An activity that helped me understand concepts was the Fraser River Rockslide Challenge. For this problem, we used math manipulatives to build bridges over the Fraser River (check out the photo of my drawings/ use of manipulatives when working on this problem!).

 

The goal of this problem was to try and cross all the bridges without going over any bridge twice. This activity seems as though with some trial and error, or strategic planning, you would be able to reach a conclusive answer. However, my struggle with this problem was that there was no answer! After continuously trying different patterns and strategies to cross all the bridges, there was no possible way to do it!

This demonstrated to me that math problems do always need a set answer, and that math is not so much about the final answer, but rather the process instead (similar to the Small Number Investigation). I learned that math questions do not always need an answer, as the process itself is an effective way to acquire knowledge about the concepts. For instance, when trying to solve this “unsolvable” problem, I used various problem-solving skills. I started by using trial and error, such as testing different patterns across the bridge. I also used some logic, such as thinking about the fact that  7 bridges need to be crossed, which is an odd number. This led me to discover that there is no possible way to cross them all without going on a bridge twice. Even though I did not finish the problem with a set answer to the question, I still challenged my brain and applied my understanding of numerous math processes.

While working on this problem, I was frustrated with the fact that I could not figure it out! I worked on it continuously and was set on the fact that there must be a solution. So, it was difficult to continue working with no success. To overcome this struggle, I thought about the broader idea of mathematics. I considered that math is not only about the answer, but more so about the process. I thought about what I gained from working on this activity and what math processes I practiced.

This type of problem is a great example to share with students. Some students (including myself before this course) think that to be successful in math, you must reach the correct answer. However, not all math problems have answers and furthermore, the process to reach the answer is much more valuable than the answer itself. This is really important to emphasize to students so that they understand the purpose behind mathematical learnings, instead of solely being focused on the final outcome and disregarding what they learned throughout the process.

Here is a photo of the Fraser River! It would be fun to include this image when working on this problem with students. (Photo by Shaylis Johnson on Unsplash).

I found a website that explains the idea that learning is more than getting the correct answer, or even an answer at all! The webpage includes some tips that considered as a teacher to emphasize this concept to students!

http://mathframework.com/numerate-environment-3/learning-is-more-than-just-getting-the-right-answer/