Flow

 I have felt flow in my math classes when I am particularly engaged or interested in a topic we are learning. I also feel flow during crocheting, singing, going on walks, and while exercising. I think being in flow depends on how interesting a topic is, or how it is presented to students. If a student is not interested they can never achieve flow. 

I think we can help students achieve flow by teaching math in engaging ways so students have an interest in the topic and are challenged by the content that is being taught to them. Teaching math through inquiry or project based learning can help students be more engaged and can help them reach a state of flow. I feel that achieving flow in math class is possible for all students, but we will need to cater to each students needs individually so they can meet flow in their own way. 

Arbitrary vs Necessary

 Hewitt refers to arbitrary as something that is taught to be memorized, something that must be done exactly the way it is taught. For example, using the + sign for addition and the - sign for subtraction is purely convention, and students are required to memorize these signs to progress further in mathematics. Necessary is referred to as content where the students do not necessarily need to be informed. For example, students can learn how to add fractions with or without mixed numbers without the convention of writing it down. Necessary knowledge can come from within or be discovered through inquiry. Arbitrary must be taught to all students, necessary can become aware to certain students through other concepts. 

The concept of arbitrary vs necessary is new to me in theory, whoever, I feel that inherently I was always known about it in theory. Using a student led approach or inquiry based approach in the classroom can help students learn the necessary and can help all students understand the arbitrary. 

In my own classroom, I could create questions that teach all the students the arbitrary but leave room for certain students to learn the necessary. We want to move beyond teaching and having students regurgitate that information on tests without having any understanding of why the concept works. 

A personal example of this for me was in grade 12 when we learned the unit circle. I remember my teacher emphasizing that we must memorize the unit circle and even having quizzes where we would have to fill in the unit circle in 5 minutes. I purely did that, I sat down and I repeatedly practiced writing the unit circle until I knew with certainty that I could replicate it on the test. I had no idea how the values of the unit circle were derived or even what they meant, I just had them memorized. If this was my own classroom, I would have focused on the meaning behind the unit circle and I would have had students find connections between how different trig values create the unit circle.    

 

Giant Soup Can of Hornby Island

 I have put a picture of my calculations and following that there is a description of my rationale. 

I started this problem by considering the average size of a women's bike, after some research I realized that the height of an average bike is hard to find on the internet, and usually you can only find the length of the frame. The frame of a bike for a woman between 5'3 and 5'5 would be 71 cm (Hudson, 2022), from there I guessed that the total height could be 100 cm. 

From the picture, the diameter of the tank looked to be about 3 times the height of the bike, so I estimated that the diameter of the tank to be 300 cm. From some more research, I found that the average bike length is 175 cm (Ellis, 2022). In the picture, the height (or length as written in my work) of the tank looks to be about twice the length of the bicycle, so I estimated the length of the tank to be 350 cm. 

At this point, I wanted to make sure my calculations were comparable to that of a regular soup can, so I took ratios of both the tank and can (height to diameter) and compared them. They were very similar, only about .3 of a decimal difference!

My next step was to calculate the volume of the tank which ended up being 24.74 m^3. Now I wanted to see if this would be enough to put out a house fire. Through some research, I found out that you need 400 gallons per minute of water to fight a house fire (Smith, 2010). I then converted my volume into gallons to find out that the tank can fight a house fire for about 15 minutes. Once again, based off of some research, I found out that it takes about 20-40 minutes to fight a house fire (Chase, n.d.). So, if there was a small fire, the tank would have enough water to fight it. 

My student bird struggled with this problem because this was really new territory for me, while I understand all the mathematics behind the problem, I have never applied it in this manner and it was a new experience for me. 

However, my teacher bird enjoyed this problem because it made me think critically, problem solve, and apply my skills outside of the box. I think this would be an excellent puzzle for students who need an academic challenge or as a problem of the week where the class would discuss and solve it together. 

Extension: 

Here is a sculpture in downtown Calgary, a head you can stand inside of! A problem I would pose to my students could be, given my height 5'1 and the average size of a human skull, what are the dimensions of the sculpture? I would give the students a picture where I am standing inside the sculpture (I just don't have one at this moment!) so they could reference off my height.   

