In contemporary education, attention to improving mathematical reasoning and building self -efficacy between students is very important. As the world becomes more complex, it is essential for students to develop strong mathematics skills. This includes not only the ability to solve mathematics problems, but also the belief in one’s ability to successfully face these challenges. To achieve this, innovative teaching methods are required. This essay will examine three main approaches: learning based on problems (PBL), contextual teaching and integration of automatic learning in education.
Learning based on problems is a method in which students learn by solving the problems of the real world. In this type of learning environment, students become active participants in their education. They work in groups, collaborate and apply their knowledge to find solutions. According to Nurlinda et al. (2024), PBL encourages the deepest thought and helps students to establish connections between concepts. While students undertake to solve problems, learn to think mathematically and develop critical thinking skills. This approach not only improves their mathematical skills, but also increases their trust when they see their progress in facing difficult problems.
The contextual teaching, on the other hand, focuses on the relative academic content with situations of real life. This approach helps students understand why they have to learn mathematics and how to apply to their daily life. When students see the relevance of mathematics in practical contexts, such as budget for a project or planning of a community event, they are more likely to interact with the material. Nurlinda et al. (2024) They argue that contextual teaching helps students better preserve information and see mathematics as a useful tool rather than a stressful subject. This connection can significantly improve their self -efficacy, since they begin to believe they can use mathematics effectively in real life situations.
Another significant aspect in improving students learning is the integration of automatic learning in education. This technology offers personalized learning experiences adapting the curriculum to meet the needs of individual students. For example, programs that use automatic learning can identify areas in which a student struggles and provide targeted exercises to improve these skills. This tailor -made approach allows students to learn at their own pace and builds their trust while getting small successful goals. As a result, students not only improve their mathematical reasoning, but also develop a stronger sense of self -efficacy when they see their improvement over time.
By combining learning based on problems, contextual teaching and automatic learning, educators can create a rich learning environment that promotes both mathematical reasoning and self -efficacy in students. These methods encourage active involvement, the application of the real world and the personalized feedback that are crucial for effective learning. While we continue to explore these innovative approaches, it becomes clear that they play a vital role in the preparation of students for future challenges in a world led by technology. Through this collective effort, students can build a solid base in mathematics and trust in the use of these skills for life., Problem -based learning (PBL) helps students learn by addressing real world problems that need critical and creative thinking. This method pushes students to be active participants in their education instead of being only passive listeners. When working together with classmates, students can explore and share different points of view. This collaboration allows them to develop their understanding of mathematical concepts, making the learning experience more significant.
Liu et al. (2023) have shown that when high school students participate in PBL programs enriched with technology, their self -efficacy and performance significantly improve. Self -efficacy refers to the belief of a student in their ability to succeed in their tasks. When students feel safe in their skills, they are more likely to get involved with challenging mathematical problems. PBL makes learning less about the memorization of facts and more about the understanding and application of knowledge to real -life situations. This change not only maintains students’ interest, but also encourages them to take possession of their learning.
In PBL, real problems can often be messy and complex. This reflects the way in which the challenges occur in the real world, which allows students to practice critical thinking and problem solving. When they find obstacles, students must analyze, find ideas, evaluate different solutions and draw conclusions. This process develops not only its mathematical reasoning but also its ability to work as part of a team to overcome difficulties.
In addition, the integration of PBL technology can provide students with various resources to improve their learning. For example, the use of software that allows simulations or visualization of data can facilitate the capture of abstract mathematical concepts. Seeing the results of their calculations in real time, students can better understand relationships between numbers and variables. This interaction with technology can also help students develop important digital skills that are increasingly necessary in the modern world.
In addition, PBL promotes a growth mentality among students. Instead of focusing on obtaining the correct answer, students learn to see errors as part of the learning process. This change in perspective is essential in mathematics, where the way to find a solution often implies proof and error. When students adopt challenges and learn from their experiences, they create resistance and trust. Over time, this approach helps improve its general self -efficacy.
