New Insights

After preparing, creating, and presenting my LPU lesson, I have discovered that teaching using the new reform based mathematics is VERY difficult. It is really hard to pose questions for students, without helping them along the way. It is in my nature to want to guide the students as they create their own understanding, instead of letting them struggle and find their own answers. During the preparation of the the LPU, it seemed really easy to teach in the new way, but when it came to actually teaching it to the class, it was very difficult.

My LPU was about introducing the concept of fractions. It is hard to introduce a concept to students who have no previous background, and get them to form their own connections, and create their own understanding. It was definitely a challenge, to say the least. However, all students have a background about fractions, they just don't know it, until it is presented in a way in which they can form their own connections. All students understanding the concept of a whole, and that there are parts to each whole. They just may not understand that a part of a whole is called a fraction.

If I were to redo the lesson plan, there are a few things that I would change in the presentation aspect of it. I still believe that my prep-work is sufficient, it was just a lot harder to present it than I had original thought. Reform based mathematics is still a new concept to me, but at least now I can say that I've done it and could do it again.

New Sights and Their Implications

So far in this course, I have learned a lot from not only the instructor, but also my peers. Each class period that there is a new group presenting, allows for one more time to see a different perspective on how to attack one of the many themes in mathematics. I have learned from my peers, how to show students to work through a problem without ever really thinking about the fact that they are doing math. The more times a teacher allows for his or her students to work in groups discovering a solution to a problem, the more success students will experience in learning taking place. On top of that, teachers need to always make sure to have different tools for the students to work with so they are receiving the hands on activities that are pertinent to learning. The more you, as a teacher, can deviate away from the fact that you are doing math work in the classroom during math, the better the outcome of learning is for the students. As a teacher, you do not need to always tell your students what they have to do in an activity or what knowledge they will gain from the activity, instead let the students explore and discover for themselves what knowledge they have gained from them partaking in the activity assigned.

The instructor has taught me all of those things mentioned above and more. If you want your students to gain the knowledge that you want them to; engage them in their prior knowledge. Teachers need to help students realize that they are familiar with the information presented to them; they just need to go back and retrieve that prior knowledge. Another important characteristic to teaching math that I have learned from my instructor is to always allow more room for work. If a student does not understand the material, make the material due a certain day, go over the material in class, and then collect the assignment the following day. If students are stuck and don’t know what to do after seeing the results to their solutions, allow them to come in and spend more time working with you on their homework; teachers need to always have a open door policy when it comes to their students.

Throughout this course I have learned a lot about myself not only as a learner, but as a future teacher. As a learner, I have learned that I do not learn well when teachers tell me instructions of how to complete a task, rather than write the directions on the board. I need those instructions in front of me in order for me to get the most out of my learning. Due to this discovery, I have decided as a teacher to always have my directions written out so my students are not confused about what is asked of them. I have also learned about myself as a learner that I need to have materials and tools in front of me while I learn to help me discover for myself the answer to the problem. As a teacher I have discovered that having tools that students can physically move/touch for themselves, with help them discover the answer at a far better pace rather than just working with paper and a pencil. One final thing that I have learned so far as a learner, is that I work best in small groups. If I am in large group learning, I feel like I am not getting as much out of the instruction because the group is so large. When groups are smaller it is easier to put your two cents in and also collaborate with your peers. As a teacher, I will allow for a substantial amount of time for students’ to work on problems and also collaborate with peers. It is my belief that it is better to work with others because then you can see the thought processes that they went through to come to the solution; it gives you more perspectives on how to solve a problem!