Let it Flow...

While I hadn’t known about the concept of flow before, watching the video made me realize that I’ve experienced it more times than I could count, especially with math. It brought back memories of working through proofs. I used to hate proofs—and to be honest, part of me still does—but the only times I managed to work through them were when I entered a state of deep focus. In those moments, ideas would start to connect and flow one after the other. Proofs began to feel less daunting and more like puzzles and, at the end, they were always satisfying to solve and made the process worth it.

 

In secondary math classes, I believe we can create these moments of flow for students. They can reach a deeper level of engagement when they face problems that balance challenge and skill and require them to push beyond their usual efforts. This method worked well for me, so I would specifically use it when teaching proofs, helping students practice reaching that focused state where things start to open up. I would encourage students to immerse themselves fully, allowing them to experience that shift where math becomes not just a subject but a meaningful challenge they can overcome.

 

One thing I realized after learning about the concept of flow while having, for years, used this process unknowingly was how important it is to be able to recognize, identify, and call on this process. Projecting mainly off of myself, but a student who learns this ability will now have an additional tool to practice when they get stuck. I can only imagine how many other types of thinking and processes there are that we all practice unknowingly. Gaining an awareness of those would truly enhance our intellectual abilities.

 I asked AI to create a flow-chart to summarize my post on flow.

 

Campbell Soup Can

 

Gathering required information:

 

Bike size:

https://www.sweetpetes.com/about/bike-sizing-chart-pg163.htm?srsltid=AfmBOopGZaJTHkPKjIna75M9zQsbKoIucEe9n3yqWKPZwpG_in-xm1ZC

 

Formula for cylinder’s volume: V=πr^2h

 

A Campbell's Soup can is 6 inches tall and has a radius of 2.5 inches

https://www.wyzant.com/resources/answers/768737/a-campbell-s-soup-can-is-6-inches-tall-and-has-a-radius-of-2-5-inches-how-m

 

 

 

 

 

Putting out a fire with this tank.

 

It is estimated that a 25 cubic metre tank can hold 6,604 gallons of water.

(https://www.inchcalculator.com/convert/cubic-meter-to-gallon/_

Working off an assumed average building size: 

"A structure 60' x 60' would figure to be 3600 square feet. 3600 divided by 3 = 1200 gpm. We would need an estimated 1200 gallons per minute of water flowing to extinguish this size area."

(https://www.linkedin.com/pulse/how-many-gallons-does-take-put-building-fire-out) 

 

These numbers tell us that the tank would be able to provide continuous water for 5 min and 30 seconds. Accordinly, I would say that yes, the Campbell Soup can may have enough water to put out an smaller sized fire, but it would take more than 5 minutes to put out a full house fire. So, it really depends on the size of the fire.

 

 

 

 

 

 

 

 

 

Thinking Mathematically

My first stop in the chapter was where the text discusses the positive feeling you get when accomplishing something. I have always tried to implement this in my practices. For example, I consider it an important part of To-Do lists to make sure you mark tasks as completed. When you go back and look at them completed tasks at the end of the day, it creates a sense of satisfaction motivating you the next day to keep on going. This same practice is especially important for students. They often get caught up in all the things they were not able to get done. Small acts like “writing AHA!” can have significant positive impacts.

 

My second stop where the text relates the story about a student who attempted some homework not knowing it was beyond his expected academic level. What really resonated me was the fact that he attempted the work thinking he was able of it. The mindset with which a student starts to work can significantly influence how they do/do not progress. Educators need to be especially vigilant of this fact, as often unsuspecting statements can alter how a student sees themselves and their abilities.

Arbitrary vs Necessary Knowledge

 

I can see how the difference between arbitrary knowledge and necessary knowledge can affect how and what a class learns. Arbitrary knowledge includes things students need to memorize because they are based on agreed-upon rules or labels. Necessary knowledge, on the other hand, involves things students can figure out using logic and what they already know.

 

I feel this practice must always first begin, as Hewitt discusses, by assessing what students already know and their level of understanding. Without this awareness, it will be very challenging to design the desired activities. It is interesting still,  that sometimes when attempting to gain necessary knowledge, it may be necessary to use arbitrary knowledge, especially labels and terms, the rationales for which were never given to students or don’t even exist.

 

I can begin to think of more ways I can include necessary knowledge into my lesson plans, especially while teaching Math. One area where I will try to implement necessary knowledge  in my lessons plan is geometry. I feel that geometry is often about instructional learning without the students every understanding why things are the way they are and how they got there. Whether the idea is related to angles, corners, sides, or otherwise, there are many activities that students can be assigned which can help them deduce rules and reach conclusions on their own. This practice will also help them retain the ideas, having understood how they got there and why things are the way they are.

