no more than constructive self-criticism of one’s actions with a view to improve ( Calderhead, 1989 ). Consequently, scholars have taken different approaches to reflective practice in teaching areas that include critical thinking (e.g., Ross, 1989 ; Tsangaridou and O’Sullivan, 1994 ; Loughran, 2002 ). These approaches had four components in common: reflecting (observing actions, reviewing, recollecting), planning for future action (thinking and considering), acting (practice, experience, and learning), and evaluating (interpreting and assessing outcomes). We propose a model that embraces these four sub-areas and three key aspects of reflection: problem-solving, action orientation and critical reflection. We align these key aspects with level of criticality in a framework with detailed descriptors. It is hoped that these elements, combined together, demonstrate the complexities of reflection in a better, clearer way so that those struggling to adopt reflective practice will now be able to do so without much difficulty.

Author contributions

MM contributed to conception and written the first draft of the manuscript. RR contributed in the discussion of the topic. All authors contributed to the article and approved the submitted version.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Reflexion: An Iterative Approach to LLM Problem-Solving

Reflexion, an AI technique for tackling complex tasks without a definitive ground truth, enhancing problem-solving & user experience.

Humans are known for their ability to learn from mistakes, refining problem-solving approaches through self-reflection and analysis. This concept can be applied to a wide range of problems that lack a definitive ground truth, such as protein design, chemical design, and architectural design, as well as simpler problems encountered in everyday life.

In this article, we explore the concept of Reflexion, as outlined in this article, an iterative method for problem-solving, in LLMs like GPT-4, that mirrors human intelligence and its applications in various fields.

Creating Internal Test Suites for Problem-Solving

When faced with a problem that lacks a clear solution, humans typically create an internal test suite based on their understanding of the context. These test suites help evaluate potential solutions and assign confidence levels to them.

Adjustments are made until a solution that satisfies most of the tests is reached, which then becomes the proposed solution. In this scenario, the solution that meets most of the internal test cases is accepted as the one likely to result in the ground truth, and the chance of success relies on the probability of an erroneous test design.

Reflexion in AI and Neural Networks

As large language models (LLMs) and other sensory neural networks advance, Reflexion may see widespread applications in tasks traditionally performed by humans. For example, an AI chef could create dishes based on your cravings, refining the recipe through continuous feedback. Similarly, an AI business consultant might develop a successful business strategy without a predefined path. By using self-reflection for iterative learning, high-confidence solutions can be developed for problems in which a concrete ground truth is unavailable.

Self-improvement through Reflection

Reflection technique in gpt-4.

The reflection technique in GPT-4 enables the AI to analyze its own mistakes, learn from them, and improve its performance. By engaging in a self-contained loop, GPT-4 can devise better strategies to solve problems and achieve higher accuracy. This emergent property of self-reflection is more advanced in GPT-4 compared to previous models, allowing it to continually enhance its performance on various tasks.

By using Reflexion to iteratively refine the current implementation, we can develop high-confidence solutions for problems in which the concrete ground truth is unavailable. This approach involves relaxing the success criteria to internal test accuracy, allowing an agent to solve a variety of complex tasks that are currently dominated by human intelligence. Future applications of Reflexion may further enable agents to tackle a wide range of problems, pushing the boundaries of artificial intelligence and human problem-solving.

Real-life Examples of Reflection

An example of the reflection technique in action is when GPT-4 was given a task to write a poem with each word beginning with the letter "e." Although the initial attempt wasn't perfect, GPT-4 self-reflected and improved its performance to create a revised poem that met the requirements. Similarly, GPT-4 corrected a math quiz it had generated upon realizing that it didn't meet the requirement of having only one correct answer per question. These examples demonstrate the power of self-reflection in GPT-4 for improving its own performance.

When to Use the Reflection Technique

The reflection technique has proven to be a powerful tool for improving the performance of AI models, particularly in the context of GPT-4. It enables AI systems to learn from their mistakes, self-correct, and generate more accurate outputs. This section will discuss various scenarios in which the reflection technique can be most effectively utilized.

• Complex Problem Solving : The reflection technique is particularly useful when addressing complex problems that require multi-step reasoning or the synthesis of information from multiple sources. By reflecting on its initial approach and identifying errors or shortcomings, the AI model can refine its strategy and generate more accurate solutions.
• Language Comprehension : In tasks involving natural language processing, AI models may need to understand and interpret context, nuances, and subtleties within the text. The reflection technique can help improve the model's comprehension by allowing it to review and refine its initial interpretation, leading to better understanding and more accurate outputs.
• Code Generation and Evaluation : As demonstrated in the Human Eval coding test, GPT-4 can improve its code generation and evaluation skills by reflecting on its initial output and identifying errors. This can be particularly useful in programming-related tasks where precision and accuracy are paramount.
• Creative Tasks : In creative applications, such as poetry or content generation, the reflection technique can help AI models refine their output to better meet specific requirements or constraints. By allowing the model to review and critique its own work, it can iteratively improve the quality of its output, making it more relevant and engaging.
• Multimodal Tasks : The reflection technique can also be applied to tasks that involve multiple modalities, such as text-to-image or text-to-video tasks. By reflecting on its initial output, the AI model can identify areas for improvement and generate more accurate and coherent results across different modalities.
• Error Correction and Quality Control : In situations where the accuracy and quality of AI-generated output are crucial, the reflection technique can help identify and correct errors. By enabling the model to review its own work, it can spot mistakes and refine its output, leading to better results overall.

