Entrance slip: Refocusing Our Efforts

From reading this article by John Sarte and Sherri Hughes, my "student bird" thought was that assigning percentages or letter grades may mean that I have to do extra well and put extra effort in achieving high percentages or letter grades. To me, as a student, these grades indicate a successful completion in passing a course or judging on how well or poorly I have done. However, it may not necessarily indicate an interest in the course that I am being assessed or marked on. It just simply means that I did the work, passed the course, and now moving on to something else. In some cases, a student with a poor grade does not mean that he/she is not interested in the course materials. Similarly, a high grade does not necessarily mean that the student is interested in the course. As often is happened to me when I was a student in secondary and post-secondary schools.

As a "teacher bird", the percentages and letter grades tell me how well a student is doing in the class. I assume that higher the grades, the higher level of understanding and/or competency a student has. I would also assume a higher interest in the course because the student is excelling. However, as argued above when I was a student, what is on the surface may not be accurately perceived. As a teacher, I believe that grades should be arrived by how well the students are doing throughout the course of learning and teaching a particular subject or topic even. Assessing their understanding on a certain day, as in most cases (i.e. unit test or exams on a certain day of the week) may not be an accurate prediction that determines the ultimate result of students' learning, as many factors can affect students' learning and thinking abilities. I believe this is the negative aspect of giving grades. The positive aspect of giving grade, however, is for teachers to keep track of where students are standing academically in a grade and subject. It also informs teachers what and how they should do to help students achieve. That being said, teachers should not disregard the stronger students just because they are excelling more than the weaker students. Teachers should give equal opportunities and promote interest among all students.


An unintended side effect of grading is that students may get pressured into thinking that just because they are being graded lower than their peers, they may feel not as motivated to learning concepts or push themselves to work harder. They may also not feel interested in the course because the grades are lower than wished or expected. This discouragement could affect students' competency and thinking abilities. That being said, grades and marks could also form a social relation in that they students can keep track of their skills and levels among their peers. It tells them which area they need help or improve, and which area they are really good at that they can help others. Motivating each other with their peers are important in establishing social relations in classrooms and higher institutions.


It may be quite difficult to not give grades to students who are learning math and/or physics, but I think that as long as teachers and the students themselves know where they stand academically, and which area they need improvement or excelling, then grades may not be very important. It is a good habit, in my opinion, if the students develop some sort of work ethics so that they are encouraged to learn and try new things without having an authority figure telling them what to do. Once they internalize this interest for learning and that they are always pushing themselves for higher knowledge, grades should not matter.

I can compare this analogy to my co-op placements at various companies during my undergraduate work terms. I had a few co-op placements in the past where it was not necessary for co-op advisors to report the school on our mid-term performances (evaluating and marking how well we do on the job). Even though my co-op advisors did not visit us during our co-op terms, that did not stop me from doing well on the job. Often times, weekly or bi-weekly, my managers would speak to me and my team (individually or as a group) on our performances, and what we should do more or less of, and what we should focus on. Their "mini-evaluations" just by speaking to us gave me a professional outlook on work that lasted me for a long time - still do even now. Their comments and suggestions have pushed me to work harder and better on the job, regardless of which profession I will be pursuing in the future. In this case, I have developed good working ethics from my employers and my team of co-workers, which I am very thankful for. In the teaching aspect, I think that if teachers can set students good examples for the students to model after, then that skill set and attitudes are definitely worth having and are more important than grades.

Exist Slip: Research for Inquiry I Project

The topic that Jacob and I will be doing is revised slightly.

Our topic now focuses on online learning in students on the subject of mathematics, with additional focus of online learning in students with special needs. Essentially, we will look at the impact of online learning in math subject on various students - students who do not have special needs and students who do.

Inquiry Project Ideas

For my inquiry project for this class, there are two main topics that I want to look at, but of course I will have to pick one to analyze.

One particular topic of interest is the idea of a flipped classroom, and the theme of online learning. I am very interested in looking from the perspective of a flipped classroom because I have designed eLearning materials, in collaboration with professors and using software to facilitate in the learning of college students. I wonder how well high school or middle school students take in concepts from the online platform. However, the concept of a flipped classroom is different than having an instructor teach through an online platform in that students are expected to learn the materials and teach themselves online first, then coming to class, knowing the materials, and apply the knowledge in the real world. So I want to examine how effective this flipped classroom and online learning is for younger students.

Another topic of interest that I may examine is poetry and mathematics. Because I have taken tons of English courses that examine poetry - particularly forms, counting metrics, finding rhythms in stanzas, etc. - these patterns in the body of the poetry amazingly tie with mathematics. Poetry has its beautiful poetic forms and so does mathematics. Poetry is an art, and we were discussing how mathematics can be used to create meaningful art, such as poetry itself. I would like to examine this topic further.

