Exit: Inquiry Project Search Plan

Entry: Refocusing Our Efforts

   As a teacher, I find letter grades to be a useful tool in assessing a student's work, especially in the context of comparing it to other students. It is an easy way to distinguish which students are struggling/excelling and which areas the average mark of the class drops. In a similar way, it helps a student to evaluate his own progress. Without a grading metric, students would be unsure of how well they are performing in the class (I personally will often feel that I did well in a test until I see my grade and realize that I had a poor understanding). However, even though grades are useful, I feel that there is too great of an emphasis on them in the classroom. I think that effort, progress, and your current understanding are all important, and grades only track the latter. They have a negative effect of discouraging kids who have a slower start and quickly evaluate themselves to being weak in a subject, which greatly affects motivation. They also affect the social hierarchy of a classroom, distinguishing the weak and strong students. This plays a pivotal role in peer pressure, motivation, effort, etc. If a student gets a reputation as being weak, they might pretend that they purposely failed (which would repeat itself) or they might lose self-esteem and confidence.

   As a math teacher, it is difficult for me to imagine a math classroom without grades. If I were to create one, I think the emphasis would shift from grades to concepts. Instead of repeating problems and getting scored on how many you get correct, I would give them their homework and ask them to return it (less questions than they get now) along with a brief paragraph that describes the method they used, what they learned, and any questions they have. Instead of grading the problems, I would just read their synopsis. If the students were understanding the material I would move on, otherwise I would reiterate the lesson. I think this would be an effective way of testing their knowledge without needing to grade them. Unfortunately, I am not sure how I would administer an exam without grading them.
 

Entry: Inquiry Project Ideas

I thought of a few that I was interested in:

• Flipped Classrooms / On-line Learning (Highest Interest)
• Cultural Influence/Differences in Mathematics
• History of Mathematics

Entry: Ancestral Genres of Mathematical Graphs

   I first stopped when a student replied that she put the x-axis at her heart, “because that’s the centre of me!” I always considered math to be mainly a universe language which develops most dependently with age, but this seemed like quite a cultural, and even personal, representation of math. It was interesting to think that different people would create a graph in their head differently depending on their personality. I naively assumed everyone would just see a graph in their head.

   I next stopped to admire 'Die gantze Welt in ein Kleberblat [sic],' and found it fascinating that "Jerusalem was taken to be the umbilical connection point between heaven and earth, the omphalos, the point where earthly and celestial axes meet." It is incredible to see the variations of maps throughout history and how they completely changed depending on history and culture.It further expanded on the idea that math isn't a simple representation of facts, but a cultural representation of facts through mathematics. It brings credence to Nietzsche's philosophy of, "Nein, gerade Tatsachen gibt es nicht, nur Interpretationen.": There are no facts; simply interpretations.

    Lastly, Table 1 of the text was very interesting to look at and caused me pause. I reread all of the tables and compared them to other cultures that I was familiar with. Thinking about how they perceived their bodies, houses, mythology, and mathematics, it was eye-opening to see the relationships. How each one is understood within the context of their culture has effects on how they comprehend and map out the others. It is something that I would be interested in reading more in-depth over a broader range of cultures.
 

Exit: Reliving an Emotional Experience

   "Checkmate!" I smirked, as I moved my queen into a perfect position across the board. My teacher looked up in surprise as realization dawned on him. For years I had been coming to the math room during my lunch break to try and win the, so far unclaimed, prize of pizza for victory against our High School's math teacher. Most likely as a byproduct his inflated confidence, he had somehow missed the infamous 4-move checkmate, resulting in his current predicament.

   "That wasn't a fair match," he replied. "I was distracted by the other student." What followed was a brief verbal argument, concluding with the firm assertion that to win the prize I would need to win again. After years of visiting, practicing, and helping in the math room, I was now quite frustrated towards the same teacher whom I had grown fond of, as I felt cheated out of my prize. Even a slice of pizza from the cafeteria would abate my angst, yet there was none.

   From the discussion in class today, in conjunction with my own reflection, I discovered that many people hold onto frustration, especially when it is derived from misunderstandings. Between the stories I heard, they all had the common factor of the student being misunderstood by either their peers, teacher, or the public. I think it is important that I bring this awareness into the classroom and try to practice empathy, or to be able to put myself into the students' perspectives to understand where they are coming from.