Personal Concerns and Next Steps

This last month of class has been fantastic. I really enjoy this class because it challenges my way of thinking in a good way. I know that most of my peers do not really like having official tests and whatnot but I thoroughly enjoyed the test that we took on Tuesday. I don't find myself being challenged to think critically often enough in my other classes so I like the constructivist structure of this class. Having to actually work through the process of creating proofs, developing formulas, etc. is great for keepin us on our toes as far as what we know but also helps us to understand what our students will be going through. On the first day of class we were told that we would most definitely be frustrated throughout the course of this class and after browsing everyone's blogs I am starting to see that coming through.

New Insights and Their Implications

Throughout this class, I have begun to understand proofs because I have to break apart a picture and find the proof for myself. In high school, everytime my teacher would say we are doing proofs, I became nervous because I did not understand how to do them; however, when I had to find a formula for a parallogram, I was more confident because I found the formula using everything I knew. Another new insight I have gained from my peers are different ways of solving mathematics. When we were given the Pick's Theorum worksheet, it was amazing to understand how many different routes people took to solve the problems. It allows me to understand that not all students in my classroom are going to learn the same way I did, and it is important to allow them to experience different routes to solving a problem. Lastly, I have learned how to make my own definitions and not rely on the definitions in the book. It is so easy to look in the book, find a definition, and write it down; however, I understand and know the definition better if I write it myself.

Personal Concerns and Next Steps

Coming into this class, I was very excited to learn how to teach math. I love math; however, now that I am further into this class, I am very concerned about teaching it to students so that they actually learn. Never have I struggled in math until this class. Having to explain myself and my thoughts with detailed information is completely different than I have done in any other math class. While completing this class, I need to keep in mind the fact that I will struggle, but struggling is what makes me learn. I need to remember to be more patient and not turn to my classmates for help right away.

Blog #2: Personal Concerns and Next Steps

This class as a whole has definitely been completely different than any other of my classes. The only concern I slightly have with this class is the midterm that we just took on Tuesday. I understand completely that with us getting behind and with Dr. Reins having to miss this week of class that no matter when we chose to do our midterm it was going to be slightly unorganized. Going into the test, I wasnt nervous at all however, when I sat down and received the test and it was 10 pages long and I only had a hour and fifteen minutes to complete it, I definitely went into panic mode. It was also hard because this was the first test we have taken in this class so as students we didnt know what to expect from Dr. Reins and once we did get the test we couldnt ask any questions. I just felt kind of helpless in a small way. It also was slightly frustrating that only ONE person actually completed the test before time was officially up. Perhaps we can discuss the test more fully once Dr. Reins gets back and maybe get a chance to make some corrections for bonus points? Either way, this is definitely a learning experience for me personally.

Personal Concerns and Next Steps

I have never experienced math in the way that this class requires. In the past, teachers just gave us the formulas and we memorized them. Knowing why to use the formula seemed irrelevant, as teachers didn't encourage this inquiry and we were given the formula, anyway. I've never had to struggle quite as much in any other class as I have in this one. When I don't understand information or can't find solutions, I tend to get frustrated, sometimes to the point that I just want to give up. What I need to remember is that by struggling, I am finding the solution for myself, thus learning in a more valuable way. Also, I need to have more patience during this process. These are some things that I need to keep in mind in regards to this class.

Personal Concerns and Next Steps

I have always been pretty good in math. I have never struggled with any concepts about math, that is until know. I have been pretty frustrated in this class. It has been may years since I have been in math class, and I have only been taught formulas. I was never taught to use different ways to approach a problem. Nor was I ever taught to question a formula. I do understand how this type of thinking may help other students, who do not get the formulas, or why that formula works, to solve problems. I have children that are in 3rd, 5th, and 7th grade, and they are changing to this type of teaching for math. This class has helped me to explain somethings to my kids. This has helped me understand somethings, by explaining it to them. However, I do feel left in the dark on some items. I am hopeful that one day it will just click, and everything will be put in place. Until that happens I will continue to struggle to understand these concepts.

