Questions and Answers

At the beginning of this semester I had alot of questions. The questions were more focused on how in the world do i think in a different way than what I was taught. I had to ask myself questions like how can I incorporate the lessons you are teaching us into our own classrooms? How to use more hands on activities in math lessons and how to make math fun for children. Throughout this semester I have gained more understanding on how to make myself think outside of the box, how to incorporate CGI, how to make math fun with hands on activities with all of the activities we have done in class.

Q and A

I liked the new methods that I have learned within this course. I enjoyed how the course stressed that students need to know why they are doing the math processes that they are told and be encouraged to find new ways and approaches to problems. I am just concerned as to how I will implement this in my classroom. I am so used to the traditional style of teaching because it is how I was brought up. This new approach will be difficult because I never experienced it until now. If a student is not understanding through this type of teaching, I feel like there are times where I might need to result to the traditional method.

Personal Concerns and Next Steps

I have learned a lot about how to teach mathematics in a better and more effective way. I think that this method of teaching is very important for teachers to use in their classrooms. I do have a question, though. I plan on becoming a middle school social studies teacher. I like the method of teaching that I learned in this class; I wonder how I can use this kind of teaching for social studies. I would love to teach in this manner and I'm not sure how to apply it to social studies classrooms.

Personal Concerns & Next Steps

A personal concern I have with this class is that so much of this information that we're learning is new to me. I was never taught in this kind of way and I just got used to learning the procedures to solve a problem and never wondering about the concept behind the procedures. I'm a little concerned that I won't be able to implement what we're learning in my future classroom; but I don't want to rely on the old way of teaching. I know my future students will benefit so much from the CGI method of teaching. I think my next step would be to continue learning about this approach to teaching and hopefully practice it while student teaching. The more practice I get with it, the better I will be at teaching in this manner.

New Insights and Implications

Since my last post I have learned alot more about how to teach a constructivist classroom. I understand that as a teacher we must just allow the students to work through the problem and task at hand. With the use of manipulatives, students can explore math and critical thinking. I realize that children can teach their peers by having classroom discussion and encouraging students to try different ways to solve problems. I also understand that children can teach me. I may be introduced to a new solution that had never crossed my mind before. Also with what we have just learned and discussed about CGI, I can look back and remember my own progression through the order of development. By thinking back and being able to visualize my own development, I think I will better understand students movement through these developmental stages.

Questions and answers

One of my concerns for this course and myself is I am worried that I will have a difficult time implementing these consructivist views into my classroom. It seems simple to do as I participate in a constructivist classroom, however I feel it would be extremely difficult to do as the teacher. I do however feel more confident in my ability to teach mathematics than I do about any other subjects. Not to trash other methods courses I have taken, but I have passed those courses and left the room wondering what I learned that will help me as a teacher. Most often the answer to that question is nothing. This mathematics course has not left me feeling that way. My next steps for this class are to take the concepts and more importantly strategies we have learned in class and implement them in my student teaching next semester. I have been placed in a Math room and I am eager to observe my host teacher as well as get going on my own.

Personal Conerns and Next Steps

I have learned a number of different mathematical teaching strategies over the course of this semester. I have been taught that as a teacher you should have your students work through math in a constructivist manner. I believe that this is truly the best way to learn math. From my own experiences, thinking and solving constructively through math has made me a better mathematician. I know that when I become a teacher it is up to me to implement the strategies I have learned in Math Methods into my own classroom. Like Professor Reins has repeated over and over again, these strategies are going to be challenging, but they can be done with hard work and determination. I believe that is my biggest personal concern. I know I have the basic foundation for teaching these strategies, but I am afraid that I will fall back on the traditional teaching styles because of my lack of experience in the classroom. As for the future, I am going to try my best to implement the mathematical strategies I have learned from class. I have become fairly interested in the CGI approach and I believe that this approach will be a good place to start.

Q and A

Most of the math classes I have been in have pertained the normal method of teaching math.. show you the most common way to complete the problem and that is how you do it. From Math Methods I have learned that this teaching style is hightly looked down upon, and I am happy about that. I feel that it is very important that multiple approaches to the same problem are displayed for students. I also think that students should be encouraged to come up with new approaches and really try to look at the problem in a new/different way. I like how this is stressed in our class and although there are times when I feel there are no more possible ways, there always seems to be a hidden approach out there just waiting to be discovered. Encouraging students to explore the possibilities of how the different problems may be answered in numerous ways will also force them to use prior knowledge and relate tasks that they have learned in approach previous problems in order to advance in their learning and develop different learning approaches to problems.

New Insights and Their Implications

This class really opened my eyes to learning math. I always thought of math as something that was really cut and dry you either got it or you did not. And I generally got it so never really struggled with it or worked with it or thought more about it, I just knew what I did. I never really realized that there was so much more in math to explore and so much of a deeper understanding to work with, and to know a couple of main concepts and be able to solve pretty much anything. The instructor and working with my peers through some problems really made this realization clear to me. I have gained a very different perspective of math through this class.

Q & A

Like many, I was hesitant about taking just another math course. However, this math course has been unlike anything most of us have ever experienced. I did come into the class with many questions, such as “How am I going to start out with limited materials and teach math in an innovative way?” and “How long will it take students to adjust to this new way of doing math?” and “How much better are students actually performing?” I have found that there are many schools starting to incorporate this new way of teaching math and I am excited that these students are no longer being drilled for hours on sets of math questions that they will learn how to do after the test.

The way my past teachers and professors usually teach math is by the though, “There is only one right answer and only one correct way to find the answer.” I have had high school and college professors both take points off for not solving the problem right [a missing minus sign, numbers messed up]. I think this is unfair I strive to never do this to my students. I always wanted to know why it mattered about making little mistakes when I knew how to solve the problem and I got the answer right. I do not know if I will ever find out an answer to that, but I hope I never make my students wonder the very same thing.

Question and Answers

How will I find time to do the constructivism method when I am a teacher? 

I have thought about this question a lot because I know that this method is hard to find time for.  I would like to do this for every period of the day, every school day but I know that in the busy world of a teacher, that is not possible.  What I will do so that I can incorporate it a little into my lessons is try doing it once a week, for one or two periods of the day.  Throughout the week I can do discovery learning and provide lots of tools that will encourage the constructivism method.  

I do wonder how all of that will work out.  It is easy to plan for something when you are not actually in the field, with all of the work that is involved with being a teacher.  Once you are actually out in the field many things come up and you may have to cut back even more then I already have on, the constructivist way.  I will have to wait and see if this can become a reality.  

Personal Concerns and Next Steps

My first concern with this course is learning the different strategies and styles of teaching. I was taught the traditional way which has resulted in me being stuck with the procedural way of learning and knowing mathematics. This class has challenged me, and made me think about mathematics in a different way. I feel the techniques we have learned in this class are preparing us tremendously for our future teaching. My next steps for this class are to take the concepts we have been learning and apply them in my student teaching and continue to learn more in the future. I really enjoy this class and I feel it is preparing me for my future teaching career.

Questions and Answers

When I started this class I had a negative view of what math and did not want did not want to have to teach it. I never understood why fractions are inverted when dividing. Why can't we just multiply across? Through the fraction bars and cosine air rods I was able to understand more about fractions and why we have to do invert and multiply. I also learned that pictures and representations of the fractions can help students understand fractions better then just given them a formula. After doing the activities in class I feel better about fractions. I am also nervous that I will not have time to to do CGI with my students and my question is how do teachers fit it into the day? I definitely want to make sure that I am using CGI with my students because I believe that it is one of the best ways to teach math. I may not be able to do CGI with my students every day but I know that I will make a great effort to do CGI with my students at least twice a week.

New Insights and Their Implications

I feel as though over the course of this class I have really come to have a new understanding of mathematics reform. I see where it is coming from (TIMSS studies)and why it is necessary to change how we are educating our students. The only issues I have with the new reform are that I think it is somewhat out of context to compare ourselves to Japan and China because we allow our children to be children, we give them summers and we want them to learn, but our cultures are very different and we cannot expect to "catch up" with those countries just by changing our methods. I think it is worthwhile to reform our mathematics I just hope that it is not expected for us to be even with Japan or China in the very near future. I will be interested to see the results of the latest tests. The other insight and implication I have is that I am training to become a special education teacher. Yes, I will be certified to be an elementary educator as well, but I want to be a SPED teacher. What I am learning in my SPED classes is that inquiry learning is not effective for students who are struggling. Direct instruction has been found to be the most effective for struggling learners. So my question is, will I be prepared to teach the traditional way if that is necessary for my students? I think I will, and I think it has been worthwhile to learn the different methods of teaching. Those are the implications and insights that I have been dealing with lately.

