Reflection: Battleground Schools

For this blog response, please comment on the fraught history of mathematics education in North America and the ways that you think this might affect your own situation as a math teacher.

I really enjoyed reading this article as it touches on many points that teachers have to deal with throughout their careers. It is interesting to see how much the change of curriculum can affect many teachers. It is also interesting how black and white math education was in the past; there was no room for expression in mathematics, and there was only room for material to be transmitted from teacher to student. It is not surprising at all that students who were not going into post-secondary studies in mathematics were not thought of during the process of putting together a curriculum standard. As teachers, we always unconsciously dream all of our students will grow to go down the same path as we did. However, this is completely not the case. Students choose the past that is best for them and that should be okay.

As a future teacher, it would definitely affect my teaching if the curriculum was to change. Looking at the new curriculum, teaching is now becoming much different than it was before. Being a student of the old curriculum, I can somewhat sympathize with the teachers discussed in the article who were not comfortable with the new curriculum standard; however, as teachers, it is our job to be comfortable enough with the material to relay it to our students. As long as the standards consider all students and not just those going to post-secondary, it is important that teachers do their best to become comfortable with the new standard so their students can also be comfortable. 

Teachable subject: Braiding hair

I really enjoyed the whole process of the teachable subjects in our groups! I thought it was amazing how we went from knowing nothing of each topic to every basic element!
My teachable was on braiding hair. The people in my group thought my lesson was overall good, but said I required a better hook. I feel that if I incorporated a better hook the overall flow of my lesson would have been much better. I also noticed most of my group mentioned I lacked organization in my lesson, so this is something I will need to work on for the future.
Overall, I really enjoyed presenting my lesson to my group and am excited for future attempts.

Soup Can Puzzle

Volume = pi x r^2 x h
Goal: To find out radius and height of the real water tank in order to figure out the volume
Photo -
Height of bike: 5.5 cm
Diameter water tank: 10.5 cm

Real Life -
Campbells soup: 11.5 cm x 8.5 cm
Height of bike: 110 cm (looking up the height of a regular bike)

Using the information above, my goal is to find the diameter and height of the water tank.
I found the diameter by finding the ratio of the height of bike and water tank in the picture vs real life:
10.5 cm : 5.5 cm = d : 110, so the diameter is d = 210 cm.

Using the information above, I then found out the projected height of the water tank. I used the diameter and height of the soup can, and the projected diameter of the real water tank in order to find a projected height of the water tank:
210 cm : h = 8.5 cm : 11.5 cm, where h = 284.12 cm.

Therefore, the volume of the soup can water tank would be
V = pi x r^2 x h
= pi x (105)^2 x (284.12) = 9840797.08 cm^3 = 9840.79708 Litres

Lesson Plan: Braiding Hair

Objective/Goals: Students will be able to braid their own hair, or another's hair.
Time: 10 minutes

Strategies to help learn: students will be able to 

Hook: Long hair can be very beautiful but very hard to manage. Today I am going to show you how many men and women with longer hair manage their hair by the process of braiding.

Materials required: ribbon, paper, tape

Assessment: Students will show understanding from makeshift "hairs" (ribbon).

Assumed prior knowledge: Some students will know how to braid already, and some will not. 

Development of idea/skill: Students will be taught how to begin by parting hair into 3 pieces, followed by bringing alternating sides to the middle.
e.g. Beginning with the right piece, bring over the middle piece into the middle, and bring the middle to that side. Follow the same pattern continuing with the left side and then the right.

Conclusion: Today we learned how to braid hair, and I hope everyone has gained 

Further extensions/Applications: Some further extensions to what we learned today are the fishtail and french braid.  

Letters from Students!

Letter One:
Dear Ms. B,
I just wanted to write this letter to thank you for all the hard work you put into teaching our class. You made exactly enough time for every student, and even though it was tough, you made sure everyone in the class felt important. There was never a point in the class when students didn't understand because you went through all the material meticulously. I always felt engaged in the classroom and felt excited to learn. I really appreciate all of the times you kept your door open in order to let us students come in and ask questions before and after school.
I just wrote to tell you thanks!
Sincerely,
Bill

Reflection:
I've always wanted to become a teacher for the sole reason that I want to make a difference in the lives of students. It has always been my goal to make sure I have as much time as possible for my students in order to make sure they are understanding everything being taught. While I know this is a dream, I want to do my best to make it a reality.

