Exit: Inquiry Project Power Point Slides

Entry: Annotated Bibliography

Phipps, R., & Merisotis, J. (1999). What's the Difference? A Review of Contemporary Research on the Effectiveness of Distance Learning in Higher Education. Institute for Higher Education Policy. http://files.eric.ed.gov/fulltext/ED429524.pdf

This book analyzes the effectiveness of distance learning in higher education. It does this by examining various research projects done which examine the validity of online learning. Though this book determines the validity to be undetermined, it offers some insight into its effectiveness.

Galusha, J. (1998). Barriers to Learning in Distance Education. University of Southern Mississippi. http://www-tandfonline-com.ezproxy.library.ubc.ca/doi/pdf/10.1080/87567559909595802

This book analyzes distance and on-campus learners' learning styles. It concludes that students who opt for distance courses are typical more independent and less traditional. It also deems online students to be intrinsically motivated and not reliant on the typical classroom structured rewards.

Cavanaugh, C. (1999). The Effectiveness of Interactive Distance Education Technologies in K-12 Learning: A Meta-Analysis. University of South Florida. http://files.eric.ed.gov/fulltext/ED430547.pdf

This book looks at the effectiveness of Interactive Distance education and finds that there is a small positive effect in favour of distance learning. This book looks at the effectiveness levels of various approaches and will be useful when structuring my own class.

St. Cyr, S. (2004). Can Distance Learning Meet the Needs of Gifted Gifted Elementary Math Students? 27(2). http://gct.sagepub.com.ezproxy.library.ubc.ca/content/27/2/42.full.pdf+html

The effectiveness of adding a technological, distance aspect of learning to elementary/secondary schools to supplement the learning of gifted students. This study looks at the benefits, downfalls, and concerns of using technology in this manner.

Exit: Sword Dance Takeaway

   It was interesting to make shapes with the sticks and then try to replicate it with the swords. It would be a nice lesson to do with younger students who are learning the basic properties of shapes and how to form them. They can discover how intersecting lines form and the fewest amount of sticks to make different shapes.

   By incorporating the dance into it after they have played with the sticks they can see the relationship with how much simpler it is by having a group perform it. Hopefully they can think about the reasons for this.

   I also find that having them draw a picture of the shape they made was a good idea at helping some students visual and understand what is happening.

Entry: Key Articles

With my partner Ying Ting, I will explore the idea of an on-line math classroom. We will likely look at the benefits this incurs, possibly for disabled or challenged students, as well as which age group benefits the most from this.

1. Dove, A. (2013). Students’ Perceptions of Learning in a Flipped Statistics Class. In R. McBride & M. Searson (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2013 (pp. 393-398). Chesapeake, VA: Association for the Advancement of Computing in Education (AACE).

- Feedback from university students after they have taken a flipped Statistics I class.

2. Lynch, M. (2002). The Online Educator: A Guide to Creating the Virtual Classroom. RoutledgeFalmer.

- A detailed look at how to create and structure an effective online classroom.

3. Ashby, J. (2011). Comparing student success between developmental math courses offered online, blended, and face-to-face. Journal of Interactive Online Learning, 10(3). Retrieved November 1, 2015, from http://www.ncolr.org/jiol/issues/pdf/10.3.2.pdf

- Comparing success in three environments: online, face-to-face, and blended.

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.

Entry: Max Van Manen (Pedagogical Sensitivity)

   The first quote from the article that stood out to me was, "A compliment should be meaningful and should not be granted indiscriminately because, if given too  readily and too freely it may lose its significance."  I found this quote raised an interesting question of how to properly raise a child's confidence and fits into what I perceive to be conventional wisdom. In regards to a pedagogical perspective, however, it would be challenging to develop the ability to incorporate this advice. Each student would react differently to compliments, and more importantly, each compliment would bear a varying significance to the student.

   The next quote which caught my attention was, "Teacher educators have generally become quite aware that the tried 'knowledge into practice' model of teacher training in universities falls short of effective professional preparation." As an aspiring teacher, I found it quite interesting how there seems to be a strong opinion that teacher training is inadequate in preparing future teachers. This seems quite contrary to what conventional wisdom would tell us. I am curious to find out how the pedagogical approach with which one takes in the classroom differs from the one taught in university and how it fits into the broader field of education.

