collaborative problem solving in education

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• Published: 04 June 2018

Collaborative problem-solving education for the twenty-first-century workforce

• Stephen M. Fiore 1 ,
• Arthur Graesser 2 &
• Samuel Greiff 3  

Nature Human Behaviour volume  2 ,  pages 367–369 ( 2018 ) Cite this article

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The complex research, policy and industrial challenges of the twenty-first century require collaborative problem solving. Assessments suggest that, globally, many graduates lack necessary competencies. There is a pressing need, therefore, to improve and expand teaching of collaborative problem solving in our education systems.

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Fiore, S. M. et al. Collaborative Problem Solving: Considerations for the National Assessment of Educational Progress (National Center for Educational Statistics, United States Department of Education, Washington DC, 2017).

Graesser, A. C. et al. in Assessment and Teaching of 21st Century Skills. Research and Applications (eds Care, E., Griffin, P. & Wilson, M.) Ch. 5 (Springer International Publishing, Cham, 2018); https://doi.org/10.1007/978-3-319-65368-6_5 .

PISA 2015 Results (Volume V): Collaborative Problem Solving (Organization for Economic Cooperation and Development, 2017); https://doi.org/10.1787/9789264285521-en

National Academies of Sciences, Engineering, and Medicine Education for Life and Work: Transferable Knowledge and Skills in the 21st Century (National Academies Press, Washington DC, 2012); https://doi.org/10.17226/13398

National Research Council Enhancing the Effectiveness of Team Science (National Academies Press, Washington DC, 2015); https://doi.org/10.17226/19007

The Royal Society Assessing Experimental Science in 11–18 Education: New Research Directions (Royal Society Press, 2016); https://royalsociety.org/~/media/events/2016/10/education-conference-report-12-october-2016.pdf

Hart Research Associates Falling Short? College Learning and Career Success (Association of American Colleges and Universities, 2015).

Critical Skills Survey (American Management Association, 2012); https://www.amanet.org/uploaded/2012-Critical-Skills-Survey.pdf

National Academies of Sciences, Engineering, and Medicine Building America’s Skilled Technical Workforce (National Academies Press, Washington DC, 2017); https://doi.org/10.17226/23472

Weinberger, C. J. Rev. Econ. Stat. 96 , 849–861 (2014).

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Fiore, S.M., Graesser, A. & Greiff, S. Collaborative problem-solving education for the twenty-first-century workforce. Nat Hum Behav 2 , 367–369 (2018). https://doi.org/10.1038/s41562-018-0363-y

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• John Douglas Buchanan
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The Australian Educational Researcher (2024)

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• Collaborative Problem Solving® »

Collaborative Problem Solving® (CPS)

At Think:Kids, we recognize that kids with challenging behavior don’t lack the will  to behave well. They lack the  skills  to behave well.

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Kids with challenging behavior are tragically misunderstood and mistreated. Rewards and punishments don’t work and often make things worse. Thankfully, there’s another way. But it requires a big shift in mindset.

Helping kids with challenging behavior requires understanding why they struggle in the first place. But what if everything we thought was true about challenging behavior was actually wrong? Our Collaborative Problem Solving approach recognizes what research has pointed to for years – that kids with challenging behavior are already trying hard. They don’t lack the will to behave well. They lack the skills to behave well.

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CPS helps adults shift to a more accurate and compassionate mindset and embrace the truth that kids do well if they can – rather than the more common belief that kids would do well if they simply wanted to.

Flowing from this simple but powerful philosophy, CPS focuses on building skills like flexibility, frustration tolerance and problem solving, rather than simply motivating kids to behave better. The process begins with identifying triggers to a child’s challenging behavior and the specific skills they need help developing.  The next step involves partnering with the child to build those skills and develop lasting solutions to problems that work for everyone.

The CPS approach was developed at Massachusetts General Hospital a top-ranked Department of Psychiatry in the United States.  It is proven to reduce challenging behavior, teach kids the skills they lack, and build relationships with the adults in their lives. If you’re looking for a more accurate, compassionate, and effective approach, you’ve come to the right place. Fortunately, anyone can learn CPS. Let’s get started!

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Exploring Factors that Influence Collaborative Problem Solving Awareness in Science Education

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• Published: 20 February 2020
• Volume 25 , pages 337–366, ( 2020 )

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• Li Chen   ORCID: orcid.org/0000-0003-0063-8744 1 ,
• Koichi Inoue 2 ,
• Yoshiko Goda 3 ,
• Fumiya Okubo 4 ,
• Yuta Taniguchi 5 ,
• Misato Oi 6 ,
• Shin’ichi Konomi 7 ,
• Hiroaki Ogata 8 &
• Masanori Yamada 7  

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This study designed a science course following collaborative problem solving (CPS) processes, and examined the effect on students’ CPS awareness. The Limnic Eruption CPS course was implemented using a Moodle system in a tenth-grade class. Considering the complex and coordinated nature of CPS, in order to improve CPS skills, it is important to identify what are related with the development of all sub-skills of CPS. Thus this study aimed to determine potential factors that affect the use of CPS skills in students’ motivational and behavioral dimensions. Multiple data sources including learning tests, questionnaire feedback, and learning logs were collected and examined by learning analytics approach. The relationships between students’ CPS awareness with their learning motivation and learning behaviors were explored. The research findings indicated a significant positive correlation between CPS awareness and certain learning motivation factors and learning behavior factors. Considering the students’ individual differences in learning abilities, we also compared the results of high and low performance groups. As a result, low performers’ learning motivation and learning behaviors were correlated with the social domain of CPS awareness, while those of high performers were correlated with their cognitive awareness.