References: 

Chase. (n.d.). How Long Does It Take To Put Out a House Fire? https://firefighterinsider.com/how-long-put-out-house-fire/

Ellis, C. (2022, August 20). What size shed do I need for my bikes? | The Best Bike Lock. The Best Bike Lock. https://thebestbikelock.com/bike-storage-ideas/best-bike-storage-shed/what-size-shed-for-bikes/

Hudson, A. N. (2022). Rutland Cycling. Rutland Cycling. https://www.rutlandcycling.com/pages/sizing-guide/

P. Smith, J. (2010, December 1). Needed Fire Flow. Firehouse. https://www.firehouse.com/home/article/10465153/determining-how-much-water-is-needed-for-effective-fire-control

Eisner and Curriculum

I found it interesting that this article talks about null curriculum and how schools only focus on math, science, social studies, and English. It makes me wonder, are we teaching practical skills in our curriculum courses? Students are learning how to learn and critical thinking skills plus problem solving skills but is it unjust to our students to not have mandatory classes on cooking, cleaning, basic concepts about automotives, plumbing, and electrical work? While some might say those are skills that should be taught to children by parents, I really do believe we should be having mandatory classes in schools on these skills. These skills are critical for students to know and understand once they are adults and I feel it is the job of high school teachers to not only teach the curriculum but to prepare students for non-academic challenges they may face once high school is over.

Along with my opinion on null curriculum, I enjoyed what the article had to say about implicit curriculum, schools teach students soft skills. I would define soft skills as people skills such as how to converse, punctuality, respect, authority, learning to work with others and people who might be difficult to work with, prioritization, etc. We as teachers should be teaching our students to be good and productive members of society. It is important we model behaviour for our students because they look up to us.

This article expanded my views on curriculum because I have never stopped to think about what curriculum should be other than the explicit curriculum. After reading this article, I realized that it is so important to focus on soft skills and life skills in schools. This ties into the BC curriculum through the core competencies. The core competencies focus more on life skills and soft skills rather than just strictly curriculum. While I think we should have a class that explicitly teaches core competencies, they are taught implicitly in our classrooms. This article raised the question of how I can incorporate soft skills and life skills into my own classroom, this is something that I am still trying to figure out and answer. Part of the reason this question is so difficult for me to answer is because our focus in our classrooms is primarily on curriculum which makes it difficult to find the time to incorporate these crucial skills.  

Pro-D Day Reflection

 I attended the BCAMT conference in person. I had an amazing time at the conference and I feel like I learned so much about math education. The three sessions I attended were Helping Students Enjoy Pre-Calculus 11, 12 and Calculus Courses, Standard Based Assessment: Proficiency Levels and Exemplars in Practice, and Curricular Competencies in Secondary Mathematics. I chose these specific sessions (particularly the last two) because my goal is to have a firm grasp on standard based assessment. The idea of using standard based assessment is so new to me and I wanted the opportunity to learn more about it and see how other teachers are approaching standard based assessment. I was surprised to see that veteran teachers are also having a hard time using standard based assessment, which made me realize this is new for all teachers right now and we will all learn together! 

Group Microteaching Reflection

 

Overall, I feel that the group microteaching was successful. I really enjoyed lesson planning for the lesson and coming with my own resources to use while we were teaching. Lesson planning really helped me prepare for how I wanted the lesson to go. I felt like the lesson ended up coming off as a bit of review since we were asking the students for definitions, rather than teaching them the definitions. In the future I want to work on incorporating more interactive activities that are not just practice problems. I also want to work on my confidence in the classroom, because I doubted myself during the lesson when I was teaching how to calculate the median when there are two numbers in the middle, and because I doubted myself I messed up the instruction and taught something that was incorrect. 

Letters from Future Students

Dear Ms. Vaid,

I was in your class 5 years ago and I want to let you know how much I appreciated your teaching method! I liked how in class we focused on why mathematics works the way it does rather than just learning how to plug and chug. It made me view math in a different light and it help me have a deeper understanding of mathematics which helped me so much when I got to university! I also appreciated how encouraging you were to everyone in class, you really made me feel like I could succeed in math class even when I was struggling or doubting myself.

Thank you for everything!

 

Dear Ms. Vaid,

I am emailing you to tell you your class was a waste of time for me. I learned absolutely nothing about math from your class. You kept focusing on why this works and never showed us how to do the problems! I still struggle with math to this day, and I wish you would have focused more on how to solve the problems rather than making us appreciate the “beauty of math”. It was because of your class that I decided to not take any math in university and maybe if you had focused more on showing us how to get the answer as easily as possible, I would have taken math in university.

 

From writing these letters I can say that my biggest worry about becoming a math teacher is students who fall through the cracks. I worry that there will be a student in one of my classes who I cannot support the way I want to, or a student whose needs I cannot understand.  At the same time, I have hope that I can teach students to love and understand that mathematics is not just a set of algorithms and that everyone can succeed at mathematics if they try!