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.

Summary & Synthesis

I am really excited about what we have been recently learning about in this class. We are finally seeing what we can do to incorporate techniques in the classroom. The CGI model will probably be something I will eventually use because I would like to be a math teacher some day. I like the ways we are learning about the CGI model and seeing how we can incorporate it into the classroom. We are in a way being students during this process but this is good because we will actually be teaching this concept someday in the future.

Questions and Answers - Blog 3

Throughout the last few weeks of instruction, I have learned how Cognitively Guided Instruction can greatly benefit student's learning. I have several questions about CGI. How do teachers use CGI in their classroom and plan for timely instruction? I understand that teachers will plan lessons that allow students to develop their own strategies to solve problems, but how to they do this in a timely manner. I am having a hard time understanding how teachers plan their weekly or monthly lessons using CGI since the teacher will not know how long it will take for the students to develop an understanding of the concept. How do educators teach the important concepts that students need to know for standardized testing? How do you encouage students to use their own strategies and methods for solving problems in a timely manner? I know that it is important for students to use their own strategies for solving problems, but in order for students to be successful on standardized tests, students must be able to solve problems efficiently. How do teachers use CGI and encourage students to seek their own answers efficiently?

Summary and Synthesis # 3

I have enjoyed learning about CGI, and I can see how this helps the students. I can see how having students use their own knowledge of problem solving to tackle a problem. This is a much better way to allow students to obtain deep understanding of the process that they will go through to solve fractions. I know that a lot of students struggle with math, and hopefully with this type of teaching, it will become clearer for these students.

I was a bit skeptical about the first half of this class. I truly thought that what was being taught was for older students. That was, until I went to my 3rd grader's conferences on Monday. They are going to start working with rhombuses, trapezoids, right triangles, obtuse angles, and parallelograms. So for those that think that they are not going to be teaching this stuff in the earlier grades, you will be. On that note I will keep the information from the first half of this class for my student teaching and beyond.

Summary and Synthesis #3

I have found this unit on CGI to be quite interesting. For most of my progression through education, my teachers have taught me one method of doing a task or a problem and I was just supposed to accept that as being the only method. Having students experiment and work through the problems using their own strategies is a great idea! Having the students share their strategies with one another foster class interactions and it can also be a learning experience for students. One student may not understand a topic and by listening to another student's strategy may begin to understand the concept. As we have discussed in class, learning stops when the answer is revealed. Students can utilize their different strategies to new situations as well and not just to that particular type of problem.

New Insights and Their Implications

Throughout the past few weeks (since our first test), I feel I have learned a lot about teaching math to students. Not only did I learn and now understand certain concepts about adding, subtracting, multiplying, and dividing fractions, but I also learned how to use models to represent them. Never before had I been taught how to use models to show my thinking. I understood the instrumental part of math but not always the relational part that really explains why and how we do things in math. I understand why we multiply fractions the way we do because of the multiplication bar method. I now feel I can teach this concept to students without questioning myself on how/why we do the instrumental parts of math.

I learned the importance of teaching fraction concepts to students through the CGI model. I think it's a great way to have students use their previous knowledge to construct their own learning. It gives more responsibility to the students and has them figure out how/why they perform a mathematical process instead of the teacher just telling them 'this is how we solve this.' Especially in the last few weeks, I feel I have learned a great deal that I will take with me to my own classroom.

Blog #3: Questions

A few questions that I have: I think CGI is a really great addition to mathematics but, I feel like it's only appropriate for lower elementary. My question is, how would you use CGI in upper elementary, or even middle school mathematics? Can you? Another question I have deals with the syllabus. It talks about "wikispace," which is something I am VERY unfamiliar with so...what is it? Also, aside from online manipulatives, which we already have looked at, what are some other pertinent technologies that should be incorporated into a math class?