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Abbreviations

Collaborative problem solving

Information communications technologies

• Learning analytics

Moodle, Mahara, and BookRoll

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Acknowledgements

This research was partially supported by Japan Society for the Promotion of Science (JSPS) Grant Number: JP19H01716, 16H06304, JST AIP Grant No. JPMJCR19U1.

This study is funded by Japan Society for the Promotion of Science (JSPS) Grant Number: JP19H01716, 16H06304, JST AIP Grant No. JPMJCR19U1.

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Faculty of Business Administration, Takachiho Univerisity, Tokyo, Japan

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Conflict of interest.

Drs. Ogata and Yamada received research grants from JSPS for this research project. Drs. Goda, Okubo, Taniguchi, Oi, Konomi, Yamada received research grants from JSPS for other research project. Drs. Ogata received research grants from Cross-Ministerial Strategic Innovation Promotion Program from Cabinet Office. Ms. Li Chen and Mr. Inoue do not have any conflict on this research.

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Chen, L., Inoue, K., Goda, Y. et al. Exploring Factors that Influence Collaborative Problem Solving Awareness in Science Education. Tech Know Learn 25 , 337–366 (2020). https://doi.org/10.1007/s10758-020-09436-8

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Teaching Collaborative Problem-Solving for 21st-Century Success

By davidlreese,

Tips on providing opportunities for students to apply problem-solving and collaboration skills. 

By David Reese, Ed.D.

As educators, it’s our job to prepare the students of today for the jobs of tomorrow.  Collaborative problem-solving is a critical part of the 21st-century workforce and essential to success.  In 2015, OECD and PISA defined collaborative problem solving as “the capacity of an individual to effectively engage in a process whereby two or more agents attempt to solve a problem by sharing the understanding and effort required to come to a solution and pooling their knowledge, skills, and efforts to reach that solution”.

This definition of collaborative problem solving incorporates three competencies:

• Establishing and maintaining shared understanding
• Taking appropriate action to solve the problem
• Maintaining team organization

After reading the research study, I was impressed by the connections to 21 st century skills. As a presenter, I often reference the 21 st Century Learning and Innovation Skills (Communication and Collaboration, Critical Thinking and Problem Solving, and Creativity and Innovation). The OECD and PISA definition incorporates these attributes within this competency.

Collaboration:

• Work effectively and respectfully
• Exercise flexibility and willingness to compromise to achieve a common goal
• Value individual contributions of team members
• Assume shared responsibility for collaborative work

Problem Solving:

• Reason effectively
• Use systems thinking
• Make judgments and decisions
• Solve problems

The research supports consideration for including collaborative problem solving as an instructional priority. Teaching students how to work together is something done frequently in elementary schools. Continuing this process in secondary school and teaching students how to work together to solve a problem is important work for teachers. One application of this could be the use of performance tasks and project-based learning.

Project-based learning encourages student groups. Teachers can use a variety of grouping strategies during the school year to help students apply collaboration and problem-solving skills. As adults, we are very aware that we do not always work with people we like, but an important part of our job is working with these people to accomplish a task as part of our work. Research frequently occurs through this process and having students become consumers of the research is crucial. They will need to understand how perspective influences the research and findings. As the culmination of the work, the group will need to consider multiple solutions to the situation and make the best decision to address the goal of the task.

As you can see, through this process students can learn how to:

• effectively divide the workload to complete the task
• construct research and gather information from many perspectives
• respectfully consider multiple solutions from group members accounting for creative and quality solutions to address the goal of the task

Reinforcing the value of working in groups is a critical understanding for educators. As schools and states consider individual testing and data it is vital that schools and teachers provide opportunities for students to have practice and learn strategies for working together and performing collaborative problem-solving. This competency is a vital workforce demand and as such NAEP (National Assessment of Educational Progress) has undertaken a study for considerations of collaborative problem solving to determine possibilities for future inclusion on a national assessment.

In future posts, I will look at practical strategies that can be incorporated into the classroom to help students become competent in all aspects of collaborative problem-solving.

