Giant Soup Can and Extension Questions

As in teacher perspective, this puzzle is pretty straightforward. By using the ratio of the bicycle's height to that of the big soup can, we can measure the corresponding position of the small soup can when lying flat. It is approximately at half the height of the 'P' letter and perpendicular to the ground. This proportion helps calculate the dimension ratio between the small soup can and the giant soup can using the scale, and subsequently, we can use the volume formula to approximate the tank's water capacity. 

When I consider this problem from a student's perspective, I realize that it is far from simple. First, I need to comprehend the feasibility of enlarging the proportions. Moreover, I must understand that volume cannot be simply scaled by a proportion of length, which is an error I have commonly observed in many of my past students. Furthermore, I would need to be aware that the soup can is a cylinder, and its volume is calculated using the formula of the square of the radius multiplied by π and then by the height. Understanding this formula would also require prior knowledge of what π represents.

The one approach of me as a student: base on the online information, the normal soup can has 6 inches as height and 2.5 inches as radius, we get a ratio of 6 and 2.5; assume the bike is standard length 1.75m, and the height of the giant soup can is 3.6 multiples length of it, then the dimension of the giant soup can would be: 1.75m*3.6= 6.3 m, with the 6:2.5 ratio, the radius of the giant soup can would be 6.3m/6*2.5=2.625 m. And so the volume of the giant soup can would be 6.3*2.625^2*π ≈136.38m^3

The application of real-life examples in teaching holds significant meaning. I have a friend whose struggle with mathematics, mainly after the 8th grade, was primarily due to the sudden abstraction in the teaching approach. Thus, I believe that for children whose abstract thinking is not fully developed, utilizing tangible objects in teaching can help them establish a more direct connection between mathematics and reality. 

An example that left a profound impression on me was from a video I once watched. A young girl asked her brother how to equally divide a quarter-damaged square cake to share with her four best friends while maintaining the same appearance. 

Pausing the video, I spent two minutes contemplating how to solve it. Eventually, I realized that the remaining 3/4 of the L-shaped cake needed to be further divided into four equal parts each, totaling 12 pieces. Then, I rearranged them as a puzzle, forming four identical L-shaped cakes. This process involved introducing the concept of fractions and engaging in a puzzle game, making the idea quite captivating.

（reference video: https://www.youtube.com/shorts/hgp-BzhkF8Y)

Another brain-teasing puzzle that astonished me was how to divide a circular cake into eleven equal parts without a protractor. Although I didn't come up with a mathematical proof myself in a short time, the solution was super amazing and incredibly surprising!

Indeed, we are aware that using a protractor can relatively accurately divide a circle into any factor of 360, or the method of bisecting to divide a circle into powers of 2. However, with the prime number 11, which is quite hard without measurement, but a clock with fixed rotating dials provides a useful analogy. Since the minute hand of a clock completes 12 full rotations before aligning with the hour hand, and, remarkably, the 12th alignment coincides with the initial one, indicating that in a full rotation of hour hand aligns with the minute hand in 11 distinct positions. Consequently, by manipulating the minute hand of a clock, we can identify these 11 positions of alignment, mark their directions, and connect the centers of the clock's hour and minute hands to divide a circle into 11 equal parts!

Example figure for a coincides

(Reference video: https://www.youtube.com/shorts/dork6Os77ek)

With this idea, I am able to introduce some angle and radian contents with realistic items. 

I could also use this to introduce my extension question: how to divide a string equally into 11 segments without using ruler to measure it?

I believe

Pro D day Takeaway

(The lovely donut wall from the conference!💖 )

This Friday I went to BC association of teachers of modern languages conference (BCATML). I am very honored to attend this conference to enrich my knowledge. Though teaching language is very different from teaching math, but I have found many similar ideas that I can implement in math class. In fostering a conducive learning environment, it is imperative to be transparent and provide students with all necessary information. Change should be introduced gradually to avoid overwhelming students, ensuring that adjustments are made without drastic variations all at once. While incorporating engaging educational games can be beneficial, it is crucial not to overuse them, as excessive reliance may lead students to prioritize winning over actual learning. I was fortunate to receive valuable resources from a generous presenter who shared an insightful game workshop. Furthermore, it is evident that grades alone do not serve as effective motivation, as they can drive students towards compensatory behaviors. An authentic assessment approach must encompass several aspects, including accuracy that does not solely rely on averages, giving more weight to recent performances. Emphasizing the value of knowledge and introducing alternative consequences for cheating can foster a sense of responsibility and integrity. Encouraging a mindset focused on hope and growth is essential, allowing students the freedom to explore the language and learn without fear of judgment for every action.  

Reflection on 'Curriculum'

The first thing stopped me is that I feel resonant when I see the author questioned about payoff system created 'award junkies' as I remember clearly when I was young, I sometimes really just focus on how to win the prize, and compliment from teacher, but not to learn things. I totally understand why he ask this question.

