Exploring the Function Educational Tools and Techniques for 21st-Century Learners to Enhance Performance in Linear Programming: A Hermeneutic Perspective

Exploring the Function Educational Tools and Techniques for 21st-Century Learners to Enhance Performance in Linear Programming: A Hermeneutic Perspective

Chrispine Mulenga Mwambazi, Simeon Mbewe, Francise Simui

University of Zambia, Lusaka, Zambia

DOI: https://dx.doi.org/10.47772/IJRISS.2024.8100170

Received: 28 September 2024; Accepted: 10 October 2024; Published: 13 November 2024

ABSTRACT

Teaching and learning activities and methods identify the process, the outcome factors and the input variables such as students, teachers and instructional materials. The skills and attitudes of the students also gauges teaching and learning activities. The effectiveness of teaching and learning may be impacted by unfavorable social and physical circumstances. Establishing a conducive atmosphere is crucial for proficient instruction and acquisition of knowledge. Additionally, in order to impart the proper knowledge to pupils, teachers must be knowledgeable about their subject and have adequate training in the use of teaching tools.

The utilization of images, objects, video clips, and internet resources fosters the pupils a realistic imagination of the setting in which the material is being taught. Learning is reinforced as a result: we forget what we hear, remember what we see, and understand what we do. Lack of readiness for the workforce, new student traits, high dropout rates and disengagement, lack of motivation, changing demands of the 21st-century labor market, and global scenarios like economic and social crises, global diversity, and inability to think creatively and be globally competent are all factors. Those who successfully receive knowledge content have transferable abilities that allow them to understand the complexities of technology and think creatively.

Keywords: teaching, 21^st learner, teachers, linear programming, competence

INTRODUCTION

Educational tools and practices play a vital role in the education of 21st-century learners by increasing their engagement, developing their comprehension, encouraging critical thinking, and getting them ready for the modern workforce. These methods and resources help students and facilitate efficient instruction so that students can grasp the material more readily. It increases motivation, engagement, comprehension, and retention. Additionally, it fosters collaboration and communication abilities. Personalized learning, accessibility, and inclusivity through workforce readiness are its main goals.

Contextual

The educational landscape has transformed dramatically evolving needs of learners. Modern educational tools and techniques aim to develop critical skills such as communication. The most productive methods and tools available today include flipped classroom, digital and online learning platforms, Interactive whiteboards and smartboards, gamification and game-based learning, virtual reality (VR) and augmented reality (AR), project-based learning, social media and networking tools, and mobile learning (m-Learning).

According to Bonk (2009) digital learning platforms like Khan Academy, Coursera, and edX provides access to a wide range of courses and learning materials. These platforms support self-paced learning anywhere.

Similarly, Schmid (2006) asserted that interactive whiteboards and smartboards are used in classrooms in order to make lessons more engaging. They support multimedia content, interactive lessons, and collaborative learning activities. Reality offer help improve comprehension of difficult subjects, as noted by Radianti et al. (2020).

Collaborative tools like Google Docs, Trello, and Slack facilitate group work and project-based learning. These tools support real-time collaboration and communication among students (Laal, & Ghodsi, 2012).

Adaptive learning technologies use algorithms and data analysis to provide personalized learning experiences. These systems adapt content and assessments based on the learner’s progress (Pane et al, 2015).

It is sufficed to mention that the integration of these tools and techniques in education prepares modern world. By fostering technological proficiency, educators can ensure that learners are well-equipped for future challenges. By adopting and integrating these innovative tools and techniques, educators can better meet the needs of 21st-century learners, creating more engaging, effective.

Statement of the Problem

The 21st century has seen a tremendous progress in both technology and pedagogy, for educators teaching complicated subjects like linear programming. Today’s varied, tech-savvy learners cannot be engaged by traditional teaching approaches, which are frequently lecture-based. Furthermore, students must be able to handle real-world optimization issues by applying theoretical notions they have learned in linear programming—a crucial field of mathematics and operational research (Aydın & Demir, 2020). Even with the availability of contemporary teaching resources like collaborative platforms, interactive software, and simulations, many students still find it difficult to comprehend and apply the concepts of linear programming. Investigating and incorporating cutting-edge teaching strategies that improve student performance, comprehension, and engagement is necessary in this field of study.

Specific Objective

The key objective explores the function educational tools and techniques for 21st-Century learners to enhance performance in linear programming.