Personal Concerns and Next Steps

I am concerned about teaching mathematics in a constructivist manner. I was taught in a different way and I think it will be extremely difficult to get away from teaching that way. This class has really taught me the importance of teaching in a constructivist manner and that is how I want to teach my future math classes. However, I feel like I am not completely prepared for that just yet. I suppose to take the necessary next steps I will study more about constructivism. I will try to learn as much about it as possible so that I can apply my knowledge to teaching math in the future. I have already learned so much on constructivism, but I feel like it is not enough to prepare me for teaching in that way. I suppose I will just have to give it a try when I get out there and hope that I can teach in a constructivist manner. I hope that I am able to be a good constructivist teacher because I know that students learn much better through a constructivist classroom.

New Insights and Their implications

I feel that I have found myself really learning about some new methods of teaching in this course. I feel that I have maybe been a little sheltered in my previous math instruction in elementary, middle and even high school and college. I feel that a lot of the methods of instruction that I have been exposed to have been very traditional and "one way". I am beginning to see that if I could start over in my math experiences, I would have had a lot better chance in success if I could think through processes on my own without having someone telling me the "one way" to complete the problem. I feel as if I am finding different and better ways to help my students gain understanding without shoving a process down their throat. Even in class periods, I have found myself learning and better grasping concepts by hearing other people's perspectives on the topics. It helps me to work through a process myself before someone tells me their process. I find that if I even see someone else's process first, it impacts and skews my perceptions of the problem and further complicates it for me. I found the videos from the book with the children working through math processes very interesting and helpful also. I realized how great and empowering this method of instruction can be for students. They have a sense of accomplishment and success after figuring out a process on their own. Also, from seeing other people's perspectives, they can change how they are thinking in a slow process to move further in their learning. I feel that our instructor has also been taking a positive role in the classroom, as he is implimenting the methods with us as a class without always directly teaching it. The examples provided from the instructor are helpful, but it is also helpful to work through processes in our own ways to be first hand learners of the method we should be implementing in our future students.

Questions and Answers

I had many questions when this course first began. How will this class help me teach math in my own classroom? How is the constructivist method used in mathematics? Is using the constructivist method really beneficil to students' learning? So far, I have found some, but I believe not necessarily complete, answers to these questions. I have learned a lot in this class about how to teach math. I have also learned a lot about the constructivist method. I can admit that I did not know very much about the constructivist method before taking this class. I have found that it could be beneficial to the student to take some of their learning into their own hands. Trial and error can be a very good learning process for students.

Summary and Synthesis

In my last blog, I discussed the importance of using a constructivist approach when teaching mathematics. In the last couple of class periods, we have begun to learn about Cognitively Guided Instruction (CGI). From our discussion in class and from reading our text on CGI, I have become very interesting in the CGI approach. I think that it is a neat way to approach teaching mathematics and can get students thinking deeper than you would expect them to. I can really see myself implementing some CGI instruction in my future classrooms. I don’t think that I could use it as a main form of instruction, but I do think that it would be a great thing to do one day a week or at least once every couple of weeks. I also think that the CGI would fit nicely into a constructivist based classroom. I really feel that these ideas that we are learning about deserve some consideration when planning instruction. They are very different from the traditional approaches that we are use to, but I have questioned the effectiveness of the instruction that I have received through the years. Thus when I am out in the field, I am going to try to incorporate the things that we have learned in this class. I know that this may not be easy, but I am up for the challenge.

Personal Concerns and Next Steps

I have some personal concerns about they way to use the constructivism approach in the classroom. This is a hard considering in the past I was taught to find the "right" answer. I do have some concerns with finding what is a good manipulative to use in the classroom considering that some of the mainpulatives that I grew up using weren't the best tool for learning. This approach does make sense in teaching math and gives students the chance to figure out the problems than rather having the answer given to them. For the next steps in my classroom I want to try and use the constructivism approach in my classroom so my students can actually learn for themselves. I think if I have a few lesson plans that are more toward this way I will have a good start. I want to find appropriate manipulatives that can help my students have more of a visual concept and understanding of a math idea.

New Insights and their implications

It is very interesting to learn new methods of teaching students. It is very hard for me to understand some of those methods, and try to think outside of the box. It is very hard for me to think outside of the box, and I will be the first to admit it. I was raised in small schools , where we were taught very traditional ways of teaching. I grew up in a small town of South Shore, and Clear Lake, South Dakota, and I do not honestly remember engaging in mathematics like they way are learning to teach our students. I do not remember doing alot of group work, or any activities that actively engaged us in our math assignments or activities. I remember doing alot of worksheets. It will be interesting to see when i am student teaching and teaching in my small school district, if i will use my old ways or if I can be able to think outside of the box and use these new methods we are learning this semester. I can definitely see my self using the different types of blocks to help teach addition, subtraction, multiplication, and division. keep up the good work!

Personal Concerns

I feel as though the class is getting better. The class itself is becoming a little bit easier to understand. I think the sometimes the directions aren't all the clear, but I feel very comfortable with going to Dr. Reins office and discussing any type of concern with him before it overwhelming. I only concern I have is time management. It is really hard to make sure that everything gets done for this class along with any other class. Also I woory about being able to understand the tpoics because it soed take me quite a bit longer to get some of the simplest terms and methods.

Questions and Answers

When I started Math Methods, I had questions. How was I going to effectively teach my future students beings I do not fully understand math? Am I going to be a good math teacher? How will I apply the knowledge I do have about math to my students? All of these questions have bothered me since I have decided to become a teacher. I now realize that it is going to take a great deal of effort and time to become the math teacher I really want to be. In order to be an effective teacher, I am going to have to retrain myself to think in a constructivist manner. This is going to be a lot of hard work on my part but very worth it. I do not want my students to go through life hating math like I have. I now realize that math can be fun and you can teach and learn math in a variety of ways that enhances learning for all. I now feel that I have the knowledge to make myself a better and more effective teacher for my students.

Personal Concerns and Next Steps

My main concern right now is the LPU assignment. I have looked at the information in the notes and I am confused on what all we have to do for the assignment. I feel like I am not sure exactly what needs to be included in the assignment. I have looked at the examples of the past lesson plans that were done and that has gave me somewhat of an idea on what needs to be done. Our group has chosen our topic, but we are not sure where to begin or what to do to even start working on our project. The next steps that I am going to take are to progressively break the assignment down into small parts to try to figure them out and better understand it. Our group is going to meet a couple more times to complete the assignment. We are going to try to finish the assignment this week, so that if we have questions we will be able to ask them. Hopefully we understand the assignment completely so that we can understanding it, so that we do not have stress out over it too much.

Personal Concerns and Next Steps

Right now, as time sits, I am concerned about the upcoming test. It really makes me worried that I can't spend as much time on it due to our LPU and my two praxiss exams on Saturday and the many project we have due next week. Most of my time now is devoted to studying for the Praxiss and trying to meet with my group members.
My next steps to solve these concerns are to meet with my group members a few times this week and try to finish the LPU; leaving time for me to study for my two exams, and the rest of the time to spend on the test. It will take alot of time and energy to do all my homework, but I am certain that I will be able to accomplish all of this, and still have time to do a great job on the test. I will be REALLY happy when this week and next week are done!!!

Personal Concerns and Next Steps

Some of my personal concerns are regarding the LPU assignment. I have looked at the assignment and feel a little confused of what all is required. It seems like there is a lot to be included, which worries me because I feel like it hasn't been discussed in depth during class. However, I do feel like the examples provided did a great job of showing what it should look like when it is completed. I also think that it will be helpful to have it peer-reviewed before the final grade.

My next steps are going to be to work through the assignment step-by-step and just break it down into little parts so it isn't so overwhelming. I also think that this will help me to understand it a little better. I am going to try to get this assignment done as early as possible to give me an opportunity to ask questions and get them answered. I am going to talk to others in the class also, to see how everyone else is doing their LPU and how they are feeling about it. I think by taking these steps I am going to be able to become less stressed and feel more comfortable about the assignment.

