Personal Concerns and Next Steps

Throughout this course, I have learned a lot about different ways to teach. I have also learned a lot about myself and how I learn. Allowing students to explore a problem and find their own solutions is what we have learned about. We have learned not to just show them how to do it. I am still not completely comfortable with teaching this way. My teachers always just gave us the solutions and stepped us through solving different problems. This is the way that I am familiar with. It will take some time to feel comfortable with teaching the way we have been learning about. Researching and practicing this method that is new to me are two things that I plan to do to help me with my concerns. Continuing to use this new method will help me with teaching. I know that I will not be comfortable with using it when I first start off teaching. I hope that I do not turn back to the traditional way and the way I was taught when I start teaching. It is important to understand the material you teach and that you know how to teach it to every student. Taking the approach to teaching that we are learning about will be difficult. However, after time I hope that I will be able to use this approach. It is difficult for me to learn how to do a math problem in a way that I am not used to. I am used to solving math problems in the way I was taught. To help with this problem, I will continue to try and practice this new style of teaching.

Personal Concerns and Next Steps

Now that we have about a month left in this class, I am beginning to feel worried that I am not completely ready to teach math in the ways we have been learning about. It is very scary to think that at this time next year, I very well could have my own classroom and group of students to teach math to. I am concerned that I might try to teach my students in the "wrong" way. I also am concerned that I may try so hard to teach in this "new" way, that I may not realize what types of instruction my students really need. I want to teach in this new way; I know my students would really benefit from it, but the thought of teaching something wrong is a huge concern for me. I am also concerned about what parents will think. Obviously my future students will go home and tell their parents about their day and I am just worried that one day I will go check my email and I will have several emails from angry parents asking me why I am not teaching their children the way we used to be taught. I am not teaching to impress parents, but unfortunately, dealing with parents who don't believe in the way I am teaching would be very difficult I imagine!
I feel the best steps I can now take are to continue to learn as much as possible about teaching math in effective ways. Just because the class is over does not mean that I know absolutely everything I need to know about teaching math! I will need to continue to learn as much as possible. Becoming prepared will also help me to deal with parents, too. There are many resources available for me to learn more about teaching math and it will be extremely important that I use those resources to help me become a better teacher. I need to realize that my teaching will never be perfect, but the more I learn about teaching, the better my teaching will be.

Concerns and the next step

Having been taught math concepts for 16ish years the traditional way with examples, homework, corrections, and tests it is concerning to me that I am suppose to stop, drop, and roll into a new way of teaching. I have become so wrapped up in trying to figure out what we are suppose to be doing and how to teach it the way our professor wants it to be taught. I look at the concepts presented to us and say I was taught this concept this way so I do not see why it is a terrible way to teach it. I see where our professor is coming from with the concept based learning and wanting students to see the true meaning behind certain parts of math. Do not get me wrong I have had an open mind these past weeks about trying to understand and learn how to teach in the concept based mind but it is so difficult to change in only a matter of weeks. I am staying optimistic in that I can continue to broaden my outlook on certain mathematical ways of thinking and teaching. I have learned many new ideas from this course.

Summary and Synthesis

This past week in ELED 330 we have been discussing CGI (Cognitively Guided Instruction). From what I know about this program so far, I think it sounds extremely effective. It is a way for teachers to understand students mathematical thinking. This program is used for grades K-6. CGI allows all students to be actively involved in problem solving. Students are able to solve open-ended questions using their own method (student generated solution strategies). Furthermore, students are given the opportunity to explain their mathematical thinking. One reason this program is so effective is because students are always given enough time to give a thoughtful answer. I definitely think more schools should use this program. Students do have the knowledge to find their own way. A student-centered program, like CGI changes the way students think about mathematics for the better.

Summary & Synthesis

For the past few weeks in math methods we have been discussing the CGI approach (Cognitively Guided Instruction). It is similiar to the reformed based math, in which new teachers are encouraged to use in their classrooms, however, several teachers dont use this beneficial approach. We learned that some of the assumptions of CGI are that students' use multiple "roads" of learning to find their solutions and that most of their solutions are developed by means of their own approaches. When using the CGI approach, the instructor acts as more of a facilitator, rather than an instructor who shares strategies and ideas with the students'. Key components of the CGI program are that students' share the different approaches in which they use with their peers and that students' are given plenty of time to thoughtfully think through and solve their problem. It is extremely important that instructors give students' that "wait time", because a lot of students hesitate to state their problem solving strategy. I feel that CGI is an approach I want to use in my future classroom and will without a doubt benefit from. Teachers need to stray away from the traditional style of teaching and allow students to "think" for themselves. By using the traditional style of teaching teachers' are depriving students of their own learning and creating learned helplessness. I am looking forward to implementing this approach (CGI) into my future classroom.