Theoretical Framework

Modern educational tools and strategies anchored in successful learning theories can be integrated into a well-structured theoretical framework to improve performance in Linear Programming for learners in the twenty-first century. Students use tools such as simulation models, graphing software, and game-based learning environments to actively engage in solving real-world linear programming problems and developing their understanding (Piaget, 1977; Vygotsky, 1978).

Students work on challenging linear programming scenarios from the engineering, logistics, and business sectors. Students are forced to comprehend linear programming ideas like limits, objectives, and optimization by working on these tasks. Using lesson plans for linear programming that are step-by-step and progressively cover key concepts while avoiding excessive complexity at first. Learning is improved and unnecessary burden is decreased when the intricate linear programming algorithms are divided into smaller, more manageable chunks. Kirschner et al. (2006) and Sweller (1988) on cognitive load management.

To sum up, this theoretical framework incorporates a number of 21st-century learning strategies and resources intended to improve students’ linear programming skills. By fusing contemporary technology with constructivist, cognitive, and collaborative approaches, educators may help students interact with linear programming in a dynamic and productive way that promotes creativity, critical thinking, and useful problem-solving abilities.

LITERATURE REVIEW

Research shows that visualization enhances students’ comprehension of abstract concepts in linear programming (Zhang & Wang, 2021).

These tools engage students while learning linear programming concepts. they engagement, leading to better problem-solving skills (Anderson & Rainie, 2020). Problem-Based Learning focuses on students working through real-world linear programming problems, such as optimizing resources for a business or logistics scenario. This approach enhances critical thinking and application of linear programming techniques (Jonassen, 2018).

Instructors use online tutorials, videos, and software alongside traditional teaching methods. Research indicates that blended learning provides flexibility and improves retention of concepts in linear programming (Means et al., 2013).

Students can collaborate on linear programming projects using these platforms, which facilitate discussion, resource sharing, and collaborative problem-solving. Collaborative learning encourages peer-to-peer learning, which has been shown to improve performance in mathematics and linear programming (Slavin, 2014).

Adaptive tools offer personalized learning, which is crucial for addressing individual weaknesses in mathematical concepts like linear programming (Smith et al., 2020). Pre-class learning materials followed by in-class problem-solving. Instructors provide lecture content before class, allowing class time and hands-on linear programming exercises.

Creating an effective contextual framework to evaluate tools and techniques on 21st-century learners in linear programming involves several key components. The 21st-century educational landscape emphasizes critical thinking, problem-solving, collaboration, and technological proficiency.

Effects of Function Educational

Using functional educational tools to teach linear programming enhances the performance of 21st-century learners. These tools leverage technology, interactive platforms, and innovative teaching (Li, & Ma, 2010).

This increased engagement can lead to higher motivation and better retention of concepts. It improves understanding and Application. Visual aids and simulation tools help students visualize complex concepts, and apply linear programming principles in practical scenarios.

According to Pane, et al., (2015) reveals that functional educational tools personalized learning. Adaptive learning technologies can tailor content to meet individual student needs, ensuring that each learner can focus on areas where they need more practice. Tools that support collaboration, such as online discussion forums and group projects, encourage peer-to-peer learning and teamwork, which are crucial skills. Immediate feedback and assessment on exercises and assessments, allow students to understand their mistakes and learn from them immediately (Thomas, & Hong, (Eds.).,2013).

It is sufficed to mention that incorporating functional educational tools into the teaching of linear programming can lead to significant improvements in student performance. By making learning interactive, these tools help students better understand and apply complex concepts. Effect of teaching techniques on 21st-Century learners to enhance performance in linear programming

Improving the performance of 21st-century learners in linear programming can be attained through techniques. Active learning involves engaging students directly through activities and discussions. This technique is beneficial for subjects like linear programming, which requires a strong grasp of both theoretical and practical aspects. This method entails having students watch videos or read books at home to absorb new subject, then using class time for assignments, projects, or debates.

Johnson, & Johnson, (1989) commended that collaborative learning strategies encourage students solve problems, promoting deeper understanding through peer-to-peer interaction. Assigning group projects where students must collaboratively solve linear programming problems can improve learning outcomes.

It is sufficed to mention that by implementing these teaching techniques, educators can boost the performance of 21st-century learners in linear programming. These methods not only equip students with the necessary skills to tackle real-world problems effectively.

According to Albright (2010), solving linear programming problems enables students to recognize the application of what they are learning. Problems related to business optimization, resource allocation, and logistics can be particularly engaging.

