Being STUCK!

 Being STUCK

 

To concisely describe my response to this reading, here are two "stops" (moments of reflection or insight) I encountered:

1. Recognition of being STUCK as a learning opportunity: The text highlights the importance of acknowledging and embracing the state of being stuck, transforming it into a productive process rather than a source of frustration. This reframing stood out as a mindset shift essential for tackling challenging problems.
2. Using systematic strategies to get unstuck: The suggestion to return to the Entry phase (identifying what is KNOWN, WANTED, and what can be INTRODUCED) provided a structured approach to navigating mental blocks, emphasizing the power of organization and reflection in problem-solving.

These points resonated as they underline growth through persistence and structure in mathematical thinking.

Two-Column Solution for the "Weighing Fish" Puzzle

Puzzle:
A fisherman caught three fish. The fish were not weighed separately, but in pairs.

• The big fish and the medium-sized fish together weigh 16 kg.
• The big fish and the small fish together weigh 14 kg.
• The medium-sized fish and the small fish together weigh 12 kg.
  Question: How much does each fish weigh?

 

Mathematical Work	Process, Emotional Reactions, Dead Ends, and Productive Approaches…
Step 1: Define variables	At first, I felt a bit overwhelmed by the amount of information, but I decided to stay organized.
Let B be the weight of the big fish, M be the weight of the medium-sized fish, and S be the weight of the small fish.	I decided to use simple letters for the fish weights to make the math easier to follow.
From the puzzle, we have three equations:	I read the problem carefully several times to make sure I understood the relationships between the fish weights.
1. B+M=16B + M = 16	This equation was simple and clear. I felt confident about it.
2. B+S=14B + S = 14	The second equation followed a similar pattern, which reassured me.
3. M+S=12M + S = 12	The third equation gave me hope that I had enough information to solve for all three fish weights.
Step 2: Solve the system of equations	I thought about how to combine these three equations to find the individual weights.
Add all three equations together:	I felt optimistic that combining them would simplify the system.
(B+M)+(B+S)+(M+S)=16+14+12(B + M) + (B + S) + (M + S) = 16 + 14 + 12	I realized I could combine the equations by grouping similar terms.
2B+2M+2S=422B + 2M + 2S = 42	I was happy to see a pattern, as I noticed a common factor (2) in all the terms.
Divide by 2:	This step felt logical and straightforward.
B+M+S=21B + M + S = 21	I now had a total weight for the three fish combined, which felt like progress.
Step 3: Solve for individual fish weights	I felt that I was close to finding the individual weights.
Subtract equation 1 from this new equation:	I decided to subtract to eliminate B+MB + M and focus on SS.
(B+M+S)−(B+M)=21−16(B + M + S) - (B + M) = 21 - 16	I double-checked my subtraction to avoid mistakes.
S=5S = 5	I felt happy to have found the first fish's weight — a small victory!
Subtract equation 2 from the new equation:	I repeated the same strategy, feeling more confident this time.
(B+M+S)−(B+S)=21−14(B + M + S) - (B + S) = 21 - 14	This approach seemed to work well, so I continued.
M=7M = 7	I felt satisfied because I now had the weight of the medium fish as well.
Subtract equation 3 from the new equation:	I felt excited, knowing I was close to finding the final weight.
(B+M+S)−(M+S)=21−12(B + M + S) - (M + S) = 21 - 12	I followed the same process, hoping it would work again.
B=9B = 9	I was thrilled to find the weight of the big fish. All the pieces had fallen into place.
Step 4: Verify the solution	I wanted to make sure my answers were correct.
Check the three original equations:	I felt that verifying my work was important to avoid mistakes.
1. B+M=9+7=16B + M = 9 + 7 = 16 ✅	Perfect! The first equation works. I felt reassured.
2. B+S=9+5=14B + S = 9 + 5 = 14 ✅	Great! The second equation is also correct.
3. M+S=7+5=12M + S = 7 + 5 = 12 ✅	Yes! The third equation is correct too. I felt accomplished.
Conclusion	I felt happy and satisfied that I had solved the puzzle using a logical, step-by-step approach.
The weights of the fish are:	I reviewed the entire process to ensure I didn't make any mistakes.
Big fish = 9 kg, Medium fish = 7 kg, Small fish = 5 kg	I felt proud of my work and the clarity of my process.

 

 

Curricular microteaching reflection

 Curricular micro teaching reflection

 

Our presentation on creating and interpreting bar graphs was engaging and well-structured, thanks to the thoughtful use of flipped classroom techniques, clear visuals, and collaborative planning. The inclusion of interactive elements like the demonstration and exit slip encouraged student participation and critical thinking. However, we could improve our time management to allow more room for student discussions and sharing ideas. Overall, this experience highlighted the strengths of teamwork and the importance of balancing instruction with interaction for better student engagement.