Questions and Answers

One of the experiences during class that I had questions on was the assignment regarding Pick's Theorem. I really had difficulty with this assignment regarding how to go about figuring it out. Honestly, the first thing that came to my mind was calling my friend who is a Math major. She ended up being the one to help me out, and I was glad she did. She showed me and a few others how to figure out the areas of the different shapes.

My next question was what I was going to need this information for. I went to class the next day and shared my answer. Dr. Reins told the class that if they had payed attention, then their following homework assignment would be completed. Then it hit me, I needed the previous information in order to know why Pick's Theorem worked. This was a good feeling.

My last question regarding this experience, was when was I going to use this information again. I was answered during the Midterm. I got to show how I understood Mathematics and how this theorem worked.

I was happy with the many opportunities I was given to use the material I learned and explored multiple times.

Summary and Synthesis

Thus far, I have learned a lot about how to better teach mathematics. I agree with the fact that the traditional way of teaching math is outdated and too procedural to accomplish major goals in mathematics, but I must say that I think it will be difficult to transfer my thoughts into a new way of thinking and teaching. It will definitely take time to accomplish major goals for how to better teach mathematics because it is first crucial for myself to become familiar with procedures. This way of teaching math does make more sense to me. I think that it is important for young students to be able to ask questions and be active participants in their learning. I think they should have the opportunity to find answers on their own and make sense of the information that is being given to them. I feel that procedures and always following rules makes students think that there is only one way to accomplish tasks and they should know that for full understanding, they need to learn all about the problems instead of just the formulas. I know that I have a lot more to learn, but I am willing to learn for the sake of my future students. I want my students to be taught the best way that I know how to teach.

Class on 10.21.08

Today in class we went over our quiz questions for Chapter five and six in our book.  The quiz is due tomorrow (10.22.08).  It was very nice of the teacher to go over the questions with us before we took the quiz because in the past not everyone has done well on the online quizzes.  The benefit of going over the questions the first part of class is that now we all know what exactly we need for the quiz, that way we can do well this time around. 

The second half of class we did an experiment.  The name of the experiment was “The leaping Egg (or Ping Pong Ball)”.  You take two glasses and put a funnel in one of the cups to simulate a wine glass, (We decided that wine glasses would be inappropriate for elementary students).  You then blew on the ping pong ball and it jumps into the next cup.  You can measure how far apart the cups can be before the ball gets out of control.  It is a very good experiment for student to understand air flow.  

Summary and Synthesis

Throughout the semester I have learned a lot of new methods of teaching mathematics. The midterm exam was an excellent way for me to put together the information we have learned so far this semester and apply it to teaching mathematics. I feel as though occassionally a method of summarizing what is happening in class, that way you can put a grasp on what you have learned and apply to teaching.

summary and synthesis

What I think so far about this class has changed in a way. I first thought that I was just in no way going to be able to get it or grasp any concept, but I have and that is good. The teaching method that you have adapted and have taught this class in is making a ton of sense now that I see how it is supposed to be done and what is expected. I do feel better know that I have the first test done with and now I know what to expect. I am sure that I still have so much more to learn and am still excited to do so. I think I need to understand more about the whole philosophy but think I will get there.

Summary and Synthesis

I have found as the course goes on, that I am remind myself time and time again that the way I originally thought teaching math or the way math was taught to me is not very beneficial. The course has taught me that there needs to be more analysis and time taken in math by the educator as well as the student. I was used to being given the right way to do a problem and then I was supposed to mimic that way within each related problem. The course has taught me that it is necessary for the student to know why they are using the formulas or why the formulas are the way they are. This is why I also have learned some activities that practice this idea, such as the more recent one where we were to develop a formula for a given shape.

Personal Concerns and Next Steps

This class made me struggle a lot at first. I feel I am still trying to grasp some ideas in this class though but not as bad as at first. This new teaching style is new to us and it is hard to take something in one semester when we have been taught pratically the exact opposite our entire lives. I think that this is a good teaching method from the expierience that I have had but yet I can not wrap my head around it completely. I might know and understand more than I give myself credit for because I thought I had gotten a C on the test but really I got an A. My personal concern is that after this semester this new teaching method will be difficult to take on or escape my mind on how to do it. My step is to absorb as much information from class and find other ways after this semester to keep the teaching method fresh in my mind and also able to use it.

Summary and Synthesis

One of the things that I have learned from this class is that they way I was taught math when I was growing up was not necessarily the right way. I was taught to use the wrong techniques, and that is why math is so difficult for me today. In class now, we are learning how to teach in a contructivist way, which is totally new to me, and sometimes frustrating- simply because it is a brand new method. In the past, I remember having to do a lot of memorization of procedures and formulas; with the constructivist method, there is much less emphasis on memorization. The students will have to do a lot of figuring out on their own, sometimes without seeing a formula first. This gives each child a chance to work out the problem for themselves first. I think this method is better because it gives the students a chance to really dig deep into the concepts of mathematics and figure things out for themselves.

New Insights and Their Implications

I think the best thing that I learned from this class is how to teach differently.  We learned from a study called TIMSS, which showed the United States that we are behind in our way of teaching that we need to do something different.  From this study we found that we need to teach like some of the other countries are teaching which is in a constructivist manner.  We also talked about why constructivism is important in the classroom.  We learned that students and everyone comes to know, with their knowledge.  Everyone needs to build off of there existing knowledge that we have processed.  If I can learn to teach in a constructivist manner then I will be helping future students. 

Personal Concerns and Next Steps

Some personal concerns for me is being able to teach math this way and do a good job at it. I do not always understand what we are talking about or how we figured out to do the problem. I think that this is because I never had to think outside the box when doing math and math has always been hard for me. I will continue to try and understand math, keep up with the readings and work through the problems and hopefully by the end of the class I will have a better grasp of things. I think that this is the best way at teaching math and hope that I will be able to successfully teach my students this way.

Summary and Synthesis

So far, this math class has taught me that teaching mathematics to students is no longer about memorization and following the steps exactly as outlined in the book. Because of studies done between countries, primarily focusing on Asian cultures and the U.S., math curriculums are being evaluated and revamped. Students are now learning in a more constructivist manner, including more hands on assignments and class discussions about problems. The math textbooks have changed in order to facilitate and encourage student learning. Unfortunately, I remember having textbooks with paragraphs of explanations about the problems which would show up later in the chapter; however, once I got to the problems, the time I spent reading was a waste because I could not figure out how to apply the book knowledge to the problems.

I have learned that much of what students gain from their school experience does not stick with them; students may also have their own preconceived notions which interfere with the correct information. This is why teaching math properly at a young age, and continuing with it all throughout their school years, is incredibly important.

Summary and Synthesis

All of the work and exploration we did with geometry and the area of shapes was really interesting. The way the learning was left to us was a good experience to have. We talk about constructivsm and student-centered classrooms in so many classes, but I have never been in one until this class. When studying for the midterm test, it was not like other classes where you go to the class notes and find definitions typed out. This class requires exploration which is honestly a new experience for me. It is a great experience though. As a teacher, I want to run my classroom similar to this because student retain information better when they have to work to find the answer and it's not just simply given to them. One more thing I want to sum up is that the midterm test was rewarding. I was expecting it to be difficult and to much, but because I studied and had learned in the class, I felt great after taking it. I hope my students can have a feeling like that. By working hard and really understanding a concept, assessments are intrinsically motivating.

Summary and Synthesis

I have learned interesting ideas from this math methods class. The most important part for me, is learning about the United States educational system. In class we have learned that the US is behind in mathematics when compared to other countries; yet, the US spends more money than these countries. I found it fascinating to learn why the US trails so many countries. Countries that are ahead of the US have a smaller focus (meaning they have fewer topics to cover) but the ideas they do teach have a higher degree of coherence (meaning the topics are linked together). The US tries to cover everything and the ideas have little coherence. Since the last blog, I have learned more ways to teach in a constructivism manner. I learned more about constructivism; it is a way that students construct their own knowledge about something. It is an inquiry and discovery manner of teaching and math learning. It was nice to have constructivism modeled for us in class. I liked the lessons and how they gave me examples of how to teach using problem solving. I have never been exposed to this much hands on math learning and I believe that this method of teaching is a ton better than the old method of teaching. I believe that if teachers adopt this method in the US, we will see improvement in our country's ranking in math comprehension. Since the last blog, I have become more of a believer in this new method math learning.

