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.