Personal Concerns and Next Steps - You may blog about genuine personal concerns created as a result of the experiences in this course. (Please note: If you blog on this item be sure to provide sound rationale for your concerns and what steps you are planning to pursue to address your concerns. This is not an opportunity to vent, be constructive and professional about it. Don't complain about something unless you offer a better alternative or solution.)

I guess the biggest concern that I have about this class is that I'm not used to learning math in this way. I am used to having Math teachers tell me how to do a problem and then turn me loose to practice they way they showed me how to do it. It is going to take me some time to reach into my own brain to try to figure out how to do different math problems. I think that by learning how to do this I will be a better Math teacher.

New Insights and their Implications

I think that this class has been very productive so far and the activities that we have done have been ery helpful. I agree with Brittany that math was taught to us in a very routine manner. I think what is most interesting is that in the past year, our classes and instructors have been telling us that there is going to be a new shift in education. I did not know what it was going to be like until this semester. I think that we, as future educators, are intimidated by the fact that what we have observed of teachers over the years growing up and going through the K-12 system, is not how we are suppose to teach. I also think that it is interesting that during class, everyone including me, is hesistant to answer questions and have an opinion. I think that this class is goign to be very interesting and a great learning experience for everyone.

New Insights and Their Implications

During the first couple weeks of class it has been very interesting. I am finding that I really enjoy this class and the approach that is being taken to teaching it. Instead of having us write 20 lesson plans to cover math concepts in what we think is a deep concept, we really have taken a step back and uncovered a completely new layer here. I can safely bet that most of my peers in this class, including myself, were taught math from projector transparencies, examples, and worksheets galore. This class is making me rethink about all of the other lesson plans I have written. Did I really achieve my objectives, or do I just think I did? I like the activities and discussions we have had thus far. The article that we read the other day about math anxiety being learned from the same sexes was astounding to me, and the fact that nearly 90% of elementary teachers are female. But, it really does start to make sense because how can we teach what we don't know? How are the kids supposed to know what we as teachers, don't even know? So, I really have enjoyed this class and I really am looking forward to the rest of the semester. I think this will enhance all of our teaching philosophies greatly!

New Insights and their implications

From the first few weeks of class I have learned a new approach to teaching mathematics or how to teach mathematics though problem solving. I currently feel that I could teach problem solving in a variety of ways, when previously my knowledge on this concept was not very good. Because I now have a strong understanding of problem solving I feel it is very important to implement in the classroom. Our in class readings and class discussions have helped me to gain knowledge and skills on problem solving as a method of teaching. I also learned that problem solving is a “way of teaching” and that when done correctly students really learn the material in depth. We also learned that there are several factor that influence problem solving and that there is no one-way to teach it. From the in class quizzes, I have learned that in order to meet the student 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” allow student to solve their own problems.

New Insights and their Implications

I have already learned a lot through just a couple of times we have had class. I guess what I first thought of math was what I was taught in grade school up to some of my college courses, which was to me was a regurgitation of the text back to the teacher with either a quiz or a test. But I think about the implications of just regular teaching to students and I can see the draw backs. I think with the help of the Timms testing we have learned that we are lacking in focus, reasoning, coherence, and sense making. I have found why students need to know this to be successful in math for a life time. I have also learned a lot about problem solving in a classroom and I think I will have one to two models of problem solving hanging up in my classroom. I think students need to know the required steps of solving a problem and also that there isn’t clearly one way of solving a problem. I think overall I have a better concept of thinking about math more constructively and I also believe that at times the STATE standards suck.

Blog #1

Personal Concerns and Next Steps - You may blog about genuine personal concerns created as a result of the experiences in this course. (Please note: If you blog on this item be sure to provide sound rationale for your concerns and what steps you are planning to pursue to address your concerns. This is not an opportunity to vent, be constructive and professional about it. Don't complain about something unless you offer a better alternative or solution.)

