New Insights and Their Implications

I find that the new insights that we are learning in math methods to be really beneficial towards our future teaching. It almost seems ridiculous that as we were students in elementary school, we were just given a problem and a formula to solve it. Since that was the scenario, we never actually learned the process of how to solve the problem on our own. Then when we were given a story problem and didn't have a formula right in front of us, we were lost and confused on what to do. This is not good teaching at all. If we want our students to really succeed, then we need to teach them how to find a way to their real solutions. I find it really impressive and cool that a 7th grader made up her own way to solve (addition of fractions-I believe it was) and especially that it worked for more than just her problem. I hope I can teach my students to use their own methods to solve new problems in their own creative thinking.

Eled 330-blog 2

The last few class periods have been very beneficial to my learning.  Watching my peers teach and give us other students insight into new material has shown me what a difference it makes to take the material into your own hands.  The worksheets they've given, the examples shown, and working in groups has helped me to understand the importance of teaching multiple ways to my future students.  I've noticed that I work better with drawing things out and my partners have seemed to benefit mostly from manipulatives.  Having both of these options has helped me to see what helps me learn best, but how useful more materials are for others.

I believe that watching other students do their LPU's I have gained a better understanding on how to show students concepts through the use of manipulatives and not simply an algorithm. I also noticed that watching my own peers teach a lesson helps me connect with new teaching ideas. I didnt realize the different ways to teach a math lesson until this class. Manipulatives play such an important role in the learning and I feel that the LPU presentations have been doing a great job of providing examples on how to teach children math.

Summary and Synthesis - Summarize and synthesize the impact of recent experiences, ideas, and/or issues encountered on Tuesdays and Thursdays in class from your perspective since the previous blog.

This past Thursday, we presented our lesson on dividing fractions. This gave us a whole new perspective on our class and how we are presented with new ideas and formulas of the class. I now understand why we have to know the ins and outs of everything that we present in math. It is important to know why concepts work they way they do and how we come to conclusions in math. Presenting the lesson helped me realize why our lessons are presented in a conceptual understanding because as teachers, we must understand why math is the way it is in order to teach students the same. 

Summary and Synthesis

The last few class periods have created a better understanding for me regarding the content we have been covering this year. I really liked the student teaching that occured on Thursday. It allowed me to better understand the fraction work that we have been doing because it was student-centered and the group broke down the steps very nicely. It taught me new ways to teach my students about fractions in ways that I hadn't thought about before. I am excited to see where the other student led teachings will go.

New Insight and Implications

Throughout the time I have been in this class I have enjoyed learning new ways to create connectedness within teaching math. I now see how important it is that students know why they are learning new math skills and where they will use them. Throughout school my teachers did a great job building from one topic to the next but I still struggled with the why question. I always loved math because it made sense to me, but I didn't know why I needed to know the information. Making story problems that are real life situations that need a solution answers that question for students. After the house project, though it was very time consuming, I understood why area and nets are needed. I remember sitting in class dreading the project, but I would rather have my students do that then sit and do area worksheets. As a teacher thinking of good projects that meet standards and are practical is a great use of my time and the students.

Summary and Synthesis

Since my last post, I have learned a great deal about teaching mathematics. My whole life, I have understood mathematics through minimal implications, connections, and relevance. I was taught mathematics in chunks instead of a whole. This teaching methodology is completely off base and needs to be changed. Through this course, I have learned that mathematics needs to be planned in a cohesive manner so that students have an in-depth knowledge of topics that can be used to have full understanding of future concepts. One way that I learned this topic was from the mean activity. It opened my eyes to see that one simplistic concept in mathematics can connect to more complex concepts that will be taught in the future. I also learned this from the most recent LPU. The students who completed doing the LPU did an excellent job at describing the reasons of WHY we divide fractions the way we do and what the purpose is of it. Doing this, placed relevancy of the topic to my life. Since the last blog, we have also learned about area. Area to me, has always been an easy concept because I was given a formula and numbers were plugged in and I received an answer. Through the teaching methods used in this class, I have learned that area is much more meaningful and that it has a great deal of knowledge behind it that can relate to other concepts such as volume. I have encountered some learning issues in this course. My issues arise from not understanding the material in the way that it is presented. This is not the instructors fault, nor my fault. This problem is directly derived from my past teachers approaching math education in chunks. Now that I am learning mathematics in a holistic approach, I am slightly confused because I have never seen it approached in this manner. This teaching method makes sense, it will take work on my work to make sense of the content.

