Examining the impact of peer collaboration on K-6 students' mathematical thinking and problem-solving skills.
This study aims to uncover effective collaborative practices that can improve kids’ mathematics learning outcomes by examining the effects of peer collaboration on K–6 students’ mathematical thinking and problem-solving abilities in a particular school district.
Mathematics is a subject that often requires problem-solving and critical thinking skills. Peer collaboration has been recognized as a valuable tool in promoting mathematical thinking and problem-solving skills among K-6 students. This literature review aims to explore the impact of peer collaboration on K-6 students’ mathematical thinking and problem-solving skills. Fifteen scholarly articles related to this research topic were reviewed to identify the current state of knowledge and highlight gaps in the existing literature.
Peer collaboration has been a focus of research in mathematics education for many years, with the potential to improve students’ mathematical thinking and problem-solving skills. The purpose of this literature review is to explore the impact of peer collaboration on K-6 students’ mathematical thinking and problem-solving skills, and to identify effective strategies for implementing peer collaboration in the classroom.
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Despite traditional direct-instruction in perimeter and area of shapes, my 4th-grade math students are struggling with applying this knowledge to solve real-world math problems that involve calculating dimensions.
What is the effects of collaborative learning strategies on real-word problem-solving abilities of 4th-grade math students?
A quantitative research approach would be appropriate for investigating the effects of collaborative learning strategies on real-world problem-solving abilities of 4th-grade math students because it allows for the collection and analysis of numerical data that can be statistically analyzed. Using a quantitative approach, it would be possible to collect and analyze data from a large sample of 4th-grade math students in a standardized and objective manner. This would allow for the comparison of the problem-solving abilities of students who received collaborative learning instruction with those who did not, and the examination of whether specific types of collaborative learning strategies are more effective than others.
Poor problem-solving abilities among 4th-grade math students is a significant instructional problem in K-6 mathematics education. This problem has the potential to impact students’ math performance in future grades, leading to math anxiety and other negative outcomes (Stevenson, 2019). One possible cause of this issue is a lack of effective math instruction that emphasizes problem-solving skills, including strategies that promote problem-solving abilities. Teachers may lack training or resources to develop effective instructional approaches to teach problem-solving skills (Sawyer & Smith, 2020). Other possible factors that may contribute to the problem include a lack of student engagement or motivation, insufficient prior knowledge, or inadequate learning environments.
To address this issue, it is essential to identify and implement effective instructional strategies that can improve students’ problem-solving abilities. Collaborative learning has been shown to have a positive impact on student learning outcomes, including problem-solving skills, in various subject areas (Alqahtani, 2015). By promoting collaborative learning practices that emphasize problem-solving skills, teachers can provide students with opportunities to develop critical thinking skills that are relevant in both academic and professional contexts.
To address the problem of poor problem-solving abilities among 4th-grade math students due to a lack of effective collaborative learning strategies, an instructional unit will be implemented. The instructional unit will focus on integrating collaborative learning practices into the math curriculum. The unit will consist of a series of lessons that involve small-group work and cooperative learning activities designed to promote problem-solving skills. The lessons will be structured to include clear learning objectives, cooperative learning opportunities, and formative assessments to monitor student progress. The instructional unit’s ultimate goal is to provide students with the necessary skills to solve real-world problems and promote long-term success in math education.
A lack of effective math instruction that emphasizes problem-solving skills, a lack of teacher preparation or resources for creating effective instructional approaches, low student engagement or motivation, insufficient prior knowledge, or an unsuitable learning environment are all potential causes of the issue of poor problem-solving abilities among 4th grade math students. Additionally, there may be other outside factors that affect the issue, such as socioeconomic position or learning difficulties. In order to create effective solutions that can address the problem’s underlying causes and aid students in acquiring the skills they need to succeed in math classes, it is essential to identify these potential reasons.
Since it is crucial for people to have adequate mathematical knowledge and abilities in today’s society, mathematics education has long been a vital field of study. Due to its potential to improve students’ learning experiences, collaborative learning has grown in popularity in mathematics classes. A teaching strategy called collaborative learning encourages students to work together in pairs or small groups to accomplish a common learning objective. By examining the existing research on the subject, this literature review seeks to determine how collaborative learning has affected the teaching of mathematics.
