Homework: Dave Hewitt & mathematical awareness

To find a fraction between 5/7 and 3/4 using a common denominator, express 5/7 as 20/28 and 3/4 as 21/28. Since there is no integer between 20 and 21, expand further to 40/56 and 42/56. One possible answer is 41/56. However, if the numerator is 11, the least common multiple of 5 and 3 is 15. In this case, we cannot find an integer that fits in.

Stop 1: Dave highlights the issue of students memorizing procedures without truly understanding the underlying concepts. This prompts reflection on the traditional teaching methods and the importance of fostering a deep comprehension of mathematical principles.
Stop 2: The discussion about the statement "2 + 3 = 5" as a profound concept that extends to various situations challenges the perception of basic arithmetic as isolated facts. It encourages educators to delve deeper into the fundamental principles and implications of seemingly simple mathematical expressions.
Stop 3: The emphasis on awareness in learning fractions, particularly the awareness of finding a common name (denominator) for addition and subtraction, prompts educators to reconsider their teaching strategies. It underscores the significance of developing students' awareness of mathematical principles rather than relying solely on memorization.

Hewitt likely began by identifying key concepts related to fractions, such as the need for a common name (denominator) when adding or subtracting fractions. This foundational understanding serves as the basis for the problems. The problems involve real-world contexts, such as comparing quantities of objects like pencils, brushes, or other items. This not only makes the problems more relatable for students but also emphasizes the applicability of fractions in everyday situations. The problems go beyond simple computation and encourage critical thinking. For instance, asking students to find a fraction with a specific numerator between two given fractions prompts them to consider the relationships between numerators and denominators. Hewitt introduces open-ended questions, such as exploring whether there is a lower or higher numerator that would still result in a fraction between two given fractions. This invites students to engage in exploration and discovery, fostering a sense of mathematical curiosity.

Providing opportunities for students to explore and discover mathematical principles fosters a sense of curiosity and ownership of learning. As a Math teacher, l will try to design activities that allow students to investigate and draw conclusions, promoting a deeper connection to the subject matter.

Comments

  1. Qiaochu (Joy)December 15, 2023 at 11:08 PM

    Hi Shawn, thank you for the insightful analysis of how Hewitt likely structured the fraction problems. Starting with foundational concepts like the need for a common denominator and grounding problems in real-world contexts makes the material relatable and emphasizes its practicality. The open-ended nature of the problems encourages critical thinking and exploration, fostering a sense of curiosity and discovery among students. How do you envision balancing structured learning with open-ended exploration in your lessons to encourage curiosity and understanding among students?

    ReplyDelete

Post a Comment

Popular posts from this blog

Final blog post

In this term's coursework, I've encountered numerous considerations that had previously escaped my attention, especially in the realm of integrating mathematics and art. Notably, the Math and Art project, among the various blogs I've composed, has left a lasting impression. It represented my inaugural attempt at blending mathematical concepts with real-world artistic expressions in a teaching context, offering valuable insights for my future endeavors in math education. Furthermore, the lesson plan assignment proved to be an invaluable resource during my short practicum. The practical application of the lesson plan in my teaching experience provided me with substantial guidance, serving as a roadmap for structuring effective lessons.  Despite the insightful experiences gained from these assignments, the overall volume of blogs this semester has created a notable amount of pressure. If feasible, I would appreciate a reduction in the workload, affording me more time to thorou...
Read more

Reflection on 'Flow'

The state of flow is a profound and fulfilling experience that transcends specific domains, encompassing various aspects of life such as art, sports, and work. Personally, I have experienced a state of flow during activities that align with my skills and provide a challenging yet achievable environment. This often occurs during problem-solving. The idea that flow can be connected with mathematical experiences resonates with my own encounters with mathematics. Mathematical problem-solving, particularly when dealing with challenging yet solvable problems, can induce a state of flow. The process of grappling with mathematical concepts, experimenting with different approaches, and experiencing the "aha" moment when a solution is found mirrors the characteristics of flow described in the talk. I believe it's entirely possible to create conditions that facilitate a flow state for students. As teachers, we can play a crucial role in designing lessons that strike a balance betwee...
Read more