Summary and Synthesis

My perspective of this class has changed a lot over the semester. At the beginning I was really worried it was going to be extremely difficult, but now since I am somewhat comfortable with your method of teaching my perspective has become a lot more positive. I still do not know if I completely understand the philosophy of the teacher, but over the year I am coming to understand it more and more. After having the first test done makes me a lot more comfortable as well because I always stress out about the first test the most with a new teacher because I do not know what to expect.

Summary and Synthesis

Overall, I feel completely different about this class now than I felt after the first week of class. After the first week of class I felt as though this class was going to be extremely challenging and overwhelming. I no longer feel that way, however there are times where I struggle to complete assignments fully. I think that is the point...that is the best way to learn. At the beginning of the year I also felt as though the class website was too cluttered with information to provide much help to students, however I have adjusted to that as well and it proves to be an excellent resource.

Summary and Synthesis

My experiences with class so far this semester, have been meaningful but at times frustrating. I feel the material we cover is somewhat difficult, but the way we participate and investigate various activities helps me understand the content. To find what is expected of me for this class, I realize looking at the session notes is the most beneficial. Taking the test on Tuesday also helped me understand that the session notes are the only way of obtaining what is expected of me to know and retain. I now know how and what to do before each class period to be fully prepared each day for discussion.

Summary and Synthesis

My experiences with the class have been all right. I find that the worksheets and the hand outs really do help me study and understand the content better. I have conquered my fear of the chop strategy, and I have found that scale factor is a weakness. Some of the experiences have been frustrating, because some of the topics covered are still difficult to handle. The directions are sometimes hard to follow, but a question is never turned down in class. I feel as thought the questions asked and answered really have helped in my understanding at times. The most important thing for me to remember is that thinking outside the box is OK, and to take risks is important when teaching and learning math.

Summary and Synthesis

To be honest at the start of this class I was very skeptical about the methods that Dr. R was teaching us. I wondered to myself how would I ever be able to teach in a manner that I had never learned myself? Throughout the course of these past weeks though, I have started to come around to the idea of it. I have been learning things that I already knew how to do, but did not know why I was doing them or why they worked the way they did! Essentially, I have always had an instrumental understanding of math and now I am beginning to (slowly) have a more conceptual understanding of math. Already I can see the benefits to this type of teaching. I hope with this new attitude I will have a more positive outlook and learn even more from this class.

Summary and Synthesis

I have learned a lot of information so far this semester in math methods. I have learned a variety of new ways to present and teach material to students. I have learned what constructivism is and how to teach in a constructivist manner. It is important to have children learn to solve things on their own without the equation or formula given to them. Students can explore the problem first to try to develop the formula on their own. When students work this way it gives them a better understanding of how to solve the problem, how the formula works, and how they acheived the answer that they got. By working this way, students are making meaning out of what they are doing. Teachers need to make sure to use the students prior knowledge and to connect that to what the students are learning. We have learned different ways in which to teach scale factor to students. We have also learned different ways to approach problem solving and ways to help students solve problems in multiple ways. Right now we are learning about different polygons and finding the area on them. I have learned a couple of different ways to find the area of a polygon; such as, Pick's Thereom, chuncking the interior, and chunking the exterior area of the polygon. We are also learning the different formulas for the polygons. This class has required to think on my own and to use my prior knowledge to connect to new ideas.

Summary and Synthesis

I have learned so many new and interesting concepts this semester through math methods, such as constructivism. I have learned that it is important to be a constructivist teacher when teaching math because students need to learn how to do mathematics on their own. They need support and guidance also, but helping them to actually do mathematics is the best thing for them. When students learn new concepts on their own they make meaning out of it and learn much better. Using prior knowledge to help construct new knowledge is extremely important and can be used to help students develop new ways of thinking about math. Constructivism is just one of the many different concepts that I have learned this semester. Another concept that I have dealt with is finding areas of different shapes and polygons. I have used my own prior knowledge to help me with finding area formulas and coming up with algorithms for areas of polygons. Pick's Theorum is just one of a few methods that I learned for finding the area of a polygon. I found it to be very useful and easy to use. Throughout this class, I have been required to think on my own and find answers to questions that I did not know before. This entire course is based in constructivism and it truly does help in the learning process.

Summary and Synthesis

Since my last blog, I have remebered and discovered new methods in finding area of shapes and what the definition of shapes are. The definition of a polygon is one of the first things that I learned by doing looking at different shapes and figuring out if they were polygons are not. I also learned different methods in figuring out the area of any polygon. One formula I learned was Pick's theorem which as a pattern toit when drawing shapes on a geoboard. There were also other qualifications for quadileterals and rectangles that I had to remember since grade school. Many of my textbooks had defined a rectangle but they defined it in a way that it was so broad and it could be another shapes definition. I think it is important to define shapes well enough so students understand exactly the characteristics of that shape and what makes that shape unique compared to the other shapes.

Summary and Synthesis

I have learned from my instructor that I am not bad at math but was taught math with all of the wrong techniques. I now realize that I should have been taught math through a constructivist manner. I was always taught math content in a broad and general way. It seemed as though I had to hurry and memorize formulas, definitions, procedures, etc. the fastest way possible just so I could keep up with material my teachers would be teaching. I now know that children need to build upon their prior knowledge in meaningful ways in order for them to gain a deeper understanding of the information that is presented to them. I also now realize that I need to implement constructivism into my own teaching style if I want my students to really and retain most of the material that is presented to them. Implications of learning and teaching mathematics is that it can have some very difficult. This is why it is important for teachers to understand how children learn best.

New Insights and Their Implications

I think the biggest thing I've learned in this class is that the way I was taught math growing up is completely wrong! I always had a very traditional way of learning math; my teachers talked about the new concept for awhile, gave us a worksheet to do, and after enough lessons, tested us on it. There weren't many hands-on experiences provided to us students. When it came time to take a test, we just memorized the equations and answered the questions. After the test was done, pretty much everything we memorized was forgotten. That would probably explain why I'm not very good at math now.

I guess I never really knew that there was a different way to teach the information. But thanks to this class, my conceptions on teaching math are changing drastically! Although there are times I get frustrated in this class, I can honestly say I'm learning so much and actually retaining the information because we're doing hands-on activities and working on constructing our own knowledge. I really see the benefits of teaching math in this manor. I hope to be able to adopt this method in my own classroom. I think my students would really benefit from learning this way!

Personal Concerns and Next Steps

My convern in this class is a personal concern which I have struggled with a lot but even more so in this class. I understand the concepts and the materials you are presenting us but I have a hard time explaining it to other people sometimes and think it could be benefital to me how to explain the whys some more rather then just presenting the right kind of problems. To help students understand the right connections.

Personal Concerns and Next Steps

Some personal concerns that i have are that I am unable to think out side the box. I have always learned a certain way to mathematical formulas and how to problem solve. I was never really given opportunities to be challenged and find different solutions. Another concern of mine is that it is so hard for me to take tests and comprehend and make connections while studying that it could eventually hurt me in the long run. Some steps that i can take into account when i am studying is to try and make those connections to real life situtations, and maybe start studying a couple weeks before the text, rather than a couple days before. It is just very hard to study so far in ahead, when we are required to do some much homework in all of my other classes. I am not complaining, but sometimes school gets a little overwhelming and i seem to fall behind in all of my studies. Some other steps i can take in order to improve would be to give myself challenges and make my self solve problems using different strategies.

Summary & Synthesis

The impact of the recent experiences throughout the Tuesday and Thursday blogs have really opened up my eyes to thinking "outside" the box. Many math classes encountered today in elementary school have made way into the old thinking of how math is run. Through this math class I am in, I have had a tremendous impact on the fact that as teachers we need to guide our students into their own thinking and help them to model and demonstrate their prior knowledge in order to build upon their new experiences in math. The thinking in itself in these classes makes known that there are MANY different strategies and skills used to be able to solve ONE problem. This is effective to the classroom because it allows students to pick and choose and experiement with all in order to find out which problem-solving tactic works for them. This is a wonderful idea, because it focuses on the independent child, and their individual needs! The issues that are brought up in the classroom, with the research encountered through Japan and other countries of the region, look at math a completely different way. The U.S. lacks in math and needs certain progress. This class helps explore dicussions through models, student to student interaction, student to teacher interaction, geoboards and many manipulations that will help us to better understand the methods of teaching math.