Examples of Situations and Prompts Using the Reflection Technique

To maximize the benefits of Reflexion when working with AI, it's crucial to tailor the approach according to the specific situation. By incorporating context-aware self-assessment prompts and providing clear guidance on the desired improvements, users can harness the AI's iterative learning capabilities more effectively. This enables the AI to adapt its responses to meet the unique demands of each situation, resulting in more accurate, relevant, and valuable output. Ultimately, the key to unlocking the full potential of Reflexion lies in the thoughtful customization and adaptation of the method to suit the task at hand.

The reflection technique can be applied to a wide range of tasks and domains, enhancing the performance of AI models in diverse situations. This section will provide examples of situations and prompts where the reflection technique can be effectively employed.

Example Prompts for Using Reflexion with ChatGPT

The following example prompts demonstrate how Reflexion can be used in conjunction with ChatGPT to improve the AI's performance through iterative learning and self-assessment:

• Prompt: "Provide an overview of the history of the French Revolution." AI Response: (First response)   Reflexion Prompt: "Evaluate the coherence and accuracy of your previous response about the French Revolution. Suggest improvements if necessary." AI Response: (Improved response)
• Prompt: "Explain the process of photosynthesis in plants." AI Response: (First response)   Reflexion Prompt: "Assess your previous explanation of photosynthesis in terms of clarity and scientific accuracy. Provide a revised explanation if needed." AI Response: (Improved response)
• Prompt: "Write a short story about a time-traveling adventurer." AI Response: (First response) Reflexion Prompt: "Critique your previously written short story in terms of plot, character development, and narrative flow. Offer suggestions to enhance the story." AI Response: (Improved response)
• Prompt: "Describe the advantages and disadvantages of renewable energy sources." AI Response: (First response) Reflexion Prompt: "Review your previous response on renewable energy sources for balance, comprehensiveness, and up-to-date information. Propose any modifications that could improve the response." AI Response: (Improved response)
• Prompt: "Give an overview of the economic theories of John Maynard Keynes." AI Response: (First response) Reflexion Prompt: "Analyze your previous overview of John Maynard Keynes' economic theories for clarity, depth, and accuracy. Recommend any adjustments or additional information that might enhance the response." AI Response: (Improved response)

These example prompts demonstrate how Reflexion can be applied to a variety of topics and domains, enabling ChatGPT to iteratively improve its performance by learning from its mistakes and refining its responses. This approach can lead to more accurate, coherent, and informative answers, ultimately enhancing the user experience and the utility of AI-generated content.

Examples of Reflexion in App or ChatBot Use Cases

Example of Reflexion in a Customer Service Scenario

Customer : "My internet connection keeps dropping. What can I do to fix it?"

AI Response (Initial): "I'm sorry to hear that. Please make sure your modem and router are connected properly and that all cables are securely plugged in."

Reflexion Prompt: "Evaluate the relevance of your previous response to the customer's issue of intermittent internet connection. Offer a more specific and helpful solution if necessary."

AI Response (Improved): "I'm sorry to hear that.  If your internet connection keeps dropping, please try the following steps:

• Reset your modem and router by unplugging them for 30 seconds and plugging them back in.
• Check for any firmware updates for your router.
• Move your router to a more central location in your home to improve signal strength.
• If the issue persists, contact your internet service provider as there may be an issue with the service in your area."

In this example, the AI initially provides a generic response that may not fully address the customer's problem. By applying Reflexion, the AI is able to evaluate its response and generate a more specific and helpful answer, enhancing the customer's experience and providing more effective support.

Example of Reflexion in a Medical Diagnosis Scenario

Medical Professional: "The patient presents with fever, joint pain, and a rash. What could be the possible diagnosis?"

AI Response (Initial): "Based on the symptoms, it could be a viral infection. You may want to consider running some blood tests."

Reflexion Prompt: "Reevaluate your previous response, taking into account the combination of fever, joint pain, and rash. Provide a more specific and accurate diagnosis, considering other relevant factors or diseases."

