Concerns

After being in this class for almost a full semester, I think that teaching math this way is a much better method than the traditional method.  However, I do not feel that one semester of being taught this method is in no way enough to prepare us for using this method in the field when we become teachers.  I think that if we are expected to use this method of teaching math, it should be incorporated earlier in our education.  This way, we are taught this method sooner and we are able to practice it throughout our careers here as students.  I do not feel that being taught this method the semester before studn3et teaching is fair to us.  Especially if we are expected to use this method of teaching mathematics.  Having said that, I will coninue to practice using this method so that I am comfortable with it because I do believe it is an excellent way to teach children math. 

New Insights and Their Implications

Throughout this last month, I learned a number of things. The most useful thing that I learned was about the test administration and the type of questions that should included on the test. Tests need to include a number of different types of questions that measure all different levels of understanding of the concept being tested over. Tests should include easy questions that most people get correct but also questions that make the students use a higher level of thinking and make inferences to get the correct answer. Also, tests should include hands on learning if it is possible to help assess the students ability to actually do the work.

Blog #3

New Insights

From the past couple of weeks, I have had a few new insights that have impacted my overall feelings of this "new way of teaching math." In general, I have a very positive outlook on how beneficial this way is to students and their understanding of mathematics, however, I wish that we would have had this method taught to us from the very start in Math Concepts. I believe that one semester is not enough for us to truly grasp how to teach math this way. It should be a technique that we should work on developing during our entire time spent in the School of Education.
Another new insight I have had is about our LPU lesson plan. I'll admit I was very nervous about whether or not we would be able to teach this correctly in way that would be understandable to students. However, after having our meeting with Dr. Reins, I feel much more comfortable with how we are going to go about our lesson, as well as how we are going to help students grasp the concept we are covering.
A final new insight is on CGI. Overall, I feel that this method of teaching math is very beneficial and would be something that students would not only be engaged in doing, but would help them to grasp a concept much better than just rote work. It has also shown me that it does take quite a bit of work and thinking to produce good CGI problems, but the class presentations were very helpful in providing me with information and examples to help make it easier.

Personal Concerns and Next Steps

Based on what I have learned, so far, about project based mathematics and CGI instruction I have a few concerns about these teaching methods. I think that CGI and project based teaching are excellent teaching strategies for deepening students’ understanding of mathematical concepts. However, I still believe that there needs to be some traditional instruction in the classroom. My reasoning for this is because students still need to know how to do mathematics on using symbols and formulas. Although using models and pictures are great ways to understand and solve problems, there will not always be time or resources available for students to solve every problem using these methods. Also, my concern may be invalid because it is possible that problem based instruction does include periods of traditional instruction and I just misinterpreted it. Right now, my strategy for mathematics teaching includes teaching students the written/symbol mathematics and showing them examples with models or allowing them to find different ways to solve the problems. My thinking has changed over the semester because now I feel that the students should discover ways to solve problems before learning the traditional method. Some concepts I just do not think students will be able to figure out without prior knowledge. Exponents would be a topic that I would be interested to see how it is taught through CGI or project based before it is traditionally taught.

-Branden

CGI

I really enjoyed learning about the CGI model. It has made me think outside the box on teaching elementary math. I think that it is a very efficient way to teach students math. I think that allowing students to figure out their own ways to solve problems is much better than just telling them how to do it because then they will have a better understanding of the solution to the problem and will have a better chance of remembering it in the future. This is ultimately better than the traditional method because down the road teacher won't have to reteach their students how to do the basics of math.

CGI

Our last few class sessions have been focused on cognitively guided instruction (CGI). I could definitely see myself using this instruction in my future classroom. I really think the student-centered activities are a great way for students to grasp a new concept. CGI does just this--it asks opened-ended questions and gets the students to create their own ways of learning. Students share their thoughts with classmates through discussions and explore other ways to solve the same problem. CGI is great for teachers and students, which can definitely be hard in a math classroom. CGI has really been a topic that I have found to be the most interesting in class thusfar. It has us thinking outside of traditional style teaching and opening new doors to how students gain understanding and how teachers teach.

CGI

This last week we have been learning about the CGI (cognitive guided instruction) method of teaching. I believe that is a very good method of teaching students that allows them to be hands on with their math problems. CGI gives the students a chance to decide their own method of doing a problem. CGI also is a great way for the teacher to hear why the student does a problem a certain way. The students are encouraged to explain their reasoning of why they did the problem the way they did, and how they got to their answer. I think that doing our presentation on CGI of multiplication and division really gave me a chance to see the CGI method first hand. I believe that writing problems on your own based on the main topics really allows the teacher to make the problem exciting for the students. It is also every important when writing a problem to make it relate to the students so they are more excited to do it. Overall, I believe that CGI is a great method of teaching, and I will use it in my classroom.