So far in this course, I am concerned with my own personal skills in math and whether that will translate well into a grade or my ability to teach mathematics to my future students. I personally have no faith in my abilities in math and at some points; I am scared to even try for fear of failure. I have had an anxiety toward math since I was little. I will also admit that I was fearful of even beginning this class considering my past relationship with mathematics. To address my concerns, I am going to do my best in this class and try to take in as much information and ideas as I can in order to allow my future students to have a better chance of success and more positive feelings toward mathematics. I resolve to take the assignments, readings, and activities one step at a time and ask for help if I it’s needed. I feel if I take an optimistic attitude toward the class I might find a chance for myself to become competent in math methods and even being to enjoy it to some extent.

Blog January 31st

New Insights and Their Implications - 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?

It becomes increasingly evident as we delve further into the semester, that teaching mathematics has to be understood and explained with a broad interpretation. As I speak with my peers, we all have a similar inclination to teach but we all learn material by a variety of methods. I understood that potential students need to have an educator who does not divulge every technique but trains a student to actively seek for a path to a solution. Professor Reins made a very valid point the previous class session. He made the remark that state standards should play a role in how one should teach but is not the absolute reference guide. Standards should be carried out with an emphasis on broadening a mathematical concept. The reasoning is that students need to know the background knowledge of the material and not just a limited amount of highlights that lack transition into other topics. I find that this class will greatly enhance the manner in which I educate. In addition, I feel that this course should have been presented to education majors before or during the math concept classes. The perspective not only teaches one how to explain mathematics, but it also gives a student more a comfortable approach to executing unfamiliar math.

Blog #1

New Insights and Their Implications - 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?

So far in this class I have learned many new perspectives on both approaching math concepts as well as teaching them. Throughout my schooling I have never really liked math. I think the majority of the blame for my dislike of the subject was my lack of confidence. I never thought I was good at math, therefore I never wanted to work on it. I realize that many students encounter the same problems. In this class I am learning to take a new approach when teaching math, which is to allow students to explore the problem before teaching them a specific way to complete it. In school I have always been taught a certain way and expected to follow the way I was shown. I do not believe this is the most effective way to teach math, however it may be difficult to learn a new way. I think my view of math in the past will help me to be a better teacher because I understand the frustration it may cause to a student. I understand that there are many different ways to teach and learn math, and I look forward to learning more new approaches!

Insights and Concerns

Adapting to change is an important skill to acquire. I love the fact that everything we are leaning in these methods classes compliments each other towards shaping our very own teaching philosophy! We have been talking a lot about the importance of shifting the balance of classroom power from the teachers to the students; the teachers' serve as guides in the students' learning not just individuals that bark the steps of mathematical computations and demand the students to repeat. We've been talking about how the South Dakota standards are vague; they're too broad being a mile wide and an inch deep of content. If you try to focus on teaching everything then nothing is really important.
Now how is this going to affect my teaching abilities? I believe if my school district adopts an outdated textbook curricilum for math, I will be faced with the biggest challenge of all time. We have been introduced to the NCTM's National Standards which emphasizes the importance of incorporating national standards with state standards in order to develop a decent lesson to teach. I was never really good with mathematics as I have been to the math trailer countless times throughout grade school. I believe that in order to be successful in this class and future classrooms, I am going to have to be vigilant and persistent in applying higher level thinking and reasoning skills in my lessons!

Blog 1

New Insights and their Implications

Just in the short time that I have been in this class, I already have a new perspective in math. I am beginning to understand that there are many more ways than I was aware of to teaching math and I realize that I need to learn these methods in order to be an excellent math teacher. I typically get very frustrated with math but I think that by learning these methods I will be able to be confident with what I am doing and hopefully portray that in my future classroom. I look forward to the variety of things that I will be learning and strengthening my math skills.

