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.