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Literature & Language
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Essay
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English (U.S.)
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Topic:
The Different Dimensions of Mathematical Proficiency in Mind
Essay Instructions:
- What have been your experiences with each of the five strands in in your mathematics education classes? • How could you and your students benefit from keeping these different dimensions of mathematical proficiency in mind? What parts could be challenging? • How can the five strands be used to assess proficiency related to mathematical models and modeling? • What would the indicators that students are achieving conceptual understanding and productive disposition related to mathematical models and modeling
Essay Sample Content Preview:
Mathematical Modeling
Student’s Name
Institution
Question One
Generally, mathematicians of the 21st-century use models and modeling to tackle real-world issues and circumstances in educational and professional contexts. They help people "think like mathematicians" rather than "perform mathematics." Students gain valuable analytical and problem-solving abilities through models, even if they are rudimentary. These skills are becoming increasingly important as the world becomes more interconnected and complex. Mathematical knowledge is more than simply being able to answer a question correctly. Students must be able to perform basic math calculations. In order to learn mathematics successfully, one must be mathematically proficient.
Assessments of higher-level skills and knowledge, such as mathematical modeling, might be guided by the Five aspects of Mathematical Proficiency developed by the National Research Council (Swafford et al., 2001). The five strands are understanding, procedural fluency, strategic competency, and adaptive reasoning. Conceptual knowledge is described as an "integrated and functional grasp of mathematical ideas," which helps students study new concepts by linking them to what they currently know or have previously learned. A person's procedural fluency refers to their ability to carry out tasks in a way that is quick while still being accurate and suitable. When and how to use a process is defined as procedure knowledge. Competence in mathematics is a prerequisite for strategic thinking. Think logically, reflect, explain, and justify ideas via adaptive reasoning. In the end, a productive disposition is a belief in one's own ability to persevere and succeed, as well as a belief in the value of mathematics.
Question Two
Typically, students can acquire new concepts by relating them to what they already know, thanks to conceptual comprehension (Hwang et al., 2019). When students acquire conceptual knowledge, they can better retain information and avoid making typical mistakes. Flexibility, accuracy, efficiency, and appropriateness are all part of what is meant by procedural fluency, which is why it is so important. It is crucial to be able to spot illogical answers right away. People can learn by connecting new concepts to ones they already understand. Recognize the similarities and differences among a group of connected facts and principles, as well as the nume...
Student’s Name
Institution
Question One
Generally, mathematicians of the 21st-century use models and modeling to tackle real-world issues and circumstances in educational and professional contexts. They help people "think like mathematicians" rather than "perform mathematics." Students gain valuable analytical and problem-solving abilities through models, even if they are rudimentary. These skills are becoming increasingly important as the world becomes more interconnected and complex. Mathematical knowledge is more than simply being able to answer a question correctly. Students must be able to perform basic math calculations. In order to learn mathematics successfully, one must be mathematically proficient.
Assessments of higher-level skills and knowledge, such as mathematical modeling, might be guided by the Five aspects of Mathematical Proficiency developed by the National Research Council (Swafford et al., 2001). The five strands are understanding, procedural fluency, strategic competency, and adaptive reasoning. Conceptual knowledge is described as an "integrated and functional grasp of mathematical ideas," which helps students study new concepts by linking them to what they currently know or have previously learned. A person's procedural fluency refers to their ability to carry out tasks in a way that is quick while still being accurate and suitable. When and how to use a process is defined as procedure knowledge. Competence in mathematics is a prerequisite for strategic thinking. Think logically, reflect, explain, and justify ideas via adaptive reasoning. In the end, a productive disposition is a belief in one's own ability to persevere and succeed, as well as a belief in the value of mathematics.
Question Two
Typically, students can acquire new concepts by relating them to what they already know, thanks to conceptual comprehension (Hwang et al., 2019). When students acquire conceptual knowledge, they can better retain information and avoid making typical mistakes. Flexibility, accuracy, efficiency, and appropriateness are all part of what is meant by procedural fluency, which is why it is so important. It is crucial to be able to spot illogical answers right away. People can learn by connecting new concepts to ones they already understand. Recognize the similarities and differences among a group of connected facts and principles, as well as the nume...
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