Entry Slip: Article on "Ancestral Genres of Mathematical Graphs"

Susan, the article you wrote is certainly interesting to read and analyze. I have also thought about why right and up indicate positivism, and left and down indicate negativism. I've encountered this especially in units on graphing and sketching equations, such as a linear equation, parabola, and many other shapes. I understand that it is common to think that right and up is associated with positive because of the points you touch on in your article. I also believe that our culture and norm definitely have something to do with the naming conventions. I mean, after all, they are supposed to be "arbitrary assignments" (15). And interestingly enough, because culture is different across the world, for instance, the North American (Western) culture may be different than South American culture, but the universality on the existence of culture leads to the same conclusion in the "genre" of mathematics. In Asia, specifically China, Chinese also associate any numbers left of 0 to be negative, and any numbers right of 0 to be positive. Again, this name convention is universal across culture.

One area that made me think more about this convention of this "hidden", "arbitrary" assignment is the CAST rule. I learned the CAST rule in high school in units on trigonometry. The CAST rule, which stands for Cosine, All, Sine, Tan, is a grid that is divided into four (4) quadrants where it tells us what trigonometric ratio (cosine, sin, tangent, or all) is always positive in a said quadrant. Counting using the CAST rule starts in a counter clock-wise fashion. First quadrant is positive in A, second quadrant is positive for S, third quadrant is positive for T, and the fourth is positive for C.

This is an image that was taken from Google to demonstrate the idea of the CAST rule. Applying the CAST rule to calculate the exact values (in fractions) of trigonometric ratios may not apply to the "right/up" positive and "left/down" negative convention, since trigonometry of a certain function follows a smooth, continuous curve that repeats itself depending on the degrees it has. The +/- sign of a trig function really depends on the angle or the degree that it is given. The angle and the exact position can be shown on a 360-degrees circle. So, I'm not really sure if the conventional naming of positive/negative still applies in this case because trigonometry deals with continuous functions, not something that is binary, which has front and back, up and down, or left and right.

While reading your article, I was also fascinated by the image included in your article of Albrecht's (1471-1528) portrayal of an artist is drawing a model through a frame using a grid system. This got me interested by the artist's sketch of human facial symmetry and the many patterns that exist in nature. I'm particularly interested in facial symmetry because body measurement, especially as seen on faces, influences judgement and qualities (e.g. positive and negative social cues) of an individual. The aesthetics behind facial symmetry in certain culture has a deeper meaning than just the appearance of the face. For instance, Chinese physiognomy used to be so popular that Chinese people assessed a person's character and personality just purely on their facial constructions. The connections between mathematics of symmetry in the human body with the culture aspect that is influenced by it is astounding and can be quite controversial. However, complex mathematics cases such as the trigonometry functions may show otherwise.

Exit Slip: Take Away From Personal Phenomenological Experiences

From our personal phenomenological experiences, the takeaway of this, in my opinion, is the concept of "human" aspect of teaching - and just human aspect of social interaction between each other. Interacting with others is all very important for us all, and that including everyone (accommodating and adapting to students' learning needs). We also talked about authority, and how students are more intimidated by teachers with high authority because they may be less likely to ask questions and seek help. So, if a teacher is more "human" and not just a "robot" (or a scary authority figure), students may be more inclined to seek help and be more interested in the topics that they teach. In all, the concept of being sociable and human-ly to others (i.e. respecting and adapting to students' needs) are very important!

Personal Experience in a Formal/Informal setting

When I was around 6 or 7 years old, my parents signed me up for swim lesson, to much of my surprise. I was never a good swimmer, and I didn't like the idea of being inside water (I was always afraid of swimming in deep ends due to my fear of drowning). I can't remember much about the first day of swim lesson, but I did remember my learning process in between.

First of all, I really did not like the smell of swimming pools, or anywhere beyond that matter. And second of all, the pool was used not for recreational purposes, so there weren't too many people swimming for leisure. I know that if I drown, they won't be in time to catch me or I won't have anyone to hang on to. As you can probably imagine, to get me actually inside the water was tough. However, as time goes by, I got used to this fear. My swimming instructor, a young woman, was very calm and patient with me. It's as if she understood my fear of water and seems to be okay with me acting this way. As well, I wasn't the only one who is afraid of swimming in deep ends. Knowing that I wasn't alone in this made me feel more comfortable. My instructor was also with me, side by side, knowing that she will catch me if I did drown. She was my lifeguard. Slowly, as time goes by, I gained confidence and independence, knowing fully well that I can swim on my own.

At the last day of my swimming lessons, I remember there was a big swim race, where beginners like me race across lanes. I remember I was competing with this other girl around my age, and I couldn't believe that I got to the end before she did! It was a rewarding feeling, and both my parents and the instructor were very proud of me.