Microteaching Reflections

 I enjoyed teaching this lesson. After assessing myself and received my colleagues' feedback, some points I will consider next time I plan a lesson:

- To start with an overview of what will be covered;

- I would explain a bit more about about the physics of countersteering;

- Share the video links with students so they can watch them again later if needed,;

- To leave time at the end for questions;

- I will end with a summary of the main points covered in the lecture. 

Microteaching Lesson: How to Countersteer on a Motorcycle

 

Download PDF

 

Lesson Plan: How to Countersteer on a Motorcycle

Lesson Overview		Instruction
Learning Objectives: • Students will understand the concept of countersteering on a motorcycle. • Students will be able to demonstrate countersteering techniques through a physical simulation activity. Curriculum Points Being Met: • Safe motorcycle handling and obstacle-evasion techniques. • Understanding of vehicle dynamics related to two-wheel transportation. Learning Objectives: 1. Cognitive Objective: Students will comprehend how countersteering allows for effective turns on a motorcycle, even though the techniques seem illogical. 2. Psychomotor Objective: Students will physically simulate countersteering in response to obstacles. 3. Affective Objective: Students will develop awareness of safe riding practices in dynamic road conditions.		How Objectives are Being Met: • Cognitive: Through verbal explanation and demonstration of countersteering. • Psychomotor: Through an interactive activity involving arm movement to simulate countersteering. • Affective: Students will reflect on how countersteering is essential for avoiding obstacles safely. Terminologies/Definitions: • Countersteering: A technique used by motorcyclists to turn by pushing the handlebars in the opposite direction of the desired turn. For example, pushing the right handlebar causes the bike to lean and turn right. • Lean Angle: The angle at which a motorcycle tilts to initiate a turn. Materials Needed: • A whiteboard or chart to sketch the concept of countersteering. • A computer to play a video • An open space where students can freely extend their arms for the exercise.
Lesson Plan Outline
1. Introduction (1 min):    Ask students to show with their arms how they think they would turn on a motorcycle. This will help identify any misconceptions. 2. Explanation (3 min):    Introduce the concept of countersteering. Explain that pushing the right handlebar will lean the motorcycle to the right, while pushing the left handlebar will lean it to the left. Illustrate using a simple diagram. Play the video that demonstrates this phenomenon. 3. Interactive Activity (3 min):    Have students extend their arms as if holding handlebars. Call or point out various directions and have them react by quickly deciding which way and how to countersteer.		4. Assessment (2 min):    Conduct the activity with students closing their eyes to simulate real-time reaction without visual input. Provide feedback based on their reactions. 5. Bonus (if time permits - 1 min):     Advanced techniques to take corners at higher speeds. Assessment: • Formative:   1. Observation during arm simulation exercise.   2. Correct and quick reaction during the obstacle simulation activity. • Summative: Feedback from students on their understanding and demonstration of countersteering.
Post-Lesson Reflections	• Was my explanation of countersteering clear, and did students grasp the concept quickly? • Did the interactive activity engage the students and help them simulate the real-life action of countersteering? • Could the students make the connection between the physical movement of their arms and how it affects turning on a motorcycle?

 

Battleground School

 The first point I stopped at was close to the beginning. While reading the discussion on the perception people have of those who excel at Math, I immediately started to think of how this is one of the main reasons for the shortage of Math teachers. It was nice to see that that discussion was coming up on the next pages. I feel its crucial to change this view of Mathematics. Without it, we will continue to see a shortage of Math teachers. And, as the paper points out, Math will continue to be taught by unqualified teachers. If the people teaching Math do not have the training on how to teach Math in a way that students enjoy and learn, then we are stuck in a vicious cycle that seems

It was very interesting to read about how Mathematics education has transformed over the past century. I found it quite surprising that the "New Math" movement of the 1960s was motivated by the need to beat the USSR in the space race. Though it's unfortunate that the changes and advancements brought into the educational systems were fuelled by politics, it helped introduce new and more advanced topics into the world of Mathematics education. Perhaps if, from then, the focus was on changing the approach to Mathematics to student-focused, we might have been in a different world of Mathematics today.

Lastly, when the discussion of NCTM came up, I decided to take this chance to look in it. I had heard the name before, but was unsure as to what exactly the NCTM does and offers. After looking through their website, I found that teachers can benefit from the NCTM website by accessing a many types of resources to help in math instruction. The site offers lesson plans, classroom activities, and professional development opportunities to improve teaching skills. Teachers can also join communities, join math education conferences, and access different research articles on new Mathematics developments and advancement. Additionally, the NCTM provides grants and awards to help teachers fund creative and innovative classroom projects. It's definitely something every Math teacher needs to be a member of.

https://www.nctm.org/