Three Curricula All Schools Teach

The first aspect of this article that stood out to me was that about competitiveness in the education system. When I was in high school, me and my friends would always compare our test scores with each other. This always felt like playing a sport, in which you have a drive to win, although it was more of a friendly game. I think that for some students competitiveness may be a good thing, to give them that little extra push to achieve marks. However, the motive behind this may be a little short-sighted. If kids are trying to get high marks due to wanting to one-up their friends, are they really studying for the right reason? Are they really learning? Competitiveness also has a dark side to it. Many students may feel inadequate if they do not perform well relative to their classmates, which could mess with their psychological well-being. As an extreme example, Japanese students who do not achieve high enough marks and as such are subsequently rejected from the top universities, may commit suicide due to the shame they feel, for not living up to expectations set by them or by others.

The overall theme of this paper was to look at what secondary schools (in the U.S.) teach, and what they do not teach, and the overall structure of the curriculum.  It never quite sat well with me that in B.C. we must complete an English 12 in order to graduate, yet no other grade 12 course was needed. Even further, it was the only provincial exam in grade 12, and was worth 40% of your final mark (at least it was when I took it in 2013). This caused me great stress as English was my worst subject, yet I had to take it, and universities placed a great emphasis on having a good mark in this particular subject, no matter what program you apply to. "Why were arts students not scrutinized by their math marks?" was my thinking. Was success in poetry a good indicator of a student's aptitude in post-secondary education?

It seems to be that the core subjects consist of language arts, social studies, mathematics, and science. Any other subjects are more fringe and are not guaranteed to be offered at every school. Yet it appears odd to me that astronomy is not taught as a science 11 or 12 course in the B.C. system, despite it being the study about the entire Universe. Instead, a small topic is inserted into the Earth Science 11 curriculum, but I don't think it does the subject justice. There is the option in the new curriculum to make the course yourself (as a teacher) under Specialized Science 12, but the issue of it not being offered at many schools still stands. I do admit that I am obviously biased regarding this topic, but to me it always seemed like the astronomy portion of general science courses is the one that teachers often gloss over and pay little attention to, and I just wonder, why? Perhaps the reason as to why I decided to major in astronomy was my yearning for a proper learning of what the subject really has to offer, since I was not given the opportunity in my secondary education.

Reflection: Curricular Microteaching

This microteaching lesson was the first one in which we looked at the BC curriculum, and as such it felt very applicable to a real secondary school classroom. My group decided on tackling the transformation portion of Pre-calculus 12. In particular, we looked at the effect of transforming f(x) to f(ax). We felt like this aspect of transformations would be the best as students historically have trouble with this, as many believe that increasing the coefficient a would widen the graph by that same factor.

We initially looked at the quadratic function y = x^2 and the sinusoidal function y = sin(x). We later came to a group decision to focus our efforts solely on the sinusoidal function, at the advice given by Susan, on the basis of time constraints. We felt that the sinusoidal function would be more illuminating in demonstrating the effect of changing a, as the quadratic function could be argued that you are stretching/compressing vertically (e.g. y = (2x)^2 = 4x^2, so you could say that the graph was stretched by a factor of 4 vertically, rather than compressed by a factor of 2 horizontally.)

We also wanted to represent this transformation using different methods. I made an interactive plot that could switch between sinusoidal functions with different values of a, to display the transformation graphically. I asked students the similarities and differences as a means to engage them and get them thinking about how this particular transformation changes different aspects of its base function. I felt like I did a decent job at having them be active participants in the lesson.

Some things I would work on for future lessons would be the incorporation of applications to make it more apparent to students as to why they should be interested in learning this material. In addition, general whiteboard layout and deciding on having the projector screen up or down with respect to students and their potential issues seeing the board are also things I will look out for.

Curricular Microteaching Lesson Plan

Lesson Plan

Interactive Plots

A Geometric Puzzle

With the numbers going from 1 to 30, there will be 30 distinct numbers, equally spaced around the circumference of the circle. In order for a number to be diametrically opposite to 7, it must be in-line with the diameter of the circle with one end on 7; this occurs when that number is half-way around the circle relative to 7. Since there are 30 spaces, half-way would be 15 spaces, and so we add 15 to 7:

7 + 15 = 22

which tells us that 22 is the number. I also decided to prove this geometrically/computationally. Using the tikz package in LaTeX, I was able to construct this problem with a grid line to further emphasize the opposite number to 7, which is of course 22.

