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.

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