Summary & Synthesis

Over the last month, I have learned a few important teaching strategies for teaching math. These ways of teaching were not how I was taught, so they seem somewhat exciting and somewhat scary at the same time. I have always enjoyed math and like figuring out why and how math works. The last month has challenged my math skills in a very different way. For the first time, I found myself struggling with math in a different way than I'd ever struggled with math before. I now somewhat understand how we're suppose to teach math to students; letting them struggle to come up with an answer. However, it's hard for me to completely grasp since I was taught math so differently. Over the last month, I have gotten frustrated with assignments and readings because it's forcing me to think about math in a completely different way. However, I still love math and am extremely excited to apply these teaching methods to my own math classroom.

Summary and Synthesis

On Wednesday, October 14, 2009, our class went to Beresford Elementary for Operation Coyote. While at Beresford, I taught not only one math lesson but two math lessons. The first math lesson was in first grade and we introduced the number line and worked on addition and subtraction. The second math lesson was in third grade and we worked on the number 5 times tables. At first, I struggled with the thought of teaching a math lesson without adequate preparation time, but once I started teaching the first lesson (in first grade), I become confident in how I was presenting the information. Later in the afternoon during my second lesson (in third grade), we taught a lesson about the number 5 times table. We gave the students a problem of the day and had them work on. Then, we had the students talk about the answers they got. Most of the students had the correct answer but some had different ways of getting the answers. We had the students talk about the different ways in which they found the answers and told them that just because you had a different way of getting the answer, does not mean your way is the only way. I found experience to be a great connection to what I am learning in this class, math methods. When I was doing math in elementary, there was one way to do a problem and that was it. When this type of instruction is introduced to students, more students will "get" math problems.

New Insights and Their Implications-Blog #2

Throughout class this month, I have learned a lot of new things about teaching students math. However, the one thing that sticks in my mind and that I found extremely interesting was breaking a shape into other shapes. For instance, it was really interesting when we found the formula for the trapezoid by breaking the trapezoid into two triangles and a square. I had never looked at shapes in that way. I had no idea that I could develop a formula on my own and didn’t believe I could until that assignment. I also found it helpful to use tangrams to see how shapes can be composed and decomposed. Overall, I learned a lot about teaching math to students and am looking forward to learning how to teach the more difficult concepts that students struggle with in the upcoming classes.

blog #2: Personal Concerns

This class is definitely unlike any other math class that I have had. Although I have gotten frustrated with this class a few times, I have learned a lot too. For example, when we did the taking apart area formulas, I struggled with this concept a little at first (proofs). Now that I can see where the formulas are coming from it will definitely help me to teach the formulas to my studnets. Going through my previous education years, I definitely just memorized formulas, but actually being able to produce the formula even if I can't remember it is a huge benefit. I just hope that as the class goes on I keep reconstructing my previous notions.

Summary and Synthesis

Throughout this course, I have altered my thinking about what constitutes best practice for teaching mathematics. Like many of my classmates, I have been challenged by this course to think in new ways and make sense of ideas without taking shortcuts. Each concept we have experienced in this course has been linked and built upon other concepts, which are all part of a "bigger picture." Teaching math is not about drilling isolated concepts and formulas to students, which are impossible to remember or understand, but is about allowing students to construct their own ideas and create a conceptual understanding about why they are carrying out procedures. Like Bridgette mentioned, I also learned the benefits of cooperative learning. In the past, working with others has usually been considered a form of cheating. From this class, I have been able to see how everyone benefits from sharing their thinking and justifying their own ideas, which strengthens each student's individually constructed understanding.

New insights and their implications

Through this math class so far I have learned a lot about how kids should learn math and how I learn math. I really like this class because I am learning math in a way that is like I have never learned before. I have always been someone who struggled to learn and memorize formulas and then know how to use them in a situation or problem becuase I did not understand them. This class is teaching me math the way I should have learned it, and is showing me how to teach kids math so they actually understand what they are learning. I have learned that students are not actually learning anything when they memorize formulas, but learn much more when they understand why and how to solve a problem rather than just memorizing solutions. I have also seen through this class how tough it may be to change the way math is taught, but in my classroom I will be able to help students learn math in a different and most likely a more effective way.

