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.