Class Reflection

This class has been nothing if not interesting for me. I do not have a day where I do not worry about going to class, nor a day where I leave feeling accomplished and confident about what I was presented. I have been pushed harder and challenged further in this class than any other class I have taken during my time here at USD and most surely have a better appreciation for the frustration I know my future students will be feeling when I am teaching them in the future. Also, I have never been introduced to the idea of the common core standards before this class, and found it extremely interesting as tool to take with me in my future as a teacher. However the most important thing that I will take from this class is all the various materials we were introduced to in regards to better teaching math with manipulatives. This was not a way that I was traditionally taught math, and therefore was an extremely new concept to me that I will most definitely be using with my students in the future.

New Insights

Watching all the LPUs in class has been very interesting for me to say the least. I was extremely nervous about my own groups LPU before watching the previous groups present, however, now I am feeling much more confident in my group and our ability to teach our chosen subject. I was extremely unsettled about this class in general and even more leery about the LPU's before I was able to watch the others perform theirs and in turn feel more comfortable about my teaching of math in general.

Class Summary

Over the course of this class I have learned new methods and ways of teaching math, but more importantly the process of how to come up with the answers. The LPU's have really given me insight to new ways to help teach students, such as the use of manipulatives. The information learned throughout this course will help me as I teach math in the future because I will be able to share with the students the reasons for solving problems the ways we do.

Summary of the Class

Now that the semester is winding down, I thought a summary of the class would be appropriate. We have covered a lot of ground thus far. I can say my mathematical foundation has definitely become more solid. I have been challenged in ways that did at times make me feel uncomfortable only because I had never been exposed to learning/teaching in such a manner. I now appreciate the course and the ways the content was presented to me. (I only wish all my methods courses reached this level of depth).

New Insights and Their Implications

Watching my peers present their LPUs in class has been really helpful for my mathematical understanding. Each lesson provides a variety of different methods to teach a single concept. By observing these lessons I am gaining new insight of a concept; in addition, I am now better able to teach the concept. I realize not all of my students are going to learn the same way. Therefore, by knowing how to teach one concept multiple ways, I am preparing myself to better teach my students. I look forward to the rest of the lessons to come!

Summary and Synthesis

(I emailed this one too you in October and I am not posting it on the blog)

This course has also opened my eyes to a new light of math. After watching the first group present on Thursday, I can honestly say I am excited to see what the rest of the classes presentations are about. Although I felt uncomfortable in the beginning of the course, I am now becoming more confident in math than I have ever been. I can't believe it has taken 16 years of schooling before someone has opened my eyes to the processes behind math. My appreciation for math is definitely renewed.

Place Value

I thought the LPU for teaching place value was a fun and new way of learning place value. Though to be honest, I was very confused at what we were learning to teach our students in place value. I am confused on why we need to teach students the base 3 and base 5 values if we only really use base 10 to teach math problems. Maybe I am just confused on part of the lesson and don't remember being taught any of base 3 and base 5 in my elementary school days. However, I thought the using the manipulatives in the game was a fun way to understand addition and subtraction. It is a great visual and hands-on way to really show your students how to "steal" in subtraction and not "borrowing." I also think it is a better term to use "steal" instead of "borrow" so that students understand that the number column is not getting anything back. I also really liked getting to see using the unit blocks in one of the previous lessons for addition and subtraction. These are some learning manipulatives I would like to use in my future classroom to help explain math as it is very confusing for some students.

CGI LPU

I feel that presenting the LPU was a great learning experience. It is a great way to practice teaching new topics as well as to learn how to be a better teacher. I really liked engaging our "students" with including their names in our catchy poems. It was fun integrating language arts with the poems into our lesson. I believe this teaches students another fun way to play around with math problems. I wish we would have spent more time explaining the definitions of the different CGI problems to help everyone understand them better because I felt our lesson would be a better review lesson for CGI instead of the first time working with it. Also, this brings up the point that not everyone reads the homework readings to understand the just of the CGI lesson and as a teacher, you should be prepared for that.