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• Oct 27, 2020

Collaborative & Proactive Solutions: This is How Problems are Solved

By Aisha Powell, CEI Intern

Disruptive behavior in children—from having an occasional angry outburst, or escalating to more troublesome actions, like lying and stealing—is much more complex than it looks. While it can range in expression, the trauma that is often at the root of such behavior can result in emotional and mental disorders down the line if children are not taught effective self-regulation skills. For teachers and educators, addressing these issues holistically can result in increased success. Studies have shown that effective treatment can include things such as early intervention and a combination of parent and schoolwide involvement (CHADD, 2018; Greene, 2018). Clinical Child Psychologist Dr. Ross Green developed the Collaborative & Proactive Solutions (CPS) Model to help adults identify, resolve, and address these problems.

CPS Model and Addressing the Problem

When there are behavior disruptions, instead of focusing on the child as the “problem,” Dr. Green contends that adults need to find a way to meet both the adult’s and child’s needs. After his long career in research and practice, he created the Collaborative & Proactive Solutions model (CPS) to help caregivers and children improve their relationships by breaking down the steps needed to come to a healthy agreement. Substantial research has proven that the CPS model works to help reduce disruptive behavior and improve parent-child relationships (Lives in the Balance, n.d.).

The first stage is about approaching the problem from a sympathetic standpoint. The four steps are:

Emphasize the problem (and solving it) and not behaviors (and modifying them). Too often, blame and guilt are put on children when a problem occurs, which causes more tension and apprehension.

Engage in collaborative, not unilateral, problem solving. “Solving” a problem without consideration from both parties is not finding a real solution. Instead, there should be a collaboration between both child and adult to find a solution that acknowledges both their perspectives. This will empower both the child, who will feel like their voice is an integral and important part of a solution, and the adult, who wants to better understand the child.

Undertake proactive, not reactive, problem solving. Do you know why a child is feeling challenged? If the answer is no, then you first need to find out when and why a child will feel challenged, in order to have a plan of action before they show disruptive behaviors.

Remember: Kids do well, if they can . Don’t assume that a child wants to be challenging on purpose. Instead, remember that—like you—they are doing the best they can. If they don’t have the skills to regulate their behavior, adult expectations may be impossible to meet until they acquire the necessary strategies and tools.

Many researchers have studied the best treatment options for children with disruptive behavior disorders. Some include early intervention, some highlight intense parent involvement, and others stress schoolwide involvement. But a combination of the three is what is needed to truly address the problem. Dr. Ross Green has studied Oppositional Defiant Disorder (ODD) and Conduct Disorder (CD)—the diagnoses given when misbehavior goes beyond mere disruption and becomes unsafe to the student or their peers. He found that a clash between child and parental or educational expectations can cause children to react in ways that are disruptive because they don’t yet have the skills to meet those expectations (Green, 2018).

Success in the Classroom

At Bloomfield Public Schools, an 11-school district in Essex County, New Jersey, implementing the CPS model proved to be a rewarding experience for parents and teachers alike. During a 9-week program , spearheaded by Dr. Greene, they were able to offer parent-teacher workshops introducing the four steps and how to effectively intervene for better outcomes. It was positively received and resulted in the CPS model being implemented in their district-wide intervention practices to help “change the lenses” of staff members and parents alike (Bloomfield Public Schools, n.d).

The CPS model can be implemented in both educational and home settings to help resolve instances of misbehavior on the spot and alleviate them in the future. To do this effectively, adults must take a collaborative approach with an emphasis on problem-solving. Green advises starting with empathy. First, gather information to identify the child’s concerns. Next, define adult concerns. Lastly, work together to find a solution that is realistic and mutually satisfactory. If necessary, you can also set the problem aside and agree to come back to it at a time when the tension has lessened.

For more information about the CPS model and tools to support your children, please visit the Lives In Balance website to download more resources.

Bloomfield Public Schools. (n.d.). CPS Model .

Children and Adults with Attention Deficit/Hyperactivity Disorder (CHADD). (2018). Disruptive behavior disorders .

Greene, R. W. (2018). Transforming school discipline: Shifting from power and control to collaboration and problem solving. Childhood Education , 94 (4), 22–27.

Lives in the Balance. (n.d.). Research etc.

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Effects of Online Cooperative Learning on Students’ Problem-Solving Ability and Learning Satisfaction

Yi-ping wang.

1 College of International Relations, Huaqiao University, Xiamen, China

2 School of Management, Harbin Institute of Technology (HIT), Harbin, China

Associated Data

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

As technology changes, it is becoming more common in education for students to acquire knowledge from sources other than just their teachers. In the face of a diverse student background, teachers have to make adjustments in their instruction so that students do not simply listen. Student-based educational philosophy aims to combine instructional methods with cooperative learning to allow students to change from passive learning to active knowledge construction, reinduce students’ learning motivation and passion, and enhance students’ self-learning effectiveness. Focusing on college students in Fujian Province as the research sample, 360 copies of a questionnaire were distributed for this study. After deducting invalid and incomplete ones, 298 copies remained, with a retrieval rate 83%. The research results showed significantly positive correlations between online cooperative learning and problem-solving ability, problem-solving ability and learning satisfaction, and online cooperative learning and learning satisfaction. According to the results, it is expected, in the digital era, to integrate information technology into the teaching environment and focus on learning objectives to create teaching software with a user-friendly interface, simple operation, learning process recording, and an interactive learning community in the teaching-learning process to develop the characteristics and effectiveness of digital teaching and learning.