In today’s rapid rhythm, skills such as critical thinking, collaboration and resilience are vital. Teaching students through problems based on problems helps prepare them for future efforts, either in higher education or workforce. By getting involved with mathematical reasoning in a significant way, students develop skills that extend beyond the classroom.
The importance of the context in learning cannot be exaggerated. When students can see how mathematics apply to real world situations, they are more likely to find it relevant and exciting. PBL allows them to explore these connections, making mathematics more accessible and pleasant. As a result, students become not only better mathematicians, but also more safe apprentices of themselves that feel equipped to handle various challenges. In general, problem -based learning offers a dynamic approach that supports both mathematical reasoning and self -efficacy among students., Teaching and contextual learning (CTL) are an effective way to support students to learn mathematics by making lessons more relatable to their daily lives. When teachers use CTL, they show how mathematics are connected to real experiences. This connection helps students understand the importance of mathematics and encourages them to engage more in lessons. Sari and Khairani (2021) have found that when mathematics learn to use this approach, students improve their skills in problem solving and feel better in their capacity in mathematics.
An important element of contextual education is that it often involves practical activities and real scenarios. For example, rather than simply solving a mathematical problem from a manual, students can budget a party or measure ingredients for a recipe. These activities allow students to apply mathematical skills to the situations in which they are outside the school. Consequently, they are starting to see mathematics as useful, rather than numbers and abstract formulas.
Cano and Lomibao (2023) also point out that when students see how mathematics relate to their own lives, they feel more confident by using it. When they realize that they can solve problems that are relevant to them, their self-efficacy is developing. This means that they believe in their ability to succeed in mathematics. This change in the mentality is crucial because when students feel capable, they are more likely to take up challenges and persist through difficult problems.
In addition, contextual education allows teachers to adapt their lessons to the interests and experiences of their students. By understanding what students care – be it sport, music or technology – educators can create examples and problems that resonate with them. This personalization makes lessons more interesting and encourages students to participate actively.
For example, a teacher could introduce statistics by asking students to analyze data from a popular sporting or musical survey. This example not only arouses interest, but also shows how mathematics can be used to understand trends and make predictions. While students solve these contextual problems, they practice their mathematical reasoning and acquire information that extends beyond the class.
In addition, when students discuss their results in small groups or with class, they learn to clearly communicate their ideas. This interaction builds a community of learners who support each other and share different ways of thinking about problems. In such an environment, students feel more safe to make mistakes and learn from them, which is vital to develop resilience in learning.
Overall, contextual teaching helps students connect mathematics to the world around them, improve their reasoning skills and strengthen their confidence. This approach creates a positive cycle where understanding leads to increased self-efficacy, encouraging students to meet more complex mathematical challenges. By incorporating real links, educators can cultivate a love for mathematics that lasts beyond school and empowers students in their future efforts., The integration of machine learning in education can greatly benefit the mathematical reasoning and self -efficacy of students. With the use of Artificial Intelligence Tools (AI), as adaptive learning platforms, students receive personalized instructions that meet their exclusive needs (DAI, 2023). These platforms collect and analyze data on student performance. For example, they can track which math problems students get right or wrong and then provide feedback that helps students learn from their mistakes. This immediate feedback is critical because it allows students to understand their strengths and weaknesses in real time. In turn, this personalized approach offers students a sense of property about their learning process, increasing their trust and desire to get involved with challenging mathematics topics.
In addition, using AI -oriented tools, students can learn at their own pace. Some students can fight with certain concepts and need more time and practice, while others may quickly understand and be ready to move on. Adaptive learning technologies can identify these differences and adjust the difficulty level for each student. This means that every individual can progress according to their own skills, which can build a stronger base in mathematics. When students see they are progressing, they usually feel more capable, which increases their self-efficacy.
However, the integration of AI tools in the teaching of mathematics does not fail to have their challenges. Egara and Mosimege (2024) point out that while tools like chatgPT have great potential, they also have obstacles that educators should address. Teachers need to develop effective strategies to implement these tools in a way that completes traditional teaching methods. For example, it is essential that educators provide guidelines on how to use AI tools effectively, ensuring that students do not become excessively dependent on technology and still develop critical thinking skills.