Summary of the class

This class has been a whirlwind for me. It has been filled with determination, frustration, and success. It has challenged me to think outside the realm of what I have been taught and pushed me to be a better learner than I felt I have been in the past. In past classes, we have been taught materials based on the State Standards. I have never been told about the Common Core Standards until this class. The idea of the Common Core and the information I have learned about altering math instruction to fit those standards is something I will take with me into the classroom. If I had to pick, I would say that those standards are the most important aspects of this class that I will take with me. That doesn't mean there wasn't other aspects that will help me as well. The idea of working in groups is something that I have always preferred in a classroom, and this class has reinforced that idea. Using manipulatives is an idea that can help students understand in-depth concepts but I have also learned that it is important to create a "bridge" between the concrete work and the symbolic work (worksheets). Traditionally, I have been taught math based on worksheets and flashcards. This class has opened my eyes to the possibilities of better strategies and the need to step up the education that I want to give my students.

Summary of the Class

The major insights that I've gained from this class are: a glimpse at common core standards to promote understand for what is to come in the future, a deeper understanding of basic mathematical skills such as finding mean, exploring area, and rediscovering scale factors as well as gaining knowledge of algorithms and teaching through manipulatives.

Overall, I'm happy with my progress in mathematics as well as the grade I believe I've earned. To be honest I was worried about the test, being that it was very comprehensive and covered more material than I found manageable. I was happy to be able to use the internet as well as my notes. This was one of the more challenging classes I've taken this year, but I did learn a lot of new methods.

Summary of the class

I found this class very informational, but confusing and even frustrating at times. The material covered was interesting and was a great refresher of processes that I learned in elementary and junior high. The biggest issue I had with the class was only having one test. There were 120 pages of notes to go over and 32 questions on the exam. I didn't think that the knowledge I learned was well represented in the test. I am happy that you are trying to prepare us for the future, but it was really confusing.

Summary of the class

When I first came into this class I thought it would just be like every other methods class and I will not learn a thing. So I started the class by not really caring what was going on. The fact that this class challenged all of us I think took us all back a little bit too. We aren't use to being challenged and not understanding so much information like for this class. I have no realized how important this information really is when it comes time for me to teach. I wish I would have payed better attention in class so that I could be more familiar with these concepts and then be able to teach them to my students. I feel like these are important aspects to teach to students and very important ones too.

New Insights and their Implications

Looking back upon this course, I really feel that I have grown and progressed as an educator of mathematics. At the beginning of this course, I felt rather overwhelmed. I agreed with new reform based mathematical teaching, but felt like I would never be able to teach in this manner. I didn’t feel like my prior educational experiences had equipped me well enough to become a high-quality math teacher. Because I cannot change what has already been, so I decided to keep an open mind and a positive attitude about figuring “all this stuff” out. I have such a passion for helping students learn and be successful. As an educator, I want to provide my students with the best possible education that I am capable of providing. Students deserve nothing less than high quality, challenging educations, and it is my job as an educator to provide just that. I truly believe that as challenging and frustrating at times this course has been, I believe that I will become a better educator because of it. This course has really helped me see the importance of helping students develop problem solving and reasoning skills. I have learned how critical it is to develop cohesion for students so that they can continue to build, develop, and refine their knowledge about mathematics. When ideas are isolated and memorized, students can’t find purpose of meaning, but cohesion can help students continue to explore, build, and refine. Although I feel that I still need lots of practice with reform mathematics, I truly believe that from this course I have gained the tools to become an effective educator.

ELED 330 Test

We just recently took the ELED 330 portion test in this class. I can honestly say that I studied much harder for this tests than previous tests I have taken, but I could not become comfortable with the material. Even knowing that it was an open book/open notes/open internet test, I was still very nervous. Being that I am an individual that has severe test anxiety, I felt as though many of my "wrong" answers were silly mistakes that I knew exactly what I did wrong once I had the test back in front of me. Even though this test made me very frustrated with this class and my overall grade, I can appreciate why we as future teachers need to take this kind of test to understand the frustration that our future students will be feeling when they are being tested over the same material, and now I can better help my future students avoid feeling the way about the material that I am currently feeling.

Eled 330

Throughout this course, my thoughts about math have gone up and down. At the beginning of this course,  I didn't like the methods Dr. Reins used and I didn't feel as though I was learning anything. As the semester progressed, I was able to see a different side to those methods and I started to like the course more. This course all came down to one thing, "the test" To a lot of us, it was the hardest and most time consuming test that we have ever taken. I walked away from that test having no idea how I did but I hoped for the best. Am I satisfied with how I did, no completely. I hoped for an A but I'll settle for a B. This test challenged us in many ways that we have not been accustomed to. We are used to answering pretty basic questions that require no critical thinking or showing of the process we used to get to that answer. After taking the test, I realize the importance of this course. I realize that as future math teachers, we need to understand the processes that are required in order to effectively teach a certain concept in math. We must know how to explain this process and also be able to teach it so that if children are ever tested like we just were, they will be able to fully accomplish a task that we couldnt. I understand the methods of this course, and are they the most comfortable? no, but if this is what the math world is coming down to, we must accommodate and learn to like it. This course has definitely taught me many different strategies and methods to put forth in math and I can now feel accomplished for all the hard wor put towards this course.