Blog 1: New Insights and Their Implications

To begin thinking about math in a new and more efficient manner, especially the ways in which it is taught, is challenging to say the least. I believe that the last few class periods of this semester have really begun to push me to try and become more positive towards the field of mathematics. Also, I have attempted to open myself up to considering different ways of teaching the content which can be especially difficult because of the more traditional ways in which I was taught as an elementary student. The instructor and the ideas/activities he has presented the class have stretched us to consider problem solving and other staple concepts of math to a much greater depth than what is currently being taught many students of the United States even today. As the country lags behind in math scores on the international spectrum, teachers and federal officials alike are concerned about the lack of progress America has been making in the classroom. It will be our job as future educators to make a difference, which, as stated before, will be a challenge in and of itself because of our lack of background knowledge in the ways in which we are expected to teach math.

New Insights and Their Implications

So far from this class we are learning about a new approach to teaching mathematics, where the teacher is not providing the students with all the concepts and formulas. Instead, the students are participating in activities where they solve problems and discover the concepts and formulas themselves. This is a hard adjustment to make in prior thinking of what mathematics education is like, and can be frustrating for the students. However, when the light bulb goes off and things start to click for the student's, that's when the method proves itself. I think that when I am teaching in my own classroom I would like for my students to solve their own problems and be the facilitators to their own learning. I am worried though that it may be difficult to encourage students to keep trying and for them to not get discouraged.

New Insights and Their Implications/ Personal Concerns and Next Steps

New Insights and Their Implications:

I have learned more about the reformed-based teaching that we are learning to teach our future children. I have learned that by simply modeling a problem or helping a child work through their own problems by showing the steps is not a good idea to teach children to understand math concepts. There are two ways for teachers to use standards; the first way is to find a standard and match it with an activity and the second is to find an activity and match it with the appropriate standards. Throughout this class I have learned a lot about using resources, especially finding multiple standards to back up the activity being used. I have really enjoyed reading and learning about the NCTM's goals and expectations and the activities it provides for teachers to use. This affects me as a future teacher because I will now use more resources to find and use in my activities. I will also work on learning the new way of teaching so that I will not be giving my students answers in a way that does not help them learn or understand the material. I want my students to be challenged and intrigued in figuring out math! I am excited to continue learning how to teach this in my classroom in this math methods course!

Blog #1 Summary & Synthesis

Summary & Synthesis Blog:
On Tuesday, we were to find a math standard that was full of difficult language and terms and come to class on Thursday with that standard on paper. So I found a standard that I thought was going to be interesting to pick apart, but on Thursday I was a bit frustrated with the standards because we were not able to match a NCTM standard with the first state standard that we had chosen. It was nice to be working as a group on this project because once we put our heads together we found a match to the standard that we had chosen. I think this is one way to show that if you keep trying at any task you will be able to come up with an answer. You should never give up on a particular task, and this is a great example because when we took the time to pick apart each individual standard we found a match. I now understand the importance of not only following State standards, but also National standard while teaching math education. I am interested to see where we are going with this project and learn more about the standards and the connections between State and National standards.

Blog #1---ELED 330

Personal Concerns & Next Steps---You may blog about personal concerns created as a result of this experiences in this course. (Please be sure to provide rationale).

When I started this course, I had some personal concerns going into this class. Math has been an enemy of mine since early on in my school experience. A bad experience with a teacher in math in second grade solidified my hatred for all things math-related and ever since then, math classes have been my worst fear. So, the thought of taking a math class where I would learn to teach math to other students seemed incredibly daunting at first. I admit, I could have been more optimistic on my first day fo class, but I found myself dreading this class before I even arrived. While I can't say that I'm feeling completely 100% competent in teaching math yet, I am feeling very much relieved after the first few classes and do feel like I can set aside all of my bad feelings towards math and focus on providing my future students with a positive math experience. Once I allow myself to realize that I can be successful in math, I can help my students realize that they can be successful as well, and ultimately, as an educator that is my goal. So, what started out as a real serious personal concern and doubt at the beginning of class has slowly started to become a resolution to be personally successful in this class not only for myself but for the future students I will teach these subjects to as well someday!