Utilize software and online tools such as GeoGebra, Excel Solver, or specialized linear programming solvers. These tools allow students to visualize problems and solutions interactively. This maximizes classroom time for hands-on practice and teacher support. Albright (2010) discussed various teaching methodologies for linear programming focusing on problem-solving and practical applications.

METHODOLOGY

Research Design

The function educational tools and techniques for 21st-century learners to enhance performance in linear programming were explored by the researcher, which made the excellent choice for this study (Yin, 2018). Because of the design’s qualitative aspect, the researcher was able to communicate with study participants and hear about their actual experiences.

Population

A population, also known as a target population, elements or cases—whether they be people, things, or events—that meet particular standards and to which the research findings are intended to be applied generally. What sets the unit or group apart from others is its feature.

Population comprised the following key stakeholders from KETA (pseudo name) district within western part of Zambia These groups were considered to have information on electoral violence in Zambia because they are key stakeholders in politics and electoral processes.

Sample Size

The sample for this study was fourteen (14) participants. This sample depended on data saturation where there was no more new information coming from the participants concerning the study themes (Patricia & Lawrence, 2015).

Sampling Technique

Sampling techniques in educational research are essential for gathering data to have an insight on tools and techniques designed to enhance student performance. Each member of the population has an equal chance of being selected. Participants were chosen to evaluate the effects of tools on linear programming performance.

Every participant was selected from a list. This method can help streamline data collection across larger populations of learners.

Instruments for Data Generation

This study used interviews and document review to generate primary and secondary data, respectively. These methods of data generation/production were appropriate for generating information.

Focus Groups

According to Krueger and Casey (2014), focus groups can provide group experiences as well as peer comments on the most and least effective tools or tactics. Students learn to openly express their perspectives, back up their opinions with evidence, listen for understanding, and be willing to change their minds when confronted with new information (Witherspoon, Sykes & Bell, 2016). To stimulate a discussion or debate among students, the teacher uses a text, thought-provoking video-clip or controversial image. They engage in class discussions by practicing their communication, collaboration and argumentation skills, researching a particular topic, defending opposing positions on global issues and raising awareness (Sun et al., 2015).

Interviews

Interviews help gather in-depth qualitative data from students on specific educational tools (e.g., online tutorials, software) in linear programming instruction. Interviews with open-ended questions to explore individual student experiences and instructional methods in more detail (Kvale, 2007).

Interviews are the predominant modes of data generation in qualitative research. The study employed semi-structured interviews with all categories of participants. The semi structured interviews were employed because they are more flexible, and they yielded extra rich information. The semi-structured interviews helped in making follow up questions and seeking clarifications on specific information (Barret, 2018). Each interview lasted for about 20 minutes.

Data analysis

Data generated was analyzed using thematic method. The data analysis began with a transcription of all the 14 interviews. This was followed by data cleaning to ensure only necessary information remains. This process required reading through the transcribed texts several times. Thereafter, themes were identified by highlighting key issues in the interview transcripts.

Data Quality Assurance

Trustworthiness was employed to ensure consistency with naturalistic inquiry since the study involved human beings. Four elements of trustworthiness were employed which included credibility, dependability, transferability, and confirmability.

Ethical Considerations

The researcher considered a range of ethical considerations as ethics are key aspect in conducting meaningful research involving human beings. participation by participants was through consent. No one was coerced to participate.

RESULTS AND DISCUSSIONS

The feedback from the participants revealed several themes, such as motivation and engagement, comprehension and retention, skill development, teamwork and communication, individualized learning, accessibility and inclusion, and readiness. Majority of participants said that solving difficulties in daily life is made easier by understanding and practicing linear programming [corporeality]. In addition to considering productivity, exam dates, deadlines, and personal responsibilities, students can make efficient use of linear programming concepts to allocate their study time among multiple subjects or projects (Hillier, Frederick & Gerald 2014).

Anderson, David, et al. (2016) found that linear programming maximizes the allocation of time among various study subjects or tasks on constraints including time constraints, subject priority, and desired aims. According to Frederick et al. (2016), using potential outcomes is the best strategy for limitations. It involves maximizing or minimizing linear inequality and equality while abiding by a set of constraints. These resources can aid in linear programming, numerous applications and techniques used to solve optimization problems.

A study by Winston (2014) found that learning linear programming makes daily management easier. Time is a never-ending resource that never runs out. The secret to success in life is to properly manage this resource, to which all have equal access, and to give planning adequate attention.