Summary and Synthesis- Blog #2

This Math Methods course has definitely caused me to think about teaching math in a new light. I have been struggling with quite a few of the concepts that we are learning, and this may be because I am used to math teachers in the past walking me and my class through all the steps that need to be taken to complete a problem. In this class we are learning through accessing our prior knowledge and using critical thinking skills to solve problems without the instructor as the facilitator. I had a hard time with finding the area's of the shapes on the geoboard, and after I asked for help I am much more confident with the concept. I have learned that I need to think outside the box and focus on what I need to be doing to solve the problem in front of me and not get overwhelmed, because that is when I run into trouble. This new way of teaching and learning has been a stuggle for me but I am able to see the positive effects that will result. If students are finding their own methods for problems and going through the entire thought processes, like we are in this class, they will be more likely to retain that information and make their learning more meaningful. This class is a struggle for me but each day I am learning in new ways and I am hoping that it will have positive effects on my future teaching of mathematics.

personal concerns...

Throughout this semester so far there have been different ways to think and understand this subject. I get frustrated pretty easy when I don't fully understand something and I have been on a rollercoaster of frustration and confusion. I try to cope with all the new learning strategies and fit them into everyday situations. This class is definitely different than any other math class previously taken. It is good to accept a challenge and work at it, but when I continue to try and don't grasp a concept, I get frustrated with myself and find myself stopping at what i'm doing and coming back to it to make sense or just leave it all together. I need to be a little more patient and look outside the box to find the answers, sometimes this is difficult for me.

New Insights and Their Implications - Blog #2

Throughout the last month of class, I have learned many valuable lessons. I believe the module and lesson on geoboards and area of a polygon were the most beneficial activities. I found it challenging to try to formulate different methods for solving the area of a polygon. During this activity, I learned how to cooperate with peers in order to solve more of the difficult problem. When we brought the worksheets back to the classroom, I realized how students could use several different methods to solve an area of various polygons. Even though I was able to view the different methods/strategies my colleagues and the professor used to solve the same problems, I understood my method best.
After completing this specific activity, readings, and modules, I realized that students can learn how to solve problems in various ways. I will use this information and carry it into my future teaching. I believe it is important to allow students the opportunity to show their method/strategy for solving a problem. In addition, I realized that I learned best by using my own method to solve these problems. I have concluded that students will learn best by using their own methods to solve problems. In my future teaching, I will give students problems and ask each student to come up with a method of solving. Even though I struggled through this activity, I believe I learned much more. In conclusion, I believe students will learn a concept more thoroughly if they apply their own ideas to finding the solution.

Personal Concerns and Next Steps- Blog 2

Math has always been extremely difficult for me and this class is a challenge too. It is difficult to look at math in a different way when I have been doing math one way for so long especially when I struggle with the way I was taught. I do believe that teachers who struggle with a concept and then finally understand it are going to be able to teach the students well. I think that teachers who struggle will teach the concepts to the students well and be able to help them with their problems. I know that it will take more than just this class to understand this type of math especially when I still have problems understanding the old way to do math.

Personal Concerns and Next Steps

This semester I have gained a lot of new insights and ways to understand math in a completely new way. I have been challenged, confused and frusturated a lot this semester because I am being taught to think about math in a totally different way than I have ever been taught. It is diffucult to try and learn something in a completely new way. I know what it feels like to be a student learning a brand new concept. The concepts that have been introduced are important but are still hard to look at in a new way.

Personal Concerns and Next Steps -Blog2

I have always enjoyed doing math and being in math class. This class has definitely been a different view on math and challenging me in different ways. I really like the activities we have been doing in class. Like finding the formulas of a trapezoid and parallelogram by breaking down the shape into simpler shapes. I have never thought of doing it this way before. I have always just memorized formulas and never knew where they came from. Looking at in a different way was very challenging for me, but it made sense. I also liked using the chop strategy for finding polygons. I have never thought of surrounding it with a rectangle and decomposing shapes from it. I really like all the new ideas that we have been learning in class.

Blog # 2--Summary and Synthesis

We have been talking about finding the area of polygons. I find this topic interesting and hard to understand. I did not learn this in grade school and never used a geoboard until now. With listening to other student methods and knowing there is more then one way to solve the problem, makes it more understandable. I also find it interesting that there is only one true written down formula known as Pick's theroem and by reading the modules and class discussion, no one knows his thinking that made him come up with the formula. Pick's theroem works wonders and anyone can find the area of a polygon on a geoboard really fast. I am learning that there is not just one way to solve a problem and students can help each other. The teacher does not need to provide the answer, but look at the student's method of solving the problem.

