I recently had an experience with a mountain that taught me a lesson about my students as well as students in general. I decided to go for an evening workout with my uncle and unbeknownst to me, my uncle chose to run a trail that was on a mountain. I was excited about this run because I had the opportunity to climb a mountain this past summer in Colorado Springs, CO and it was a great experience. Our run started off wonderful, and we eventually reached a certain point where my uncle decided we should head back down the mountain because of the sunset. At first he was unsure about what path to take so that we could head down the mountain, but I was unbothered because the sunlight was still quite visible from the position we were at on the mountain. A few minutes later, we seemed to have found the right direction, but eventually my uncle explained to me that he hadn't been up this particular mountain in a few years so he was somewhat unsure how to get back to the bottom. At this point I was concerned because it was getting even darker outside and our vision of the trail was getting hazy. My concern was not so much being stuck on the mountain, it was the fact that we couldn't clearly see the trail, and I didn't want either one of us to get an injury due to all of the debris and uneven ground on the trail. We happened to pass a gentleman on the trail whom appeared to be going up the mountain and he gave us his version of directions to get back. Unfortunately, his directions became confusing after only a few minutes. By this time, it was dusk outside and we were trying to read the signs on the trail for help. We decided to go left just as the last gentleman had told us, but shortly after, there was another fork in the road. We stopped and had no clue which direction we should follow. Instead of getting too worried, we decided to remain still for a few minutes. Then, we looked up and saw two lights and to our surprise, it was a biker. We inquired about directions and thankfully about ten minutes later, we were finally able to exit the trail.
After arriving back where our journey began, I felt great about the fact that we didn't have to call 911 to get rescued from the mountain. While driving home, I realized how that experience with the mountain can be very similar to a child's experience in a mathematics classroom. Often times students begin a task with confidence because of their past experiences and/or performance. Things start out well for them with working on a task, but at some point, things begin to get dark and hazy in regards to what direction is needed to arrive at the solution. In a child's mind, once they begin to struggle, they are often reminded of the dark places that aren't mathematically familiar. It doesn't necessarily mean they don't know the content, they just may be having trouble recalling the specifics of that particular concept. The student will likely request help from a peer, which results in them being able to proceed a little further with solving the task. Later they may arrive at another point in the task where they are unsure or unaware of which direction to take. At this point, once the student has reached for the help of their peers already, the teacher should be the next line of help. Hopefully after the teacher's directions, the student gains the confidence of knowing that they are headed in the right direction and are not far from the solution. When the students arrive at the solution, they should be mindful of their experience with working through a productive struggle. At no point on that mountain were my uncle and I worried about getting off of the mountain, we were only concerned about visibility to help us arrive at our destination. As teachers, we should seek to build up the confidence of our students so they surely know at some point they will arrive at the solution to a task. However, when lessons are effectively facilitated, the teacher sets themselves as the last line of help for the students, just like the random stranger that happened to cross paths with us while we were lost. I took notice that this gentleman was not only riding his bicycle on the trail, but he also had a light on his helmet as well as his bicycle. This reminded me of the significance of having the proper tools and resources to work with on a task. I encourage all math teachers to establish a climate that facilitates the problem solving process allowing students to productively struggle on their own before helping them. It will help build confidence in their own mathematical ability as well as force them to be critical thinkers which is a critical skill needed for life.