ELED 330 Test

The recent test we took was at the higher level of thinking. I studied quite a bit for the test yet I did not feel 100% comfortable with the material. When the test was in front of me I seemed to struggle to come up with the answers. The part that was the worst for me was time. I felt very rushed even after staying fifteen minutes late before I turned in my test because I had to get to my other class. Even after turning the test in, I had no idea how well I did on it. This test did make me feel like a fifth grader who was getting overwhelmed while taking a hard test. As a teacher, we need to make sure the students are well prepared for exams by giving them study strategies as well as ways to use the resources that are available.

Test

Throughout this class I learned how to teach mathematics differently. When studying for the test, I went over the entire study guide and filled it out. I also looked over my notes and tried to work out problems. Since I was gone for a week it was harder for me to figure out how to work out what I missed. Going to the review session was helpful. Going into the test I wasn’t a 100% comfortable with all of the material, but I didn’t know how else I could study. After taking the test, I was exhausted. I haven’t taken a test that made me think that hard before. It felt like I was taking the ACT again. Overall though this course, has helped me develop a better understanding of teaching mathematics.

Summary and Synthesis

In the last few class periods, we had groups of students teach us. I have never really learned from other students teaching, but these last few times I have learned and understood the concept. Also I feel like I understand these topics better than I have in the past. When peers teach each other, I feel like they are able to get on our level to help us understand.

Blog 4

After taking the test I felt like I had been deflated and I remember you said that this is what a student feels like after taking a standardized test and I completely agree with that statement. I want to be sure to help my students as much as possible so as not to feel this way after taking an exam.

New Insights and Their Implication

The double number line was a very interesting subject to learn about. It made sense to use it for something like shopping for the "best deal".

New Insights and Their Implication

CGI addition and subtraction was actually a lot easier than I thought it was going to be and I learned that I don't necessarily need to be scared of something I don't know about yet. I didn't want to get the CGI LPU because I had no idea what it was but it turns out it was relatively easy material.

Summary and Sythesis

After taking the exam I felt like I did the best I could. I had applied everything that I remember from lectures and interpreted it to the best ability I could. Some parts of this exam was challenging that definitely had me thinking hard. Then seeing the results of that exam hit me in a different place. Thinking that "wow" I felt completely different opposed to how I did when I finished the exam. I thought that I have done better than what I have received but that could have been true if I would have prepared better. I am still happy with the result because it could have been worse but I also believe that it is quite hard to study for math besides just memorizing equations. I also have a better view on the course and how it is taught. There is quite a bit of logic behind it all.

Eled 330-blog 2

Taking this class has been very frustrating at times and not so pleasant but I feel that I have learned a lot in such a short amount of time. Sometimes it is overwhelming, but I have remained confident and optimistic. The class has given me the opportunity to expand my thinking no matter how much or how little I already know we can always learn more. I think that the LPU's have been beneficial for me because it allows me to be engaged with others and gather information together with different input. I also feel that the presentations have been helpful for me because not only do I get the chance to present, but I get the chance to observe. I feel that this is important as a future teacher to take what I have learned and some how incoorperate into to my classroom.

#3

I thought that the test was at the higher level of thinking. I wasn't sure for the most part of the test if I was completely sure of my answers. I didn't like the feeling of not knowing a for sure answer on some of the questions. I am generally a student that feels confident when taking a test, however I didn't feel very confident when taking this test. I felt like I studied, but wasn't sure at times what I was really studying. I thought that the multiple choice were not at all hard in any way, but the other parts of the test were at times confusing for me and I wasn't real sure on what was expected of an answer. More times than not though I thought I was doing fine, but the reflection of my grade showed that I was more unsure than originally thought. As a teacher it is important that we make sure that our students are making connections with what they are being taught and as a teacher I plan to use plenty of strategies to help ensure that my students have all and any resources available for them to use.

