October 25 Class Reflection- Helping Joel

     In my mathematics education class this week I learned about how to develop rich problems that can benefit my students. We discussed the features of an effective problem and how they help students in their learning. These features include whether or not everyone can get started, its challenge level, its relevance, and a question that allows for multiple ways to find a solution. In order to demonstrate this, we looked at Joel's kitten problem which asks the student to find the best deal on kitten food. Below you will find images which depicts the different ways that students completed the problem and their thought process that they went through to solve it.

     As I looked at these images I thought to myself, what can I learn from these different methods of solving a problem. From this I have learned that students work their way through problems with methods that benefit their learning style. For example, one student had to draw out each piece of currency in order to visualize the problem. My best guess would be that this student is a visual learner that enjoys using images to complete questions. Other students, like the two above it, might think through the problem logically and apply their knowledge in other math topics. These students must show their work and work through the calculations in order to finish. All in all, if I was the teacher in this class this activity would show me how each of my students learn. This is important to note because I could differentiate my instruction so that each student can learn at their maximum potential. I believe that teachers need to alter their instruction in order to make sure that the needs of each student are equally met.
     Another activity that we completed was that we met in congresses in order to present to our classmates how we arrived at the solution we did. This taught me an effective way that students can not only demonstrate their knowledge orally, but also gives students a chance to learn from each other. This is a tactic I believe I will use in my placement because it benefits students with a variety of learning styles and gets the students more engaged in what they are learning.
     One key lesson that I learned during this class is that students gain a deeper understanding when they are allowed to struggle with the problem and come to a self revelation. Unfortunately, throughout my experience as a math student I was always taught to just memorize math "rules" and practice them until I knew them well. To me, this is an ineffective method of instruction because it only allows for a shallow understanding and does not give students the chance to explore. Problems are the key to mathematics education and it is the duty of an effective teacher to know how they can be used to enrich the understanding of their students.