AI Response (Improved): "Considering the symptoms of fever, joint pain, and rash, the following differential diagnoses should be considered:

• Lyme disease: If the patient has been exposed to tick bites or has been in a wooded area, consider testing for Lyme disease.
• Rheumatoid arthritis: While the symptoms may resemble a viral infection, rheumatoid arthritis can present with similar symptoms. Check for elevated rheumatoid factor (RF) and anti-cyclic citrullinated peptide (anti-CCP) antibodies.
• Dengue fever: If the patient has recently traveled to an area with known dengue transmission, it's important to consider dengue fever and run appropriate tests.

Please remember that any AI-based suggestion should be used as supplementary information and not as a replacement for a medical professional's judgment."

In this example, the AI initially provides an incomplete diagnosis. By applying Reflexion, the AI reconsiders its conclusions and offers a more accurate and comprehensive assessment, thereby better assisting the medical professional in the diagnostic process.

Example of Reflexion in a Literary Analysis Scenario

User: "Analyze the theme of identity in 'The Catcher in the Rye' by J.D. Salinger."

AI Response (Initial): "In 'The Catcher in the Rye,' the theme of identity is explored through the protagonist, Holden Caulfield, as he struggles with adolescence and the transition into adulthood."

Reflexion Prompt: "Reevaluate your previous response on the theme of identity in 'The Catcher in the Rye.' Provide a more in-depth and nuanced analysis of how the theme is developed in the novel."

AI Response (Improved): "The theme of identity in 'The Catcher in the Rye' is intricately developed through Holden Caulfield's journey of self-discovery. The novel delves into the challenges faced by adolescents as they attempt to understand their evolving identities. Holden grapples with his own sense of self, often oscillating between a desire to preserve his childhood innocence and the pressure to conform to societal expectations of adulthood.

Throughout the story, Holden's encounters with various characters, such as Phoebe, Sally, and Mr. Antolini, force him to confront his own identity and .... (went on to provide a more complete analysis).

In this example, the AI initially provides a surface-level analysis of the theme of identity in 'The Catcher in the Rye.' By applying Reflexion, the AI is able to reevaluate its initial analysis and generate a more in-depth and nuanced interpretation of the theme and its development in the novel.

Reflexion Takeaway

Reflexion presents a powerful approach to enhancing AI models' problem-solving capabilities in situations where definitive ground truth is unavailable. By mirroring human problem-solving strategies, this method enables AI systems to iteratively refine their solutions through self-reflection, evaluation, and feedback. The various examples and scenarios discussed in this article illustrate the broad applicability and potential benefits of incorporating Reflexion into diverse domains, including customer service, medical diagnosis, literary analysis, translation, and recipe creation.

As AI continues to advance and play a greater role in our daily lives, it is crucial to develop models that can adapt, learn, and improve their performance through reflection. By integrating Reflexion into AI-powered applications and services, we can ensure that users receive more accurate, relevant, and helpful responses, fostering trust and satisfaction in these systems. Ultimately, the Reflexion technique offers a promising avenue for unlocking the full potential of AI, enabling it to tackle complex tasks and challenges that have traditionally been the domain of human intelligence.

Good example of us not seeing max GPT-4 capability yet, imo. Prompt design, tool use, meta cognition strategies (eg idea of attempt, critique, retry, capabilities model, etc) are very likely to go a long way. https://t.co/0quKagQECZ — Andrej Karpathy (@karpathy) March 26, 2023

A Guide to Chatting with ChatGPT - Tips for Natural Dialogue

Ask Me Anything (AMA) Prompting

How Self-Critique Improves Logic and Reasoning in LLMs Like ChatGPT

Optimizing Large Language Models to Maximize Performance

The Black Box Problem: Opaque Inner Workings of Large Language Models

How to Evaluate Large Language Models for Business Tasks

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Ray Optics: Reflection and Mirrors

Calculator pad, version 2, reflection and mirrors: problem set.

A light ray approaches a mirror at an angle of incidence of 25°. What is the angle of reflection?

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A light ray approaches a mirror at an angle of 22° with the mirror surface. What is the angle of reflection of this light ray?

Angle B = 38° Angle C = 52° Angle D = 38°

Anna Litical is doing the Plane Mirror Lab in physics class. She places a pin a distance of 4.9 cm from a plane mirror. How far behind the mirror can the image be expected to appear?

Baldwin Young stands 68 cm from his dresser mirror, inspecting his scalp. How far is the image of his scalp located from his scalp?

A meter stick (object) is placed in an upright position in front of a plane mirror as shown in the diagram at the right. The image of the meter stick is equidistant from the mirror. Suppose that the meter stick is equipped with a working eyeball capable of viewing the top and the bottom of its image. The eyeball is located at the 90-cm mark on the meter stick. Using either a ray diagram or geometry, determine … a. … the location of the intersection of the eye's line of sight with the mirror as the eyeball sights at the top of the image. b. … the location of the intersection of the eye's line of sight with the mirror as the eyeball sights at the bottom of the image. c. … the amount of mirror required by the meter stick to view the image.

a. 95 cm b. 45 cm c. 50 cm

A spherical concave mirror has a radius of curvature of +62 cm. What is the focal length of the mirror?