New Insights and their Implications

I think that the most important thing that I learned during this first half of a semester is how to teach mathematics in a more reformed way by taking a constructivist approach. By looking that the TIMSS data, I learned that we do need to take a different approach in mathematical instruction in the United States. But knowing a change is necessary and knowing how to make that change are two different things. That is where the constructivist approach comes in. From what I have learned about constructivism during class and from the readings, I believe that this approach is a good step toward reformed mathematical instruction. By allowing students to construct their own knowledge we will be allowing them to again a deeper understanding of the concepts. Also, a classroom following the constructivist approach will have better focus and coherence. I feel that if I am able to implement a constructivist environment for my students to learn in, I will be doing my part in the reformation of mathematical instruction. I feel that the learning that takes place during a lesson built with a constructivist approach mirrors that type of learning we want our students to be having based on the results of the TIMSS study.

What does it mean to "Do Mathematics?"

Doing mathematics means that you are involved in the science of pattern and order (pg 13).  You are always exploring different ways to solve math problems.  You have to look at multiple angles of the problem to see if it is the correct way to solve it.  The old way of doing mathematics is “listen, copy, memorize, and drill” (pg14).  This is one way to do mathematics however the new way is more efficient and helps you learn why you get an answer not just, this is the formula, solve the problem.  The new way to do math is to have the students think of the problems and formulas and start from the beginning.  When you are doing this the students actually remember the process more and understands why something is the way it is.  This is doing mathematics because you are looking at the science of pattern and order.    

What does it mean to "do mathematics"?

When students are doing math they are engaging in the science of pattern and order. The students are exploring and explaining different ways that they used to come up with the answer to the problem. They are making sense of and figuring out the problem. The environment also has to be one where math is not threatening and every student is respected for their ideas.

What does it mean to "do mathematics?"

According to Van De Walle, "doing mathematics" means that students are engaging in the science of pattern and order, and doing mathematics is effortful and often takes alot of time (13). I think that in order to be able to"do mathematics" children should be actively involve in the process of understanding how the problem works, how they can connect it to their lives, and how they can solve the problem in not just way but in maybe several ways. We are taught in school that there is only one way to do a problem, but in all reality there could be several ways to solve the problem and get a probable solution. "Doing mathematics" also means that it shouldn't always be easy, we should be able to dig into it and struggle a little bit. According to Van De Walle there are many verbs we can correlate to "doing mathematics." For example, we can correlate explore, investigate, conjecture, solve, justify, etc (13). When students are engaged in these verbs it is very impossible for them to be passive learners or observers (13).

What does it mean to "do" mathematics?

Please add your comments to this question raised by chapter 2 of Van de Walle. Comment directly to this post about what it means to be involved in "doing mathematics."

What does it mean to "do mathematics?"

Doing mathematics means that one is actively engaged in solving problems. While doing mathematics, one is looking for patterns and order to come up with the answer. When doing mathematics, one is not just following rote procedures that were previously taught by a teacher. By doing mathematics, one is able to understand why they got the answer or why a formula found works in the given situation.

Personal Concerns

Since coming to college math has not been the easiest thing for me, I never used to have a problem with it, it was always a subject that I understood. However, I believe the teaching styles have changed since I have come to college, that they assume we as students know more than we do. So far this class has been easier to follow then most math classes I have taken in college. I believe it is the style of teaching used in the classroom, it is broken down and you give us a way to find the answer ourselves. It makes learning more enjoyable and less stressful.

Personal Concerns and Next Steps

I, honestly, have been a little worried about this class because it's math. In the past, I have never been given a good reason to enjoy math. I've always struggled with some mathematical aspects, so, I have grown to actually dislike math. However, I am doing my best to have a positive outlook for this class. I'm trying my best not to judge this class based on other math classes that I've taken. I have to say that, so far, I am very interested in this math methods class! I am very anxious to learn much more about how to teach my future students. I look forward to learning many different methods of teaching my future students.

Personal Concerns and Next Steps

This class has offered a lot of valuable information. Perhaps almost too much, but I think that is the point. I can definitely see myself using some of the resources, such as the National Library of Virtual Manipulatives. Also, I enjoy the projects because they are not as belittling as other class’ projects, such as coloring and gluing. I also appreciate having the standards being related to what we are doing within the class, mostly so we know how to start choosing them on our own as we will have to do this very soon. I just worry that in the future I will have trouble finding projects and assignments that accurately fit all of the standards. However, having more experienced teachers and good resources will be a great help.
[andrea]

Personal Concerns and Next Steps

Currently my only concerns in the class are figuring out where to find each piece of information and apply it to my learning and future. With all of my other methods courses and classes being on D2L, everything is new to me and is taking time to get used to. I find myself in class trying to pay attention and figure out where everything that was covered was recovered at, however, when I return home to review the information, I find myself confused as to what was read and where to click into. The class has been both informative and stressful. I feel that since we only meet twice a week, there is a lot of information being covered in class each meeting. Some of the information that we began class with, always has the potential to slip my mind by the time I walk out of the door.

Personal Concerns and Next Steps

Personal Concerns and Next Steps
-We are currently rounding out our third week of classes and I feel like this class has already given me a run for my money. I have been given more information in this class the last couple weeks than any of my other courses thus far. I am concerned because I feel like I sit in class and pay attention as much as possible, but yet the information is going in one ear and out the other. I feel like during lectures we don’t get down to the nitty gritty and that’s what I need to feel comfortable with what is important and what is just additional information or resources. I want to be able to listen during lecture and have it all click instantly, but there is just so much information. During class I am finding it hard to pinpoint the important facts to store away into memory. My solution to my problems is to study alot and read the chapters once and maybe even two or three times to understand the materials presented. It looks like I’m going to need to adjust my way of learning and adapt to this new and challenging course.

Personal Concerns and Next Step

I believe that class has been going well so far. I am pretty good at understanding math if I have a little time to look at it. I have encountered both good math instructors and instructors that were so bad that I had to help teach the class. I believe that this class can better prepare me for teaching than the old way of just showing it for memorization and then forgetting about it. I do not have any concerns at the moment. Just enjoying myself. It is amazing that in our world today we have only now come to really look at the standards and how to do things better than we did before.
Adam Jastram

Personal Concerns and Next Steps

The main concern I have with the math class is that I have not been taught to enjoy or like math. I am also not very good at math, so it makes it really hard in this class. The math teachers that I have encountered throughout my math history always just showed me how to do what needed to be done in class. The teachers also just gave me answers a lot of the time instead of explaining to me how to think logically through the problems. Though this class is taught with totally different methods that I am not used to, I believe that I will be able to learn more about math and really enjoy it. Through this class, I think I will be able to think more about math logically and use reason. Also in this class, I plan on really trying to understand math rather than just getting by.

Personal Steps and Next Steps

I have really liked this class so far and it has been very interesting to me. I have already learned a lot more in these few weeks than I have in other math classes on how to teach math. I know that this is a new way of learning and a teaching way that most of us have not been exposed to at the university. It is a bit difficult for me but not too hard that I am not learning. I just wish we maybe had more time to discover things like we have been but also have more time to talk about things and go over the right answer. I like that were are going over the standards because in all the method classes we are needing to look at them more and more and most teachers just expect us to know how to find the right one. In this class we are going more in depth with what to really look for in standards. I have always liked math, maybe have not been that good in teaching it, so I am looking forward to being able to know how to teach it better and to help other people understand it better also. How do you change the standards for special need students? This is one question that I am interested to learn more about in the last couple of weeks. I know that each student is different in their own way and am excited to learn more about fitting the concepts, the individual, the standards and the new way of teaching all together.

Personal Concerns and Next Steps

A concern I have within teaching math, as well as other content areas is the standards. If I am teaching a third grade class math, science, social studies, and language arts, there are a large number of standards I will need to be aware of and make sure I am meeting. This past Thursday in class (Sept. 18) helped me realize that it really is not to difficult. The standards, both state and national, are easy to find, and for the most part, easy to look through. I found the assignment to find the 7th grade math standards for the activity we did in class to not be very difficult. The standard websites have links to go directly to the grade and directly to the strand. Finding the 7th grade standards in geometry and measurement just took a few minutes of reading. Though I am realizing it's easier then I initially thought, I want to find a way in which I can make sure I am effectively finding all standards for every content. I also want to learn a way in which I can sort the standards myself in order to have easier access.