Introduction

As times progress and technology improves, teachers are no longer the only channel for students acquiring knowledge. Students in this generation are stimulated by distinct and diverse cultures to show more active and flexible characters or responses than students before them, and are even brave enough to challenge existing values. Students in a traditional learning model with passive lectures will not concentrate in the classroom. Examinations have been a core part of education for a long time. It is the best time to practice cooperative learning. The curricula show that the ideas such as taking the initiative, engaging in the public, and seeking the common good are important. Engaging in the public and seeking the common good is a result of the characters of positive independence and face-to-face fostering of interactive and interpersonal skills mentioned in cooperative learning. In this respect, it can be stated that cooperative learning guides students to be well and develops various interactive abilities with ego, others, society, and nature. It also helps students in applying and practicing their knowledge, experiencing the meaning of life, being willing to devote to the sustainable development of society, nature, and culture, and seeking reciprocity of each other and common good. Information technologies are material tools that learners should actively and broadly apply to a the positive interaction channel between oneself and the environment to effectively engage the public with others and the environment ( Li et al., 2021 ).

In the face of diverse student background, teachers have to make adjustments in their instruction to stop students from simply listening. Educational philosophy should be student-based to promote each student’s thinking. In this case, cooperative learning allows students to change from passive learning into active knowledge construction, could reinduce students’ learning motivation and passion, and enhance students’ self-learning effectiveness. Most students are digital natives born after 1980, while most of their teachers are digital immigrants and even “digital refugees” escaping from technologies and being afraid of new knowledge. The overlap between such two generations is limited, meaning that their values and morality are distinct. Modern students are digital natives able to use mobile phones, televisions, computers, laptops, and tablets since childhood, and highly dependent on new technologies. Information-technology-integrated instruction with multimedia equipment and materials means teaching and learning is no longer restricted to dictation and paper-and-pencil ( Vaz et al., 2021 ); the class climate has changed to cooperative learning. The operation of cooperative learning is smoother through information technology, and a communication and interaction bridge can be built through information technology so that cooperative learning could cultivate students’ problem-solving ability to further promote learning satisfaction. As a result, the effects of online cooperative learning on students’ problem-solving ability and learning satisfaction are discussed in this study, expecting to integrate information technology into the teaching environment in the digital era, focus on learning objectives based on learning theory, have teaching software with a user-friendly interface, simple operation, learning process recording, and an interactive learning community in the teaching-learning process to develop the characteristics and effectiveness of digital teaching and learning.

Literature Review and Hypothesis

Constructivists regard gaining knowledge as a comprehensive and reflective thinking activity through students’ independent exploration and observation and highly praise learner-centered learning environments. Teachers’ roles of propagating the doctrine, imparting professional knowledge, and resolving doubts change into knowledge building facilitators. The superordinate-subordinate relationship of “Learning from Teacher” is changed into the equal relationship of “Learning with Teacher.” The learning perspective of constructivism facilitates the development of current learning technology ( Cortez et al., 2021 ).

Dozens of instructional strategies are developed for cooperative learning, and each grouping method presents the characteristics and applicable teaching situation. Teachers could flexibly apply the difference according to instructional objectives, student characteristics, and course attributes. Researchers, in the interview with collaborative teachers, also reveal not being restricted into a grouping method, but extracting the advantages of various methods, and making flexible adjustments in consideration of teachers’ personality traits and class attributes and characteristics ( Akdemir et al., 2020 ). Major cooperative learning strategies are classified into three types, including one suitable for leading sharing and discussion among students, another for assisting students in mastering learning content, and the last for leading teams for theme-based inquiry. Each type shows various strategies to cope with different teaching styles, or more than two strategies could be changed and applied depending on the demands ( Hafeez, 2021 ).

Li and Keller (2018) mentioned the significant effects of using web problem-based cooperative learning and on the problem-solving skills of the children. The results revealed the better performance of students compared to traditional problem-based learning. Del Gaudio et al. (2021) used online cooperative learning to discover the advantages and strengths, solve problems according to collaborative interaction, comprehend the roles, integrate the discussed ideas, clearly master the tasks, coordinate the allocation of team members’ reports, complete reports according to previous discussion results, discuss and modify successive measures together, inspect cooperation results, track back problem-solving processes, and reflect team organization and roles, problem-solving ability as to independently complete tasks with high-level thinking, and cooperative problem-solving ability as to create the value of synergy, solve problems and complete tasks together, and create good performance beyond the expectation ( Wu et al., 2019 , 2022 ). Ingrid (2019) explained that independent thinking and analysis ability allowed dealing with daily life and even life problems. Teachers applying information technology to cooperative learning to enrich students’ life experience, being good at asking questions, creating problem-solving teaching situations, applying technological tools to speculate and deduce problems, effectively solving problems with cooperative discussions, and enhancing adaptability to life could help students become problem-solving experts. For this reason, the following hypothesis is established in this study.

