Shawn-EDCP-342

Dear Mr. Fan, Your passion for mathematics was infectious, and it ignited a spark within me that continues to burn brightly to this day. Your teaching style was not just about equations and theorems but about fostering a deep appreciation for the beauty and logic that mathematics embodies. You had a unique way of making even the most complex concepts seem approachable and engaging. The problem-solving skills and mathematical mindset that you instilled in me have been invaluable throughout my life. They not only helped me excel academically but also in my career and personal endeavors. I often find myself thinking back to the lessons you taught and the way you encouraged us to think critically and creatively. I want you to know that your influence has extended far beyond the classroom. I chose a career in mathematics, and I'm currently working as a research mathematician. I owe much of my success to the strong foundation you provided me during those formative years. Thank you for be...

Every 2 guests used a dish of rice. Every 3 guests used a dish of broth. Every 4 guests used a dish of meat. Let r, b, and m be the number of dishes of rice, broth, and meat, respectively. r + b + m = 65 Every 2 guests used a dish of rice, so 2r represents the total number of guests. Every 3 guests used a dish of broth, so 3b represents the total number of guests. Every 4 guests used a dish of meat, so 4m represents the total number of guests. So, 2r = 3b =4m = g represents the total number of guests g/2 + g/3 + g/4 = 65 g(1/2 + 1/3 + 1/4) = 65 g(13/12) = 65  g = 65(12/13) = 60 which gives the total number of guests is 60. This puzzle can be solved without algebra by carefully considering the relationships between the guests and the dishes. However, using algebra helps formalize and generalize the solution process. Offering examples, puzzles, and histories of mathematics from diverse cultures can significantly impact students. It not only promotes inclusivity but also helps student...

I agree that mathematics, like other art forms, should be subject to critical appraisal based on criteria such as soundness, elegance, and simplicity. This aligns with the idea that mathematics is not just a mechanical exercise but a creative pursuit where the quality of mathematical arguments and solutions can be assessed and appreciated in much the same way as the quality of a piece of literature or a musical composition. This perspective can foster a deeper understanding and appreciation of the aesthetic aspects of mathematics. I would disagree with the statement that mathematics is completely irrelevant to our lives. While some aspects of mathematics may seem abstract and disconnected from everyday experiences, mathematics plays a fundamental and essential role in various practical applications and real-world problem-solving. Mathematics is not only an abstract pursuit but also a powerful tool used in fields such as science, engineering, technology, finance, and many others. It h...

My favourite math teacher among all the teachers I have ever encountered was my grade-12 math teacher. He explained complex mathematical concepts in a way that was easy to understand. He had a knack for breaking down problems step by step, ensuring that every student grasped the fundamentals before moving on to more advanced topics. He also went beyond the curriculum to show us the real-world applications of math, making the subject relevant and exciting. Whether he was demonstrating how algebra played a role in everyday budgeting or showcasing the beauty of geometry in architecture, he made sure we saw the practical value of what we were learning. Moreover, he genuinely cared about his students' success, offering extra help during lunch hours, and organizing study groups before exams. His dedication went far beyond the classroom, and he motivated us to reach our full potential in mathematics. My least favourite math teacher was my grade-10 math teacher. He would rush through les...

 Lockers are only touched by students who are factors of that locker number. For example, locker #5 is only touched by students 1 and 5. Student 1 closes it and student 5 opens it. In fact, because factors come in pairs, the first factor student closes it and the corresponding factor student opens it. When factors don’t come in pairs, the locker will be left close. And factors don’t come in pairs when numbers are multiplied by themselves. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…) are the only numbers whose factors don’t come in pairs because one set of factors, the square root, is multiplied by itself. This means that only perfect square lockers will be left close. Therefore, locker # 1, 4, 9, 16, 25, 36,…, 961 these perfect squares numbers are left close whereas the rest of lockers are left open!

It is often beneficial to introduce relational understanding before instrumental understanding. Starting with relational understanding helps students build a solid foundation by emphasizing the underlying principles and connections between mathematical concepts. However, the order of introduction may vary depending on factors such as the complexity of the topic, the developmental stage of the learners, and individual learning styles, and in many cases, a balanced approach that combines both relational and instrumental understanding is most effective. In teaching math, our aim is multifaceted, encompassing the development of procedural fluency, fostering excitement about mathematics, and cultivating a deep understanding of mathematical concepts. To address these diverse goals effectively, teachers must employ a balanced approach that integrates these aspects into their teaching methods. This balance involves teaching students the practical skills and techniques needed to perform mathe...

  While reading this article, I have also been reflecting repeatedly on whether, in my teaching process, I predominantly use instrumental mathematics or relational mathematics. I stopped when l read at “Because area is always in square centimetres.” A similar situation has also occurred in my classroom. I also stopped when l read at “It is more adaptable to new tasks.” and “It is easier to remember.” When I taught new concept, I sometimes connected it to previous knowledge, but students often expressed that they have forgotten the prior knowledge. I believe this is because they haven't fully understood the connections between these pieces of knowledge. Instead, they tend to memorize formulas, which makes it very easy for them to forget what they've learned before. I prefer to apply relational mathematics when teaching higher-level mathematics. In higher-level mathematics, a significant amount of knowledge is interconnected. If students cannot understand the relationships betw...