New Insights and Implications

Since this class started I've learned several things in regards to concepts about math education. I've always viewed math as a very dry subject with only one right answer; when in fact there are several ways to approach one problem. It's important to encourage students to come up with a solution in their own way rather than paving the path for them. When doing this we teach students problem solving skills. We also talked about the importance of using the right math standards for both state and national. We also learned about what standards mean and how to analyze each standard and put an appropriate assignment with each standard.

New Insights and Their Implications

Over the past few weeks, we have learned many aspects about math. The block activity stands out the most for me and I feel I learned a lot during those two days and trying to solve the problem. The activity helped me develop problem solving skills and really think about how I was thinking. I was shocked when we tied this activity to the standards. It fits multiple standards but only pieces of each standard. When we broke down the standards, I found it very interesting how you need to really look into the wording of the standards to get the real meaning out of them. I think it is crazy how much money is spent to revise the standards when we already know in two years they are going to change.

New Insights and Their Implications

This class has been quite an eye-opener so far. I thought this class was going to be fairly simple because math has always been one of my better subjects but I have come to find that this class is more than math concepts. Instead of simply finding an answer and moving on, I've learned to take a step back and think about the why's and how's. For instance, the activity we did with the shapes seemed very simple, until we discussed it in class. I never noticed a pattern with our data at all until the class discussion. Even then, it wasn't about finding the pattern, it was why and how this pattern existed that was important. It's not always about the right answers but the methods and strategies used to get that answer. Also, I've learned that the content standards used for mathematics in South Dakota are not very well written. The discussion we had the other day about state and national standards was pretty interesting. I never really thought about standards in that much detail - always took them for what they were. I have really learned to consider both standards in order to give my students a more thorough education.

The past few weeks in the class has been something I have not experienced before. I usually do very well in classes, I normally understand concepts and complete them to the best of my ability. I have never have a major struggle with any school work, until this class. I am used to just looking for the answer and then once I get the answer I could truly care less about how I got the answer, as long as I got the credit for the right work and right answer. This class has turned that all upside down for me, which I feel is something that all students should experience. The way you teach math is the way that math should be taught, I am actually building on my knowledge instead of just "floating" through the class with the correct finished product. In the past few weeks I have really been testing my knowledge with a different way of thinking, even though it is extremely frustrating that it does not just come to me, I feel that I will benefit from this class. While sitting in class I try to think of ways to teach like you, as in to really get my students thinking, not just saying "here is the answer."

New Insights and Their Implications

Through this class I have a better understanding of the standards, state and national. I had thought I did understand them and what they ment, but after this week I am shocked as to how much I do not know. When we looked at the activity and tried to find standards that would fit with the activity, I thought I had done alright. As a class, we looked at other standards and talked about them. This was wonderful, as I got to hear what other studetns were thinking when they chose the ones they did. With the implications standards being what they are, I am supprised that they are so vague in their attempt to let the teacher know what to teach. I now know that I need to look at the national standards with the state standards to produce quality lessons that my studetns can learn from. What I need to do now is to take this new found information and apply it to all my classes.

Blog One: Insights & Implications

I have already learned a lot in this class about how to teach math and how students learn. First off I have learned that giving students time to solve problems themselves is the best way for them to learn. Like my peers in class I too was taught math in the manner of here's the problem, here's how to do it, now practice by doing a worksheet filled with problems. Even though I may have been able to learn math this way, not every student thinks the same way as their neighbor. I have also learned a lot already this semester about the standards. It is now quite clear to me that the state standards are much different from the national standards. It is interesting that the state standards are so vague. I had never realized that to be so until we spent time picking them apart in class last Thursday. What I hope to continue learning in this class is how to connect the standards to my teaching successfully. Successfully to me means that a lesson is one that the students were able to relate to, connect prior knowledge to, and understand.

New Insights and Their Implications (Blog #1)

This month I have learned a lot about how to teach mathematics. Going into this class I was unsure how to explain concepts to other students. I really enjoy how we are discussing with each other how to explain different concepts. Every student learns differently and by showing us all of the different ways we can solve problems we can keep this information in our notes so when we teach it to students we can show them that there are more than one way to solve a problem. I also learned that it is important to have a variety of questions to show examples of when teaching mathematics. As a teacher, I need to have students perform a multitude of easy, moderate, and difficult questions and also show them how to do some of each for examples. I also need to find different ways to get students to have hands-on learning when it comes to mathematics so they can perform trial and error for themselves without the aid of the teacher. The final thing I learned this month was that teachers need to give little help to students when they begin their work. We need to let them try things for themselves and not just give them the answer.

