Looking back at how I perceived group work before this unit, I felt that there was little to gain from other people's perspectives. I felt that the purpose was to arrive at an answer and unless I needed help, what could be the benefit in having others to work with? But as I progressed through the unit, I realized that there was a great deal to learn about how to learn. When exploring mathematical concepts there is much to gain from looking at other people's thought processes and see how they would go about solving the same problem as I was working on. Group work has become more of an exploration tool rather than simply a different way of working. It helps me to find new ways of grouping students in order to expose them to new thought processes. I used to feel that group work was best when you were working with people who all thought just like you did, but now I realize that the true benefit to group work comes from working with those who are completely different thinkers. They are the ones who will challenge you, redirect your thoughts, and allow you to explore additional paths of understanding. From these groupings we have also discovered new methods of presenting our findings to the class.
It has been fascinating to me to see how different each of my peers presents information. We have all been experimenting with our iPads and looking at new apps to demonstrate what we have learned. I feel that as you take the limit as time approaches infinite, the function expressing the number of ways to express one's learning diverges to infinity. In other words the possibilities are endless! The board in our methods classroom seems to have been barely used. We have been experimenting with oral presentations, slide shows, posters, and the iPad apps. I feel that the act of putting together a presentation allows students to reflect on their learning but also connect the dots for the observer. So a presentation seems to be more of a conversation rather than a one sided transfer of information. I hope to be working with additional presentation methods as we continue to explore mathematical thought processes.
In looking at the thought processes of students through observations as well as becoming a student myself, I have felt there are many more ways of thinking through problems and situations than I realized. To be successful in a classroom, it is important for a teacher to open the pathways of different forms of thinking processes and allow students to journey through mathematics in their own style and form. It seems that one thing the students all had in common was their desire to express things visually first and their success could be tied to their ability to first see what was happening, essential applying the problem in a basic setting. This can be accomplished through drawings, diagrams, manipulation of physical objects, or even conversations with other students. This universal thinking tool manifests itself in poorly drawn symbols. When working with other people, I have noticed that I, like many students, need that first few minutes to think to myself before collaborating. In order to build up that familiarity with the problem, I need some time to focus and concentrate on what is happening. After this happens, my collaboration conversations become so much richer and relevant. I think students will always need this time to reflect in order to take their next steps from independent work to group work. Learning how to duplicate this in a classroom on a daily basis is one of the goals I have for myself to work on during my studies of education.
Adding to the list of things that I need to work on, I have been fortunate enough to be placed in a subject that is making great efforts to engage students. In consultation with students, teachers, and educational specialists, I see how the richness of the curriculum is more important than simply making things fun. In our study of the IMP curriculum, I have been taking notes on how the curriculum sets up learning goals, connects concepts, and applies skills from math into applicable situations. My primary focus will be how to combine this style of studying math with aspects of social justice. I want to learn how to nurture students in their exploration of using math as a form of measuring justice and equity. This is part of my social justice plan and to accomplish it I will need the support of community members, curriculum specialists, educators from various grade levels and most importantly the support of my students.
Ultimately the students are the ones who are to be benefiting from any learnings developed in this field of study. My experiences with students throughout the unit have allowed me to see what ways to ask questions, how to set up activities, and create independent investigative minds that explore math rather than simply do it to get an answer. The richness that math can contain is what I will be taking away from this unit the most. I have thoroughly enjoyed working through problems that can be extended, investigated, furthered, and deepened on. An answer to a problem does not have to be an end result but can be the midpoint to further discussion and study. A practice that I want to take with me into the classroom is the ability to extend problems. I feel that most of math is written out on scratch paper, crossed out and rewritten to follow a series of thoughts that only the mathematician at work can follow. But in presenting the material, one must provide clarity and organization to those following along. If the mathematician at work is to create extensions to the problem, they must be even more organized in creating the situations and working through them to be sure they make sense. This process of bringing clarity to math is something that I have gotten to experience throughout this unit and as my personal growth continues, I will be organizing my own thoughts more and more.