Summary and Synthesis

I have enjoyed learning more about math and can not wait until we talk about the CGI program, or at least I hope we talk about the CGI program. These last couple of weeks we have been talking about the process of problem solving, scale factors, and both the NCTM goals and expectations and the state standards. One of the first things that we did was the handshake problem. This was interesting because we were asked to write down what we were thinking while trying to solve the problem. For me it was harder to figure out why I was doing what I was doing because it seemed to be so automatic for me. I immediately started to solve it by using diagrams but could not tell you why I decided to you this strategy to solve the problem. I also appreciated the activity on similar shapes. This was great because we had the opportunity to work in groups and we also had to try many different things to find out how to enlarge the shape by a scale factor of both 2 and 3. I hope that we continue to do hands on activities that we could also do with are classes when we begin to teach. I have always believed that hands on learning is a great way to teach and learn different things.

New Insights and Their Implications

Prior to this class I had never really seen myself teaching mathematics. If I were put in the position to teach Math I would have taught it the only way I knew how, the way I was taught. However my views have already drastically changed. I have learned about the deficiencies that we as the United States face when compared to other countries. I think that the problem solving approach is a very practical way that I can teach Math effectively. When we began discussing the problem solving approach and how much more time it takes and the amount of time the problems take i had serious doubts. I personally thought that this was going to be a discussion about how we SHOULD teach that was not practical whatsoever. I have been enrolled in classes in which we have been told how to teach but there is no way that we can teach that way and meet goals and standards that have been set forth. It seems now that I am confident that i can use an approach that can increase student learning as well as meet state and national standards.

Personal Concerns and Next Step

So far the class is really interesting to me, and I have learned quite a bit about how math is taught and how it should be, but I do not feel as though some things are gone into depth as much as I like. I know that letting the students explore how they think and what their methods are are important, but at the same time I need to worry about the standards. I feel it is a bit over whelming knowing that there is a new style of teaching, but the standards have stayed the same. Knowing the standards is not going to make students better learners, or even meeting them. However, I think that teaching is about the students and what they can do and pushing them to a new level of learning. The standards are important, but as far as students with disabilities are concerned how do they fit in the learning process?
I think that the standards are important, but implementing them in a way that makes learning fun and meaningful for the students is the challenge and I would love to learn more about different ways to do this. Students should be the center of our teaching process and fitting the standards into that process sometimes seems to be a challenge because they are so unclear.

New Insights and Their Implications

So far I have learned that our Math scores here in the United States are quite poor when compared to a country such as Japan. I have also learned that the United States does not devote more than five minutes to any one math problem. When we look at a country like Japan and find out that they spend fifteen or more minutes on just one problem, we begin to see why the United States might not be scoring well on these tests. I have learned quite a lot of information in Math Methods these last few class sessions, but this is the one bit of information that really got me to listen. Seeing how poor the United States scores on these tests makes me realize that it is more important than ever to be looking for different ways of teaching math to students. We need to start letting the students find ways of coming up with the answers for themselves, rather than just telling them how to arrive at an answer. Obviously, Japan is doing something different and the United States needs to step up and start doing the same. We need to incorporate more actual thinking into mathematics, rather than using the traditional, here's the problem, here's how you do it, and here's the answer technique. If we as teachers don't start changing things, then our students and the United States will suffer the consequences.

New Insights and Their Implications

Attending class these past couple weeks have been a great learning experience for me, because I now know more about the many ways to teach mathematics to students. I was very impacted by the data that was shown to us about how the United States differs from many other countries when it comes to mathematics. I have always felt that we as a country have high expectations for our teachers and education is put on a pedestal which creates a well rounded learning environment for students. After learning about the statistics I have a new outlook on mathematics instruction. All students learn in a number of ways, especially when it comes to mathematics. We as teachers need to be knowledgeable on the content area so we know how to reach our students. This class so far has prepared me for many types of situations that I may encounter as a teacher, and I look forward to learning more about how to teach students about the many aspects of mathematics.

New Insights and Their Implications

I have already learned a lot of new information pertaining to the concepts of mathematics, but the piece(s) of information that captured my attention the most so far in class were the test results. I have always considered the US to be on top and be successful when it comes to comparing us to other countries, but that was not the case when it came to the test scores. Not only were our test scores lower, they were extremely lower in some cases. This was an eye-opener and pure evidence that we need to step it up and start bringing some fresh, new ideas to the classroom instead of the boring traditional teaching styles. I strongly believe that we need to let students understand the different approaches to solving math problems and encourage them to explore different approaches. Students should also be rewarded for showing creativity and developing or experienmenting with new learning styles. I feel students also need to absorb more of the information by going more into depth on the material they are learning. As a future teacher, I want to do more than just simply demonstate the problem and then send homework home with the students. Taking a fresh new approach and a step further into the learning material will make a difference in how the students learn and retain the information!

New Insights and their Implications

Before this class I knew that the US as a country needed to help and improve our school systems, but I did not realize that we needed as mush help and improvement like we do. Barely touching base on something in math or another subject then trying to move on (expecially when you have to build on it) is hard to accomplish and that is probably one of the reasons we such low test scores and improvement in our classrooms compared to some of the other countries. We need to be diving into deeper meaning in our content. Instead of assigning a lot of problems to a student we should only do a few and pick them apart more than try more problems to review and make sure we have the concept down. Instead of doing a chapter a day we should focus on a chapter a week and make sure the transition from one to the other is clear.

So far in math class I have learned a lot.  I have noticed that I really need to keep up on my work, because I think it would be very easy to fall behind.  I have never been all that good in math class, but maybe this new way that you are going to be teaching us will help me understand things a little better.  I am also kind of confused about that standards I should be using, there are the State and National standards, however you said that one was better then the other.  I want to be the best teacher I can be and I want my future students to have the best education from me.  My goal in this class is to find the best way for them to learn.  

We have been taught about shapes, which was a really fun, but confusing activity.  I did get the hang of it when you explained the activity about scale factors to the class.  One of the examples that I will remember is that, if you have a scale factor of 2 and multiply the variable by 2 squared you get the new area.  When I am reading about all of these concepts in the book it is hard to understand, I am glad that we have a class where there is hands on activities to help me learn better.  I have also learned about many different studies that show how the United States is really far behind from the rest of the world in out test scores.  I think this class will be a challenging but fun class to be in.  

Summary and Synthesis

Personal Concerns and Next Steps

A combination of two topics discussed in class creates an area of concern for me when I think about implementing them in a classroom situation. These two topics are the need for reform in the way we teach math and standards. I have always been a little nervous thinking about how I am going to make sure I cover all the required standards in all the subject areas and make sure that my students are proficient in them. Our class discussion about standards has not made this nervousness any better. I have learned that on top of the state standards, I also have to look at the national standards to make sure I am also covering them. Then we have to add in the fact that the method of teaching math that I am most familiar with through my experience as a student is not the most effective and I will have to learn a new method. So now I am thinking not only do I have to concentrate on meeting the standards, I also have to come up with a new way to teach those standards.

This seems like it could really be a hard thing to do, but I know that it is very important to do it. Thus, I really want to work hard so that I can successfully teach all the state and national standards in an effective method of teaching. I am hoping that the remainder of the class will be able to really help me gain some reformed methods of teaching math as well as help me ease my nervousness with the standards. I also know that I will have to be thinking of ways that I can really organize myself so that I can find a way to effectively monitor the standards that I have covered and the ones that I still need to work on.

Summary and Synthesis

I have felt pretty good about class so far. I am noticing that there is a lot of things about math that I need to touch up on before I try to teach it in the schools. I have never been very good at math and it is a little overwhelming to have so much information at once. I think that this class is going to be good for me because I need to start to understand some more content as well as some effective strategies for helping my students who may struggle with math as I did. I keep thinking that I want to find a way that I can make math better for my students than it was for me. I always dreaded math class and I want my students to feel that they understand what is going on and I hope they can always be open about sharing ideas and suggestions. In all math classes I have had, I have felt that I shoudn't say what I think because I don't want to be wrong. I always thought of math as a right or wrong subject, but I am learning that there isn't always just one right way to solve a problem. Just because the teacher shows one way to solve a problem, that doesn't mean that there isn't another way to solve the same problem to get the same answer. I feel that I have already learned some valuable things in class and I am looking forward to what will come in the future.

-Brianna

Summary and Synthesis

Since my last blog I have learned alot about our new math methods and we should teach them to our future students. I have also learned alot about the different kinds of math standards that we are expected to tie into our curriculum. It is a little confusing with all the standards, and i should tie them all into my curriculum. How do i decide whether or not to use the National, State, or the NCTM's standards. I am very focused on my future and all of these standards are a little imtimidating. It is very helpful though to talk about standards and how to appropriately use them.

