Personal concerns and the next step

In this class we are learning a new way to show students how to do math. I am finding this interesting but very challenging. It is making me think outside the box and look deeper into the understanding of math. I find that things are being very well explained in the class which, I feel, is the reason for it being so difficult. To take the next step, I think that more explanation is needed for me to fully understand the different teaching methods. This would help because I feel like I am being presented an idea and that is it. I don't understand much beyond that. I think if more time was taken to make sure that everyone is understanding the concept this class would be more successful.

Summary & Synthesis

Throughout this semester, Dr. Reins has used many methods and strategies for helping us understand that the processes and reasoning students are using to solve a problem is more important than the product. The goal is for students to practice reasoning skills in order to create a deep understanding of a math concept, understand how it relates to all other math concepts, and know how to apply the math concept in real-world contexts. Also, throughout the semester we have been discovering how manipulatives and other models can help students further explore, understand, and develop deep mathematical understanding. Particularly over the past few days, we have been learning about how to bridge the gap between symbolic math work and manipulative math work. Traditionally, many teachers will try to use one or the other to help students learn math concepts. Some teachers will only use manipulatives to help students build mathematical knowledge, but when it comes time for the students to show symbolic mathematical work on paper, the students struggle. On the other hand, some teachers simply teach the mathematical algorithms, expecting students to memorize procedures in order to “show” symbolic math work. Today, a group presented a lesson on dividing of fractions. First, the group demonstrated the mathematical algorithm and taught us why we use the algorithm the way we do. After explaining the symbolic mathematical work behind dividing fractions, the group extended the learning by having us use manipulatives to demonstrate dividing fractions. Using manipulatives provided a concrete, visual picture of how to divide fractions. By demonstrating the algorithim and then supplementing the symbolic math with manipulative work, the group was able to successfully bridge the gap between manipulative math and symbolic math. After seeing seeing how well, this process can works, I now understand more clearly what Dr. Reins meant by bridging the gap between manipulatives and symbolic math work. The most successful reasoning, problem solving, and learning occur when both are used, and I believe this is true because it is provides differentiated teaching. The more ways a teacher can activate students’ brains, the more likely students will understand the concept more fully.

Personal Concerns and Next Steps

I see many people who are stating there personal concerns with the overall success in the class. My personal concern however, is about my future success in teaching math in this new way. I understand that building off of a students previous knowledge and having them realize what concept builds off of another concept is really important. My fear is am I going to be effective at teaching in this method since I have not been prepared by my previous teachers and instructors? My overall goal is to be a middle school math teacher or a middle school science teacher. However, if I am not able to teach math effectively like we have been shown over the last seven weeks, I am not sure that I should teach math. One main thing that I think is going to be very helpful is teaching the lesson that our group has picked out for December 1st. I think in order to teach math this way, it is great to see other groups teach in this method, but most importantly get some practice for yourself. Another thing that I have been doing is writing how each concept fits into another concept, and how we have been building off of the simplest concepts. I feel like the type of math processes that we have been learning in class have been allot more fun than the average and boring math problems. I think that in order to teach math in this way, we as the future teachers are going to have to do allot of research and learn from our mistakes. I know mistakes are not the worst things that could happen to you as the teacher, but by limiting them you will be better for the students. I am hoping through practice, research, and hard work I can become very efficient at teaching math using this new method we have been taught since the beginning of the semester.

Summary and Sythesis

Today's class we learned how to divided fractions. The one difference from this class than any other one is the fact that it was taught by my classmates. They used a different strategy to represent the model and algorithm. They taught a process of division of fractions by looking at the algorithm first instead of the model first. I personally thought this way was beneficial because we were able to see how the numbers were divided and made moving into the models a bit easier to understand. Some of the problems were hard to use manipulatives but was eventually seen how after seeing other examples other people did. I did like how on one example they us use our bodies to show the problem, which was very interesting and fun.

New Insights and Their Implications

I was fully prepared to struggle with the concepts and the processes of this class, but I have found this new style of teaching much more difficult to understand than I originally had thought. I realize how important it is for students to make connections between concepts that they are learning. In contrast, I feel that through my education, I have lacked gaining these connections, which makes them that much harder to teach them. I do value the knowledge that we are gaining by learning how to make these connections, but it seems as if there is too much to teach and too little time. I hope that I learn enough about the subject so that, when it comes time for me to teach, I am able to take what I have learned and apply it in new contexts.

New Insights and Their Implications

Throughout the entire semester, Dr. Reins has been drilling us with the concept that "it's all about the processes, not the product!"  Growing up I was always corrected on having the correct answer while being told to show my work.  I could have shown work that had nothing to do with the problem but as long as I had the correct answer I was good.  So when Dr. Reins began drilling us with that concept I began to chuckle to myself because it's something completely new to me.  The whole concept has really grew on me and I now firmly believe that it is indeed all abut the processes and not all about the product.  Krushie Mamma, Brandi, and Amber did an excellent job today breaking down the processes we must look at to divide fractions.  They really challenged the class to look at the problem in entirely different ways and were very successful in doing so.

New Insights and Their Implications

Today a group presented about diving complex fractions. The point was not to learn about how to divide complex fractions but why do you do the processes that you do. A lot of this math class is wondering why do you do what you do and not what is the correct answer. Once students understand the why of the process they will understand the process more. A lot of math teachers do not do this, and it makes students question, why is this important? If the teacher stresses on the importance of the subject material and why it is important in real life scenarios then the students will be more willing to participate.

Summary and Synthesis

Today in class we learned about divided fractions. The difference with today's method was that it was being taught my our classmates. They also used a different strategy to represent the model and algorithm. We learned the process of division of fractions by first looking at the algorithm form instead of model first. I believe that is way was benifical to the class because we were able to see how the numbers were divided. When moving onto the models. I struggled to understand how to represent the concept using manipluatives. Until is was shown by examples to the class I could not see it visually. I did however think that by having the students use themselves to represent the problem was a creative way to show the problem. Students are able to show different ways instead of just using one manipulative. Before I did not really understand how the manipulative can help instead instead of the algorithm, but today it made sense.