First Blog--Eled 330

New Insights and Their Implications - 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?

I learned many new things since class has started. I have learned that I will need to teach many different ways to solve the same problem, and that different students will use different entry points. I l earned how important it is to not just give solutions to problems but to encourage the students to find a solution. It is very important to allow the students to struggle for a little bit before helping them. I also learned that I am very nervous to teach math to my students.

Blog Four: Questions and Answers

My question is: How do we as new teachers keep ourselves from falling back on the "old way" of teaching math?
I think there are many ways to confront this problem. Some of these could be:
-Never be afraid to try something new
-Learn from the students
-Collaborate with other teachers
-Learn from other teachers
-Never be afraid to ask for help

Blog Three: Summary and Synthesis

I think the Cognitively Guided Instruction that we have just learned has been the most beneficial part of this class. I wish we would have spent more time in class on it. I think this class has helped me understand how children think about math and also that there are many ways that children think about math. This math class has also helped me understand some math things that I previously did not understand completely. Now it is up to me to put my knowledge from this class into motion in the future.

Questions and Answers

Questions and Answers - Questions raised as a result of the experiences and include your personal thoughts as to a solution/answer to your question. (These could be inquisitive questions, musings, wonderment questions, or future research questions.)

After finishing the first half of the course, I have some questions. One question I have is about the tests. I did not do nearly as well as I thought I would on the 2nd test, and I am wondering what all is taken into consideration when grading them? After the 2nd test, I thought I would do much better than I did, and was very disappointed when I saw my score. My views on teaching mathematics are certainly going to be different than the instructors at this point as I am still a student myself, and I found a lot of the questions to be rather open to interpretation. I also question what else is taken into consideration for grading in this class? I know it may sound as if I am only concerned with grades, but when you are this close to the finish line, it would be extremely disappointing to take a class over and delay graduation. Some solutions I could find to these problems would be to take into consideration the students response to the test questions, and realize that they may be viewing the question froma different point than the instructor, and to put yourself in the students shoes to understand their rationale. I would also hope that the small in class assignments are taken into consideration while grading, though I don't know if they can make up for the lost points on the test. Anyway, these are my questions and answers for now, and I'm sure I'll have many more as the semester goes on.

Summary & Synthesis

I feel that now we are actually getting into what we will be using in teaching Math to elementary school students. I feel this way because, in my opinion, what we have been doing since the begining of this class is just being students... not becoming teachers. I know that CGI is being used in classrooms now, so why not teach us future teachers this instead of Math Concetps all over again? I am glad that we finally were able to view our exams, as I felt a little more prepaired for the final that was just days after. I really hope that the next class we have is more beneficial to becoming a teacher.

Personal Concerns & Thoughts

I feel much better about this class after I saw my first exam score. I did much better then I thought I would and I'm very proud of myself since I have been struggling a little in this class. Now I'm worried about the exam we just took, so I can't wait to see how I did. I look forward to the next part of this class and I also look forward to working on the LPU assignment with my group. I guess what I've learned through this class is to never give up and keep on trying.

synthesis

This last bit of class has been really interesting. I like that we are finally getting into the specific ways to teach more difficult concepts like multiplication and fractions. I'm not very good at articulating mathematical processes or explaining how they work so the strategies that we worked on in class were a little bit tricky for me to figure out but they really helped me to grasp how to explain the concept. CGI is also something that I really liked learning about. It makes so much sense for students to figure out and present their strategies to the class!

Concerns and Thoughts

This class was frustrating. However it feels like one of the few classes that I'm learning something that's relevant and useful. I was a little worried about the tests but we got to fill out and use the study guides. Even though this class was frustrating I couldn't really imagine it being any other way.