The second thing stopped me as I saw the name 'Null Curriculum'. From the further explanation I get the point where the 'null' word is like what school ask for but neglected or absent on curricula. Which is quit interesting because base on my understanding, the word 'null' usually used for 'nothing' or something 'useless'. Well, I guess it is different between my understanding and different between the languages.

I like Eisner's article brings that schools have implicit and 'null' curriculum which school were looking for but not included or shown on the older curricula, and now BC curriculum is more inclusive, becoming more general base on time. I can see the pedagogy idea is updating and keep change in mind that, there are lot of things other than just school subjects that the educators really want, nurturing kids to be engaged and curious about the world, and to create a caring society.  

Reflection on Microteaching

 

During our mini-lesson, it became apparent that the sheer volume of material we attempted to cover within the 20 minutes timeframe was very excessive, so that make our teaching extremely challenging. I believe that my group mates in effectively  elucidate the terms and concepts and created very engaging warm-up questions, I recognized that my contribution, particularly in the formulation of questions, exceeded the practical constraints of our activity duration. Reflecting on our experience, it seems crucial for us to engage in a thorough discussion concerning the appropriate workload for a 10-minute session before students engage in active learning. This discussion would make sure we use our time well and teach in a way that works best for the students, making learning more interesting and effective.

Curriculum Micro Teaching Lesson Plan

 Lesson Plan Workplace Mathematics 11

Unit:

Financial Literacy 

Topic:

To purchase, own, or lease and to operate and maintain a vehicle

Big Ideas: 

Mathematics informs financial decision making

Curricular Competencies:

• Model with mathematics in situational contexts

• Explain and justify mathematical ideas and decisions in many ways

• Reflect on mathematical thinking

• Connect mathematical concepts with each other, other areas, and personal interests

Prescribed Learning Outcomes (PLO’s):

• Describe the difference between buying and leasing a vehicle

• To understand and know how to apply the factors that involve buying or leasing a vehicle

• Defining the positives and negatives of both buying and leasing 

• Use rational decision-making by comparing buying vs. leasing a car

Materials and Equipment:

• White board

• Marker

• Activity Handout

Warm up questions:

• How many people do you know have cars?

• Do they buy or lease them?

• Do you know what factors to consider when debating between buying and leasing?

Lesson components + Activities

Beginning (~5 minutes) : 

• Warm up questions

• Definitions of buy / lease

• Buying: outright buying vs financing

• What factors do we consider 

• Go over formulas

Middle (Activity) (~10 minutes):

• How to calculate the approximate total cost of either buying (outright or financing) or leasing including operating and maintaining the vehicle 

End (Wrap up) (~5 minutes):

• Summary

(Think - Pair - Share):

• Advantages / disadvantages of buying and leasing

• How different circumstances affect this decision

TPI - Reflection

It is good to have a different perspective of how to assess one's teaching. I have noticed that my teaching is weak on social reform, which I still don't really have an idea of how to do in math teaching, or maybe I did somehow but I don't really consider my teaching including social reform. And I have noticed that this sort of expertise report base on the questionnaire which mainly focused on self-assessing. While I taking the questionnaire, I know that knowing how to self-assessment is valuable, but it has its limitations. Relying solely on one's own perception of their performance can be influenced by biases and subjectivity. It might not be effective for self-reflection if someone believes they are excelling when they are not or vice versa. To enhance the effectiveness of self-reflection, a more comprehensive approach is essential. This includes utilizing a well-structured questionnaire that covers various aspects of performance, seeking input from professionals in the field, and incorporating objective criteria and feedback from peers, mentors, or supervisors. 

Micro Teaching Topic/Plan and Reflection

Lesson Title: Five Line Staff - Basic Western Music Notation Recognition

Learning Objectives:

Students are able to read basic treble staff as sol-fa after this lesson

Materials Needed:

Printed handout and five line blank paper to compose short music

Lesson Outline:

Introduction (2 4-5 minutes):

Briefly introduce the rules of reading staffs and engage students with guiding couple questions.

(Background knowledge check: Is there any student know how to read staff already?)

"Do you see any patterns in music?"

Group Activity I (1-3 minutes): Recognize provided five line staff notes 

(Scaffolding with exercise, the key point here is to let student familiar with the lines and notes position. With guiding questions follow along with the note reading, introducing to the composing activity.)

Group Activity II (4-6 minutes): write short staff and share with group members to see what are the song trying to express. 

Short on time, only 1 minutes for this group activity. Lacking of time to do scaffolding, time management of course plan was not well designed

The Goal of Group Activities is to get familiar with the five line staff 

End (1 minute):

Wrap up what student learned from this little lesson. 

Introducing music notes somehow relevant with math.

Reflection:

Based on recent classes, handouts provide excellent guidance for students, and it is easier to scaffold their learning with worksheets. The content information should be clear and concise; avoid introducing a large amount of knowledge at once to prevent students from feeling overwhelmed. According to peer reviews, the amount of information is considered acceptable among my groupmates. However, I didn't plan the group activity well, as I can do, but my students usually lack the same level of experience as a teacher. Based on this mini lesson, I have learned that when designing activities, considering them from the students' perspective and determining the appropriate duration of the activity are essential points to be careful about in the future when designing my lesson plans.  