A decorative garden sphere has a diameter of 44 cm. The reflecting surface of the shiny sphere makes a great convex mirror. What is the focal point of the convex surface?

In a physics demonstration, a concave mirror having a 50.0 cm focal length is used to create images of a candle located at various locations along its principal axis. Beginning from a distance of several meters from the mirror, a candle is moved forward and its image is projected onto an opaque screen. Determine the image distances (distance from mirror to image) for object distances (distance from object to mirror) of … a. … 125.0 cm b. … 100.0 cm c. … 75.0 cm d. … 50.0 cm (Be careful with your math; the result is surprising.) e. … 25.0 cm

a. 83.3 cm b. 100.0 cm c. 150.0 cm d. No image. A solution to the mirror equation does not exist for this object distance. e. -50.0 cm

Problem 10:

Obtaining a large spherical mirror with a focal length of 0.654 m from the Physics Storeroom, Mr. H takes his last period class outside for a fascinating demo. A student volunteer holds the mirror at an angle such that the face of the mirror is directed towards the Sun - roughly 1.46x10 11 m away. Mr. H then uses a piece of paper with George Washington's picture on it to focus the image of the sun on the sheet of paper. Before the paper engulfs in flames, a bright image of the sun can be seen on the paper. Use the mirror equation to calculate the distance from the mirror to the image of the sun.

Problem 11:

Every morning Bob Gillette uses a shaving mirror with a focal length of 72 cm to view the image of his face. Supposing his face is 18 cm from the mirror, determine the image distance and the magnification of his face.

d i = -24 cm Magnification = 1.33

Problem 12:

The infamous Chinese magician Foo Ling Yu places a 56-mm tall light bulb a distance of 124 cm from a spherical concave mirror with a focal length of 62 cm. a. Determine the image distance and image height. b. Describe the orientation and type of the image.

a. d i = 124 cm and h i = -56 mm b. The image is inverted and real.

Problem 13:

In a physics lab, Anna Litical and Noah Formula position a small night light bulb at several locations along the principal axis of a concave mirror. Using a note card, they locate the image of the light bulb. The mirror has a focal length of 32.0 cm. What image distances would you expect Anna and Noah to observe when the object is located at distances of … a. … 85.3 cm from the mirror? b. … 64.0 cm from the mirror? c. … 48.1 cm from the mirror?

a. 51.2 cm b. 64.0 cm c. 95.6 cm

Problem 14:

Ima Primpin uses a cosmetic mirror to magnify her eyelashes during the traditional morning painting session. Her 1.2-cm long eyelashes are magnified to 1.6 cm when placed 5.8 cm from the mirror. a. Determine the image distance for such an upright image. b. Determine the focal length of the mirror.

a. -7.7 cm b. 23.2 cm

Problem 15:

In the Fall of 2006, the Sky Mirror sculpture was opened in Rockefeller Center in New York City. Standing three stories tall and weighing 23 tons, its concave side faced the Rockefeller Center and its convex side faced Fifth Avenue. a. A taxi on Fifth Avenue is located 38 m from the convex side of the sculpture and its image is one-fifth the size of the taxi. Determine the focal length of the mirror. b. Estimate the image size and image distance of the 260-m tall Rockefeller Center if it is located an estimated distance of 95 meters from the concave mirror surface. Assume the focal length of the concave side is the same magnitude as the focal length of the convex side.

a. -9.5 m b. d i = 11 m (rounded from 10.55 m) and h i = -29 m (- indicates inverted image)

Problem 16:

A convex spherical mirror has a focal point located a distance of 24.6 cm from the surface of the mirror. (You will have to decide for yourself whether f is + or -.) a. Find the image distance (in cm) for an object distance of 76.8 cm. b. Determine the magnification of this image.

a. d i = -18.6 cm b. M = 0.243

Problem 17:

A convenient store mounts a convex mirror in the corner of the store to serve as a security mirror and reduce the frequency of five-finger discounts . When Robin Storz is positioned a distance of 4.8 m from the mirror, her image is magnified by a factor of one-half. Determine the focal length of the mirror.

Problem 18:

Kerry Uss is studying the convex side of her soup spoon. She notices that her 3.8-cm tall nose appears to be 1.2 cm tall when positioned a distance of 2.4 cm from the spoon. a. Determine the image distance for this particular object distance. b. Determine the focal length of the convex side of the spoon.

a. d i = -0.76 cm b. f = -1.1 cm

Problem 19:

A large spherical mirror sculpture is constructed in the town square at Physicston, Illinois. The sculpture consists of a large sphere with a diameter of 24 meters which is coated with a reflecting material. A 1.8 meter tall photographer stands a distance of 38 m from the concave side of the sculpture and takes a picture. Determine the image distance and the magnification of the photographer.

d i = 7.1 m Mag = -0.19

Problem 20:

Baxter Nachure lives in the country along Sinewave road. It is difficult to pull out of the driveway onto the road since the road is curved and trees prevent him from seeing around the corner. He recently installed a large convex mirror at one of the curves to give him a wider angle of view. It has a focal length of -1.54 meters. Determine the magnification of an oncoming car located 35.8 m from the mirror.