Kamuke said that,

“ I feel engaged and motivated with the current educational tools and techniques that teachers use when teaching linear programming. I study more than I have fun. I make care to maximize the temporal aspect of my study time” (Kamuke, 04.11. 2023).

The application of contemporary teaching methodologies and technological tools to enhance student interest and engagement can significantly boost linear programming proficiency. These tools increase the accessibility and engagement of abstract or difficult mathematical ideas like linear programming by utilizing contemporary technology, interactive tactics, and learner-centered approaches. This aids in problem’s boundaries and feasible region. Observing real-time changes while adjusting variables can help learners better understand concepts such as objective functions, feasible regions, and optimal solutions.

Iqbal et al. (2018) claim that interactive tools boost motivation and conceptual understanding by letting students study mathematical models on their own. This increases student engagement.
By gamifying linear programming tasks, teachers can make problem-solving into a quest or challenge where students can earn incentives for smart thinking or right answers. With the drive of competitiveness or self-actualization, it promotes continuous practice and increases comprehension. Dichev and Dicheva (2017) found that gamification in education substantially improves student motivation and performance by establishing an engaging and joyful learning environment.

Prior to class, students watch videos or read books that go over linear programming theory and fundamental problem-solving strategies. During class, they engage in hands-on exercises and solve problems with an instructor’s help. This methodology makes the most of the time spent on higher-order thinking activities like delving into intricate problems using linear programming, debating different approaches to solving them, or using linear programming in practical situations. According to Bergmann and Sams (2012), by giving students additional opportunities to encourage better recollection and application of concepts in problem-solving.

Collaborative learning environments where students tackle linear programming issues in groups, exchange diverse ideas, and clarify concepts by using tools such as Google Classroom, Padlet, or forums. Collaborative learning makes complicated concepts more relevant and concrete for students by encouraging peer engagement and creating a shared learning environment. According to Gokhale (1995), students who work in groups typically perform better than those who work alone, particularly when it comes to difficult assignments that call for critical thought.

These platforms are able to modify task and provide focused feedback in linear programming. With personalized learning, every learner is working on level-appropriate linear programming challenges, gradually boosting confidence and proficiency. According to research by Pane et al. (2014), adaptive learning platforms customizing training to each student’s needs.

Augmented and virtual reality technologies; students can view problems related to linear programming in three dimensions. In which virtual reality environments highlights boundaries and limits and encourage students to explore potential areas in a more engaging way. This could significantly increase conceptual understanding, especially for visual learners who might have trouble seeing abstract ideas in two dimensions. Bacca et al. (2014) claim that virtual reality technologies in the classroom helps students comprehend and remember difficult topics, which is particularly useful for disciplines like linear programming.

Project-Based Learning

This method increases students’ interest in linear programming and strengthens their problem-solving skills by showcasing its practical applicability. Thomas (2000) found that Project-Based Learning encourages students to apply theoretical knowledge in real-world scenarios, which enhances performance and comprehension. This encourages in-depth comprehension. Suffice it to say that 21st-century educational technology and methods enhance students’ success in linear programming by making learning interactive, collaborative, and practical.

According to Muke,

“The use of contemporary teaching methods and resources for twenty-first-century improve comprehension, recall, and linear programming ability. These resources make use of interactive and captivating approaches that meet the modern student’s cognitive and technological needs” (Muke, 04.08. 2024).

The findings support the claims made by Johnson et al. (2016) that gamified learning environments, virtual reality, and interactive software are examples of contemporary teaching strategies that can raise student interest and engagement. These technologies enable a range of learning methods and maintain student motivation since they provide instant feedback on their progress. Tools for interactive instructional technology boost student interest.

Enhanced Comprehension and Memory

Contemporary instructional strategies and resources for 21st-century learners can be extremely important in enhancing comprehension, retention, and performance in linear programming. These resources make use of interactive and captivating approaches that meet the modern student’s cognitive and technological needs.

Students may test out various situations and see the results instantly, which improves their comprehension of how dynamic linear programming problems behave (Anderson & Krathwohl, 2001). Students can be motivated and engaged when learning is infused with elements of games, a concept known as gamification. This could involve employing tests, challenges, or simulations in linear programming to have students solve optimization issues in a competitive setting. The accomplishment that comes from reaching new levels or receiving incentives motivates people on an innate level.

Their comprehension of limitations, solutions, and optimization methodologies are communicated to others through group projects, partnered conversations, or peer teaching sessions. Group discussions and debates compel students to explain their thinking, which improves retention and expands their comprehension.