Summary and Synthesis

Over the last couple of months, I have learned some important teaching strategies for teaching math. This way of teaching, was not the way I was taught growing up. I am very scared about this new teaching strategy. I hate math, and I am concerned that my attitude will rub off on my students. In learning this new strategy, it’s scary, because of what I was used to, now I have to change the way I learned, so I can teach my students. In this class, I have really been challenged to understand the material. Over the last couple months, I have gotten frustrated with the assignments and readings because it’s forcing me to think about math in a completely different way. This class is a struggle for me, but each day I am learning little by little. Hopefully this new way will have a positive impact on my future teaching of mathematics.

Synthesis

We have been learning about the Cognitive Guided Instruction (CGI). The key components of CGI, observed from two in class videos, happened to be that students are using their own methods to arrive at a solution, the students are explaining step-by-step their methods, the questions are open ended, and the students are capable of higher level thinking when solving the problems. The assumptions that go along with this teaching style are that the students are capable of explaining themselves clearly, there are multiple approaches to solving a problem, and that students have the knowledge to find their own methods for solving a problem.

We have learned about addition, subtraction, multiplication, and division using this teaching style. The addition and subtraction are placed together are given different categories. There is join, separate, part-part-whole, and comparison for the main categories of the types of problems. Join problems are generally addition problems, and separate problems are generally subtraction problems. Compare can be subtraction or addition, but are saying that "y" has more of "n" than "x". Part-part-whole problems are usually involving a problem that seems it could be a fraction or ratio. There are three different subcategories for each problem and are the same for three of the four categories. The three subcategories are result unknown, change unknown, and start unknown. Part-part-whole has two subcategories, those being part unknown and whole unknown.

For the multiplication and division portion of CGI, There are four categories of the type of problem and then three categories for the problem. The three categories for the problem are multiplication, measurement division, and partitive division. The first category obviously deals with multiplying, and the last two obviously deal with division. Multiplication deals with the missing total for the problem, measurement division deals with one missing group within the problem, and partitive division deals with missing objects in a group. The four problem types are grouping/partitioning, rate, price, and multiplicative comparison. Grouping/partitioning is dealing with students placing items into a group and figuring out the answer from grouping. Rate deals with time and distance, normally miles per hour. Price is dealing with the unit price or price per pound/gallon. Multiplicative comparison is saying that something is some many times taller, longer, wider, etc. than another like object/person.

I like how easy this teaching style seems to be for students, and we are asking students to do something most are naturally able to do, such as grouping objects together or using drawings to figure out the answer to a problem.

Personal Concerns and Next Steps

While going through this course, I have learned a lot about the way that I learn in the area of math. Math has always come very easy to me and I have always taken a liking to it. However, after experiencing this course I have found that I do not enjoy math as much as I used to. I think that I don’t enjoy math as much anymore because I am so confused on how I will someday teach my students. I know that what we are learning in class on how to teach math will help students to really grasp the concepts that they are taught, but I struggle with the fact that sometimes it takes me awhile before I understand what is going on in the class. At times I never really figure out how to do what we are learning until we have moved onto a new concept, and it is then that I finally understand what we were supposed to take from that new “idea.” I think the reason that I am struggling so much in this class with understanding what is going on, is because I have never been taught this way. I was taught the traditional way of using worksheets to figure out how to solve problems; I never really got a whole lot of interaction with manipulatives. I fully intend to someday teach as the way that we were taught in Eled 330 and Eled 432, but as already mentioned, I will have to do a lot of practice working with different models and thinking of different activities before I am able to teach the way Dr. Reins teaches. I am a little concerned that I will become frustrated with learning/teaching my students deeper level thinking process and turn back to the “traditional” way of teaching.

Blog #3- CGI

The last couple class meetings we have centered our learning and focus on the CGI method of teaching. Alot of the aspects of this teaching model we have have been incorporating into Math Methods, but it was interesting to learn about CGI and compare it to project based learning methods.
Cognitively Guided Instruction is student centered with limited teacher interaction. In order for CGI to work students need to have prior knowledge of the topic at hand and they need to be able to develop their own models and strategies to solve various problems. Some key elements that i feel are important to CGI are: recognizing multiple approaches to solving a particular problem, allowing students to show the entire class how they arrived at their answer and owning the work that they have done, and the problems and questions need to be open-ended. These elements and assumptions are important if teachers want to get the most out of CGI.
I plan on using CGI as much as possible. It is a great way to get students proud of their work and claim their findings. I think it is an important tool to use especially with younger students. We could use this tool to shape and form their way of thinking early on.