ELED 330

After taking the exam, I feel that I have grown during this class. When the class first started, I felt as though the information was very abstract and difficult for me to understand. I did not think I would ever make sense of the way that Dr.Reins taught us. As the class progressed, I changed my state of mind and began thinking in a different way as the student. I also feel that through the LPU's I have learned a great amount on how to teach students in a way that is inquiry based and project based. This is definitely a class where I have learned from my peers. Before the test, I spent time with classmates going through the study guide and studying problems and concepts taught in the class. Although a lot of topics did not make sense to me at first during class, reviewing them with others and hearing my peers talk about these concepts really helps me to make connections I need to make. The exam we took last week was by far the hardest exam I have ever taken in the Ed School. I realized that by studying hard and conversing with peers about the content it was possible to succeed and grow. I cannot say that I have felt this way in any other class in the Ed School. Overall, I do not feel that I am super confident in my knowledge with how this class is taught, but i can say i have grown as a student through the challenges this class has to offer.

Summary and Synthesis

All I could say when I finished taking the test was "wow."  The test was very challenging and required a great amount of deep thinking and sense-making.  I felt like I was prepared to take the exam because I went over the study guide countless times and read the chapters/readings that were assigned to us.  But after taking the test I realized that the study guide wasn't going to help me on the test because it was all about the connections and sense-making.  This was very different from every other exam and I believe that was a reason why I thought it was more difficult.  This test, however, taught me so much from simply going over the exam in class.  When I saw my mistakes, I could go over the thought process I took to find the answer and compare it to the thought process I should have taken.  This helped me because I can use the information I gained to become a better test taker and teacher.  As a teacher, I must require my students to use deeper thinking to develop a deeper understanding of the material.  I must also be able to show my students the connections that need to be occur in order to develop the deeper understanding.

Eled 330 Test

I thought the test was very challenging.  I remembered learning and at least seeing all of the information that was on the test, but it definitely challenged me in my higher order thinking.  In class today (Nov. 8) you mentioned a comment that this is exactly how a 5th grader would feel during a standardized test on material that was challenging to them.  This really impacted me.  It made me think back to when I struggled with math and how I brought that same math anxiety into this class.  I hope that I continue to remember this feeling when I become a teacher so that I can prevent any student from feeling this way.

Summary and Synthesis

Since we have now all taken the exam, I feel that it, as well as preparing for it, is fine to blog about. I usually have a pretty set routine when I study for exams. I read, complete the study guide and review the information until I know it backwards and forwards. I tried to use the same strategy with this test, but soon found that I would need a different approach. For example, I usually would rather do a study guide myself before asking for help, but for this study guide, I felt that collaboration was needed. I usually study alone, and for this test I was studying with other people. For me, and this material, it seemed like there were some questions that I needed to discuss with others to get their take on it. It was helpful to get others' perspectives to widen the way I thought about any one problem. Overall, I did think the test was a little more difficult, but I think I will retain the information that was on this test better than others because of the way I studied for it.

Summary and Synthesis

These past few weeks have definitely been an eye-opener for me. Math has always been my favorite and best subject, so I never really worried about having to teach math. It comes naturally to me and I feel comfortable with it, so I just always figured teaching it would come naturally to me as well. After spending this last few weeks talking about manipulatives and different ways to make students think less about the answer and more about the process, I am now developing doubts that so many of my peers (from college and high school) have experienced for so long. I understand the importance of the concepts we have been talking about as well as the necessity for teaching reform mathematics, but I am feeling more frustrated than ever before and I can feel myself shutting. I suppose this is beneficial in the long run because I can now understand how my future students may feel when they aren't understanding. I have full faith that I will get a grasp on this way of teaching eventually, it's just hard to think of math from a different perspective.

Summary and Synthesis

The past few class periods we have been discussing CGI and what that means to the teacher and to the student. It seems as though a teacher can be doing CGI and not even know it, if they do not know what it means. CGI can be very beneficial to the student and to the teacher. Group presentations are also beneficial to our class as a whole. Sometimes students learn more from their peers.

Summary and Synthesis

After doing research on my presentation for CGI math (addition and subtraction) I gained a deeper insight to the way students comprehend and mentally solve math problems. Students use a variety of manipulatives, drawings, and other hands on objects to help compartmentalize areas of a story problem. The videos that were shown of a classroom using CGI math were helpful because it is easier to see CGI math being done hands on rather than having the concept explained verbally in our class.