Letter Two:
Dear Ms. B,
I am writing to let you know that I had a lot of problems with the way you taught me. You constantly pressed the class about attending before and after school sessions, even though no one was ever interested in coming. I felt you were not personable with your teaching, and didn't make it apply to anything we would ever use in our lives. I constantly battled with myself over if I even liked math in high school because I was so bored in your class. I don't mean this to be harsh, but just wanted to let you know so you could improve for the future.
Sincerely,
Bill

Reflection:
This letter is based on fears I have as a teacher. I always go back and forth about whether I even want to do before and after school sessions for the reason that I feel most students would not want to attend. I also worry that students will not like my approach to learning and shut down and end up not liking math in the future. In my eyes, all it takes is one bad teacher to turn a student away from a subject, and my ultimate concern is becoming that teacher for a student.

Hyperboloid Structure: Reflection

The project my group did on our hyperboloid structure was one of the most memorable presentations I will have done during this program, and this I know for sure. I knew immediately I wanted to do the hyperboloid structure from the beginning, since it was the one that stuck out most to me.

Building the structure was inspiring as it did not take us long to figure out our own method of creating it. It was very easy to find the materials as well, as the skewers were from a market and the rubber bands were from a beauty supply store! Instead of the method shown online using paper to hold the skewers, we attached pairs of the skewers together and added more and more to the attached sets. We worked on two different models in order to find out which model would work better. Doing this allowed us to see faults in one model and see the strengths in the other. It was a great chance to work as a team, as me and Jacob worked on one model, while Etienne and Deeya worked on the other. Instead of two people, or one person, working on one model, we did something so everyone could work together!

The math art project we did has large correlation to conics – taught in secondary mathematics. When teaching this subject, it may be helpful for students to create the structure in order to better understand conics like hyperboloids and paraboloids. It would be a great way to teach and to learn the subject. Students could do extensions of their own in order to gain further understanding as well.

Furthermore, I feel that students of many ages can gain something from an experience of building our structure. It is simple enough that younger children can build it, as well as older students in later years of secondary school.

Dishes puzzle

I began my problem by writing out the constraints I had to work with:

- 2 people shared 1 dish of rice,

- 3 people shared 1 dish of broth,

- 4 people shared 1 dish of meat

I then noticed that in order to find out the number of people, I could see this relation:

1 dish/2 people + 1 dish/3 people + 1 dish/4 people = 6 dishes + 4 dishes + 3 dishes/ 12 people 

(by finding the LCM)

which would lead me to an answer of 13 dishes/12 people.

Since we know that there are 65 dishes, 

we can see that if we divide the number of dishes by the 13 dishes/12 people relation, we can cancel the "dishes" and get a result containing only the number of people.

Doing this,

65 dishes ÷ 13 dishes/12 people =  5 65 dishes x 12 people/13 dishes = 60 people

Therefore, without using algebra, you can see that there are a total of 60 guests.

I don't think cultural context has any effect at all because the problem would be just as doable for any student if there was no underlying cultural context. I think it is a good problem to have, but I do not think there is any strong, underlying cultural effect left.

Article Reflection: Math that Matters

Questions:

•Is mathematics 'neutral', or is it connected with social/ environmental justice?
•What are your ideas about the author's intentions in writing this textbook?
•Can these ideas from middle school math inspire teaching ideas for your secondary math classes?
•Are there topics in mathematics that are more or less possible to connect with social justice issues?

Reflection:

I feel that math is definitely driven by social and environmental change and justice, or it can be. It is ultimately up to the educator to decide whether to touch on outside factors related to math, or to just teach the basics. The intention of the author, in my eyes, was to open up the eyes of teachers in order to show them that there is more to teaching math than meets the eye. There is a definite way of incorporating the outside world to math. David Stocker's purpose was to give teachers the option of being able to bring social awareness into their teaching; this is wonderful as I feel that most teachers maybe feel confused about how exactly to incorporate these things into teaching, but Stocker gives great examples along with his writing. 

In secondary math classes, it can definitely be harder to incorporate social justice into teaching, but again, it is up to the teacher to attempt to do so. Personally, thinking of senior level math classes, I feel it would be more difficult to associate lessons with social justice, as students would just want to focus on the concepts in order to get a good mark for post-secondary. A teacher could try to connect probability with social justice issues, but topics like logarithms and transformations may a bit harder to relate to real-world problems, though this does not mean they are impossible to relate. 

Pro-D-Day Plans: BCAMT Conference

I will be attending the BCAMT conference in Whistler!