Summary and Synthesis

The past few weeks in math have brought more clarity into the focus of the class. I really enjoyed the student led teaching session on Thursday. I felt the lesson was very student-centered, and the pattern blocks shed some light into the fraction work. The paint project, though tedious, was a real life example that aided the classroom in learning about nets. I definitely feel less lost in the class the further we get into the curriculum, though I wish I had some indication of where I stood, grade-wise in the course.

Summary and Synthesis

This class is really starting to open my eyes about how to teach my future students, and how not to teach. When we were learning about multiplication and division of fractions just recently in class, I learned many new ways to teach my students including activities that I never thought about before. Just because I learned best by writing fractions out on paper, doesn't mean that my students will learn that way, so it was nice to learn about various ways to teach my students.

New Insights and Implications

I found this class to be a little confusing when we first started the semester. I was unaware of how to teach or learn math in the different methods that had been brought up in class. As the semester goes on, it is becoming easier to understand this new form of teaching and learning. I also feel that the LPU projects are going to be another way that we can learn how to teach different areas of math. Having our peers teach us is also a great way to learn.

Summary and Synthesis

I like the idea of having us as a class teaching some of the topics to each other and then having Mr. Reins add in his perspective and then teaching us at the end of the class period. I actually did learn a lot Tuesday from getting information from the group that presented. And then we get to use the items that Mr. Reins uses in his lessons too. For instance the group was able to incorporate in the fraction bars and pattern blocks. This makes learning and knowing how to teach a topic easier.

New Insights and Implications

For me, this class is about learning new techniques and strategies to teach elementary math to students. I feel that I know, generally, how to do math problems, but I lack the strategies on how to TEACH it. That is where I get a lot of insight through this class. For example, a new insight I have learned recently in this class has to do with the use of manipulatives. I have learned that by allowing students to use tangible objects to better understand problems, you are allowing them to work more indepth with the problem and allowing them to see the problem from a different angle. By doing that, they are more likely to remember it. I will use this idea throughout my classroom because I have learned in this class that it is important to have a higher level of thinking in math and it is important to teach my students to value that higher level of thinking.

New Insights and Implications

I enjoy learning new ways to teach mathematics to my future students. When I was an elementary student, I don’t remember learning the way that Dr. Reins has taught us. My teacher just gave us the algorithm and had us practice it. By not learning through manipulatives, it makes it hard for me to understand how to do everything, but when I finally grasp the concept, I know I will be able to teach my students different ways. Also it is necessary for a teacher to know why we use a certain algorithm. This way he or she can teach their students and they will truly understand.

New Insights and Implications

Math Methods has been much different then any course I have taken up to this point. It has encouraged me to think way beyond the knowledge I have learned in the past. I feel the class is very difficult because in many cases I am having to relearn the math as well as how to teach it in great detail to new learners. I do wish that this course could be two semesters long instead of just one so that not so much information would have to be crammed into one semester. Math has always been my most troubling subject. I feel that if my teachers in elementary school had thought me the reasonings behind math then maybe math would have been a more positive experience. I hope that with Math Methods I will learn ways to better teach math and help my future students learn math. My goal is to help students understand and enjoy math. I would like to take my negative experiences in math and build on them to help my students have a more swuccessful learning experience in math throughout school.