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!

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.

New Insights and Implications

I am a notoriously poor math student. In high school, math was constantly the one class waging war against my GPA. Naturally, I dread all things math when it comes to college. This class is nice because it breaks down mathematics into coherent pieces which all fit together. I am beginning to develop a view of math in which all of the elements are interconnect. The activity we did with mean and standard deviation really cemented that concept. I think I will always be slightly uncomfortable with math, and there is no way I would be qualified to teach it at a high level, but at the very least I am confident that through this class I will build skills necessary to teach it at the elementary level, and convey connected ideas to students.

New Insights....

Before taking this class, I was very nervous about the course. Because I have always struggled with math, I think I have began to build a wall up. I am looking forward to continuing to learn how to break down the concepts of mathematics so that I can be confident when it comes to teaching effectively. I have learned a lot through the readings in the text; however, for me I have gained the most out of the class lectures. So far my favorite activity was estimating the mean using the rulers and washers. Because I am a visual learner I found myself really connecting and making sense of the task at hand. I think the biggest challenge I am having in this class is to think simple. I often find myself making the task harder than it needs to be.

Personal concerns and the next step

This class has already been a challenge for me.  I have always had a little math anxiety and I wasn't looking forward to coming into the class.  What I have been learning so far has been very interesting.  I am having a hard time applying it as a student and how I would be able to explain this material to my own students.  I think it is such useful and helpful information that I would love to get better at it.
I think the next step with this is just to work harder and go in for extra help and questions.  I want to be the best teacher I can be and hopefully bring my students to love math.  I do not want students to feel helpless in math

New Insights and Their Implications

Prior to taking this course I considered myself good at math. I have always succeeded in it and have always understood how to get the answer. This summer I took both math concepts 1 and 2 and aced it with very little effort. Since I have been in this class I have realized that I am good at plugging in numbers but not good at understanding why I did what I did. I have been deprived of exercising my critical thinking skills. I have had some of the same problems in this class that I had in math concepts and could not figure out how to come up with the answer without following procedural steps. My implications for teaching and learning math are to first try and understand the problems as a whole for myself and then allow my students to come up with their own techniques for solving problems and to provide them with that foundation that I was never introduced to.

Personal Concerns and Next Steps

It is always difficult to transition from one form of learning to another. I feel that in this class, we are doing the opposite of what we've done for so long and it's difficult to get the proper mindset to make the change in thinking. My concern is that I'm not fully connecting the material we learn in class. I get the main points and how we get solutions, but sometimes I can't quite correlate how those steps come together in the end. I think that it is great that this class is based upon us working to find our answers rather than doing things from the book, but it will just take time for me to switch gears, and I'm afraid that it will take too much time, and I'll miss out on important information. It's just not quite comfortable learning for me yet, but it will get better!
I think the next step with this concern is just to work a little harder, participate a little more in class, and seek help if I feel I don't understand. If I put more effort into the activities, I'm hoping the connections in material just present themselves! I'm confident that I will overcome these issues, it just may take time.

New Insights and Their Implications

At the very beginning of this class, I thought I was in way over my head and was unsure of what was happening. Now that I think I have understood this method of teaching, things are getting better. I like the different activities we are doing and class because we are able to do learn them and actually do them so we can teach our students some day. I have realized that this teaching method is completely different from anything I have ever learned, and I am excited to see where it takes us. I enjoyed teh laft activity and finding out how to teach students about standard deviation. Once we went over how to do that everything started clicking in my head about how to reach students with these concepts. In this class I am starting to learn something unique and different from most of my other method courses. Sometimes I still feel confused, but I just allow myself time to think outside of the box and then I can fully understand these concepts and activities. I am anxious to see what is to come next for this class and to get started on our projects.

New Insights and Their Implications

          Starting this class off the first  couple of days I was a bit intimidated at how we were going to be learning to teach math. The style of progressive learning and teaching the understanding of mathematics rather than the memorization of formulas is foreign to me. However, after working through and completing the scale factors and areas assignment I can see how this style of teaching math is much more beneficial for students. In our math content courses, I struggled with the concept of similar shapes and their ratios, after going through an assignment that dealt with the same concepts I was surprised to see at how well I was able to learn and understand the math behind scale factors, similar shapes, ratios, and so on. The math became much more clear to me and I was also able to reflect on how I thought about it before and what mistakes I made in my previous thinking. I am still slightly uncomfortable with the style of teaching math this way, but experiencing it as a student has opened my mind up to seeing the many benefits it has.