H1 : Online cooperative learning presents significantly positive correlations with problem-solving ability. H1-1 : Online cooperative learning shows significantly positive correlations with problem-solving ability. H1-2 : Online cooperative learning reveals remarkably negative correlations with problems-solving ability.

Oates and Ritók (2018) explained that learners being able to effectively enhance their problem-solving ability after going through the curriculum arranged by the school, course content of teachers, and effective promotion of knowledge acquisition in the learning process, with consistent expectation and anticipation, would appear satisfactory; on the contrary, dissatisfaction would be delivered. Metin-Orta and Demirtepe-Saygılı (2021) stated that education aimed to help individuals live their life; in real situations, an individual using critical thinking to solve complicated and messy dilemmas and problems was the core task of modern education. Teachers in the teaching process did not simply transmit knowledge, provide guidance for study, and dispel confusion, but had to help students associate old experience with new knowledge to further solve problems through tight cognition structure to form meaningful learning in order to effectively enhance learning satisfaction. Wu et al. (2021) regarded cooperative problem-solving ability as an individual with sufficient ability communicating and dialoging with more than two companions to share knowledge and skills, collaboratively and effectively participate in an activity, and develop teamwork ability to solve problems. Collaborative problem solving referred to several partners collaboratively completing a task where each partner had to positively participate ( Chiao and MacVaugh, 2021 ; Min et al., 2021 ), mutually coordinate, and pull together to solve problems in the task with teamwork so as to effectively enhance learning satisfaction. Accordingly, the following hypothesis is establishment in this study.

H2 : Problem-solving ability shows remarkably positive correlations with learning satisfaction. H2-1 : Problem-solving ability appears to have notably positive correlations with learning satisfaction. H2-2 : Problem-solving ability presents significantly negative correlations with learning satisfaction.

Wu et al. (2020) applied interactive APP to analyze learning satisfaction with idiom teaching; the students, regardless of gender and learning achievement, were satisfied with the use of interactive APP for idiom learning. The use of information-technology-integrated cooperative learning for the learning achievement of students in the experimental group did not outperform students in the control group, but the learning satisfaction was better than those in the control group. Kurilovas and Kubilinskiene (2020) mentioned that students in the experimental group with cooperative learning outperformed students with general cooperative learning on learning achievement and learning attitude and presented positive learning satisfaction. Haidar and Fang (2019) explained cooperative learning as teachers effectively applying information technology to smooth cooperative learning; for instance, dynamic information materials and real-time team performance could assist in students’ learning motivation, learning ambition, learning satisfaction, and learning effectiveness and create a quality learning environment with peer teamwork and teacher-student interaction. The following hypothesis is therefore established in this study.

H3 : online cooperative learning reveals notably positive correlations with learning satisfaction. H3-1 : Online cooperative learning shows remarkably positive correlations with learning satisfaction. H3-2 : Online cooperative learning reveals notably negative correlations with learning satisfaction.

Methodology

Operational definition, online cooperative learning.

Online cooperative learning, as the independent variable in this study, is measured with positive interdependence, promotive interaction, social skills, and group processing, according to the blended learning model proposed by Liao et al. (2019) .

• Positive interdependence: mutual dependence, mutual responsibility, mutual help, acceptance of assistance, and cheering up team members.
• Promotive interaction: mutual assistance, sharing information, and providing clear explanation in the team.
• Social skills: leadership and communication.
• Group processing: evaluating the cooperation effectiveness of each other.

Problem-Solving Ability

Problem-solving ability, as the dependent variable in this study, is measured with exploration and comprehension, planning and execution, and monitoring and reflection, according to the problem-solving ability model proposed by Lin et al. (2018) .

Learning Satisfaction

Learning satisfaction, as the dependent variable in this study, is measured with student aspects, teacher aspects, and school aspect, according to the blended learning model proposed by Travis and Bunde (2020) .

• Student aspects: including students’ interests, learning motivation, learning attitude, personality traits, gender, needs, experience, learning ability, learning effectiveness, and peer interpersonal relationship.
• Teacher aspects: covering teachers’ professional ability, traits, teaching methods, curriculum arrangement, teaching content, difficulty in material design, attitude towards students, and teacher-student interaction model.
• School aspects: containing school equipment, learning environment, environmental safety and health, teaching resources, and transportation.

Research Object and Analysis Method

College students in Fujian Province, as the research sample, were distributed 360 copies of a questionnaire for this study. After deducting invalid and incomplete ones, 298 copies were valid, with a retrieval rate 83%. After confirming the applicable online cooperative learning strategy, the actual teaching activity is practiced as planned. Four teachers practicing cooperative learning in the school were invited as the collaborative teachers to deliver the 10-week (total 50 sessions) teaching activity to 500 students in 10 classes of a university in Fujian Province. The questionnaire data collection is preceded after the end of the course.