CGI

I think that Cognitively Guided Instruction is a great idea.  I always learn better when I'm able to come up with my own way of doing the problems, and actually have time to do them.  It makes you look at math instruction in a completely different way.  What is the point of having the teacher stand in front of the class and work the problems out for the students.  It makes more sense to have the students figure it out on their own and learn the problems by doing it themselves.  I thought the video (as funny as it was) was a great way to show effective CGI demonstrations.  I thought it was great to have each student show how they got the answer to the problem because it shows the other students other ways and ideas of solving the problem.  I will definitely be using CGI in my classroom.

Cognitively Guided Instruction

Cognitively Guided Instruction has fallen in line with the rest of the ideas that we have discussed throughout the semester. Having the student showcase their skills and ideas for approaching a problem and figuring it is far different than what I have been exposed to in the past. Rather than focusing on what the student cannot do, the teacher needs to find out what they can do and work backward from the student's problem in order to help them develop the skill necessary to solve the problem. With this program, we have discussed again that the teaching really needs to be student centered and they need to find ways to figure out the problem or strategy.

Blog # 3: Reflecting on CGI

For the last few classes we have discussed CGI and from what I saw in the videos and learned through the discussions and the book CGI is something I could defiantly see myself using in the classroom. CGI makes more sense to me and is something that I think would be very valuable for my students. The videos we watched I found very interesting. Watching the students figure out the problems using their own methods was really eye opening, it just goes to show that students have their own ideas about numeration and numbers. Instead of giving them the formula to figure out 2X5 or 16-9 we can give them time to think through it on their own and come up with their own solutions. The bee question that was posed in the video really caught my attention, if one bee has 6 legs how many legs do 5 bees have. Instantly after asking the question students moved around the room finding the tools they want to use to help them solve the problem. One young boy grabbed a ruler and counted groups off the number line, another grabbed cubes and even used separate cubes to represent the bees themselves, and one little girl started using tally marks on her paper not needing the manipulatives that had been set out. Watching them solve these problems using their own strategies really got me thinking about the way I was taught multiplication. We were shown the proper way to multiply and given problems written out on a sheet of paper, there was not word problems or critical thinking skills being used. Using the CGI approach really opens the door for higher level critical thinking skills that allow student to formulate their own connections to math. After seeing the difference and reflecting on the studies we looked over on the first day of class I can’t understand why we don’t all teach math in this way.

last blog post, GURL!

During the past few class sessions we've been discussing CGI-- cognitive guide instruction. I can totally see myself using this in my classroom someday (God forbid I ever teach math). I really believe in student-centered activities and approaches, CGI does just that. It is built around open-ended questions, students working on their own then eventually sharing their thoughts and ideas and ending with a small discussion. CGI is very teacher and student friendly, which isn't the case with all math approaches.
I think this has been the most helpful topic we've covered so far in K-8 Math. Each and every one of us should be motivated and intrigued by the idea of stepping away from traditional strategies-- especially considering how many of us have shared that the root of our hate for math comes from how we were taught it as children-- and moving forward, finding ways to help our future students succeed.

Personal Concerns and Next Steps

Throughout this semester I have been introduced to many different teaching strategies when teaching math. However, I still feel lost, and concerned about how I will be able to use these strategies when I become a teacher. Math has never been my strong suit, but I do know how I learn math, and the different approaches we have learned this semester are not any of them. My guess is because I have only been taught the traditonal way of learning math when I was in school. In a way I believe this has hurt my confidence and understanding in this class but it is important to learn different approaches because all students learn differently. Although this class is very frustrating for me, I still want to learn this way of teaching because it can benefit the students I have in the future.

Personal Concerns and Next Steps

I have a concern that math is definitely different from when I was in elementary school. I need to continue learning the best ways to teach math, in order for my students to learn. I am a little nervous that I will either not use the right technique with my students or I will not use it appropriately. Both project-based learning and CGI are new to me, but I think there are great benefits in using those methods of teaching. Teaching maths seems a little overwhelming to me right now, but I know that if I continue learning the great ways to teach math in this course, that it will not as bad as I think (or at least I hope!!) I think I will have to find a way to integrate all the ideas into one: project-based learning, CGI, and some traditional teaching. Since each student learns differently, it might be beneficial to vary my approach, which is why I need to make the most of each topic during this course.