Homework reading and response: Arbitrary and necessary

In the context of the article, "arbitrary" refers to those aspects of mathematics that are based on conventions, names, or memorization. These are elements that students must accept and adopt without much room for interpretation. They include things like mathematical notations, terms, and established rules. As a teacher, I need to recognize that these elements are essential, and my role is to inform students about them. However, I should also be aware of the potential challenges in this area, especially for students who may struggle with memorization. To address this, I could consider innovative teaching strategies, mnemonic devices, and frequent practice to help students grasp and retain these arbitrary elements effectively.

Conversely, "necessary" elements in the article refer to mathematical properties that can be understood and worked out through reasoning and problem-solving. These are the underlying principles, relationships, and concepts that form the foundation of mathematics. As a math teacher, I see the importance of nurturing students' awareness and understanding of these necessary elements. I should create a classroom environment that encourages critical thinking, exploration, and discovery. Instead of providing all the answers, I can design tasks and activities that help students uncover these properties themselves. This approach empowers students and fosters a deeper and more meaningful comprehension of mathematics.

As a Math teacher, I should maintain a balanced approach, acknowledging the need for students to learn both arbitrary and necessary elements. While memorization is important for certain aspects, I should strive to make mathematical concepts accessible through understanding and problem-solving.

For necessary elements, I can design lessons that engage students in critical thinking, encouraging them to explore, question, and reason. This not only enhances their mathematical understanding but also fosters a sense of ownership and curiosity.

My assessment strategies should reflect this duality. I can include assessments that evaluate students' understanding of necessary concepts alongside their ability to apply arbitrary elements accurately.

In conclusion, the article's distinction between arbitrary and necessary elements in mathematics serves as a valuable reminder for math teachers to balance the acquisition of conventions and memorization with the development of deep mathematical understanding. By being mindful of these distinctions, I can plan lessons and units that empower students to become not just memorizers but also critical thinkers and problem solvers in the world of mathematics.