Two-stage analysis in Structural Equation Modeling (SEM) is applied to analyze goodness-of-fit and test the model in this study. Confirmatory Factor Analysis (CFA) is first used, aiming to test the existence of independent variables in the model in order to delete dependent variables with bad effects on causal analysis. Path analysis is then preceded after the modification. Path analysis aims to estimate the relationship of model paths among variables. Without Confirmatory Factor Analysis to test independent variables, the use of path analysis might be affected by independent variables to result in bad goodness-of-fit or insignificant model paths. Goodness-of-fit test in Amos18.0 is utilized in this study. CMIN/DF of the measurement result being smaller than 5 is acceptable and being smaller than 3 is excellent; GFI, AGFI, NFI, IFI, TLI, and CFI are better higher than 0.9; and RMR, RMSEA, and SRMR are better when smaller and ideally smaller than 0.05.

Factor Analysis

The online cooperative learning scale in this study, with factor analysis, extracted four factors of “positive interdependence” (eigenvalue = 2.633, α  = 0.84), “promotive interaction” (eigenvalue = 1.875, α  = 0.86), “social skills” (eigenvalue = 2.236, α  = 0.81), and “group processing” (eigenvalue = 1.633, α  = 0.87). The cumulative covariance explained achieves 75.923%. The problem-solving ability scale, after factor analysis, extracted three factors of “exploration and comprehension” (eigenvalue = 3.251, α  = 0.86), “planning and execution” (eigenvalue = 2.407, α  = 0.88), and “monitoring and reflection” (eigenvalue = 2.716, α  = 0.83). The cumulative covariance explained reaches 77.493%. The learning satisfaction scale, with factor analysis, extracted three factors of “student aspects” (eigenvalue = 1.577, α  = 0.80), “teacher aspects” (eigenvalue = 2.281, α  = 0.85), and “school aspects” (eigenvalue = 2.388, α  = 0.90). The cumulative covariance explained achieves 80.762%.

Empirical Analysis Model of Structural Equation

Regarding the Confirmatory Factor Analysis (CFA) results, the convergent validity of the observation model could observe the reliability of individual observed variable, construct reliability (CR), and average variance extracted (AVE); the reliability of individual observed variable is better higher than 0.5. The factor loadings of observed items in this study are higher than the suggested value. The construct reliability is better higher than 0.6, while other researchers suggest higher than 0.5 being acceptable. The model calibration results reveal the construct reliability higher than 0.5. Average variance extracted is suggested higher than 0.5; the average variance extracted of the dimensions in this study is higher than 0.5, conforming to the suggested value.

In terms of the structural formula calibration results, χ 2 / df , RMSEA, GFI, AGFI, RMR, and NFI are suggested to be ≦5, ≦0.08, ≧0.9, ≧0.9, ≦0.05, and ≧0.9, respectively. This study shows χ 2 / df  = 3.142≦5, RMSEA = 0.032≦0.08, GFI = 0.967≧0.9, AGFI = 0.934≧0.9, RMR = 0.031≦0.05, and NFI = 0.918≧0.9, revealing good overall model fit. Under good overall model fit, the structural formula parameter calibration results are shown in Table 1 and Figure 1 . The research results present online cooperative learning → problem-solving ability 0.327 *** that H1 is supported, problem-solving ability → learning satisfaction 0.423 *** that H2 is supported, and online cooperative learning → learning satisfaction 0.386 *** that H3 is supported.

Structural equation modeling result.

Model path diagram. *** p  < 0.001.

The research results prove that, in the practice of online cooperative learning, information technology makes up for the insufficiency of cooperative learning, enriches courses, promotes students’ learning motivation, and drives learning effectiveness to form a positive cycle. Students’ learning motivation comes from the advancement of performance and the learning confidence comes from the ideal performance. Teachers use online cooperative learning to facilitate group discussion skills and the understanding of students. They also use Google Forms to conduct digitalized tests, and mind maps and tables to improve students’ problem-solving skills ( Simamora, 2017 ). In the teaching-learning process, instructional objectives are inspected to return the teaching profession. Teachers are good at asking questions to enhance students’ cooperation and encourage thinking. Especially in comprehension and analysis, the top-down relationship should be broken and the subjective consideration of teachers’ cognition, ideas, and interpretation as being better than students should be avoided so that it would not come out with teachers’ expected answers ( Phillips et al., 2014 ). Students’ answers could be typed with computers to respect the answers, enhance the confidence without losing students’ creativity, and present brainstorming; teachers ensure the focus and integration at the end. The application of online cooperative learning could reconstruct teachers’ teaching profession, and the experience and constant rolling correction could improve teaching skills to face changeable students and present the value of online cooperative learning. The intervention of information technology could change the resistance to the online cooperative learning process into assistance, helping it to become a powerful backup force of online cooperative learning, induce learning motivation, and promote problem-solving ability and learning satisfaction as the final instructional objectives.