New Insights and Their Implications

Learning why we do things and not just how to do them have made me realize the importance of doing math for understanding not just product. Fractions have always been one of those confusing topics but seeing why I flip the reciprocal helps me better understand the concepts and now know why I should teach students not to pass the test but understand the topic. I also have developed a liking for project learning and how learning can be greater from that than just lecture listening.

New Insights and Implications

I'm really excited to be able to have all these new ways of doing different problems under my belt. This class is still difficult for me to understand everything that's going on, but I find I'm understanding the new concepts better and better as time goes on. It's great to be able to find all these new ways for math related problems that I can share with my students. With every child learning differently, these concepts are going to be very useful in my future classroom.

Summary and Synthesis

This math course has been different then ones I've taken in the past. Over the semester, we have learned the reasoning and processes behind math concepts. Instead of learning how to do math concepts, we are learning why we do the problems and how to make connections. Dr. Reins has used a variety of methods to help us learn about connection and how to help students make connections. If, we as, educators don't know the process behind math problems, we can't help our students to discover them or make connections. With the help of manipulatives, students can see concrete models of the problems they are doing. Instead of teaching students an algorithm, we should be using activities that allow students to discover it on their own.This semester has helped me to discover just how important it is to understand the "why" in the math problems we are doing. Knowing these things is important so we can help our students deepen their understanding of math concepts.

New Insights and Their Implications

I never thought I would actually learn an easier method in math when I was in college that I was not previously aware of. I thought my ELED teachers did an okay job teaching me math as a child (although I was never very good at it). Now I'm wondering: is the reason I wasn't very good at math because my teachers were taking the wrong approaches to teaching me? I have always struggled with math, but while doing the area exercises a "light bulb" came on in my head - and I suddenly understood the concepts of finding the area for ANY figure. I never knew the trick of boxing out the figure, then finding the area of the boxed figure, then the area of either the figure or the empty space around the figure to come up with a total area. Although it seems like more work than just plugging in a formula, it seems to make a lot more sense. I also realized WHY area formulas are written how they are. After breaking down the figure to find smaller figures that I was familiar with finding the area of, it made creating a formula and figuring out the area of any figure simple. I wish my math teachers would have provided me with those types of examples when I was in school - I think it would have made my experiences with math much more enjoyable.

After realizing how much of a difference learning a new method now, as a senior in college, can make on my math career - I can now see the importance of explaining the why you do a math problem the way you do to students, not just giving them the way to solve a problem. Having an insight of why you're doing the formulas and problems the way you are truly helps create a much deeper understanding of math that sticks with you; it is much more effective than just memorizing formulas and plugging in numbers to get answers.

Summary and Synthesis

In yesterday's class we learn how to show our process on dividing fractions. I can easily divide fractions given a problem and using the method that the group showed in class. When it comes to teaching students how to divide fractions I am not sure I was aware how to show the process to students. After their lesson, I had some ideas and realized that this may be helpful to me in a special ed classroom. I like how Dr. Reins shows us the manipulatives during his lesson and can give us different ways to teach different concepts. I am going to have to show my students how to get to the answer or break the problem for them to understand it. Especially in a resource room I am going to need as many ideas as I can get because not everyone learns or understands the same way. The class is fairly fast paced and it is still sometimes difficult for me to grasp the concepts right away, but after some extra time I begin to understand more fully what exactly the processes are.

Personal Concerns and Next Steps

Each teacher has a different learning style, and it is always hard to get used to all the different ones. I think this class is completely different than how we have been taught math in the past, which is what makes it hard. When we are learning a new concept in this class I feel I understand it, but as we go more in depth I find myself becoming confused as to the process of how we came to get the numbers or formula we do. I think it is just different than simply memorizing formulas and problems like I have done in the past. The next step would just be to keep trying and working hard! If I do not understand something the best way to fix this is to go in for help and asking questions. Hopefully if I keep applying myself and putting in effort in our activities, the connections will be made!

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.