In addition, teacher training is crucial. Teachers should understand how to interpret the data collected by these AI tools to improve instructions. They need to feel confident of their ability to integrate technology while still providing a classroom environment that encourages collaboration and problem solving. In addition, it is important to build confidence among students when using AI tools. If students perceive these tools as useful allies on their learning journey, they are more likely to embrace them completely.
Another important aspect of machine learning integration is its role in real -world applications. When students use AI tools that simulate real life problems, they begin to see the relevance of mathematics in everyday situations. This contextual approach not only enhances mathematical reasoning, but also enhances students’ motivation to learn. If students understand how mathematics applies to various fields, from engineering to economy, it is more likely to get involved with the material and persist through challenges.
In short, the effective integration of machine learning in educational practices can significantly improve mathematical reasoning and self -efficacy among students. Although there are challenges in implementing these technologies, the potential benefits of personalized learning experiences, immediate feedback, and real -world applications suggest a promising path to contemporary education., Problem -based learning (PBL) and contextual teaching and learning (CTL) are two teaching methods that greatly affect the way students mathematically reason. These approaches encourage students to engage in mathematics in a practical way, allowing them to explore real -world problems and make connections to what they learn in the classroom. This active involvement is crucial for the development of strong mathematical reasoning skills.
In problem -based learning, students work on complex problems that have no clear and direct solutions. When confronted with these challenges, they use research and analysis to find answers. This process encourages students to think deeply about mathematical concepts. For example, instead of just solving an equations of a book, students can address a project in which they need to create a budget for a school event or project a park layout. Such experiences require them to apply significant mathematical principles. Research shows that students who learn from these types of practical problems improve their ability to solve mathematical issues and think critically about solutions (Alali & Wardat, 2024).
Similarly, contextual teaching puts mathematical concepts in real life situations with which students can relate, making the learning experience more relevant and engaging. Seeing how mathematics applies to everyday situations, students are more likely to understand and remember the concepts they are learning. For example, when students learn about percentages by calculating sales tax while buying or understanding statistics through sports data analysis, they understand the usefulness of mathematics in their daily lives. This method not only helps them better understand mathematical concepts, but also encourages them to think critically about how these concepts can be applied.
Both PBL and CTL increase students’ self-efficacy, which refers to their belief in their ability to succeed in tasks. When students actively solve real problems or apply mathematics to real -world contexts, they gain confidence in their skills. This confidence is essential because it motivates them to face new challenges and persist through difficulties. When students see their efforts lead to successful results, their belief in their mathematical skills gets stronger over time. As a result, they become not only better in mathematics, but also more willing to get involved with complex mathematical ideas in the future.
In addition, these teaching methods help build a student community. In PBL and CTL, students usually work in groups, where they share their ideas and strategies. This collaboration promotes a support learning environment where students can learn from each other’s successes and errors. Through discussions and group work, they develop communication skills and learn different perspectives on problem solving, which further enhances their mathematical reasoning.
In short, problem -based learning and contextual teaching effectively involve students and raise their mathematical reasoning, connecting mathematics to real -world situations. As students sail in complex problems, their analytical skills and their analytical skills grow, leading to a better solution of problems and critical thinking skills. Combined with confidence with these successful experiences, students are ready to become confident mathematicians who can face a variety of challenges in contemporary education., Self-effectiveness, or the belief that success can be achieved, is very important for students when it comes to school performance. When students think they can succeed, they are more likely to face challenges and persist in their efforts. Problem -based learning (PBL) and contextual teaching and learning (CTL) are two teaching methods that help build this belief in students. By using these approaches, teachers create a safe environment where students are encouraged to solve difficult problems without worrying about failing. This is significant because when students feel supported, they are more willing to experience new things and take risks in their learning (Yohannes & Chen, 2024).
