Summary and Synthesis

For this first section of the class, I had thought I learned a lot of useful information until it was test time. I put multiple hours of hard work into the study guide and had study sessions with my peers. I feel like I have learned alot from my peers during the LPU's. Their instruction is at my knowledge level and can teach me in ways that I can understand. I have learned alot about making connections and pointing out the process that got me to an answer. These past few weeks have been great and I feel like I am going to start understanding the concepts that will be presented these next few weeks better than I have the previous weeks.

Summary and Synthesis

This week we had a review session and a test. After the test, we had a group present and did very well presenting CGI. I felt that I learned more from group presentations in the class than ever before. The groups are doing a good job presenting the information in a way that makes sense to the whole class. I feel that class should always be like that. On days when groups are presenting I get nothing out of it. Class sessions feel like we are being talked at and not explained to. This is very difficult to learn from because nothing is explained properly enough for me to take the information and put it to good use. Some ways that could be changed is having the material presented in a way that all of us understand. I know this is a new concept to everyone but something needs to be similar so we have a basic understanding when we start. Another way is for the teacher to really help us with our questions. I feel that for me to be more successful in this class we need more help and better explanations of the material.

New Insights and Their Implications

I have learned the more from my peers in this class then I have ever really experienced in a class before. The classroom discussion, the presentations, and group work have helped me to better understand the material being taught. I have learned through other people’s experiences what works and what doesn’t as well as what I need to do better. I have learned that in this class it is important to teach beyond the norm for students. Reaching out to students and having new ways for them to learn is a big deal in this class. I have also learned that being able to justify any mathematical process is a great way of checking your work. All these things are new items of interest for me in the world of math.

Summary and Synthesis

This class has been a very insightful time for me to learn about different ways of teaching kids, and helping them learn new ways to learn connections to different types of math. I've really enjoyed getting to learn all the new ways to help kids learn, and have taken a lot from the class with the different manipulatives I can use in the classroom.

Summary and Synthesis

After many hours filling out the review guide and a couple long nights studying for the midterm, I feel that I did well on the test. By truely learning why you do something and not just how I was able to recall more than normal becasue it was better established in my mind. This completely proves the idea that teaching towards the process and not the product allows students to retain a great rate of the information. hopefully I dont have to eat my words with a bad grade on the test.

Summary and Synthesis

This class has brought out new ways to do math and teach students. The hands on math lessons will help engage the students and allow them to apply knowledge and demonstrate comprehension. It is important that students enjoy learning so they will see math as a positive and exciting subject. Relating math to topics and real world experiences is also important. The way that Dr. Reins has taught this class will allow us to pass this knowledge and method onto our future students.

Summary and Synthesis

For the summary of this first class I would say that I learned alot. This class took alot of thinking, hard work, and more hard work. I feel that this class taught me alot about teaching math and will really help me become a better teacher. Before this class I thought that math was all about answers and steps that were set in concrete. I now know that Math is not about that, math to me is now about challenging students to achieve in their own ways, connect new knowledge, and share what you know with others to try and find new ways of doing things. There were many things that I learned throughout this class, there were alot of things that surprised me, and there were many things that I would not have known to do without this class. I am hoping that this will help me be a better rounded teacher not only in math, but also in other subjects.

New Insights and Their Implications

So far from this class, I have learned a great deal from my peers. I have learned from my peers during the LPU's and from group work and in-class assignments. I have also learned a great deal about making connections from education from my peers. I have learned how others personal experiences have shaped their mathematical understanding and how those can shape my mathematical experiences. From the instructor in this class, I have learned how to go beyond teaching students with an instructional understanding approach and move them to a relational understanding. The instructor of this course has taught me how to teach students not just the how, but the WHY behind mathematics. When we help students understand the why, we are deeming their understanding of the continent. From the readings, I have learned how students learn, and various activities and math experiences that I can use with my students to help the understand the content. I have also learned about CGI and how students need to be given authentic math experiences that provide them with opportunities to use manipulatives, find the answer, and show justification for their process that they choose. This class has taught me that in the past, I have learned a great deal about instructional understanding, but was never given opportunities for relational understanding. The teaching of mathematics in an elementary school classroom is not only important, but essential. It must go beyond the how, and combine with the WHY. The justification process of mathematics is important and gives students that relational understanding.

Questions and Answers

When going through the process of CGI. One question that came up was how is this any different that regular teaching? I understand that students have a variety of different ways to answer questions, but I as a teacher would have my students explain how they came to get answer. However, when I learned more about addition and subtraction. Now, I see how children will solve problems differently. I now understand how CGI, but I believe that I would use a mixed form of instruction and CGI.

Summary and Synthesis

On Tuesday of this week I participated in the study session instead of taking my test. I really feel like this benefited me. Almost everything we did in that study session I did not know how to do before. I'm not sure if it was because it was at a slower pace so that I was able to work through it better and understand or why I was better able to understand the information we talked about better after this study session. Hopefully the knowledge I gained at that study session will really help me receive a better grade on the exam on Thursday. I know what we went over was only a small portion and there is still so much I need to study and think about, but I think going to this study session really helped me. So I should also thank you for giving us the opportunity to have this review session and better understand the information and problems we will need for the test when I take it on Thursday.

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!