Blog 3- New Insights and their Implications

One thing I am learning from my peers is collaboration. Sometimes, I might know how to do a math problem and get stuck in the same spot and they might be able to help me with that. Peers have different insights on things and can help me. I am usually one that likes to do things on my own and definitely not work in groups. I know I can count on myself to get things done and partners are not also accountable. But, this semester so far has showed me working in groups can be very beneficial to the learning experience and deeper the learning to a new level.

One thing I have learned from Dr. Reins is mostly all students are being told the answers. I never thought of that being wrong until I realized the amount of education I have missed out on and the many things that I do not remember from grade school or high school. I am learning that each student must struggle a little to endure learning and further knowledge. I know how I want to teach to better my student's future and help them live in a society that is always changing. Who knows when someone will need to use the area formula or be able to cut a pizza in 12 slices. But, if they remember the information the task will be very easy.

I'm glad I'm learning a new way of teaching and cannot wait to implement the learning into my teaching style.

Personal Concerns & Next Steps

In the beginning, I didn't think this class was going to be that bad. Math definitely isn't my strongest subject area but if I try hard I can usally do pretty good. I did not realize how challenging this class was going to be. I'm so used to the cut and dry math where you just memorize formulas/equations, so this form of math is very new and challenging to me. I thought the midterm exam was frustrating because I felt as though I didn't know how to do a lot of it and found myself guessing. I guess I should put those feelings aside since it's over and try to work harder for the next one.

Personal Concerns and Next Steps

I thought that our midterm exam was actually a fun exam to take and work through. It made me think in a different way and I actually got “to do” math instead of worksheets – which is what I enjoy. Math has always been my favorite subject and I hope to teach it someday. This class is starting to help me make connections and show what the important aspects and concerns of math education are. I am starting to think about teaching from the starting point instead of showing students a formula or equation and telling them “this is the way you solve this problem. If you do it this way then you will get the answer right.” I’m looking forward to learning more and walking into the classroom with a different mindset each day.

Personal Concern and Insight

Usually math is not a problem for me. I can understand how to solve problems, but once I solve them I usually just put the equation or the solution out of my mind. That is my concern for the class because this class is something that I am not used to, in this class we have actually learn the problem which is difficult but will help me in the future. After the mid-term I am feeling even more uneasy about this class. I don't think that I did well on the exam but am hoping that I start understanding the material and doing well at it. Time is something that I feel hurt me on the exam, I felt rushed and don't think I completed the test to the best of my ability because I knew I was running out of time, but will set up a time to finish the exam.

Blog Two: Personal Concerns & Next Steps

The number one concern on my mind right now is the midterm test. I am slow when it comes to taking tests, especially math tests, and this one definitely required more than the allotted time. So therefore I am hoping that there will be a time during which I can finish the test. I felt I was adequately prepared for the test, I just did not have the amount of time necessary for me to complete it. Other than that, I do not have many more concerns. The math class is an eye-opener. Though just today I sat in on a freshman/8th grade algebra one class and it was still being taught in the way that I had learned math. The teacher is only in his second year of teaching too, so it makes me wonder when this whole math thing will switch over/gradually change/whatever. Anywho, moral of the story is that I am concerned about the test. I feel my next steps for the next test would not change much just maybe more aware of the time. Which would help if there was a clock in the room.

Personal Concerns and New Insight

At the beginning of the year, I was not worried about this math class because math has always came easy to me. I expected this class to be like any other methods type course and expected to learn how to teach math. After the year has progressed, I feel like this class has nothing to do with math and has more to do with the thinking process in general. Sure, we are thinking about math but it involves thinking more outside teh box. I know I have learned information but I feel more confused and shambled after class. The quizzes are not a highlight of the class. I understand that they are designed to think outside of the box but I feel they are to confusing for ELED teachers. For example, I believe it was quiz 3 when not one person in the class correctly answered the first question on a quiz. I have not talked with one person in the class who has got a 100% on a quiz. The midterm is another topic that makes me want to pull my hair out. One hour and fifteen minutes was enough time for only TWO people finish the test. The proctor was not aware of allowing additional time to complete the test therefor in the last ten minutes I struggled to fill in the answers on the test and not have any blank. I feel the midterm was very unorganized. I am trying my best to stay positive about the course and I am sure it can only get better.