Collaborative Learning in Mathematics Education
In the field of mathematics education, collaborative learning has become a popular and successful teaching strategy. It has long been understood how crucial collaboration is to the teaching of mathematics since it can give students the chance to improve their communication, problem-solving, and mathematical thinking skills. Due to the constant evidence that collaborative learning can increase student performance in mathematics, educators are implementing collaborative learning techniques into their lesson plans. Collaborative learning has been shown to have a positive impact on students’ achievement in mathematics (Tokac, Novak, & Thompson, 2019). A collaborative learning environment can provide opportunities for students to discuss mathematical concepts, work together to solve problems, and engage in higher-order thinking (Lahann & Lambdin, 2020). Research has shown that students who engage in collaborative problem-solving activities show greater gains in mathematical achievement than students who work individually (Slavin, 2014).
Teacher Interventions in Cooperative Learning Mathematics Classes
Effective implementation of cooperative learning strategies in mathematics classrooms requires the active participation of teachers in ensuring that students are engaged in meaningful discussions and are able to construct their own knowledge (Ding, Li, Piccolo, & Kulm, 2007). Teachers can especially help discussions by clearly defining the goals and objectives for the cooperative learning activities and by giving students the chance to express their thoughts and viewpoints. Teachers can keep an eye on the conversations and offer targeted feedback to specific students or groups as needed to ensure that students receive timely feedback and support. Also, teachers can promote participation by creating a welcoming and encouraging environment in the classroom where all students feel appreciated and at ease participating in the learning process. Giving students the chance to work in pairs or small groups, designating tasks or responsibilities for group members, and utilizing questioning techniques that encourage a deeper grasp of mathematical topics may all be part of this. By actively engaging in these teacher interventions, students are more likely to develop a deeper understanding of mathematical concepts and to build the skills necessary for success in future mathematics learning.
All students, regardless of background or ability level, can have mathematical futures, according to Boaler and Staples’ (2008) argument. By promoting cooperation and conversation in the classroom, teachers can foster a sense of community and inspire all students to engage in the learning process. Boaler and Staples (2008) discuss about the idea of “mathematical futures” and how an equitable teaching strategy might aid students in acquiring the knowledge and values required to realize them. The authors talk about their experiences working at Railside School, where they established a teaching strategy that prioritized student autonomy, collaborative problem-solving, and a growth attitude. This method encouraged students to persevere despite challenges by enabling students of all abilities to engage with tough mathematical issues. Boaler and Staples argue that this type of teaching can help break down the traditional hierarchies and stereotypes associated with math education and open up opportunities for all students to succeed. Their work provides valuable insights into how teachers can create a more inclusive and equitable math classroom.
Crespo and Harper (2020) recommend that teachers should educate students to develop their own mathematical problems as a beneficial strategy for fostering peer collaboration in mathematics education. Students may benefit especially from this method since it empowers them to take charge of their education and promotes critical thought about mathematical ideas. Students can discover areas of difficulty and push themselves to tackle challenges that are pertinent and meaningful to them by developing their own problems. While students must develop original, intriguing questions that are nevertheless based in mathematical concepts, this method can also encourage creativity and critical thinking. Students are more invested in the learning process and are more likely to actively interact with the subject when they collaborate to solve issues that they have generated themselves. Through this method, students can gain a deeper comprehension of mathematical ideas and acquire critical problem-solving abilities that they can use in various aspects of their lives.
Effects of Collaborative Learning
In a study by Summers (2006), it was found that collaborative learning significantly affects students’ mathematical goal orientations. According to the study, students who engaged in collaborative learning were more likely to adopt a mastery goal orientation, which places an emphasis on learning the material and developing skills, as opposed to a performance goal orientation, which places an emphasis on getting good grades and outperforming others. This shows that, in addition to encouraging a greater grasp of the material, collaborative learning also fosters a more deep-seated and innate motivation to learn, which can have long-term advantages for students’ academic success.
