New Insights and Their Implications

I have learned many things over the first couple of weeks of class. I first thing that I learned is that we need to start teaching math to our students in different ways. We cannot just give our students the answers and expect them to memorize everything. We have to allow our students to problem solve and find solutions on their own. By doing this, the students will better be able to retain the information that is being taught to them. It is good to have a student-centered classroom and allow the students to have hands on experience and be part of the discussion in class.
The next thing that I learned from the first couple weeks of class was how to read and interpret the South Dakota Standards. We have to align our lesson plans with the SD standards in every subject. That use to be the part I hated about writing lesson plans. I could never find a SD standard that matched my lesson well enough. It is good to know that there are the NCTM expectations and the focal points that are available to that you are better able to interpret the SD standards for the subject of math.

New Insights and Their Implications

Over the past few weeks I have learned a lot about new and improved ways to plan and teach math. When we began talking about national and state standards I was like here we go again. Having completed lesson plans for many classes in which we had to list the standards we were covering I thought I had a good idea of what they all consisted of. But I was wrong. Over the past few class periods I have started looking at standards and the websites we have been talking about much more closely. The one area that really left an impression on me happened today in class actually. While we were looking at the content standards for math I was very impressed with what the teacher resources sections all entailed. Never looking at that before I just figured it was a list of other websites we could explore if we were confused with the standards. Little did I know it consisted of lesson ideas that could really help students. With tons of standards to cover it can be difficult developing lessons. Now knowing there are ideas directly related to the content standards I feel much more confident in developing lessons if I ever get stuck and am not sure what activity I should engage the students in. This could be very helpful in the future and I look forward to learning much more in class.

Personal Concerns and Next Steps

One of my concerns is using the standards correctly and aligning them with and activity that will benefit my students and engage them in learning, but also align to the standards. I think that the discussion we had in class today about aligning to the standards and using the many tools that are available to teachers will help greatly when trying to match assignments to standards. I am still concerned and curious about a couple of things. The standardized tests that we take are aligned to our state standards, what happens if the tests change and they match the national standards, but no teacher is covering those because they are not "supposed" to. After the discussion today I am worried that many of the students either aren't being challenged enough according to our standards or many teachers are still teaching to the test/text and finding the closest standard and matching it to their lesson.
As a new teacher I feel that I will use both sets of standards because I realize how important it is to include both. This will take more time when preparing a lesson, but I feel in the end it will benefit my students. I am concerned about those teachers that don't feel the same way, how will their students fair when the tests change or if the tests change will our standards change so we can still be "teaching to the test"? I did gain allot through class today, and I think that that is what has caused me to realize how important incorporating more than just the state standards into the lesson is. But, whether or not the tests will change along with the standards or if we will ever be required to document both sets of standards still concerns me and makes me wonder what will happen in the coming months before I begin teaching.

New Insights and their Implications

The first couple weeks of class, we had talked about a new aproach to teaching mathematics though problem solving. When asked my level of understanding and knowledge on problem solving on a scale from 1-5, I said I was about a 2. At the time I didn't feel very confident in my knowledge of what problem solving was and how to use the skills of problem solving. This is not a good thing, considering I will need to have a strong understanding of problem solving in order to teach my students mathematics. After reading the chapter on problem solving and discussing it in class, I feel like I have gained knowledge and a better understanding about problem solving.

I learned that problem solving is a "way of teaching." Althought there are many factors that influecne problem solving, there is no prescribed method for teaching problem solving skills. Problem solving is student-centered, rather than teaccher centered; it begins with and builds on student's understanding. From the senteo quiz, I learned that in order to meet the student with where they are at in their mathematical knowledge, is important for teachers, when selecting activities for problem solving task, to choose activities that have multiple "entry points." From class discussion we also formulated ideas for ways a teacher should teach problem solving. First and formost, is to be well produced in your own problem solving in order to teach students. It is important to spend time teaching students how to use different routues-which is done by giving them time and opportuinities to find and use these different strategies. Other ideas we came up with, that are important to consider are, encourage students to verbalize their thinking process to help make them aware of the strategy/process they are using. Lastly, it is important to teach the structure of the problem in order for students to apply it to other problems to see and understand how matehmatical problems are/can be realted. From the reading I also learned about the teachers purpose in a more specific way as far as what they do before, during and after the phases of a lesson on problem solving. During class, I was also learned about 3 different tools ( George Polya's Steps to Problem Solving, Ten Problem-Solving Strategies, Processess of Mathematical Inquiry) that I can consider and refer to when teaching my students mathematics through problem solving.

Through reading and class discussion I have gained a greater understanding of what problem solving is and ways in which I, as a teacher, can teach students mathematics through problem solving. I can now say that on a scale of 1-5, on how comofortable I am with problem solving, I would say I am about a 4.5 :)

New Insights and Their Implications

Q. 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?

A. The most fabulous piece of information I gain within the first few weeks we've been in class was how to read the South Dakota Content Standards! I was extremely suprised to find that besides just the content standards I've always been looking at for the last two years, there are unpacked standards that (for the most part) effectively define key terms or direction of the standard itself. The content standards themselves do not provide specific information on what to teach exactly. I also was excited to find out that South Dakota Content Standard page provides sample lessons or activities that clearly alligns the standard with the task/activity. This was the most useful information I've learned in a while! :)

I learned that it is necessary to allign tasks in the math field with the standard. This allignment can be even more in depth through the standards at the national level as well, and the focal points book will describe grade by grade what exactly can be done to allign content standards with the lessons.