At PBL, students work together to solve real -world problems, which makes learning more relevant and engaging. They learn not only from the teacher, but also from each other. This collaboration allows students to discuss their thoughts and strategies, which can lead to a better understanding and stronger belief in their skills (Simamora and Saragih, 2019). For example, if a student fights a math problem, his colleagues will be able to share different methods to solve it. By hearing and discussing these methods, students can get new ideas and strategies, which helps improve their trust in their mathematical skills.
In addition, the CTL reports the learning of real -life situations. When students see how mathematics applies outside the classroom, they begin to understand the usefulness of what they are learning. This connection not only helps students understand important concepts, but also encourages them to believe that they can use math in their daily lives. When students can relate mathematics to their own experiences, they are more motivated to learn and more likely to feel able to master complex topics.
Research supports the idea that these teaching methods improve self-efficacy. Studies show that when PBL and CTL are used in classrooms, students report they feel more confident about their skills. For example, the work of Aprisisa et al. (2024) finds a strong connection between the use of these methods and increased self -efficacy. Students who engage in PBL and CTL usually develop a growth mindset, where they consider challenges as opportunities to grow, not as threats to their success.
In addition to increasing self -efficacy through real -world collaboration and connections, these teaching strategies also offer feedback opportunities. When students work in trouble and receive constructive comments from teachers and colleagues, they can see their progress and areas to improve. This continuous feedback loop helps create confidence as students can celebrate their small hits and learn to overcome their struggles.
In general, PBL and CTL not only make learning more engaging and relevant, but also promotes a positive learning environment that can significantly improve students’ self-efficacy in mathematics. Believing in their skills and feelings supported by their classmates and teachers, students are more likely to take risks in learning and finally achieve greater success in their academic journeys., In this world that changes rapidly, we can see that education is also changing. Teachers always look for better ways to help students learn, especially in subjects such as mathematics. A promising way to improve learning is through the use of problem -based learning (PBL), contextual teaching and automatic learning. These methods not only make learning mathematics more interesting, but also help students have more confidence in their skills.
Problem -based learning focuses on situations that require students to solve real -life problems. When students work on these types of problems, they are not only memorizing formulas or rules. Instead, they are using their brains to think critically and make decisions on how to address challenges. This approach encourages students to explore several solutions and explanations. As a result, students develop stronger mathematical reasoning skills because they learn to apply mathematics in practical situations. They see that mathematics is not only a subject in school, but also a tool they can use in everyday life.
Contextual teaching goes hand in hand with problem -based learning. Connect mathematical issues with real world contexts, which makes lessons more identifiable and significant. When students see how mathematics connects with their lives, such as using mathematics in the budget, kitchen or even sports, they are more likely to participate in the learning process. This approach helps demystify complicated mathematical concepts and makes them easier to understand. As students realize that they can use mathematics outside the classroom, their belief in their mathematical skills or self -efficacy grows.
The role of automatic learning in education is becoming increasingly important. Automatic learning can customize the learning experience for each student, adapting to their strengths and weaknesses. With smart tutoring systems, for example, students can receive instantaneous comments about their work. They can take questionnaires that fit in difficulty depending on how well they work. This means that if a student fights with a specific topic, the system can provide additional resources and practices to help them improve. By using these technologies, educators can make sure that each student obtains the support he needs, which further increases their confidence in mathematics.
Hutchins’ research (2022) and Al-Thani & Ahmad (2025) emphasizes the importance of integrating these innovative teaching strategies in the classroom. They discovered that when teachers use PBL, contextual teaching and automatic learning, students not only understand mathematics but also develop a more positive attitude towards their studies. This improvement in attitude is crucial. When students believe they can succeed in mathematics, they are more likely to persist through challenges, seek help when necessary and enjoy the learning process.
In contemporary education, the combination of these approaches can lead to a significant transformation in the way mathematics is taught and learned. As students carefully involve mathematics and receive support adapted to their needs, they build their reasoning skills and increase their trust. This is vital to prepare them for the future, where mathematics plays a key role in many daily careers and situations. In general, the integration of problem -based learning, contextual teaching and automatic learning presents a promising path to improve the experiences of students in mathematical education.
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