Sharpen your pencil!
Here is a sketch of the famous Konigsberg Bridge Problem.
Can you solve it? Rules: 1. Starting on any land mass (A, B, C, D), cross to another land mass using any bridge (a, b, c, d, e, f). 2. Cross ALL bridges only once. 3. If you crossed all bridges only once, you solved the problem! Congratulations!!! |
Please watch at least the first two minutes of the video below.
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So how did you make out?
The first time I tried to solve the Konigsberg Problem was May 17, 2018 at the 8th Annual Aboriginal Mathematics Symposium at the University of British Columbia. First Nations University professor, Dr. Edward Doolittle gave the key address, where he had participants of the symposium attempt the problem.
I was at a table of very mathy individuals who were determined to crack this historical mathematical problem. After a handful of failed attempts, I announced:
"Why can't we just go around the whole river?"
I was being facetious at the time, as I was not feeling very well, and admittedly, I get a bit nervous when I am around really mathy types. (I recognize that I am technically a math teacher with a degree in math, but hey, we all have our insecurities.)
Well, it turns out you can go around the whole river! Who knew?
That is, when you analyze the problem through an Indigenous lens.
Dr. Doolittle explained that from an Indigenous perspective, one would take a few steps back from the problem so that the source of the problem could be determined.
What would be the source of this particular problem?
The source of the river, naturally! If one were to travel to the river's source, thus bypassing the need to cross a bridge, one could cross every bridge once, regardless of the number of land masses with odd number bridges. Easy peasy; problem solved!
I was at a table of very mathy individuals who were determined to crack this historical mathematical problem. After a handful of failed attempts, I announced:
"Why can't we just go around the whole river?"
I was being facetious at the time, as I was not feeling very well, and admittedly, I get a bit nervous when I am around really mathy types. (I recognize that I am technically a math teacher with a degree in math, but hey, we all have our insecurities.)
Well, it turns out you can go around the whole river! Who knew?
That is, when you analyze the problem through an Indigenous lens.
Dr. Doolittle explained that from an Indigenous perspective, one would take a few steps back from the problem so that the source of the problem could be determined.
What would be the source of this particular problem?
The source of the river, naturally! If one were to travel to the river's source, thus bypassing the need to cross a bridge, one could cross every bridge once, regardless of the number of land masses with odd number bridges. Easy peasy; problem solved!
Different ways of seeing.
Finding a third space.
Crossing bridges with and without maps.
I am not Indigenous.
I am of White settler identity, adopted by my Norwegian family at birth and to my knowledge, I am mostly Italian with a splash of English. I live and work on the traditional territory of the Lkwungen people and my Indigenous students are mostly from the Songhees First Nation and the Esquimalt First Nation.
It is my ultimate goal to reflect on the learning presented and acquired during my time in MET through a lens that is not native to me and through one that is. I recognize that I may make errors along the way, but if the goal is to learn, I must not be afraid to make errors. I trust that the people I surround myself with, will guide me through this reflection process, should I misstep.
I am of White settler identity, adopted by my Norwegian family at birth and to my knowledge, I am mostly Italian with a splash of English. I live and work on the traditional territory of the Lkwungen people and my Indigenous students are mostly from the Songhees First Nation and the Esquimalt First Nation.
It is my ultimate goal to reflect on the learning presented and acquired during my time in MET through a lens that is not native to me and through one that is. I recognize that I may make errors along the way, but if the goal is to learn, I must not be afraid to make errors. I trust that the people I surround myself with, will guide me through this reflection process, should I misstep.
For my capstone project, I will reflect on my learning from both an Indigenous and Western lens.
Ideally, through this reflection process, I will broaden my third space where both worldviews are present, yet neither are dominant. I will attempt to broaden my third space by focusing on the following Indigenous worldviews: |
- Focusing on relationship within my reflections. Relationships with my readers, to be specific. My writing style is somewhat casual; sometimes there are sentence fragments and Dana-made words. This is not to imply that relationships can only be achieved via a more conversational tone; it is more of a reflection of the skills within my wheelhouse. My writing within this site is academic in nature but also sometimes emotionally driven.
- Focusing on collaborative learning. As collaborative approaches to learning represents one of my goals for MET, I have included space within my project to comment via my Next Steps Blog and a feedback survey. I am hoping that this site will encourage readers to contact me with their questions, concerns and suggestions. Although I am ending the formal component of my learning in MET, I am not ready to stop learning and sharing with others.
- Focusing on storytelling. Embedded throughout my project are personal micro-stories that are relevant to the artifact that they are found within. My artifacts are presented in a timeline in which my MET story was unfolded, albeit in a linear fashion. I would like to mention, however, that my site can be navigated in any order one may wish to travel.
- Focusing on place. Admittedly, this is where my site is the weakest. To quote Dr. Michael Marker, "There is no place of nature; there is only nature of place." Perhaps it is permissible to have a bridge left uncrossed in one's learning? I feel like this is where I still have more to learn...
Until this degree, I had been randomly trying new approaches without knowing any research to back my pedagogical decisions.
It was as if I was crossing bridges, without knowing what was waiting for me on the other side.
I began my degree in January 2015 with the intent of learning how to effectively use technology in the classroom. It was such a simple goal! Over three years later, my capstone project will hopefully demonstrate that I am walking away with so much more. I must remind myself that it is sometimes best to NOT cross bridges, as they present themselves. Pausing, and possibly stepping back to see situations from alternative perspectives, can bring alternative forms of knowledge, that we may not have been even looking for in our haste to cross bridges.
It was as if I was crossing bridges, without knowing what was waiting for me on the other side.
I began my degree in January 2015 with the intent of learning how to effectively use technology in the classroom. It was such a simple goal! Over three years later, my capstone project will hopefully demonstrate that I am walking away with so much more. I must remind myself that it is sometimes best to NOT cross bridges, as they present themselves. Pausing, and possibly stepping back to see situations from alternative perspectives, can bring alternative forms of knowledge, that we may not have been even looking for in our haste to cross bridges.