New Insights and Their Implications

I have never been one who enjoys math, and it's by far my toughest subject. Growing up I always remember doing worksheets or problems out of a book. My math teachers taught a concept and then we did a worsheet or x amount of problems out the book. Basically I was memorizing concepts, just to get through to the next lessons. In this course I have found how important it is to help students make connections. I don't believe I ever learned how to make connections and I think that is why I have struggled through it. Helping our students make connections will help them to succeed in lessons that follow, since in math you are always building on previous knowledge. I have also found in the course that when we allow students to do hands on concepts, not only will they be more willing to want to learn about math, but they will also be able to make stronger connections. Learning math and practicing math through worksheets is okay, some of the time, but it should be mixed with real life problems and activities.

New Insights and Their Implications

Throughout elementary and up to my college career, I have always enjoyed math and have been pretty successful. I think very linearly, so math has always seemed to fit into my ways of thinking and understanding. All throughout my schooling, I was pretty successful at memorizing formulas and knowing the procedure for solving them. On the contrary, my husband is a person who does not enjoy math and has struggled with math his entire life. He has worked very hard to try to understand math, but has never been able to understand why he struggles with math so much. Throughout our college career, I would always try to help him with his math homework, and he would ask me questions such as "Why do you use this formula?" or "Why does it have to be done this way?". I was never able to answer his questions because I simply didn't know the answer. All I could do was show him the procedure for solving the equations or problems, and all I could say was, "This is just how you do it. I don't know why it is this way, but you just do it." After talking about and beginning to understand reformed mathematical teaching, I feel like I was "ripped off" throughout my education. Had I been taught this new reformed math, I would have been able to answer why you use specific formulas or why you solve things the way you do. I may know how to solve a math equation, but in many cases, I have no clue as to WHY you use certain formulas or WHY you solve certain problems certain ways. I truly believe that had my husband been taught with this reformed style teaching of mathematics, he would have never struggled with math. His brain is one that functions solely off of meaningful connections. If he doesn't understand how a concept is related or why it is important (for example a formula taught in isolation), he doesn't grasp it. His brain NEEDS coherency, meaningful connections, and meaningful context to build understanding and knowledge. Having realized this, I am super excited about figuring out how to effectively teach this reformed mathematics to my future students. I have come to realize that reform taught mathematics can have far reaching affects for students. Although, I don't feel anywhere near proficient at this style of teaching yet, I believe that if I can master this method of reformed mathematical teaching, my students will not struggle with math because they will understand how all mathematical concepts are linked together and they will have built their own knowledge in a meaningful context. Throughout this semester, I look forward to learning how to execute this style of teaching and learning how to develop lessons that make meaningful connections for students.

Personal Concerns and Next Steps

So far in this course, I have learned to look at education in a whole new light. Unfortunately, not all methods courses that I have taken have provided me with this same insight. Since, I have not been educated myself in the approach that Math Methods takes, I feel somewhat behind. I do my best to keep up on the readings, but when understanding the problems presented in class, I seem to struggle. I do not feel as if that is this course, or the instructors fault. I feel that in order to succeed in this class, I as a student, need to learn from this new teaching style, but most importantly, I need to learn how to incorporate this teaching into my own lessons. If I can grasp the basic concepts and style and apply it myself, I will be able to better demonstrate and aid my future students. So far though, I have learned that I should not just sit back and remain confused, I need to be an active participant and be more vocal with my concerns. Although, my personal concerns may be few, I do think that I have a great deal of construction to do with my own personal teaching style to succeed in this class and as an educator.

Personal Concerns and Next Steps

When I first entered this class I was very concerned that I would not be able to understand the concepts because of the 'new' way of thinking we are supposed to do. Math is not something I have ever been very good at so when I was told I was going to have to forget everything I already knew about math and learn it a different way, I was not pleased. I am starting to become more comfortable in the class but I'm still not sure I am learning the material with a 'new' of thinking. I wish I had a more open mind about math but it is really hard for me to enjoy this subject. I hope that this class gives me the ability to look at math with fresh eyes. Maybe if I learn how to look at math with an open mind I will enjoy the subject more. Hopefully, if I begin to understand the subject better I will reflect that onto my students in the future.

