New Insights and their Implications

In the first couple weeks of math class I have learned some new techniques I can use in the future to teach math. We have discussed how it is important to build confidence in our students so they will believe in their own math skills. As teachers it is also very important to access their students’ prior knowledge and build on that.

I also have obtained a lot of new resources that I can use when I am writing lesson plans to include important information that I feel the students should know while aligning the activities to the state and national standards. One of the resources that I found particularly useful was on the state standards website, I was previously unaware of the assessment section as well as being able to access sample lesson plans that explicitly aligns with the standards. I am sure that I will be using these sections to give me ideas about lessons that I can teach as well as be able to focus on the sections that the students will be tested on when taking the standardized tests.

New Insights and Their Implications

I have learned many new concepts about teaching standards, where they have come from, and how they can affect me as a future teacher. The new concepts that I have learned about teaching standards is that it is important to know and understand all of them before you can properly teach them or the content in them. I have learned that our state standards come from the teachers in South Dakota and that they do not always aligne to the national or NCTM standards. For me, this is an important topic because I think that it is much more important to aligne the state standards to the NCTM standards. These standards have more of a clear focus and cover the material that needs to be covered in more depth. Other concepts that I have learned about so far are how to teach in a different method such as helping the students get to the right answer and not just stating the answer that they need to pass a test. This method will help my future students learn the concepts in math and help to retain them longer then if they were handed the information.

New Insights and their Implications

Within these first couple weeks of math class, I have obtained much important information pertaining to the teaching of math. The first area that I have gained much insight into is the teaching methods of mathematics. I have always been used to "drill and practice". In other words, many of my elementary and high school memories of math class consisted of here's the formula, here's how you do it, and here is your assignment. However, as I have learned from reading chapter four and classroom discussion, this method is not benefiting our students. The graphs presented on the first day of class really helped me to gain an understanding for this information. It seemed as though we were doing everything wrong in relation to the countries that were showing success in the area of math. These statistics implicate that we need to go about teaching mathematics in a more beneficial way to our student I am slowly developing an understanding for the teaching methods being presented in this class both from the reading, and the group assignment we have just completed. I am eager to learn more.

The second area of study in which I have gained much insight into revolves around the state and national standards. When we first began talking about these standards I was somewhat overwhelmed. However, through class discussion I was able to develop an understanding for the reasoning behind involving the national standards into the math cirriculum, and the importance behind them. As we have learned, the state standards are somewhat broad, giving us no area to pinpoint our lessons. However, by referencing the national standards and the focal points, we are provided with more direction into what our students should be studying.

New Insights and Their Implications

I have been learning a lot about state and national standards. In all the classes before this we have had to write lesson plans with standards, but these standards have never really been explained. I knew that they were to help teachers make sure they were on the right track with what they were teaching thier students. This is the first time where I have had to go through the standards and be able to understand what the standard want and what they mean. Also I have learned where to go online to find information about standards if I do not understand what they mean or to just make sure I am understanding them right. I also like working with my peers, when we are going over standards, because that helps me understand what we are suppose to do or get something that I missed.

New Insights and Their Implications

I would say the newest insight that I have received from this class is the knowledge on standards. I have learned about how the state standards are created, I have actually now seen the national standards I have never seen these before, I have learned of the importance of alignment with these standards in my future classroom, and I have learned how to better navigate around South Dakota State standards website.
First, learning about the process of reviewing the state standards and then every 5 years making changes to them was new knowledge for me. Second and third I will put together, sadly this is the first time I have actually seen the national mathematical standards. It was very interesting to me how they are very different than the State standards in wording and how the state standards have left some of the national standards out. By me now knowing how to get access to both standards, in my future classroom I will be able to better align my classroom curriculum. Not only meeting state standards but taking a look at the national standards and finding ways to better educate my children to a larger scale. Finally, I have been to the South Dakota State standards website many times, but I never knew of all the different things I could do there. Like accessing the blue print to the Dakota Step, and ways to unpack the standards to get a better understanding of what is expected.
Everything we have covered so far in this class I see as being something that is going to be very important to my career as a teacher. Even if we have been running out of time and not covering all the material Dr. Reins wants to. I am glad that we have gone into a lot of detail over most of this material, and not just brushing it leaving me with the sense of not gaining any knowledge.

New Insights and Implications

The insight I received from the lesson on standards, was that it has helped me to see that the task of aligning could be very complex, but it is matter of looking at the big picture and finding the focus of the standard. There are many resources out there to help you to align and understand the language, the purpose, or how it will be tested. When you utilize your resources it will only enhance your teaching and benefit your students. I also was able to see how the whole system of standards really works together and how it is tested within the schools.

When applying this to the classroom situation, teachers should always be reevaluating their teaching and activities for accountability purposes. Regardless of the situation, it is important to stay on top of your curriculum and evaluate it from every aspect and ask yourself how could I make it better even if it went smoothly. If you truly care about your students and their learning you should want to give them the absolute best learning experience; good instruction should align to the standards and prepare students for content on state and national tests.

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?

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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.