Battleground of Math Ed - Reading Reflection

The first part made me stop while reading this article was that I didn't know the misconception about math had formed long time ago. Common sense often constrains individuals when it comes to mathematics, impeding their progress in the subject. Many people perceive math as a realm of rote calculations and formula memorization, aligning with their notion of "common sense." This limited perspective acts as a barrier, discouraging them from delving into the deeper, more abstract facets of mathematics. In reality, math encompasses critical thinking, creative problem-solving, and broad applications across diverse fields. Overcoming this common sense hurdle requires a shift in perspective, recognizing math as a tool to understand the world and tackle complex problems. Cultivating a growth mindset and providing hands-on learning experiences can help individuals break free from these constraints, allowing them to appreciate the beauty and versatility of mathematics beyond its surface-level computations.

The second part made me stop was while I read this article is that during 1960s the textbook was designed schools are essential because US needs more scientific elites. These institutions cultivate creativity and critical thinking among students in fields like engineering and design. In an age where technological prowess is paramount, we must equip the next generation to drive innovation and maintain our global competitiveness, much like the need for scientific excellence during the Cold War.

The third part made me stop was: in the 1990s, America's secondary-level math ranking fell behind fast-developing nations, causing anxiety about international competitiveness and the nation's ability to prepare students for a technology-driven world. This prompted calls for educational reforms and a renewed focus on math education, not as standoff between different political view.

***Revise***

The way of math education changed so much that it made it tough for students and their parents to adjust. This shift also left parents feeling confused, as they found it difficult to help their children learn in this new educational environment. With such a strong focus on math, students felt a lot of pressure and had a hard time keeping up with the changes in the curriculum. Since teacher is empowered in classroom and students grade very lean on reports from their teacher, the qualification of teacher is very important. A math teacher's proficiency and passion for the subject significantly impact students' math learning experiences. I had many students have expressed disliking math due to previous encounters with unskilled or dispassionate teachers. A teacher's expertise and enthusiasm can make math more engaging, accessible, and enjoyable, fostering a positive learning environment. Base on that, I think designing a math course thoughtfully is essential to engage students in meaningful learning and address their practical needs in daily life. It's important to structure the curriculum to not only impart mathematical knowledge but also to demonstrate its real-world relevance, helping students apply math skills to their everyday experiences and challenges.

***Revise***

Reflection on Extend Mathematical Artwork

Group Work Reflection - In our group project, we embarked on an intriguing collaboration to expand upon a mathematical artwork inspired by the works of Carlo H. Séquin, which closely related to knot theory. 

Our choice of this artwork stemmed from a desire to introduce young learners to the notion that mathematics extends far beyond mere numbers and arithmetic; it encompasses a rich world of graphics and intricate patterns that can evolve into advanced applications in our daily lives. Séquin's artistic focus centered on the mesmerizing figure 8 knot and the enigmatic 5_2 knot, which served as the foundational elements of our creative exploration. By introducing these knots, we discovered an effective way to illustrate complex 3D structures through 2D projections, offering an engaging educational tool for students intrigued by the captivating realm of mathematics. Drawing inspiration from Séquin's approach, we concentrated on utilizing four strands of different materials to create repetitive knot patterns, resulting not only in captivating artwork but also in edible creations. 

This multifaceted endeavor highlighted the idea that artistic representation knows no bounds, transcending traditional formats. Through our collaborative efforts, we learned how to the profound concepts of mathematics can be translated into visually captivating expressions.

Individual Reflection - It's truly fascinating to see how many different artworks can be created from a single idea, and knot theory is a prime example of this versatility. As we explored this concept, we realized that making simple knots, like the figure 8 knot, is not as easy as it seems. Our group spent many hours working together to figure it out and try to come up with suitable idea. We also wanted to develop fun activities for young kids, but it turned out to be more challenging than expected. Simplifying and introducing knot theory for young learners is tough. Though, there are some difficulties of how to expand the art work, it is eventually turning intriguing to create braids using various techniques and explore the endless possibilities, especially when combined with my personal passion for baking!

Extended Thought - Combining math and art can make learning more accessible and exciting for students. It's a fantastic way to get them engaged and interested in what might initially seem like a daunting subject. For instance, as someone passionate about baking, I've discovered that incorporating mathematical concepts into the kitchen can be both fun and educational. Instead of intimidating jargon, we can explore math that directly relates to our daily lives, like measuring ingredients or understanding baking ratios, knots that used for climbing or working, specific series of numbers to create beautiful patterns, etc. By making these connections, we not only make math more approachable but also show how it plays a crucial role in the things we love, like baking delicious treats. The key is to create a comfortable and enjoyable learning environment where students feel encouraged to ask questions and explore, fostering a love for math that lasts a lifetime.