We also have been talking about similar shapes. I am going to be honest with you, I was so lost at first, but once figured out the concept of similar shapes the concept was fairly easy to understand. If we were to increase the scale factor by 2, all we would have to do is multiply the variable by 2 squared. The activity that we did in class would be very helpful to use in our classrooms. They are given situations, in which they are able to solve and discover their answers. They are also given a chance to explore and investigate their answers, so hopefully this learning process would eventually go into their long term memory and later in life they can make connections through this activity.

New Insights and Their Implications

What I found out most interesting thus far in our classes, was the fact that the United States is lacking in Mathematics. As such a diverse and advanced nation, it makes me think where we are leading our students in the future. Although, in our class, we are learning about the methods it takes to solve these problems that the United States are facing. For instance, the amount of time the United States has for each problem, compared to Hong Kong or China who take 15 to 20 minutes in just ONE problem. In the United States, we compare with just one to two minutes PER problem. We are learning more about the thinking and discussing part of math right now and how each child needs to investigate more deeply or how we as teachers can help provide a deeper understanding for that specific child.
What I also learned was that we should not only be looking at the South Dakota Standards of Math for our students, but we also need to be looking at the NCTM's standards. By looking at both of these types of standards, we will be teaching better and our students will be learning more math in depth. The NCTM's standards take an in depth look at what our students need to be learning for each standard. This is very informative in the fact that it outlines specific cases and examples of what we SHOULD be teaching our students and is detailed in the account of what each specific standard means. These two standards put together a more detailed look at what needs to be taught and a not so vague look at what each one is presented to be.
All of these insights have implications. They are all implicating that as pre-teachers we need to take a better approach at teaching mathematics in our classrooms. This class will help better our knowledge and teach us methods and strategies of math so that we are able to be the best teachers for our students!

Summary and Synthesis

In Tuesday's class we discussed area, perimeter, and scale factor. At first I thought the activity we did was really confusing but once my group started discussing it, I started to understand it and that made me really excited! I know I learned this information when I was younger but I must have completely forgot about it because at first I didn't have a clue what we were talking about. We discussed that if there are two similar objects and we increase the scale factor of the original object by two then the new area for the larger object is original area times two squared. If we increase the scale factor by 3, the new area is original area times three squared. Therefore, we found that the general rule for area in terms of scale factor is Area x's scale factor squared. I thought the way we did this activity was really beneficial to us students. It was a great hands-on experience; we got to actually use different manipulatives and create the new areas with the shapes. I think this is a much better way of learning the information than just reading about it in a textbook!

New Insights and Their Implications

From the few class meetings we have had, I have learned a lot. From my instructor I am learned more about the constructivist approach, which I did not know very much about. I have also learned about the TIMMS study. I think this did a great job of opening my eyes and realizing how to change some teaching habits that may be to familiar. One such habit is that of trying to teach too many different things. I as a teacher need to spend more time on one topic until it is fully understood. I also have learned about the the National and State standards, from both the text and the instructor. These are extremely important to understand because of their high importance in the classroom and because of NCLB. I have also learned about how to use SENTEO quizzes in the classroom. This tool and technology seems like a great thing to use in the classroom regarding not only Math, but other content areas. I also loved the Virtual Manipulatives. These are great for lots of activities and do a great job of involving the students and using a visual to teach the lesson for students.

One of the main things we have been focusing on in class is regarding how to incorporate the standards and use them in an activity. I think this is important because there are certain things that need to be taught and certain activities students are going to enjoy. It is important for activities to be engaging and fun, yet still possess the necessary information that is taught to students. This class has taught me, already, lots of things regarding teaching practices. I think that if I continue to use the standards, think creatively, and be passionate about my teaching, that I could create a very conducive environment to learn in.

New Insights and Their Implications

I have learned a lot of new information in class already. It is hard to take in everything that we have learned. It seems like there is so much information in such little time. One thing that I learned today in class is the difference between the state content standards and the NCTM standards. The NCTM standards have a lot of detail compared to other standards that are too vague. It was interesting to look at the NCTM standards because they have a goal and expectations. Another thing that I liked about the site is that they list activities that can be used in classrooms. There are links that you can click on to learn more about the activity. I have also learned a variety of things from other members of the class. It is always interesting to learn the different ways in which students learn math. Teaching has changed a lot from when we used to be in elementary school. It may be difficult to learn the new styles of teaching and to be able to use them in my classroom because I will be so used to learning from the old ways.

New Insights and Their Implications

I learned from todays lecture about the SD content standards and National Math Standards. These standards are the important to include in every lesson plan to make sure students are learning not falling behind according to NCLB. I learned today that most teachers focus only on the state standards. I cannot see how they can focus on just that because those standards are so broad. Any activity or assignment could fit under a number of the standards. I think teachers need to focus on the National Standards as well. These standards are much more specific and certian activities can align with these standards. The activity we did in class with the shapes fit under the National Standards and the National Standards were much easier to figure out how the activity relates to each expectation of each standard because the standards were so specific. I thought it was interesting that the National Standards were much more specific than the State Standards because previously I thought the State Standards were more specific.

New Insights and Their Implications

So far in this math class I have learned a lot of new ideas. The idea that has made the biggest impact on me is the use of problem solving to teach math. This method of teaching is entirely new to me. However, it makes a lot of sense, even though right now it is hard to learn because I have never been subjected to it. All the research findings in countries all over the world have shown what an impact teaching using problem solving has on students; it surprises me that the United States hasn't adopted more of the techniques of other countries and is still using most of the old methods of teaching. Also, I had never thought about how, in math classes, the teachers try to cover everything. It makes sense to me now why I struggled so much with math: I barely had time to learn the material before the teacher switched to another topic. I have forgotten so much from my math classes because we never spent enough time on any one subject. By using problem solving to teach mathematics to students, students will be so much more likely to understand the material and remember it, in part because they were involved with the material and had a chance to make connections with it. In math, depth is more important than breadth.

Personal Concern and Next Steps

Thus far, I have found the class quite interesting. However, I do have a couple of concerns. The first one is that the terminology is going to go straight over my head and I am going to be lost all semester. Everything seems so particular, for example from today’s class there are expectations, standards, and focal points. They all so sound so similar to me. My problem solving strategy for this though is quite simple, I need to spend more time focusing on figuring out the differences and if I still do not understand them then I need to talk to someone else and get some extra help. My other concern is that I won’t understand the new style of teaching since I grew up learning the old style mathematics. The only solution I see for this is to simply try as hard as I can and just try to adjust my thinking in a different manner and hopefully learn from the modeling that goes on during the class period. Overall, my concerns are not huge, but I still need to address them soon.
*Amanda

Constructivism

I think of Constructivism as Student Directed instruction. Concepts that keep gaining more discussion on. The students are engaged and keep discussions going and getting to the depper meaning of ideas.

Constructivism

Constructivism is building knowledge by using prior knowledge. Through constructivism, students learn new information by building upon their prior knowledge. A classroom that uses constructivism is student centered. A student centered classroom consists of hands-on projects, group work, field trips, etc.

Constructivism

When I think of Constructivism, I think of a building on to prior knowledge. Students learn by connecting new information with what they already know. A teacher who runs a Constructivist classroom tends to focus on student centered instruction. The classroom is hands-on and deals with a lot of group work. Constructivist teaching actively involves students. They are adding on to what they already know.

Jessica Murphy

What is constructivism?

Please comment to this post (by clicking on the "comments" link below), do not start a new post. Write your initial feelings as to what constructivism is to you. Do not ask anyone, look up anything, or read your colleague's comments. It is important that these are YOUR preconceived notions of what constructivism is to you!

Personal Concerns and Next Steps

You may blog about genuine personal concerns created as a result of the experiences in this course.

These last few weeks of class we have been listening to different peers present about different topics. We have mostly followed a progression from beginning number sense to learning about different probabilites. While everyone has done an excellent job at their presentations, I still feel like I do not have a full understanding of the different topics. I tried my hardest to follow what they were saying and complete the different activities. I would have liked a little more. I'm not exactly sure what, but something could be changed. At times everything felt very disorganized. We also nine times out of ten ran out of class time for further clarification.

