Personal Learning Experience

From MathWiki

Personal Reflection – MATH 4000


Over the past summer, I have been enrolled in a course with Professor Whiteley, whereby we completed many different projects, discussed many different topics and in the end learned about many different issues in regards to mathematics education, specifically in relation to geometry and spatial reasoning. This course has taught me about my own learning style, which has impacted my understanding of what it means to learn about mathematics.

The following is a reflection commenting on the different facets of the course and the ways in which they have impacted my learning over the past summer:


Visit to the Arrowsmith School and Presentation

In the beginning of the course, a fellow student and I were compelled to visit The Arrowsmith School of learning in Toronto. Together we ventured into the city for a very eventful day of learning about the history of the school, its creator and the programs that they offer to the public. I found that this visit was an excellent way for me to learn about the style of lessons and exercises that took place in this very special school. Interestingly, since this visit, I have had the chance to tutor many students who would benefit from this school, and I have re-counted my experience at The Arrowsmith School to many teachers, professors, peers, parents and even students. Not only did the content of the visit benefit me in my learning career, but also the report that Mordy and I completed once we returned to York was a learning experience for me. It was wonderful to know that we were responsible for conveying information to our professors regarding the visit.


Weekly Discussions (in person, via email or wiki)

I have also been responsible for reading articles about Mathematics Education and posting information on the course’s wiki site. This is a brand new experience for me since I have never used wiki prior to MATH 4100, and even then I was not responsible for posting discussions, reflections or reports. It was interesting because I was constantly aware that the words I was posting were to be read by other professionals in the field. It was great to meet with Professor Whiteley on a weekly/bi-weekly basis because it constantly gave me a focus and direction in my studies. It was also a new experience for me to be having a course where there were only a few other individuals enrolled. It was slightly difficult to be able to bounce ideas off my peers due to summer schedules, but the corresponds via email was fantastic. It was very encouraging to see fellow peers take an interest in the articles I was reading and the topics we were discussing. It was also great to discuss the topic of geometry and spatial reasoning in a small group environment. I found it interesting how our ideas would often benefit from the discussions. The overall dynamic of the group, when we were able to work together, was very strong and I believe that we fed off eachother’s ideas and questions.


Reporting about mathematics textbook for teachers

In completing my first formal report on the wiki site regarding the mathematics geometry textbook for teachers, I found that I learned a lot about what it means to create a report. It needed to be well organized and easy to read. Despite the fact that I had taken the textbook home simply to “skim-over,” I found it to be very educational and full of resources. One of the difficult aspects of reporting about a lengthy textbook was that I easily got stuck on trying to report on how the textbook was organized rather than the content of the book itself. I would have like to add some more examples from the textbook, which may have sparked questions and discussions. It was a great experience, and when I did it again with the Froebel text, I made sure to try and add some “beef” to my report in order to strengthen the substance of the work.


Learning about Froebel

When I first was asked if I wanted to write a report on Froebel, I told Professor Whiteley that I had no interest in the topic. This was mostly because I knew that I was not going to be teaching kindergarten, therefore it did not immediately connect to my own life. Despite this fact, I took the book anyway, and ironically this study became one of the most interesting topics for me in this course. I learned how, to not only provide substantial information in order to support the report, but also how to include other resources, ask more questions and write about my own understanding of the topic. It was a struggle at first to be able to know how to summarize such a lengthy and informative textbook. I quickly learned that providing quotes from the book was not enough to make the report worth reading. Professionals want to see the history behind the theories and the “aftermath” of the theories. In other words, it is very important to not only give the information about the gifts of kindergarten, but also the historical and social context of its creation.


One of the aspects of my report that I feel could have been stronger was its relation to mathematics and teaching geometry. I tried to add some more information as to how Froebel intended to use the gifts, but I feel as though there are still many more questions that need to be asked and topics which can be discussed about Froebel’s theories about teaching geometry to small children. For example, at what age did Froebel hope that the concepts he was teaching should have been learned by? Or, at what age is “too” early to start teaching these concepts? Or, is there a difference between the children we are teaching today than those Froebel was teaching in his day? It is a topic worth discussing, and I hope to see that this topic may appear in future related courses. Teaching about geometry starts with teaching the young, getting their minds focused on the world around them and the objects they are experiencing with their senses.


Researching topics and contacting other professionals for research purposes

Towards the end of the course, I began to finally ask some questions which were of personal interest to myself in relation to the topics of the course. I wanted to learn about how video games affect our spatial reasoning skills. In attempting to complete some research on this topic, I found myself contacting other professionals, teachers and researchers. This was a very new experience for me. It was great to know that past professors were still willing to reply and help me in my efforts. Professor Whiteley also helped in my researching. I believe that with slightly more time in the course, or if I had begun researching earlier, I would have found ample information in order to create a substantial report on the wiki site.


Nonetheless, I still created a link, in which I discussed some of my own ideas in relation to a short article I read on the topic. I also found it to be a great place to ask more questions. As I began to literally force myself to really question what exactly I was researching, I found that I was able to formulate, organize and clear my thoughts about my curiosity on the subject. This was a great learning experience because I was able to focus my attention on what I was thinking about in order to create and write out the questions. I would recommend to anyone beginning research to start with this exercise of asking questions. It helped me to organize my own thoughts and if I had done that before I began researching, perhaps I would have come up with many more related articles.


Critiquing a research paper and comparing to other scholar papers

One of the best learning experiences of this course was being responsible for reading and critiquing a research paper from an unknown source. The paper was given to me in order to read, question and discuss its content. At first, it was a long article, and I began to read it with an extremely “technical” eye. In other words, I was crossing the t’s and dotting the i’s instead of really trying to read the content of the paper. The clarity of the argument was not very strong, and it was very empowering to try to read between the lines as if I was critiquing someone else’s proof. At first, I didn’t know if it was a good idea for me to know that Professor Whiteley thought it was not a strong argument. I was afraid that I was going to already start reading the paper with a bias. Perhaps sub-consciously I did have a bias, but I desperately tried to read the article without any pre-conceived notions. In the end, I found that by being told to read the article specifically to look for consistency and clarity in the arguments made the whole experience that much better. I knew that I was not trying to look for ways to convince myself that the article was completely correct, but rather I learned how to read a paper with a critical eye. Furthermore, by comparing this article with another very well written article about mathematical research the educational experience was enhanced. I was able to see for myself what it meant for a research paper to be based on solid evidence and supporting claims. It was great to finally learn how research in the realm of mathematics education takes form – a great experience!


Thank you for taking the time to read this personal reflection on the events, lessons and experiences in this summer course.

Tanya Trevisan September 2007