Personal Concerns and Next Steps

For the most part, I understand what is going on in this class. The reasoning for this teaching style is completely understandable, and I wish I'd been taught this way. It is however, difficult for me to catch on to what's happening and what is due each day, because I wasn't taught with this teaching style in all my years of education.

One thing I think would make it easier to understand what is going on in this class is if there were a syllabus or schedule that was up to date and said exactly what is due for the next day. I do understand that we are slightly behind schedule, but whenever I look at the syllabus, I get nervous because I have no idea what needs to get done, what's actually due, and activities we do not need to do because we've not arrived at them yet.

I think as class goes on, I'll be able to figure things out, and have a better grasp as to what's going on. I'm confident that I understand the content for the most part right now, it's just the scheduling and due dates that I need to figure out.

Personal Concerns and Next Steps

Although I'm not the best with math (but I'm not completely horrible at it either), I am a little concerned on how to succeed in this class. This class has taken me out of my comfort zone many times when it comes to math, and I think it is because it we are looking at teaching and learning math in a completely different way than I was taught up to this point. As for short term concerns, I am worried about succeeding in this class (I feel a little lost - like I'm not completely "getting" it or thinking outside of the box enough). For the long term, I am very concerned with teaching my students math in this new reformed way. I'm worried that if I do not grasp the topics and concepts enough in this class, I will not succeed in teaching my students math (and will further confuse them instead of help them). I know it is usual to feel uncomfortable at first with something you are not use to, so I'm hoping that in a short while I'll start catching on and feeling more confident in my abilities to succeed in this class and as a teacher.

Personal Concerns and Next Steps

I have a hard time following what we are supposed to do for this class. Many times when I come for class I wonder if I have everything prepared. So far I have had very good luck with keeping up, but at times I think I am missing something. I understand that you have three classes in a row but there are assignments and suggested materials, and its hard to tell what you want prepared. My next step is to figure out your style. I may be over reacting and I just have to get used to how you run the class, but for now I am very nervous that I will miss something. I look forward to class everyday and hope that I am fully prepared. I look forward to the rest of the semester and can't wait to learn more about constructivism in math!

Personal Concerns and Next Steps

I will be straight forward and say that math is my least favorite subject. I have never been good at it and it has ALWAYS been a struggle with me. I have just always found it hard to connect ideas and honestly, just be interested in learning it. I find it very hard to believe that we will use any of this in the future (besides teaching it to other students), so I have always found math as almost pointless. This class, however, is unlike any other math class I have taken. It is more based around "constructivism" instead of instuction and plugging in things to a formula. If I do not understand something in math, it is very easy for me to give up and not try. This has always been a problem of mine with this subject. My steps for this class is to try my hardest to understand what we talk about in class and truely make sure that I am on the same page as everyone else. It is just hard when everyone in the class understands and you are the only one that is clueless. I will, however, make a better effort in approaching this subject with an open mind and will make it a point to come in for help if I truely am still lost in the subject matter. All I can promise is to try my hardest and we will see where that goes. Fingers crossed!

How has this course changed or not changed your perceptions of teaching math?

This course has so far completely changed my perceptions of how I will teach math to my future students. Thus far, I never questioned how I would teach math because I never before saw a flaw in the way that I was taught. However, being that this course requires me to think so much more in depth than I ever had to in my elementary, middle, or even high school days, I have realized that I was probably not taught the best way. I personally like the new way that I am being taught to teach, because I think that it is a better way for my future students to learn. When students need to use their peers and their own mind when learning, I think that the actual learning process is then better than just having a teacher stand at the front of the class and talking about concepts. This new way of teaching will in my mind be better because it allows students to connect concepts instead of just move on front one concept to the next.

New Insights and Their Implication

I thought that this course would be way over my head at the start of the semester, but I enjoy doing activities and problem-solving strategies that are still challenging but still have a relation to teaching elementary students. I am looking forward to the rest of the semester and though the two big projects will be challenging they will be beneficial and a good way for us to stay responsible and hold leadership for ourselves in this class. I have especially enjoyed the 'laft' activity in relation to the optimal mean concept because I had no idea we would be learning about standard deviations and understanding formulas by simply estimating a spot on the 'middle' of the laft where a certain number lies. These situations will help us instruct our future students and be able to find ways of explaining various reasoning strategies and math implications in ways they are familiar and comfortable with. I believe this course will be still a challenge for me but it will be good to be forced to take the type of math we are learning to think about it as if I would be teaching my class someday!