Platforms personalize learning paths for every student according to their development. Platforms can determine how well students grasp a subject and modify the way it is taught or how difficult problems are presented to them. This way, students can gain mastery over basic ideas before going on to more complex subjects. By giving students focused practice where they need it most, adaptive learning tackles individual shortcomings and enhances comprehension and retention (Brusilovsky & Millán, 2007).

AI-Powered Tutoring Programs

Tutoring tools powered by artificial intelligence provide personalized feedback and support to students studying linear programming. Depending on how well pupils do, these systems can reduce complex problems down into manageable steps and offer hints or explanations. AI tutors enable real-time feedback and continuous practice, which is crucial for learning optimization techniques and understanding how constraints affect solutions (VanLehn, 2011). Note that students’ understanding and retention of linear programming can be significantly improved by using instructional strategies and resources that are tailored for 21st-century learners, such as gamification, collaborative learning, adaptive systems, immersive technology, and interactive learning platforms. These approaches support active learning, focused instruction, and sustained attention—all necessary for understanding the complex mathematical ideas required for linear programming.

According to Kamu,

“Because it efficiently builds abilities and improves performance in linear programming, 21st-century learners can take advantage of instructional resources and strategies designed for contemporary pedagogical approaches. My study time exceeds my leisure time. I take care of my study time in terms of time” (Kamu, 04.08. 2024).

Modern pedagogical approaches have produced a variety of instructional materials and techniques that 21st-century learners can use to effectively improve abilities and boost performance in linear programming, and develops critical thinking abilities that are crucial for grasping.

Interactive Software Instruments

When students can modify constraints and variables and see the changes’ immediate impact, geometric interpretation of linear programming is improved (Zaslavsky, 2016). Using step-by-step solutions for linear programming issues allows students to explore various approaches to problem solving and test their work, which enhances comprehension (Alpers, 2013).

Learners can enhance their performance in linear programming by gaining a stronger conceptual grasp, encouraging critical thinking, and honing their practical problem-solving abilities by employing these 21st-century instructional methods and practices. In addition, these tactics foster a dynamic and captivating educational setting, which is crucial for grasping intricate mathematical subjects like linear programming.

According to Muka

“Teachers employ instructional approaches and technologies that inspire cooperation and communication to help 21st-century students perform better in linear programming” (Muka, 04.08. 2024).

Students’ performance in linear programming for students in the twenty-first century, teachers use various instructional strategies and resources that encourage cooperation and dialogue. Enhancing students’ comprehension of linear programming requires collaborative learning. They exchange diverse viewpoints and methods for addressing problems. Each member contributes special ideas to the problem-solving process. Eric Mazur invented this technique, in which students teach their peers about principles related to linear programming, thereby reinforcing their understanding. Collaboration is encouraged via projects that use real-world optimization issues.

According to Strogatz (2019), learning linear programming requires mathematical concepts clearly. Understanding is improved when teachers encourage students to properly explain their reasons in both written and spoken forms. Pupils may demonstrate to the class how they modeled the problem, used constraints, and arrived at the best solution by presenting their linear programming solutions. Their comprehension and communication of mathematical concepts both improve as a result.

Enhancing Performance Through Feedback

Solvers for linear programming are examples of instructional tools which can give students quick feedback on their answers, assisting them in seeing mistakes and comprehending the reasoning behind optimization strategies. Students can evaluate one another’s linear programming solutions and provide comments on correctness, lucidity, and approaches to problem-solving. Analytical and communication skills are improved by this practice (Mazur, 1997). By using these strategies and resources, educators may make sure that students acquire the hard and soft skills required for success in linear programming and other subjects.

According to Kake,

“It utilizes a variety of contemporary instructional strategies and resources that are tailored to the unique of individual students, personalizing learning and improving performance in linear programming for learners in the twenty-first century” (Kake, 04.08. 2024).

Teachers apply modern instructional strategies and technologies that match the specific requirements to optimize learning and increase students’ performance in linear programming (He, Wu, & Li, 2018). These platforms provide courses that are specifically catered to each student’s learning style and level of comprehension by using algorithms to evaluate each student’s strengths and shortcomings. Students can solve optimization problems in a cooperative or competitive game-like environment by using linear programming. According to Dickeva et al. (2015), this method boosts motivation and gives abstract ideas a more concrete sense. Linear programming models and linear inequalities can be graphically represented using programs such as GeoGebra. These platforms are designed for visual learners; they let them work with graphs, modify parameters, and observe instantaneously how their changes impact feasible regions and optimization solutions (Wilkerson-Jerde, Gravel, & Macrander, 2015).