Problem 21:

A virtual image is formed 26.9 cm from a concave mirror having a radius of curvature of 48.1 cm. Determine the object distance.

Problem 22:

An 4.9-cm tall object is positioned 14.8 cm from a mirror. Determine the radius of curvature which the mirror must have in order to produce an upright image that is 7.2 cm tall?

Problem 23:

A dentist uses a spherical mirror to produce an upright image of a patient's tooth which is magnified by a factor of 4.5 when placed 1.8 cm from the tooth. (a) What type of mirror - concave or convex - is being used? (b) What is the focal length of the mirror?

a. Concave mirror. Convex mirrors do not magnify the image; they only reduce the image. b. 2.3 cm

Problem 24:

The real image produced by a concave mirror is observed to be six times larger than the object when the object is 34.2 cm in front of a mirror. Determine the radius of curvature of this mirror.

Problem 25:

A shiny bauble (ornament) hangs on Mr. H's Christmas tree. The bauble has a radius of 4.8 cm. Matthew looks into the bauble and observes an image of his face which is one-eighth the size of his face. How far from the bauble is Matthew's face?

Problem 26:

A child at an amusement park stands in front of a concave mirror with a focal length of 73.9 cm. With great amusement, the child holds her cotton candy close to the mirror and observes that its image is magnified by a factor of five. Determine the object distance which creates this magnification of five.

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Total Internal Reflection Problems and Solutions

On this page, all aspects of the total internal reflection phenomenon are explored in the form of problem-solving.  

For reference, total internal reflection occurs when the incident light is in a medium with a higher index of refraction.  

In this situation, if the angle of incidence is greater than the critical angle, then the refracted ray totally internally reflected back into the original medium. 

Total Internal Reflection Problems

Problem (1): An unknown glass has an index of refraction of $n=1.5$. For a beam of light originating in the glass, at what angles does the light $100\%$ reflected back into the glass? (The index of refraction of air is $n_{air}=1.00$). 

Solution : When light moves through a medium with an index of refraction $n_1$ and strikes a boundary of a region with an index of refraction $n_2$ such that $n_1>n_2$, then total internal reflection can occur if the incident angle equals or is greater than a critical angle $\theta_c$ given by the following formula \[\sin\theta_c=\frac{n_2}{n_1}\] If the incident ray equals the critical angle, then the refracted ray exit along the boundary at the angle of $90^\circ$. 

For incident angles greater than the critical angle, $\theta_1 >\theta_c$, the refracted ray vanishes at the boundary, and $100\%$ is reflected back into the original medium. This process is called total internal reflection. 

In this problem, we are told that light is initially in a medium with a higher index of refraction and wants to enter a medium with a lower index of refraction. So, the necessary condition for occurring total internal reflection is satisfied. 

Thus, we must first find the critical angle whose magnitude is obtained as below \[\sin\theta_c=\frac{n_{air}}{n_{glass}}=\frac{1}{1.5}\] Taking the inverse of the sine of both sides, gives \[\theta_c=\sin^{-1}\left(\frac{1}{1.5}\right)=41.8^\circ\] Hence, if the angle of incidence in the glass exceeds about $42^\circ$, then all incident rays completely return back into the same medium. 

Problem (2): A ray of light traveling through glass with an index of refraction $n=1.5$ strikes the interface of the glass-water. Let the index of refraction of water be $n=1.33$. At what angle, the ray does not enter the water? 

Solution : We want no ray to exist in the water. We know that when a ray of light strikes a boundary of two different media, part of it is reflected back into the same medium and part of the ray enters the second medium (or refracted). 

In this question, we are asked to find an angle at which the refracted ray is removed. This occurs when the refracted angle in the second medium (here, water) becomes greater than or equal to $90^\circ$. Applying Snell's law of refraction , we have \begin{align*} n_1 \sin\theta_1&=n_2 \sin\theta_2\\\\ (1.5)\sin\theta_1&=(1.33)\sin 90^\circ\\\\ \Rightarrow \quad \sin\theta_2&=\frac{1.33}{1.5}\sin 90^\circ\\\\&=0.887\end{align*} Next, take the inverse of the sine to find the angle whose sine is $1.128$ \[\theta_2=\sin^{-1}(0.887)=62.5^\circ\] This incident angle at which the refracted angle becomes $90^\circ$ is called the critical angle. Any ray, in the glass, striking the boundary with an angle that exceeds 40 degrees, totally returns back into the same original medium. This phenomenon is also called total internal reflection.

Problem (3): Find the critical angle for a ray of light traveling from Ethyl alcohol to Benzene. Ethyl alcohol has an index of refraction $n=1.361$ and Benzene has $n=1.501$. 