New Insight and their Implications

I am starting to gain new insight into the standards. I was not aware that one needs to take into consideration both the National and State standards when planning a lesson. So far with my education I have looked at the standards and written down every one that might pertain to the lesson plan. I see how this does an injustice with our students. It is better to pick a couple of standards, both from the state and national standards, to focus your lesson on. This way one can make sure that you have taught all standards required. Listing a bunch of standards, on a certain lesson, may lead you to believe that your already taught a standard but you have not.
I have new insight into realizing that I have not had math for a long time, and the old addage 'if you don't use it you will lose it' may be applicable. This class will help me learn and remember what I have already learned. I have noticed in the schools that they are teaching differently from when I was taught in school. My children are in 3rd, 5th, and 7th grades and their homework is a bit different than I remember. For example, my 5th grader is not allowed to line up math problems on top of each other for multiplication. There are at least two other ways they are learning to do multiplication. They use a table to solve the problem. I am anxious to learn these new ways both for teaching and helping my own children with their homework.

New Insights & Their Implications

Since this class has started, I have already gained many new insights in regards to teaching. I now understand how important it is for students to be able to think for themselves and engage in a learning process in which they are able to independently create solutions from the information and material given. As we have talked about numerous times in class, it is beneficial to students' learning if the teacher lets them struggle a little to figure out solutions instead of giving them the answers. This way, the students are more active learners and will take responsibility for their learning. We also discussed in class how it is extremely important to not only refer to state standards when planning lessons, but also consider national standards. It was made very clear in class how the state standards are very vague and may be missing vital components. The national standards are more detailed and help provide a better description of the learning that is expected to take place at each grade level. In other classes, we have not talked much about national standards, so it was very helpful that we covered this in class. These are some of the new insights that I have gained so far in class.

New Insights and Their Implications

Since the beginning of this class, the main idea that I have learned is how to teach math. Growing up I was taught math, but ALL my teachers taught me the same way. They would present the problem, do an example on the board, and make us do like 15 for practice. However, since being in the class I have come to understand there is another way to teach math. If more students were able to understand math, by struggling through math problems and using their own solutions then math would not be a scary subject like it is now.
Another insight I have really learned a lot about through this class is standards. Before coming to this class, I though of standards as state standards and that is the only information I NEED to worry about teaching. However, once again I was wrong. When I teach, I need to look at National as well as State standards. If I look at both, as well as APPLY both it will allow my students to score better on tests, and dig deeper into certain material, rather than of the idea of "a mile wide and an inch deep."
The last insight I have really learned from this class already is the wording and choosing standards. With the exanple we did in class, it allowed me to realize to choose one or two standards and teach those, rather than trying to teach seven different standards as one time. In addition, I need to research the meaning of the words in the standards and not just use my defination of them.
I have learned about myself that I am closed minded when it comes to math. I was always taught a certain way, that I assumed if I ever taught math that would be the right way to do it; however, I need to be more open to math and allow my students the opportunity to struggle, learn from others, as well as from the teacher.

New Insights and Their Implications

I have lerned many things from my peers and the instructor so far in this course. I have learned that there are a variety of ways to teach math, and no one way is the correct way. I have learned that you have to allow students (and yourself) to struggle in order to come to a solution to a problem, and to truly understand the concept. I have also learned that there are many ways to approach problems, and various ways (or ramps) to take when solving a problem to get to the correct solution. Some implications for teaching and learning mathematics are to allow the students (and yourself) time to figure out the problem independantly. The students and individual must struggle a bit if they are to understand the concept presented before them. Students must be allowed to test different ways of reaching a solution to a problem, as well as understand how they came to the solution. The same can be said for learning mathematics; you must concentrate, and struggle with problems before coming to a solution to further your understanding. Through this course, I have also learned a lot about myself and my own struggles with mathematics. I am not the best math student, but I find that talking with peers and asking questions about reaching solutions is a great way to learn because it allows me to understand the concept for myself, not just simply coming up with a correct answer. As the semester progresses, I hope to obtain more insight into the teaching and learning of mathematics.