Cooperative learning methodologies, according to Zakaria and Iksan (2007), may be useful in the teaching of science and mathematics, particularly in nations where standard teaching techniques may not be as effective. To guarantee that every student participates actively in cooperative learning, divide the class into small groups and give each group a role, such as leader or recorder. Moreover, Tarmizi and Bayat (2012) contend that collaborative problem-based learning is a successful method of teaching mathematics because it lessens the cognitive load placed on individual students and enables them to work together to solve problems. You can adopt collaborative problem-based learning by posing a difficult problem to your students and letting them work together to discover a solution. These approaches are especially relevant in the K-6 context, where developing critical thinking skills and teamwork are important learning outcomes.
According to Moss and Beatty (2006), knowledge building, a type of cooperative learning, can be a successful strategy for fostering students’ mathematics comprehension and problem-solving abilities. Through inquiry, discussion, and reflection, students will collaborate to build and hone their knowledge using this method. The teacher’s job is to foster a friendly learning environment in which students are encouraged to share ideas, ask questions, and build on one another’s contributions. This method encourages students to participate in deep learning and get a more comprehensive comprehension of mathematical ideas.
Using Collaborative Learning to Develop Mathematical Thinking Skills
Buckley and O’Gorman (2011) suggest that collaborative learning can be an effective strategy for developing mathematical thinking skills, by providing opportunities for students to work together, share ideas, and learn from one another. Collaborative learning can also help students develop communication skills and learn how to effectively collaborate with others, which are essential skills in many aspects of life. Additionally, through collaborative problem-solving, students can develop a deeper understanding of mathematical concepts and improve their problem-solving abilities.
Teachers can create a collaborative learning environment by providing opportunities for students to engage in meaningful discussions and by scaffolding their interactions. Webb, N. M. (1992) highlights the importance of teacher feedback and the need for teachers to be aware of the social dynamics in the classroom.
According to Brown, Collins, and Duguid (1989), the best way to understand learning is as a social activity that takes place in a cultural environment. They put forth the idea of situated cognition, which holds that learning and application of knowledge take place in contexts. This implies that learning in the context of mathematics education involves more than just understanding mathematical ideas and practices; it also entails creating a mathematical identity and joining a mathematical community. According to the authors, this community should be seen as a social and cultural space where students can collaborate with one another and their teachers to solve problems and have dialogues. Students can gain a deeper knowledge of mathematical ideas and how they are applied in the real world by participating in such activities. According to this viewpoint, it is crucial to establish a welcoming and cooperative learning atmosphere where students may actively engage in the learning process and hone their mathematical thinking skills.
The book “Learning Together and Alone” by Johnson and Johnson (1999) offers a thorough examination of collaborative, competitive, and individualistic learning. The authors go over the advantages of each method and offer useful advice for putting cooperative learning into practice in the classroom. They contend that encouraging critical thinking, problem-solving, and communication skills through cooperative learning can be successful. Moreover, cooperative learning can encourage the development of a supportive and valuable learning environment in the classroom. According to the authors, when students collaborate, they can do more than they might on their own, which can enhance academic results. Their research offers insightful information about how teachers might employ cooperative learning to improve students’ classroom learning experiences.
Despite the prevalence of constructivist, discovery, problem-based, experiential, and inquiry-based teaching methodologies, Kirschner, Sweller, and Clark (2006) contend that minimal assistance during instruction is ineffective. They contend that these instructional strategies fail to offer the required assistance for students to acquire novel and difficult ideas because they place an undue emphasis on students’ past knowledge and skills. The writers argue that a more successful strategy is to give students precise direction that includes justifications, illustrations, and practice chances. This strategy is especially crucial for difficult courses like mathematics, where students may struggle without the right support. The authors place a strong emphasis on the value of utilizing evidence-based strategies to guide instruction and enhance student learning outcomes.
Conclusion:
This literature review highlights the importance of peer collaboration in promoting mathematical thinking and problem-solving skills among K-6 students. The research under evaluation show the benefits of several collaborative learning strategies, such as cooperative problem-based learning, equitable teaching techniques, and game-based learning. Peer collaboration in mathematics education is also greatly aided by efficient teacher interventions, knowledge development, and problem posing. To determine the best strategies for encouraging peer cooperation and to examine the effects of peer collaboration on particular K–6 student subgroups, more study is required.