Solution : There occurs no totally internal reflection because there is no critical angle for this configuration. In this scenario, light is traveling from a rare medium (low $n$) to a dense medium (with high $n$) and this is contrary to the criteria for the formation of a total internal reflection. 

Thus, total internal reflection occurs when light traveling in a medium strikes the boundary of a medium whose index of refraction is higher than the original medium. 

Problem (4): The speed of sound in a room filled with air is $343\,{\rm m/s}$. The walls of this room are made of concrete, in which the speed of sound is $1850\,{\rm m/s}$.  (a) Find the critical angle for total internal reflection of sound waves striking the air-concrete interface.  (b) If we want the sound to undergo total internal reflection, in which medium must it be traveling?

Solution : To find the critical angle for a total internal reflection problem, we must use the following equation \[\theta_c=\sin^{-1}\left(\frac{n_{rare}}{n_{dense}}\right)\] But in this question, neither of indices of refraction are given. 

Recall that Snell's law of refraction is also written in terms of velocities instead of indices of refraction. Thus, the alternate form of Snell's law is given by the following equation \[\frac{\sin\theta_1}{\sin\theta_2}=\frac{v_1}{v_2}\] where the subscripts $1$ and $2$ refer to the incident and refracted rays. 

(a) We know that the critical angle is the angle at which the refracted ray becomes $90^\circ$. So, setting $\theta_2=90^\circ$ in the above equation, and solving for $\theta_1=\theta_{cri}$, we get \begin{align*} \sin\theta_{cri}&=\sin\theta_2 \left(\frac{v_1}{v_2}\right)\\\\&=\sin 90^\circ \left(\frac{343}{1850}\right)\\\\&=0.186 \end{align*} Now, take the inverse of sine from both sides to find the angle whose sine is $0.186$ \[\theta_{cri}=\sin^{-1}(0.186)=10.7^\circ\] Hence, if the sound waves strike the wall at angles greater than about $11^\circ$, then all is reflected back into the wall without any waves passing through the wall. 

(b) As you know, total internal reflection occurs when mechanical waves (sound) or electromagnetic waves (light) are incidents on a boundary of a medium having a lower index of refraction than the original medium. 

We can modify the above statement to accommodate the velocities in both mediums where the indices of refraction are not known. In this case, the total internal reflection occurs when the waves strike the boundary of a medium, in which the speed of the waves is greater than the original medium. 

In this problem, the total internal reflection can occur when sound waves travel from the air and strike the wall at an angle greater than the critical angle found above, i.e. $\theta>10.7^\circ$. 

Problem (5): The boundary of the two mediums is shown in the figure below. The angle of incidence with the horizontal is $30^\circ$. The incident ray refracted parallel to the interface. Find the index of refraction of the second medium. 

Solution : We are told in the problem that the refracted ray is parallel to the boundary of two mediums. We know that this situation always occurs when the incident ray is in a dense medium and strikes the boundary of a less dense medium. 

So, the second medium must have a lower index of refraction than the original medium. Note that the incident angle is measured with a line perpendicular to the boundary. Here, the incident angle is $\theta_1=90^\circ-30^\circ=60^\circ$. 

Setting the refracted angle as $\theta_2=90^\circ$ in Snell's law of refraction, and solving for the index of refraction $n_2$, we will have \begin{align*} n_1 \sin\theta_1&=n_2\sin\theta_2\\\\\sqrt{3}\sin 60^\circ&=n_2 \sin 90^\circ\\\\ \sqrt{3}\left(\frac{\sqrt{3}}2\right)&=n_2\\\\\Rightarrow n_2 &=\frac 32 \end{align*} As expected, the second medium must be less dense than the first medium. 

Problem (6): A beam of light moves from air into an unknown glass. The angle of incidence is $30^\circ$, and the angle of refraction is $22^\circ$. For a beam of light originating from the glass, find the critical angle. 

Solution : Critical angle is defined when a ray travels in a dense medium and strikes a boundary with a lower index of refraction. Its magnitude is calculated as \[\theta_c=\sin^{-1}\left(\frac{n_2}{n_1}\right)\] where always $n_1>n_2$. 

When a beam of light strikes the interface of the two media at the critical angle, the refracted ray exits parallel to the boundary. In this case, the refracted angle is $90^\circ$. 

Here, we want to find the critical angle when the light is in the glass and enters the air. The index of refraction of the glass is unknown. 