Personal Concerns and thoughts

I really do not have any concerns, I was worried about how I did on the first exam but after viewing the test I did better than I thought I had. I really enjoyed the CGI method and feel that I have a good grasp on that and that it will be a very useful method to use in the classroom.

Personal Concerns and thoughts

As you know, the students in the class and myself have learned math differently than we should teach our students. I think that this is going to be something that I struggle with as a teacher, because I am used to "here is the equation, now plug in the the correct numbers and get the answer." Now, we are learning to teach math, to actually have our students learn math instead of memorize an equation for the test, I think it's great, but I am very nervous for when I get out into the field and trying to 'actually' teach math.

Summary and Synthesis

From what we've discussed in class, the CGI model for instruction seems like it would be extremely beneficial to students' progression through learning. Allowing students to work with multiple strategies will help them decide which method will work best for them. In doing so, the students are able to choose the strategy which makes the most sense to them and helps them better understand the concept. Another important part of the CGI model is to give students opportunities to share their strategies with their peers. This allows students to learn from one another and to gain deeper understandings. These two aspects of the CGI model are very important in providing successful learning experiences for all students. Because this model for instruction is being practiced more often, I think it is very important that we were introduced to it. Hopefully, we will all be able to successfully implement this model into our future instruction as teachers.

Summary and Synthesis

Over the past few weeks of class I have really actually enjoyed this different type of learning that is being presented in this classroom. As I stated before in my first blog, I was slightly unsure of how this new way of teaching being done by Dr. Reins was going to go. Now after experiencing it first hand and realized just how much this has worked for me I have now rethought my teaching method for mathematics. By allowing students to struggle just the right amount with the information it allows them to feel a sense of accomplishment when they do finally figure out the answer. It makes it that much more worth the time and effort when you had to work at it rather than to just be given the formula and plug the numbers in. In addition to that, I have also enjoyed learning abou the CGI method and how that helps students as well. By giving the students a problem and allowing them to figure out the answer in their own unique way and then letting them share their answer with the class, it also helps students take pride in their learning and whent that happens it creates a much better learning atmosphere as a whole. In the end, I am definitely stepping out of the box and allowing my self to see a whole different side of teaching and am truly enjoying it.

Personal Concerns and Next Steps

Throughout this course, I have looked at math differently. I have learned that just giving students the answers and equations is not going to do anything for them except help with their memorization. With the CGI model we have been learning about, it is important to allow students to create their own strategy on how to get to the problem, which is a great idea. However, I am worried that I will not give students enough time to develop their own strategies or I will give them too much time, and it will make us fall behind. If we fall behind, then we will not be ready to take standardized testing. Another concern I have is that by the time I get students in my class, other teachers will have taught them the same way I have been taught, which is memorization, and then I will spend the whole year trying to get them to develop their own strategies. Which will make students frustrated because it is nothing they are used too. In addition, after they leave my class how can I know for sure that they will continue to use CGI.

New Insights & Their Implications

I have never really thought about developing specific types of addition, subtraction, multiplication, and division problems, but I now see why this is necessary. Although we confront problems with more abstract thinking, students who are just learning math really do perform specific strategies based on the problem type. Being able to create each problem type will help me challenge my students to take risks and try new strategies.

Throughout the class, we have learned a lot about developing a relational understanding in mathematics. Although I have learned the relational understanding of fractions and other concepts in this class, I feel that I only have an instrumental understanding of many math concepts we have not discussed. I may know exactly what to do when confronted with a math problem, but have no idea why. I plan to develop in my students a relational understanding of mathematics so they don't end up confused about why they are performing operations like me.

New Insights and Implications

Over the past few weeks, I have learned a lot about fractions. Coming into this class, I did not like to do anything with fractions. I wasn't good at adding or subtracting them and hated doing it. Now, after learning about models and manipulatives, I understand the process of equivalent fractions and adding and subtracting fractions. I learned a lot about how to compare fractions and teach my students how to add, subtract, multiply, divide, and compare fractions.