Boaler, J. O., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of railside school. Teachers College Record: The Voice of Scholarship in Education, 110(3), 608–645. https://doi.org/10.1177/016146810811000302
Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational researcher, 18(1), 32-42.
https://www.johnseelybrown.com/Situated%20Cognition%20and%20the%20culture%20of%20learning.pdf
Buckley, S., & O’Gorman, J. (2011). Collaborative learning and mathematics achievement. International Journal of Mathematical Education in Science and Technology, 42(7), 849-857. doi: 10.1080/0020739X.2011.579405.
Crespo, S., & Harper, F. k. (2020). Learning to pose collaborative mathematics problems with secondary prospective teachers. International Journal of Educational Research, 102, 101430. https://doi.org/10.1016/j.ijer.2019.05.003
Ding, M., Li, X., Piccolo, D., & Kulm, G. (2007). Teacher interventions in cooperative-learning mathematics classes. The Journal of Educational Research, 100(3), 162–175. https://doi.org/10.3200/joer.100.3.162-175
Johnson, D. W., & Johnson, R. T. (1999). Learning together and alone: Cooperative, competitive, and individualistic learning. Allyn and Bacon.
https://eric.ed.gov/?id=ED369778
Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1
Lahann, P., & Lambdin, D. V. (2020). Collaborative learning in mathematics education. Encyclopedia of Mathematics Education, 94–95. https://doi.org/10.1007/978-3-030-15789-0_23
Moss, J., & Beatty, R. (2006). Knowledge building in mathematics: Supporting collaborative learning in pattern problems. International Journal of Computer-Supported Collaborative Learning, 1(4), 441–465. https://doi.org/10.1007/s11412-006-9003-z
Slavin, R. E. (2014). Cooperative learning in elementary schools. Education 3-13, 43(1), 5–14. https://doi.org/10.1080/03004279.2015.963370
Summers, J. J. (2006). Effects of collaborative learning in math on sixth graders’ individual goal orientations from a socioconstructivist perspective. The Elementary School Journal, 106(3), 273–290. https://doi.org/10.1086/501487
Tarmizi, R. A., & Bayat, S. (2012). Collaborative problem-based learning in Mathematics: A cognitive load perspective. Procedia – Social and Behavioral Sciences, 32, 344–350. https://doi.org/10.1016/j.sbspro.2012.01.051
Tokac, U., Novak, E., & Thompson, C. G. (2019). Effects of game‐based learning on students’ mathematics achievement: A meta‐analysis. Journal of Computer Assisted Learning, 35(3), 407–420. https://doi.org/10.1111/jcal.12347
Webb, N. M. (1992). The teacher’s role in promoting collaborative dialogue in the classroom. British Journal of Educational Psychology, 62(1), 41-55.
https://goglobal.fiu.edu/_assets/docs/collaborative-dialogue-1-1.pdf
Zakaria, E., & Iksan, Z. (2007). Promoting cooperative learning inscience and MathematicsEducation: A Malaysian perspective. EURASIA Journal of Mathematics, Science and Technology Education, 3(1). https://doi.org/10.12973/ejmste/75372
To answer the research question of how the use of collaborative learning strategies impacts the problem-solving abilities of fourth-grade math students in a rural Minnesota elementary school, the proposed data collection method is a pre/post assessment using a math problem-solving test aligned to the Minnesota State Standards.
The study will involve collecting data from a sample of fourth-grade math students to compare the problem-solving abilities of students who received collaborative learning instruction with those who did not. To accomplish this, a pre and post-study assessment will be designed and analyzed to gauge the current problem-solving abilities of participants before and after receiving collaborative learning instruction.
This study follows many aspects of the action research model. Specifically, I am conducting research to investigate and improve a specific educational practice, namely the use of collaborative learning strategies to improve problem-solving abilities of fourth-grade math students. The data collection method chosen, a pre/post assessment, is common in action research as it allows for a comparison of outcomes before and after the intervention.
For this proposed study on the effectiveness of collaborative learning strategies in enhancing problem-solving abilities in fourth-grade math education, 19 fourth-grade students from a rural elementary school in Minnesota will participate. The participants will represent a diverse range of academic backgrounds, cultures, and socio-economic statuses to ensure the study’s findings are representative and generalizable. The students in this 4th grade classroom are from farming families and may have unique experiences and perspectives related to this background. Additionally, the class includes students with a range of learning needs, including ELL students, students with IEPs, and students working on a 504 plan. The study will strive to account for these differences by incorporating strategies that accommodate different learning styles and provide equitable access to materials and resources.