From the first part of the question, we can find the glass's index of refraction by applying Snell's law of refraction. \begin{align*} n_1 \sin\theta_1&=n_2 \sin\theta_2\\\\ (1)\sin 30^\circ&=n\sin 22^\circ\\\\ \Rightarrow \quad n&=\frac{\sin 30^\circ}{\sin 22^\circ}(1)\\\\&=\frac{0.5}{0.375}\\\\&=1.33 \end{align*} By having the index of refraction of the glass, the critical angle is found for this total internal reflection problem from the following equation \[\theta_c=\sin^{-1}\left(\frac{n_2}{n_1}\right)=\sin^{-1}\left(\frac{1.00}{1.33}\right)=48.8^\circ\] Thus, if light originated from the water incident on the boundary of air at an angle greater than about $49^\circ$, then light is totally returned back into the water and does not enter the air.

Problem (7): The critical angle of a specific glass in the air is $\theta_c=37.8^\circ$. Now suppose that we put it into a tank of water. What will change its critical angle?

Solution : In the first case, the boundary is composed of glass-air. Using critical angle formula, we have \[\sin\theta_c=\frac{n_{air}}{n_{glass}}\] In the second case, the glass surrounded by a water. So, the interface is glass-water. Again, its critical angle is found as \[\sin\theta'_c=\frac{n_{water}}{n_{glass}}\] The index of refraction of the glass is unknown. Dividing the second relation by the first one,  gives \[\frac{\sin\theta'_c}{\sin\theta_c}=\frac{n_{water}}{n_{air}}\] Setting $n_{water}=1.33$ and solving for the unknown angle $\theta'_c$, we get \begin{align*} \sin\theta'_c&=\sin\theta_c \left(\frac{n_{water}}{n_{air}}\right)\\\\&=\sin(37.8^\circ)\frac{1.33}{1.00}\\\\&=0.816\end{align*} Take the inverse sine of both sides to find the angle whose sine is $0.816$ \[\theta'_c=\sin^{-1}(0.816)=54.7^\circ \]

Problem (8): A light bulb is placed 5 meters below a swimming pool. What is the diameter of the circle of light formed on the surface seen directly from above? 

Solution : We can assume the light bulb to be a point source. Rays emit in all directions from that point source and strike the water-air interface. Some rays are incident on the boundary at less than the critical angle, refracted, and enter the air. 

The rays have an incident angle greater than the critical angle, do not enter the air, and $100\%$ reflect back into the water. 

These completely reflected rays are responsible for the formation of a circle of light on the surface of the water. 

The diameter of the circle of light is the distance between the two points at which the rays reach the surface at the critical angle. First, using critical angle formula, we find it as below \[\theta_c=\sin^{-1}\left(\frac{1.00}{1.33}\right)=48.7^\circ\] As you can see from the geometry, and using the definition of sine function, the radius of the circle of light is found as \[\sin\theta_c=\frac{r}{H} \Rightarrow r=H\sin\theta_c\] where $H$ is the pool's depth. So, the radius or diameter of the circle $D=2r$ is computed as below \[D=2H\sin\theta_c=2(5)(\sin 48.7^\circ)=7.5\,{\rm m}\] 

Problem (9): A beam of light is incident on the surface $AB$ of a prism surrounded by air at the critical angle, as shown in the figure. Find the angle of incidence, $\theta_1$. 

Solution : we are told that the ray is incident on the surface $BC$ at the critical angle. Thus, the refracted ray must be parallel to $BC$. 

To find the critical angle in a total internal reflection problem, using Snell's law, we arrive at the following formula \[\sin\theta_c=\frac{n_{rare}}{n_{dense}}\] Here, the prism is surrounded by air, so $n_{rare}=1.00$. The index of refraction of the prism, $n_p$, is not given. 

Thus, the critical angle at the boundary of $BC$ is found as below \[\sin 42^\circ=\frac{1}{n_p} \quad (I)\] Now, we must apply Snell's law at the entering point into the prism for the incident ray, but the angle of refraction at that point is not known. 

From geometry of the figure, we have $\beta=90^\circ-42^\circ=48^\circ$. On the other, recall that the sum of angles of a triangle equals $180^\circ$.

Thus, the angle $\alpha$ is determined as below \begin{gather*} \alpha+\beta+60^\circ=180^\circ \\ \alpha+48^\circ+60^\circ=180^\circ\\\Rightarrow \quad \alpha=72^\circ\end{gather*} Now that we have angle $\alpha$, the refracted ray at the entering surface $AB$ is simply found as below \[\theta_2+\alpha=90^\circ \Rightarrow \theta_2=18^\circ\] Applying Snell's law at this surface $AB$, we get \begin{align*} n_1 \sin\theta_1&=n_2 \sin\theta_2 \\\\ (1)\sin\theta_1 &=n_p \sin 18^\circ \quad (II) \end{align*} From equation $(I)$, the index of refraction of prism is $n_p=\frac{1}{\sin 42^\circ}$. Substituting this into equation $(II)$, we can get the incident angle as below \begin{align*} \sin\theta_1 &=\frac{\sin 18^\circ}{\sin 42^\circ}\\\\&=0.462 \end{align*} By taking the inverse of sine from both sides, we can find the angle whose sine is $0.461$ \[\theta_1=\sin^{-1}(0.461)=27.5^\circ\] 

In this article, some problems about total internal reflection were presented along with detailed solutions. 