 

 

 

 

Flow

 Flow 

Mihaly Csikszentmihalyi's concept of "flow" is deeply inspiring. The idea that happiness stems not from external rewards but from becoming completely absorbed in meaningful activities resonates strongly with me. As someone who loves soccer and and a former football player, I’ve often experienced flow on the field—those moments when time slows down, and everything aligns perfectly. The focus is so intense that distractions fade, and I feel both challenged and completely in control.

In soccer, flow is prompted by the combination of physical skill, mental focus, and the clear goal of outmaneuvering an opponent or scoring. It’s a balance between challenge and competence—pushing myself without feeling overwhelmed. Interestingly, this flow state reminds me of certain mathematical experiences as well. Solving a complex math problem can evoke a similar feeling of deep engagement and satisfaction, especially when the problem is challenging yet solvable with effort and creativity.

As a math teacher for fifteen years, I have always believed and still believe that it is possible to create conditions for flow. it’s possible to create conditions for flow in math classes. However, it requires careful attention to the structure of lessons and the individual needs of students.

Balance Challenge and Skill: Problems must be neither too easy nor too difficult. Differentiating tasks to match students’ skill levels is key to keeping them engaged without inducing frustration.

Set Clear Goals: Students should understand what they are working toward in each lesson or activity. Clear objectives and step-by-step guidance can help them focus. Students should know when they are on the right track. Encourage Intrinsic Motivation: Relating math problems to real-world scenarios or personal interests (e.g., using statistics from soccer games) can make the content more engaging and relevant.

Minimize Distractions: Creating a classroom environment that supports concentration—free from unnecessary interruptions—can help students focus deeply on their work.

Challenges in Achieving Flow

Despite these strategies, achieving flow consistently in a classroom can be difficult. Each student’s "flow threshold" is different, and some may lack intrinsic motivation for math. Additionally, external pressures like time constraints and standardized curricula can limit the opportunities for creative, immersive problem-solving.

Finaly, Csikszentmihalyi's talk reminds us that as educators, we have a unique role in shaping experiences that could lead to flow. By designing lessons that challenge and engage students, we not only help them learn math but also offer a glimpse into a deeper, more fulfilling way of engaging with life.

Giant Soup Can

  

Giant Soup Can

 

                                        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

We will use the approximate dimensions of the bike to estimate the dimensions of the soup can:

 

Mathematical Work	Process, Emotional Reactions, and Reflections…
Step 1: Use the bike’s width to estimate the tank’s width(L)	I used the approximate dimensions of the bike and visualized the tank’s width as 3 times the bike’s width.
- Bike’s width: 142 cm.	I felt confident about using the approximate dimensions of the bike.
- Tank’s width L = 142×3 = 426 cm	I appreciated how the photo helped in visual estimation.
Step 2: Use the bike’s height to estimate the tank’s height (Diameter)	I moved on to calculate the height proportionally. I used the approximate dimensions of the bike and visualized the tank’s height as 2.5 times the bike’s height.
- Bike’s height: 91 cm.	I felt confident about using the bike’s height since it was clearly stated.
- The tank’s height is approximately D = 91 × 2.5 = 227.5 cm	I felt good about using a clear proportionality factor here.
Step 3: Calculate the tank’s diameter	I calculated the diameter based on the previous details.
- The tank’s diameter is approximately equal to its height: D = 227.5 cm	I made this connection since the tank is cylindrical, and its diameter is effectively its height.
Step 4: Calculate tank volume (V)	I proceeded to calculate the volume using geometry.
- Formula for cylinder volume: V =	I was ready to plug in the numbers and complete the calculation.
- Radius of the tank: r =  =  = 113.75 cm	I confirmed the radius calculation.
- V =  =	This felt straightforward, though the numbers are large.
- V ≈ 17,321,664.24 cm³. If you convert this to liters: 1 cm3=0.001 Liters V = 17,321.66 Liters	I converted this to liters.
Step 4: Determine if the tank holds enough water to fight a fire	I compared the result to typical firefighting requirements.
- Water needed for a house fire: ≈ 12,000 L. https://www2.gov.bc.ca/assets/gov/environment/air-land-water /laws-rules/interim_guidance_fire_prevention-water_use	This value gave me a benchmark for the tank’s capacity.
- V = 17,321.66 Liters > 12,000 Litres	The tank’s capacity is sufficient to put out a house fire. I was satisfied with this conclusion.