Using the constructivist approach to teaching seems very important in this class. For me to feel comfortable teaching somewhat in a constructivist approach, I need to feel comfortable with the materials presented in the classroom. I know I am going to have a variety of students and that I am going to have to present a variety of levels to a topic. I will have to review materials and hope that they sink in. I almost feel that there was too much material and not enough time.

Personal Concerns and Next Steps

Now that we are starting the last week of classes this semester, I find myself looking back at the semester. My views on math have changed along with how I will teach math. Especially after conducting the clinical interview, I feel that my views on teaching math have changed. I never realized how huge a process it is. I always thought it was a bunch of memorization. It was either you got it or didn't. I would like to conduct some sort of clinical interview on my students someday. I think it would be very beneficial for teachers to do this with their students. I sure wish one of my elementary teachers would have done a clinical interview. I wouldn't have struggled so much with math my whole life had one teacher realized the way I was thinking about math was wrong or needed clarification!
After teaching a lesson to our class, I have also realized how hard it is! You really have to know your stuff. How can you effectively teach without knowing the material. That scares me. I'm scared I won't be able to teach math in a way that my students will truly understand and comprehend. I know it will take a few years to get into my groove of teaching math and other subjects. But what about those poor students who get those first years of teaching?

Personal Concerns and Next Steps

I have had a lot of thoughts about class today (we talked about the Equity Principle) and I just wanted to talk a little about that topic. It very clear to me that much of what we do in teaching is better "said that done" and one has lots of ideas about what should be fixed or what should be done, but when it comes down to it, it's really hard to implement. I find this to be a struggle within my heart and my head because I have a true passion for helping students get to their full potential. I was watching a program last night about a district in Washington, D.C. and they were talking to a principle in this district that said if he could he would fire over half of his staff. I found this to be very interesting and he said his main reason is because they don’t set high standards for the students (they teach in an impoverish neighborhood) and they don’t believe the students can achieve high. To me that was very upsetting those teachers think and believe that way. In that case maybe it would be a good idea for him to fire them. It is important for people would WANT to help students and who CARE about students and take this seriously to be teachers. It really bothers me to see people who could careless TRYING to become teachers and passing some how... I think it would save our school districts a lot of headache and stress if we weeded out the teachers who don’t actually care about the students and being a good teacher. Teaching is a life changing experience and by that I mean we have the ability to change lives. We can all recall a time when we have had a "bad" teacher and it scars us or helps us, but either way it affects us. I just want everyone to stop and seriously think about why we want to be teachers and do what it takes to be the best that we can be, not only for ourselves but for our soon to be students also.

New Insights & Their Implications

I want to talk about Cognitively Guided Instruction and how much I love it. My internship teacher used this approach with her first graders. So I have seen it modeled several times. When she first asked me about it I was very unfamiliar with it and felt so behind. Little did I know that I would learn about it soon.  The principal asked my field based supervisor to go toa a training workshop and teach it to the other staff in the school. I remember one day she got a substitute and I observed her teaching math to other classes other than her own using the CGI approach.  I watched her use CGI with her students and demonstrate it for other teachers but never really understood until this class. What I particularly like about this approach is how students have a choice for which strategy they want to use in solving the problem. I also like how they can choose to use or not to use manipulatives. What I really like about this program is how all the students come together at the end and a select few will share how they worked through the problem. It helps us as teachers know their understanding of the content and helps kids think of other ways work. One thing that I loved is that my teacher used Math Journals. She would print off a story problem for each child and they would glue them in their notebook. These stories were made fun by using different the names of her students.  She would then ask them to write in marker because she wanted to see their thinking and that it was okay to make mistakes. I would never have thought of that! It is a great idea! I feel so fortunate to have been able to learn about this approach in class and to be able to see it in action. I know that a lot of teachers out there are now just learning how to implement CGI. As future teachers we will be able to go into the schools with the training already under our belts! This is something that we are going to need to know because Math will most likely not be taught the traditional old way. More and more schools are adopting this approach. 

New Insights and Their Implications

I have learned a nimber of things in this class. I think that it has been helpful to see different ways that we can teach the students. I really enjoyed the CGI approach. This approach has really made me think about the different ways I can teach in my own classroom.
I really liked how the CGI approach allows the children to work on their own ways to solve problems. I think this makes this task more interesting to the children, rather than just having the answer told to them. I also liked how they can share their ideas, so they can see what else may work, and also that there may be a better way to solve it than what they had done.
It was interesting to see the videos about this approach. This helped me to see a real example of this, making it more understandable and usable than just reading the text. I was also given the opportunity to see this approach used in a real classroom in my internship. The children really seemed to enjoy using this in their classroom, and using the children's names in the problems really got them interested in the problems. The children also were able to keep these problems in a journal, so they can look back at the old problems and explore other ways to solve problems. I think that this will be something that I can use in my own classroom that the children can carry on with them as they continue through their schooling.

New Insights and Their Implications

What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?
First, I just want to say that I feel that I have a new appreciation towards math in general. I really had a "math fear" for a very long time and this class has helped tear away at that fear. I can't say I love math, nor can I say I love learning about it quite yet, but I think in time I will eventually feel that way. I can say for certain that I have an amazing group of classmates. They have all made me feel like I was part of the group and I feel comfortable speaking out in front of the class because they have made me feel like what I have to say is important. In the past that would have been hard for me to do. So I want to thank you all for that. Also, I have learned so much from all of you and everyday I keep on learning more. Dr. Reins has taught me to become a very deep thinker. I have never had to think so much on a math problem in my entire life before. I like his way of teaching and I think he does a remarkable job doing so. Finally, I hope that I can someday teach in a way that my students will be able to not only know and do a formula to get an answer, but have a deep understanding on the significance of that formula. Plus, I hope that my students will be excited to learn math and that they don't develop a "math fear" like me.

Questions and Answers

Questions and Answers - Questions raised as a result of the experiences and your personal thoughts on a solution/answer to your question. (These could be inquisitive questions, musings, wonderment questions, or future research questions.)
My partner and I have been continually working on our LPU. One question that has come up is how detailed does the lesson script actually get? We have looked at previous LPU's and there is a wide-range. Some students described almost everything and others kept the script concise. How in-depth should they truly be?
I know what I DO NOT want as an answer for this question (ex) "It should be however long you think it should be or take."). The reason being is that this kind of answer will not help me. I am confused by how much actually should be typed into this section of the LPU or what main characteristics this section needs to have. Does anyone have any solutions or suggestions from they have already done on their LPU or are planning to do? Let me know! Thanks!-Kristin

New Insights and Their Implications

During this class we have worked with different types of manipulatives that I have not been in contact with before. I remember working with rods but not the many different types that we have encountered in class: Cuisenaire rods, pattern blocks, etc. I have learned that it is important to provide many different options for students to be able to learn fractions. I do not have fond memories of learning fractions when in elementary school myself but now I think that it would be easier if students were presented with the many different manipulatives and strategies to find the solution to fraction problems.
Reading the blue CGI book has also presented many different ideas to work with in the classroom. I never knew that the CGI program even existed before reading the book. I never realized that problems needed to be categorized even within the category of the type of problem, for example addition having the different types. From reading the book I now know that it is important to have a variety of different problem types and structures. Also, the foundations of a CGI program are things that I would like to be able to incorporate into a math class that I may have in the future. Through this method I believe students would learn best. It would definitely have been better than some of the math classes that I have had.

Summary & Synthesis

During the last month we have been talking about fraction concepts, which is definitely not my favorite subject but I feel I have learned a lot through the class activities. I think many children don't like dealing with fractions because of the way they were taught and they don't have the relational understanding as to why it must be done the way it is. This class has shown me a variety of ways to learn and understand fractions, yet our schools are all teaching in the same manner, it doesn't make much sense to me. I really liked using the pattern blocks and cuisenaire rods to complete those worksheets because I could see how the problems made sense instead of just completing the problem in the way I was taught. I think many students enjoy working with manipulatives but teachers need to ensure that that is not the only way students can solve problems, they need to reach the symbolic stage of working. I was a little confused when using the dot paper to solve fraction problems but I can see how it may be beneficial for some students.
I really like the blue CGI book that we are reading because although I have used these types of problems and can teach it, I didn't realize that each strategy has a name. The error patterns book that we did some problems out of was also really neat and gives some great ideas for helping struggling students. It seems like the past month we have been doing a lot more hands-on activities that could easily be used in the classroom and I feel like I get a better understanding of the concepts by doing these activities.