From a teacher perspective, so far I have been provided with great information to ensure that my lessons planned in the future have purpose and involve students to think at higher levels. It has also became apparant the meaning of "a mile wide and an inch deep". After this class I do think teaching math will be more difficult than I had imagined but I am willing to face the challange ensure my students are comprehending, investigating, and making sense of the math they will be learning and why math is useful and not just hours of completing times table worksheets.

New Insights and Implications

The first few weeks of class have been very useful. In the future, we are going to need to be able to align state and national standards to make sure that we are teaching our students the correct material, not only in math, but in other content areas as well. It had never occurred to me that the state and national standards didn’t exactly match up. I guess I had always assumed that they were similar enough to be interchangeable, but it turns out I was wrong. This class has taught me that you have to look for the similarities between state and national standards and to try to line them up according to how they are explained. I also learned that the South Dakota Content Standards website has unpacked standards, which have helpful activities for teaching specific standards.

New Insights & Their Implications

I learned so much from today's discussion on how state standards and NCTM standards differ and how they are the same. I learned many things about state standards that I never seen or thought of before. I also found it very interesting to compare our country's fourth and eighth grade testing scores with other countries. That was a great eye opener to me to see that children aren't being taught what/how they should be. Knowing and understanding how to fix our troubled areas so that we are setting higher expectations for students is the begining of how to fix our systems.

Summary and Synthesis

I found it interesting to learn about the national standards and focal points. In every class we have only ever talked about the SD standards and doing lessons that adapt to them. It was interesting to see how different the national standards are from the SD standards. I enjoyed the activity we did where we looked up the standards for the activity we did. I was surprised that the SD standards actually had very little to do with what we did even though the national standards specifically stated that activity needs to be met. I now know that I need to be comparing the national standards to the SD standards to fully give my students a good education.

New Insights and Their Implications

I thought the first few weeks of class were very informational. In all of my other classes we have been expected to know a lot about the state and national standards and how they work, but we have never really gone over them as a class. I thought that reading about the NCTM standards outside of class and having class discussions were very helpful to learn more about how standards work. It was also interesting to look at the comparisons of the tests that were done internationally and to see where exactly the United States stands compared to other countries. I would have never guessed that our educational teachers scaled as low as they did compared to other countries. Learning about this information gave me a different view of how teachers should be teaching and how I want to teach in the future.

Summary and Synthesis

So far in this course, I have learned a ton of new things about the standards that teachers are required to meet. In other methods courses I have always been told just to meet certain standards; never why the standards are written the way they are or other sources that could be used to make sense of the standards. It was interesting to learn that the state standards were recently implemented. I guess I constantly thought that teachers were ALWAYS required to meet state standards in the past.
Also, becoming aware of national standards such as NCTM has opened my eyes to the fact that there are other resources that teachers should be using when choosing content or activities for their classroom. One thing that came to my mind today during discussion was how those who contribute to the state standards are the teachers who know what the expectations are for the standardized state tests. It seems like if they are always teaching towards the standards, which are formed to meet the state tests, then they are going to get what they’ve always got as far as results and student knowledge are concerned.

Personal Concerns and Next Steps

My personal concern or fear is will I be able to integrate all the standards into my classroom in a given year. The standards and expectations just for math seem so overwhelming that I can't imagine having to do that for every single subject area. It seems that it would be easier just to teach one specific subject like math, so that you only have to worry about the math standards. Where as if you are a 3rd grade teacher you have to look at standards from every content area and make sure that you are meeting all those standards for each. It makes me think about what type of teaching job I want in the future.

New Insights and Their Implications

I learned alot from the scale factor and area worksheet we had to do. As our group started filling out the chart, we had a hard time finding out what the general rule was for each shape. We were able to find the area and perimeter for each scale factor. One person in my group noticed that the area and perimeter was the same for each same number of side shapes. Our group had trouble increasing the scale factor for some of the shapes but we worked together and helped each other out to make sure that it was the correct scale factor. At the end of the worksheet we figured out the general rule. We took a couple different approaches to solving the problems on the worksheet. We learned from the readings that there are different ways you can think about solving problems and different steps you can take to get an answer. Some of us had the same thought process and others had something a little different but in the end we used all of our thought processes to come up with an answer.

Constructivism

I believe it is a cult of construction workers... Just kidding. I believe it is the theory that people "construct" their knowledge from experiences they have. The many times I have heard about Constructivism was in the argument for preschools, and what is define as kids just playing for fun or are they gaining knowledge from their play.

Constructivism

What I know about constructivism is that it is a method of learning that takes place by doing. It means to be a life-long learner. Basically by living we are being constructivists because we are continually learning. Constructivism is very important when helping students learn.

What is constructivism? Constructivism is providing students with the opportunity to construct meaning through a variety of learning experiences including hands on activities, differentiated instruction, etc. Constructivism is activating prior knowledge in order to allow students to understand and relate new knowledge. Constructivism is exploration. A constructivist classroom doesn't just happen. It is created through the teacher and the students working together.

Math Methods

I am writing for my intial blog and have choose to write about the geometry and probelm solving experiement done in class. I thought this was a very concrete expeience to help me see the learning involved in the exponental growth of shapes. I enjoyed working together with my classmate to problem solve. Great experience. Kelli

Constructivism

Constructivism is the ability to continue to add new material and build off of previous knowledge. You continualy connect new material to old material. You can use constructivism to teach. Connect the knowledge you are giving to students to things they know and can use. This makes the learning easier.

What is constructivism?

Please add your personal response to this post by clicking on the comments link below or the little pencil. Do not start your own new post - make sure that you are "commenting" to my post.

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.