Code:
    \begin{tikzpicture}
        \def \n {30}
        \def \radius {5}
        \draw circle(\radius)
              foreach \s in {1,...,\n}{
                  (-360/\n*\s+84:-\radius)
                  circle(.4pt) circle(.8pt) circle(1.2pt)
                  node[anchor=-360/\n*\s+84)]{$\s$}
              };
        \draw[help lines] (-5,-5) grid (5,5);
    \end{tikzpicture}

You could extend this puzzle for sure, either possible or impossible. To make it impossible, we can make the numbers run from 1 to an odd number, in which there are no opposites. I think there are some scenarios in which impossible puzzles may be appropriate; the act of finding out a puzzle is impossible could be viewed as solving it in a way, as it shows that the student understands the problem well enough to realize there is no solution.

A geometric puzzle can usually be solved using diagrams, whereas logical puzzles require more number theory.

Battleground Schools

At the beginning of the article, the contrast between the two polarizing views of mathematics really caught my eye. Politics is an aspect of life that really envelops a lot of society, and many people feel passionate about their viewpoint over another. Here it is highlighted as such, even in more (or so I would've assumed) apolitical topics such as mathematics. It just goes to show that people will always have different viewpoints, and debates will always be had when it comes to education and the most effective method of instruction.

The second part that resonated with me was when the article talked about math being for 'nerds'. Throughout my post-secondary education, when talking to people outside of a school context, the topic of my studies would come up. I would tell them the courses I was enrolled in, and they would always reply to me that I must be really 'smart' for taking all of these math classes. I always thought, why is it that math out of all the core subjects is seen as for 'intellectuals'? Does this say something about the way our society views mathematics? I can't really say for sure if I am as smart as people believe I am, I just happened to click well with mathematics and less so for the other core subjects taught in the public school system.

On another note, I found it sad, yet humorous, that the catalyst as to why the US decided to overhaul its mathematics education system is due to the "Red Scare" of the Soviets making advancements in scientific technology. Never mind worrying about the education of the youth for the students' benefit; the government was just eyeing the potential benefit these young kids could one day provide to them, which ties into the military obsession that America still has to this day (serve your country!).

The Dishes Problem

The first thing I did when I saw this problem was set up an algebraic equation, where n is the number of guests. I looked for the sum of the dishes, with each term representing a different dish (e.g. n/2 is the number of dishes of rice, since every 2nd guest gets one):

n/2 + n/3 + n/4 = 65

Multiply both sides by 12:

6n + 4n + 3n = 780

Gather like terms:

13n = 780

Divide both sides by 13:

n = 60

And so the answer I got was there were 60 guests in total.

I think it is important to offer puzzles from different cultures, so that students are able to understand mathematics from a different perspective. It is very helpful for students from that particular culture as most of the problems they deal with are from the Western culture, and may not reflect their experiences in life. Showing them that their stories have a place in the classroom too is imperative to show that they and their background matter. 

I think a story helps with setting up the problem. A lot of students complain that math is too rigid and boring, and if every problem just had a simple algorithm to solve I would tend to agree. However, problems with stories attached help in both visualizing and enticing the reader to solve the problem, as it may give the student more enthusiasm since they are invested in the story, and want to find out the conclusion.

Reflection: Microteaching

The big takeaway from this lesson for me is that 10 minutes is not a lot of time. The most common suggestion I had was to allow for a bit more time for people to write their name. When preparing, I gave 3 minutes for my group to write their names, which was manageable. However, I ended up teaching about 9 people, and as such some students needed help but I was off busy helping someone else. I will give myself the benefit of the doubt considering I was not aware of the amount of people I would be presenting for (assumed to be 3). I made the decision to emphasize Japanese linguistics by getting everyone to repeat some sounds after I explained them, in order for more participation with the students, so that they were not just passively listening. Overall, I am very pleased with how many people enjoyed the lesson and the amount of people that were able to successfully write their name!

Microteaching Lesson Plan

LESSON PLAN: How to write your name in Japanese

Time: 10 min

Objectives: 

• Learn Japanese pronunciation
• Understand Japanese kana and rules with changing sounds
• Be able to write your name in Japanese 

Materials:

• Whiteboard & markers (teacher)
• Pen & paper (students)

Beginning (1 min)

• Greeting and objective in Japanese then English
• Ask anyone if they know what language I am speaking/writing
• Mention Japanese has 3 writing systems; we use katakana for foreign words
• Tell students to consider how their name is pronounced, not spelled

Middle (6 min)

• Go over the katakana chart
• Explain how to pronounce each sound (emphasize 'f' & 'r')
• Talk about voiced sounds ('g', 'z', 'd', 'b', 'p')
• Mention blended sounds (*ya, *yu, *yo) giving examples
• Explain double consonants (tt* = ッ*) and vowel prolongation (horizontal bar ー)
• Indicate what to do with single consonants (* = *u, except for special cases 'n' & 'r')
• Talk about special cases with no Japanese equivalent sound ('v' = ヴ, 'l' = 'r', 'w' = ウ)

Ending (3 min)

• Ask students to get out a pen and a piece of paper
• Have the students write their name using transliteration
• Assist students having issues