To answer the research question of how the use of collaborative learning strategies impacts the problem-solving abilities of fourth-grade math students in a rural Minnesota elementary school, the proposed data collection method is a pre/post assessment using a math problem-solving test aligned to the Minnesota State Standards.
The assessment will consist of a total of 5 open-ended real-life math questions. The questions will cover various real-world problem-solving skills related to perimeter and area, such as finding the area and perimeter of different shapes and solving multi-step word problems involving area and perimeter. The pre-assessment will be administered before the collaborative learning strategies are implemented, and the post-assessment will be administered after the completion of the instructional unit.
In analyzing the data collected from the pre- and post-assessment, descriptive statistics will be used to compare the average problem-solving abilities of fourth-grade math students before and after the implementation of collaborative learning strategies. The descriptive statistics will be used to provide a summary of the data and to identify any patterns or trends in the students’ problem-solving abilities before and after the implementation of collaborative learning strategies.
The students are utilizing non-name identifiers, which effectively dissociate their personal data from their academic assessments and contributions within the scope of this study.
To ensure data confidentiality, all data and assessments will be kept in a locked file cabinet located in a secure area. Access to the cabinet will be restricted to authorized personnel only. Additionally, all data will be de-identified to protect the participants’ privacy. After three years, all data will be destroyed in a secure and confidential manner. As the data and assessments are collected, they will be immediately placed in the locked file cabinet and retrieved only as needed for the purposes of this study.
The data collected from the pre/post-assessment of fourth-grade math students indicates that collaborative learning strategies have had a positive impact on their problem-solving abilities. Out of the 19 students assessed, all but four showed improvement in their post-test scores, with 2 students increasing their score by one point, four students increasing their scores by two points, six students increasing their score by three points and one student increasing their score by four points.
On average, the students’ post-test scores were higher than their pre-test scores, indicating an overall improvement in their problem-solving abilities. The average pre-test score was 2.947, while the average post-test score was 4.368. This suggests that collaborative learning strategies have helped students to develop their problem-solving skills, as they were able to apply what they learned in the collaborative setting to the post-test assessment.
The data collected supports the conclusion that the use of collaborative learning strategies can have a positive impact on the problem-solving abilities of fourth-grade math students in a rural Minnesota elementary school.
Using descriptive statistics, the average pre-test and post-test scores for each student were calculated to determine the overall change in problem-solving abilities. This allowed for a comparison between the average pre-test and post-test scores for the entire group, providing insight into the effectiveness of the collaborative learning strategies on improving problem-solving abilities. This analysis identified any patterns or trends in the students’ problem-solving abilities before and after the implementation of collaborative learning strategies.
Based on the data analysis, it can be concluded that the use of collaborative learning strategies had a positive impact on the real-world problem-solving abilities of the fourth-grade math students in the rural Minnesota elementary school. The average pre-test score of the students was 2.947 and the average post-test score was 4.368, indicating an overall improvement in problem-solving abilities after the implementation of collaborative learning strategies.
The mode pre-test score was 2.5, while the mode post-test score was 5. This suggests that there were a greater number of students who scored lower on the pre-test, but were able to improve significantly with the use of collaborative learning strategies. Additionally, there were a higher number of students who scored a perfect score of 5 on the post-test, indicating that they were able to apply what they learned through collaboration to the problem-solving assessment. These results demonstrate the effectiveness of collaborative learning strategies in improving problem-solving abilities among fourth-grade math students in a rural Minnesota elementary school.
These findings are consistent with existing research on the benefits of collaborative learning strategies, which emphasize the importance of promoting teamwork, communication, and problem-solving skills in the classroom. This study highlights the value of incorporating collaborative learning strategies into math education in rural elementary schools, and suggests that such strategies may be effective in improving students’ problem-solving abilities in real-world contexts.
Based on the data, it appears that there were 4 students whose scores dropped from the pre-test to the post-test. Further analysis may be needed to determine the reasons behind this decline and whether it is significant. It could be beneficial to gather additional information, such as feedback from the students or their teachers, to understand any potential factors that may have affected their performance.