Teachers can adjust their training to fill in specific knowledge gaps and give students personalized feedback by analyzing student data, such as the amount of time spent on tasks and the kinds of mistakes committed. According to Gašević, Dawson, and Siemens (2015), analytics has the ability to pinpoint the precise parts of linear programming that pose the greatest challenge for students and suggest tailored retraining.

Understanding the requirements and utilizing technology and creative approaches to deliver customized education and feedback are essential components of successful personalized learning.

According to keka,

“I have improved my linear programming performance by utilizing contemporary instructional resources and methodologies” (Keka, 04.08. 2024).

These technologies modify content according to each student’s unique learning style and speed using algorithms. By attending personalized learning routes assist students in achieving better results (Pane et al., 2017).

By using modern instructional methodologies and tools, significantly increase the linear programming ability of 21st-century learners (O’Neil & Perez, 2013). These tactics should strongly emphasize inclusivity, accessibility, and student-centered learning. Modern educational technologies and practices support learning by giving students personalized, interactive, and interesting experiences. These linear programming tools deciphering complex concepts and researching real-world problems. Students can accommodate their diverse learning styles. Students who struggle with mathematical abstraction can benefit from more real-world applications of linear programming, and more experienced students should look into difficult, real-world linear programming issues (Meyer, Rose, & Gordon, 2014).

Teachers can dramatically improve students’ performance in linear programming by utilizing interactive tools, advocating for inclusive learning approaches, and implementing cutting-edge teaching tactics like project-based. This method not only takes into account the pupils, but it also gets them ready for the practical application of linear programming sectors.

Hamu said that,

“I participated and made sure the training matched the skills needed for the workforce of the future. I study longer than I enjoy myself. I used all of my study time” (Hamu, 04.08. 2024).

Aligning skills needed for the workforce of the future is a key component of improving performance in linear programming using instructional tools and strategies created for 21st-century learners (Kizito, 2015).

The use of linear programming challenges or competitions to gamify learning promotes problem-solving abilities and engagement. According to Subhash and Cudney (2018), incorporating competitive settings in which students are required to optimize resources, such as in business simulation games, promotes real-world application. An example of using linear programming concepts in decision-making could be a business simulation in which students use to allocate resources and compete to maximize profits.

They practice specific areas they find difficult and eventually become proficient in (Johnson, & Adams Becker, 2015).

Modern educational tools and techniques provide a rich and diverse environment for learning linear programming. By making use of interactive software, real-world issues and blended online-offline models, students gain a more practical and in-depth understanding of linear programming, which equips them for the future workforce.

These approaches create an active, engaging learning experience, and real-world problem-solving skills.

Muhe, said that,

“Using modern educational tools, can develop digital literacy, coding skills, and familiarity with tools and technologies they are likely to encounter in their future careers” (Muhe, 04.0. 2024).

Using modern educational tools, students can develop digital literacy, coding skills, and familiarity with tools and technologies they are likely to encounter by integrating technology in education helps students develop essential digital skills (Voogt et al., 2013).

CONCLUSION

These methods and resources are educational paradigm of the twenty-first century, which places a strong emphasis on technological integration, real-world application, and student-centered learning. Students’ engagement, problem-solving abilities, and general comprehension of difficult linear programming ideas will all improve when these techniques are incorporated into a curriculum for linear programming. Education should prepare students to develop transferable skills such as collaborating among themselves to solve scenarios of real-world challenges, reflecting on their ideas, strengthening their critical and creative thinking capacities.

RECOMMENDATIONS

Combining various traditional teaching approaches with modern technologies is essential to research effective teaching strategies and resources for 21st-century students that can enhance their performance in linear programming.

1. Interactive solutions that let students see how changes in goals and constraints affect them in real time should be used to engage students.
2. Competitive learning and interest can be encouraged by rewarding completion of linear programming tasks with prizes, badges, or recognition.
3. With the flexibility that mobile learning offers, students can interact with linear programming content whenever and wherever they choose.
4. Students can better visualize complex data and gain familiarity with industry-standard software by using these tools, which are frequently used in the workplace.
5. Teachers to blend learning methods, which also enable in-depth study of difficult subjects.
6. Students may swiftly correct errors and embrace learning when they receive immediate feedback.

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