The necessary conditions for total internal reflection are as below: 

(1) Light must travel from a denser medium to a rare medium. 

(2) The angle of incidence in the denser medium must be greater than the critical angle at the boundary of the two media. 

Author : Ali Nemati Date Published : 9/3/2021  

© 2015 All rights reserved. by Physexams.com

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Solving complex problems with technology, diversity at sphere las vegas.

• Apr 1, 2024
• Andrew Husband

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Something new, large, and round has dominated the Las Vegas skyline since last summer: Sphere .

After debuting this summer, the state-of-the-art entertainment venue became instantly recognizable thanks to pictures and videos on social media and Reddit. Some of the most viral posts depict the 580,000-square-foot fully programmable LED Exosphere projecting a giant yellow emoji that smiles, sleeps, and follows airplanes flying overhead with a look of wonder.

According to Jared Miller ’98, LGO ’03, Sphere’s growing popularity long before its official opening in September 2023—when the Irish rock band U2 began its months-long residency—is a testament to the work of the creative team that made it happen.

“The team we have assembled in many ways reflects my experience at MIT,” says Miller, who is executive vice president and CIO at Sphere Entertainment.

“We have deep technology experts, engineers, scientists, artists, creative technologists, and people who have worked in many different industries who have come together to embrace this vision,” adds Miller. “The diversity of the people you’re surrounded with … brings different perspectives [and an] enthusiasm to come together and collaborate on a solution. This is what’s really special about Sphere, and it applies to MIT as well.”

Technology and Experience

As an undergraduate, Miller majored in chemical engineering and interned in the oil and gas industry, after which he decided to pursue an alternative career path. This led to a job at Intel during the race to build the first microprocessor capable of achieving 1 gigahertz.

Miller learned a lot about himself and his professional interests during the experience, and he was eager for more. “I wanted to learn more about the business aspects; to move from being an engineer into a broader management and strategy role,” he says.

He applied to the program then known as Leaders for Manufacturing (LFM) and matriculated in 2001. The program was then focused on “Big M manufacturing,” but as Miller recalls, LFM was growing and evolving toward its eventual renaming as Leaders for Global Operations (LGO). As a result, the student experience was expanding far beyond manufacturing and into other disciplines.

For Miller, this meant the airline industry. “The intersection of technology and guest experience was taking hold in the industry because it required a pretty rapid shift in how airports and airlines were thinking about … how they were moving people through their journey,” he says.

LGO students participate in six-month internships at LGO partner companies that serve as a basis for their thesis projects. Miller interned at Continental Airlines, where he studied the use of self-service check-in kiosks and their impact on traveler experience.

After graduation, he remained at Continental—which merged with United Airlines in 2010 —for almost a decade, until he pivoted to designing and building new venues in the sports and entertainment industry.

“MIT constantly encouraged and challenged us to think very openly about the opportunities that lie ahead. In my case, these pivots didn’t seem that odd or awkward between the different engineering fields and industries. It was just another step in the journey,” says Miller. “The intersection of technology and the guest experience was at the heart of what I was doing.”

Invention and Diversity

Until the venue’s official launch, all the public knew about Sphere was what they could see displayed on its massive Exosphere. Once U2 played their first of 40 shows and filmmaker Darren Aronofsky’s “Postcard from Earth” premiered as part of The Sphere Experience, audiences were granted access to what Miller and his team had also been working on.

These include a fully immersive display plane with 16K x 16K resolution, 4D technologies like haptic systems and atmospheric effects to influence what guests are literally feeling, the world’s largest beamforming audio system, and more.

“So much of what we’ve done at Sphere has been about invention,” says Miller.

By “invention,” Miller means the sense of identifying potential experiences for the audience and working back from that point when developing the necessary technologies—though he is quick to explain that technology is not always the solution to a problem, but simply one of many tools that can be used.

“A lot of it comes through process improvements,” explains Miller. “You’ve got to analyze what didn’t work, using a lot of data to come back and say, ‘You know what? This is what needs to change. This is why this approach didn’t work.’ Then get right back up and find another way to tackle the problem.”

From using systems thinking and data analytics to address complex problems—like how to guarantee that 18,000 people in a spherical structure will have the same experience—to building diverse teams that collaborate to produce possible solutions, Miller credits many of the tools at his disposal to his learnings at MIT.

He learned how to think about complex problems more broadly, and how to think collaboratively with others from a wide variety of backgrounds—much like the team at Sphere.

“At LGO, we discussed and worked on problems that hadn’t been solved yet. We needed a diverse group of people to come together and use all their experiences and expertise to create that solve,” says Miller. “It’s bringing together that diverse group of people to work together that ultimately gets to a great solution.”

This story was originally published by the MIT Sloan School of Management .

Photos: Sphere Entertainment

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