Blog # 3 Questions and Answers

For my third blog, I decided to ask some questions. A few questions that I have is how are teachers implementing the CGI model into instruction? How do teachers use technology in a math classroom? I have talked with my aunt, who works at a middle school in Sioux Falls, and we were talking about how math instruction has changed throughout the years and how it is totally different. She told me that how they teach math is fun for the students to engage in. I understand that using the geometric shapes on the internet and using the camera deal to display group activities on the board are being used but my question is how else is technology being used?

Blog # 3

Questions and Answers...
What is Wiki space? How will using this website benefit us as students who are becoming educators in the near future? Do a lot of teachers use this technique/ method? And do they generally enjoy it? Just trying to get a heads up on the lesson.

New Insights and their Implications-Blog #3

I have never loved math, but have always gotten through it with help from others. I can relate to using CGI because hearing how somebody else does a problem has almost always helped me. As a result, I will use cognitively guided instruction in my classroom because I know the benefits of using it. Additionally, I learned there are even books that use CGI that teachers can include in their classroom libraries. I think students can really benefit from trying to solve the problem on their own, using their own processes, and sharing their ideas and strategies with one another. As a future teacher, I would like to be able to see how math is taught using CGI. I do like the idea of CGI, but I have one concern with using it, which is the time. As a teacher, we have to cover so many topics for students to be able to do on the standardized tests, so letting them discover the answers and develop the formulas on their own takes a lot of time. I am just curious how teachers use CGI but still cover the entire curriculum. Overall, I think CGI is a good thing, I just don’t know how it works out in an actual classroom with all the content there is to be taught.

Personal Concerns and Next Steps

Throughout my entire education, I have always struggled with certain aspects of math. Geometry was one part of math that I have always done well in. However, when the questions about why we use the area formulas came up, I had no idea how to even think of a reason. This class has taught be a lot about what is behind the basic fundamentals we were all taught to memorize. I worry, though, that I am not fully aware of how to teach such ideas because it is still so new to me.

The CGI model that we have been talking about is a great tool to keep in mind and to think about when it comes to teaching math. I look forward to seeing all of the different and creative strategies my future students can come up with when solving problems.

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.

Summary and Synthesis- Blog 3

Since the midterm we have been talking about CGI (Cognitively Guided Instruction). I personally have never seen or been introduced to this instruction before. After learning and watching videos over it, it makes sense. Why would you tell the students the answers before they begin? Why should there only be one way to solve a problem? There shouldn't. Having the students explain how they got the answer to the questions to each other, is more beneficial to them. They are talking with their thinking and mind which can relate better to their peers. Telling the students how to do a problem limits their learning. The model you teach may not make sense to them, but the way their peer does it, does! I am glad that we went over this and I will definitely use this in my classroom. It's a great way for teachers to understand the student's mathematical thinking.

Personal Concerns and Next Steps- #3

Throughout this course my main concern has been that I am afraid that I am not going to be a successful teacher of mathematics. This is not because I feel that the class isn’t teaching me enough, but I am worried that my own personal fears about math are holding me back from reaching my potential. I think this is due to the new way in which we are taught mathematics in this class. I have struggled with math through my entire educational career and this new way of learning has definitely showed me how I have somewhat developed learned helplessness over the years from my school years prior to college. My past teachers did not challenge me to find solutions on my own and when I asked for help they would basically give me the answer and I still had no idea how I got that answer, and sadly, I was satisfied with that way of learning. This class has made me realize what I need to work on in order to break my learned helplessness habit in math. If I do not fully understand the concepts (or even if I do) we are working on in class I go back through the material after class and try to make sense of it. I have started using the online manipulatives and they have really helped me to understand why we add and subtract fractions the way we do and different ways that it can be done. I feel like by going over the information and using different materials I am re-learning the math facts, which is very helpful to me. Reading the textbook assignments has also been helpful to me. I am beginning to feel like I can be successful at math and I need to continue pushing myself to make sure that I understand and think about what I am doing and why I am doing it when it comes to solving mathematics problems. I am thankful for this new way of thinking about mathematics because I feel that my struggle will help me to better understand and relate to my future students who are struggling

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.