Alves et al. (2019) explained collaborative problem solving as an individual or more than two companions with sufficient capability sharing knowledge and skills through communication and dialogue, collaboratively and effectively participating in activities, and developing teamwork to solve encountered problems. Collaborative problem solving referred to a task being collaboratively completed by several partners. Each partner had to positively participate, mutually coordinate, and help each other in the same situation to solve problems with teamwork so as to effectively enhance learning satisfaction. The intervention of information technology could make the best out of a bad situation in the online cooperative learning process to support online cooperative learning, induce learning motivation, and promote problem solving capability and learning satisfaction as the ultimate instructional objectives. The research result conforms to the points of view proposed by Munawar and Chaudhary (2019) and Haidar and Fang (2019) .

Teachers need full training to guide students with “stretching and jumping” opportunities in the “interactive relationship.” Meanwhile, teachers need full wisdom to help students move from conflict compromise to positive trust ( Ramdani et al., 2019 ). What is more, multiple evaluations outside the classroom, such as completion of team assignments, quiz performances, and sectional examination performance, help teams not to slack. Besides, each member is important that no-one is confident of the winning ( Hafeez, 2021 ). Students would search network data, discuss grounded arguments, focus on discussion through information technology, and save a lot of time for groupwork. Teachers, with statistics, would announce team performance with data at any time to induce competition and crisis awareness of teams. There might be conflict in a team, but a contest with multiple evaluations allows individuals to give up personal prejudice and unite to make effort for the team. It naturally reinforces the group process of cooperative learning ( Akdemir et al., 2020 ).

The research results show that the item of “ Teachers currently use the instructional method of online cooperative learning to make courses interesting and active ” receives the highest score in online cooperative learning strategies, revealing the acquisition of student identity. The item of “ I think the use of platform[s] for Internet communication media could help the communication and teamwork between team members and I in the cooperative learning course ” receives the highest score in problem solving capability, revealing the acquisition of student identity. The item of “ I think the application of online cooperative learning could enhance learning ability and confidence ” receives the highest score in learning satisfaction, revealing the acquisition of student identity.

The research results prove that students’ responses in class are a mirror reminding teachers of the need to adjust the instructional methods. In traditional didactic instruction, students’ academic achievement decides teachers’ success. In the use of online cooperative learning, students’ learning motivation awakes teachers’ passion. Teachers could continuously retain the original instructional methods; nevertheless, modern students are active and there are special students who are extroverts or introverts. These students may challenge teachers’ authority. Teachers can easily get tired if they do not adapt their instructional methods according to the diverse needs of students. The assistance of information technology in the practice allows seeking consensus from online resources in the team discussion. Under the situation with a well-grounded argument, students are convinced by each other to contribute to the successive discussions. The research result conforms to the points of view proposed by Weaver et al. (2019) and Ingrid (2019) . With online cooperative learning, teachers simply combine the original computer software with cooperative learning courses through the Internet, rather than re-learning brand new and strange computer software. Teachers who enjoy learning and self-growth could challenge themselves and activate teaching with advanced functions. However, it should be kept in mind that information technologies are only tools; using media can attract students’ attention in a short period, but having students internalize knowledge is the goal. Karakus Taysi (2019) mentioned the aims of education as helping individuals live their life. The development of individual critical thinking and problem-solving skills are the main aims of contemporary education. Teachers did not simply propagate the doctrine, impart professional knowledge, and resolve doubts in the teaching process, but had to help students link old experience with new knowledge, make tight cognitive structures for meaningful learning, and further solve problems to effectively promote learning satisfaction.

Online cooperation learning method is important for cultivating students’ independent thinking, interpersonal communication, competition awareness, and teamwork ( Cortez et al., 2021 ). Teachers and students are good at utilizing information technology to have students focus on discussion content and direction, instantaneously acquire the answers and feedback and correction, and improve team performance with data ( Mutua and Ong'ong'a, 2020 ). When making effort in the learning process, the learning result would not be lower than the expected performance and students would reflect this with their learning satisfaction.

Data Availability Statement

Ethics statement.

This study was reviewed and approved by the ethics committee of the Huaqiao University. Written informed consent was obtained from all participants for their participation in this study.

Author Contributions

Y-PW performed the initial analyses and wrote the manuscript. T-JW assisted in the data collection and data analysis. All authors revised and approved the submitted version of the manuscript.

This research was supported by the National Natural Science Foundation of China (71702059).

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 potential conflicts 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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The Algebra Problem: How Middle School Math Became a National Flashpoint

Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it.

By Troy Closson

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system. Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly four in five poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12 percent of Black and Latino eighth graders do, compared with roughly 24 percent of white pupils, a federal report found .

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research . A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Mass., the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside of school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, Mr. de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80 percent from 60 percent. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s current schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won both support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Mr. Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Mr. Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100 percent, yes,” he added. “That was not something that I could live with.”