New Insights and Their Implications/Personal Concerns

Like it was stated in the beginning of class, this class has become frustrating. Both good and bad. Good because I believe you must struggle with a concept in order to make the connection to the learning that is taking place. I also think that it is important for us as teachers to understand the "why" behind math, if we don't understand how can we teach our students? However there have been some bad frustrations. I am never exactly sure what is going on in class, what topic we are specifically covering, or even what homework is being assigned, and even when homework is assigned I am never sure what exactly is being expected of me. I also never know if what I did for my homework or answers that I have given in class are correct or on the right path. I think that sometimes some feedback is good. I know there are multiple ways to get to the answer of a problem but I would like it if maybe you would show us some of your methods, or how you came to an answer...or if we are going in the right direction.

On the other hand I have learned some useful information. I have learned the importance of being able to show "why". I think as children it is not an obvious question, usually younger children will accept that you do things just because that's how you do it, especially if they aren't taught why. In my job I teach adults who are trying to get their GED or just improve their skills. I have realized that these older students really want to know why we do the things we do in math, and from this class I have gone out of my way to help them see "why" we do what we do in math. I think that it really helps them grasp the concept. I have actually used the fraction bars that we made in class with one of my students to explain equivalent fractions, and it worked pretty well.

Personal Concerns and Next Steps

The reason I chose this to blog about was as a result of the recent test I just took. My main concern is that I did not finish it! I really wanted to do well on it, so I took my time, and the time got away from me! I hope that I will be able to finish the questions I did not get to. Another concern I have deals with actually teaching mathematics in the classroom. Wednesday of this week I participated in project Coyote in which I helped teach in a first grade class and a third grade class for the day with fellow classmates. It was a great experience, but it did kind of worry me about actually teaching in my own classroom someday, and because math is by far my least favorite subject, I hope that as I go through this course, I will be shown examples of an effective way to teach elementary level students in ways that they understand. Other than those two, I have no concerns and have found this course to be very helpful, and I know that as it goes on, I will continue to learn new things and carry that information with me into my own classroom.

Personal Concerns and Next Steps

The test we had last class period was an eye opener. Although we were able to use notes I felt that I did pretty horrible on it. It gave me a starting point for the next test however and what I will need to do to better prepare myself for it. Overall this class has been way different than any I have had and I see how this will prepare me for teaching math to students.

Personal Concerns and Next Steps

Lately, I have been thinking about how I was taught mathematics throughout school and how it is different from what we are learning now. I have always known the cut and dry math-- you memorize a definition or a formula and use it without questioning "Why?" I think it will be very hard for me to change how I think about and do mathematics in order to teach it differently. I wonder if I will be able to learn math in a constructivist fashion despite the ways I have been taught. It will take a lot of work!

Also, I am very concerned about that midterm! Ouch! I had completed my study guide and studied and studied! I read the book, read the modules, read my study guide... rinsed and repeated! And still, I didn't get close to finishing. I have always been one who takes a long time on math tests, because math is not my strong subject I like to think things through very, very thoroughly. I don't even know what I could do differently next time. I studied everything as best as I could and still had trouble. Although this experience was difficult for me, it made me realize that every student, even in college, has different strengths and weaknesses. It is important to work with these students so that they don't fret and stress over something so much that it impacts their performance on any kind of assessment.

--P.S. I don't know how the time-stamp works... I know for my K-8 Sci. Methods blog, it shows up as 12 hours or something later than when I post. I don't know how to change my timezone on this thing! Sorry!

Personal Concerns and Next Steps

I am wondering how I will be able to teach mathematics to my students in a way that they will be able to understand the how and why of the problems. I am wondering this because I am not sure I know the hows and whys. I believe that I am learning more and more with this class. I have learned how to find ways to understand the standards I am going to teach. I believe that I am learning how to think through problems in a way that I can deliver my thinking to my students. But waht I am struggling with is the whole process of how can I link the mathematics I am teaching to real life... why do we need to do mathematics and what purpose does it have in real life. Maybe the answers will revela themselves when I am planning the lessons for my classes. Maybe I need to take one problem at a time and think about one thing at a time.

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.