   Finally, I was fascinated by the final quote of, "We might even say that the practical knowledge of teaching resides in the things that surround us: the physical dimensions of the classroom that I recognize as my room to which my body is adapted." I feel that it is quite unconventional that teachers could consider themselves simply a part of the classroom, rather than the classroom to be a tool to be used at the teachers' discretion. I feel that this is quite significant and not simply semantics, and would drastically alter the methods that a teacher would find themselves using in class.

   To develop these skills as a teacher, it is necessary to have several requirements: (a) to have experience in the role as educator, (b) to read and discuss with other educators, and (c) to reflect upon one's own teaching in relation to (a) and (b). These practices have a great impact upon students, as they directly affect the methods and tools through which to acquire knowledge and modify their learning environment. By reflecting and adjusting their methods, in conjunction with the shift in students' attitudes and behaviour, the teachers will also have a completely new experience.

Exit: Alfi Kohn and Jo Boaler

   I found Kohn's opinion on positive reinforcement to be incredibly interesting because I am not sure where I stand on this matter. Part of me immediately thinks, "that's common sense, because if we give positive reinforcement for sharing, then the gratification of sharing is replaced by the positive reinforcement from our parents/instructors". But then another part of me has a knee-jerk reaction in opposition which says, "we should give positive reinforcement when children do the correct thing, so that they know that society approves and encourages the behaviour and by extension, we discourage selfishness". I hope that this is a subject that we can discuss in class in more detail.

   In contrast, I was very much in agreement with Boaler's opinion of multi-dimensional teaching. I can understand why some people like the traditional method of teaching the subject and then letting the students listen and practice it, as that is what they are familiar with. However, I think that that method would only work for people who either understand math easily or only know how to learn material in this manner. By incorporating multi-dimensional teaching, you can encourage students of all levels to play with it, share opinions, see more worldly uses of math, and become active learners. This would engage a wider variety of students and seems like a better method all around.

Entry: On Becoming a Reflective Teacher

   The article may be old, but it is hardly telling as the ideas have not changed. As a candidate teacher, it made me consider what I did as an EFL teacher and whether those actions were routine or reflective. Being a new teacher, I obviously had to reflect on what was and wasn't working in my classroom so that I could fit into the school nicely. However, was this reflection under the definition proffered by Grant and Zeichner? I would answer that as a no. Firstly, I don't think that I practiced pure open-mindedness. I was trained by the headmaster of the school and followed their methods, as I had no prior experience. When things did not work, I asked for their advice and followed from that. It is true that I was open to new ideas, but by only pursuing one avenue of new methods, I was not fully open-minded. In a similar way, I was not partaking an attitude of 'responsibility', as I was adhering too closely to my mentor's practices and did not consider the consequences of my methods.

   I feel that this article helped me re-examine what reflection truly is. Prior to reading it, I would have told you that I was reflecting and evaluating myself as a teacher. Now, however, I feel that reflection is a deeper process which involves a more rigorous method of critically analyzing your processes and their effectiveness. I hope to become more critical, re-assessing teaching methods and curriculum in new ways regardless of their popularity or support from other teachers, as this gives a constant avenue for growth and continual learning and improvement.

Exit: Frank McCourt

   I feel that McCourt cherished teacher inquiry, and he shows this by putting so much focus on understanding his students and putting his effort into helping them rather than teaching to them. His experiences with letting angry students vent and agreeing with them, rather than stopping them, was the most enlightening to me. In my own experiences I have found it rather difficult to not take things personally and realize what a boon it would be to harness that trait and use it to help the students' understanding by releasing their frustrations.

   He also demonstrated his views on inquiry by placing an emphasis on educating himself about his students' lifestyle and culture. I think that this is an often overlooked aspect of teaching, which is crucial to create a connection to the students. You don't need to "act like" the students, but it is important that you understand their perspective so that you can tailor your teaching towards them.

   You need to constantly update your methods and keep them in touch with your students. In summation, I would quote the words of McCourt: "If you are teaching and not learning, you are not teaching".