Troy Closson reports on K-12 schools in New York City for The Times. More about Troy Closson

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Marines say no more ‘death by PowerPoint’ as Corps overhauls education

WASHINGTON, D.C. ― Marines and those who teach them will see more direct, problem-solving approaches to how they learn and far less “death by PowerPoint” as the Corps overhauls its education methods .

Decades of lecturers “foot stomping” material for Marines to learn, recall and regurgitate on a test before forgetting most of what they heard is being replaced by “outcomes-based” learning, a method that’s been in use in other fields but only recently brought into military training.

“Instead of teaching them what to think, we’re teaching them how to think,” said Col. Karl Arbogast, director of the policy and standards division at training and education command .

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Arbogast laid out some of the new methods that the command is using at the center for learning and faculty development while speaking at the Modern Day Marine Expo.

“No more death by PowerPoint,” Arbogast said. “No more ‘sage on the stage’ anymore, it’s the ‘guide on the side.’”

To do that, Lt. Col. Chris Devries, director of the learning and faculty center, is a multiyear process in which the Marines have developed two new military occupational specialties, 0951 and 0952.

The exceptional MOS is in addition to their primary MOS but allows the Marines to quickly identify who among their ranks is qualified to teach using the new methods.

Training for those jobs gives instructors, now called facilitators, an entry-level understanding of how to teach in an outcomes-based learning model.

Devries said the long-term goal is to create two more levels of instructor/facilitator that a Marine could return to in their career, a journeyman level and a master level. Those curricula are still under development.

The new method helps facilitators first learn the technology they’ll need to share material with and guide students. It also teaches them more formal assessment tools so they can gauge how well students are performing.

For the students, they can learn at their own pace. If they grasp the material the group is covering, they’re encouraged to advance in their study, rather than wait for the entire group to master the introductory material.

More responsibility is placed on the students. For example, in a land navigation class, a facilitator might share materials for students to review before class on their own and then immediately jump into working with maps, compasses and protractors on land navigation projects in the next class period, said John deForest, learning and development officer at the center.

That creates more time in the field for those Marines to practice the skills in a realistic setting.

Marines with Marine Medium Tiltrotor Squadron (VMM) 268, Marine Aircraft Group 24, 1st Marine Aircraft Wing, fire M240-B machine guns at the Marine Corps Air Station Kaneohe Bay range, Hawaii, March 5. (Lance Cpl. Tania Guerrero/Marine Corps)

For the infantry Marine course, the school split up the large classroom into squad-sized groups led by a sergeant or staff sergeant, allowing for more individual focus and participation among the students, Arbogast said.

“They have to now prepare activities for the learner to be directly involved in their own learning and then they have to steer and guide the learners correct outcome,” said Timothy Heck, director of the center’s West Coast detachment.

The students are creating products and portfolios of activities in their training instead of simply taking a written test, said Justina Kirkland, a facilitator at the West Coast detachment.

Students are also pushed to discuss problems among themselves and troubleshoot scenarios. The role of the facilitator then is to monitor the conversation and ask probing questions to redirect the group if they get off course, Heck said.

That involves more decision games, decision forcing cases and even wargaming, deForest said.

We “put the student in an active learning experience where they have to grapple with uncertainty, where they have to grapple with the technical skills and the knowledge they need,” deForest said.

That makes the learning more about application than recall, he said.

Todd South has written about crime, courts, government and the military for multiple publications since 2004 and was named a 2014 Pulitzer finalist for a co-written project on witness intimidation. Todd is a Marine veteran of the Iraq War.

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Retired firefighter teaches problem-solving skills to Indy-area kids

Retired indy firefighter teaches problem-solving skills.

INDIANAPOLIS (WISH) — A retired Indianapolis firefighter is igniting leadership in Indianapolis. He created an organization to teach problem-solving skills to as many kids as possible.

In 1992, Anthony Williamson co-founded a youth leadership and development program named after Saint Florian, the patron saint of firefighters.

The Saint Florian Center began as a summer camp and evolved into a year-round youth program. Their motto is “to foster leadership opportunity and respect in all neighborhoods.”

“They have to be able to think about what they do before they act and then they can go and respond in an appropriate way. So many times our kids get into trouble because somebody steps on their shoes or they call them out of their name and they just respond and react and we don’t want them to react,” Williamson explained to News 8’s Brittany Noble.

The center now offers a variety of  programs including youth employment training, college prep, Readers are Leaders , and Rites of Passage.

“We were contacted by (a school) principal because they had some young people, specifically boys, that seemed to not understand community, not understand how to remain focused on their classwork and not be disruptive in the classroom, therefore, they were sent to the office on multiple occasions. So they were looking for ways on how to empower young people to understand why education is so important,” Williamson said.

The  Saint Florian Center  thrives on volunteers to expand their reach. So far, Williamson says he’s worked with more than 30,000 kids but he hopes he can reach more children.

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