New Insights- Blog 3

The new insight I have gained from our work with the CGI method will not go to waste in the future!  It seems to me that with this approach, we are giving students a real shot at understanding and appreciating mathematics.  In the classroom, this method could be a valuable tool for figuring out how each student learns by what methods they choose to use to solve a problem.  By understanding the different methods used in addition, subtraction, multiplication, and division, students would be better able to see why different pieces of a problem go where they do in a mathematical sentence.  I cannot imagine how I could not use this method in my classroom since it proves to work so well in studies and with myself, who previously didn't appreciate the importance of CGI in the classroom.

Personal Concerns

CGI

CGI is something that I really like. I love that students are not told what is right or wrong in the method of finding their answers. Being someone who struggles with math I can see how I would have been encouraged through the process of learning addition, subtraction, multiplication, and division. I love seeing that there is a method of teaching that focuses not only on the answer but the different paths to get there. I dont think that you can just decide to use CGI one day, and teach it the next. I think that it has alot more to do with the way that teachers are approaching their classrooms with the freedom of creativity, and students feeling open to express their paths. These concepts must be instilled into children so that they will not fear the wrong answer, and will try even if they are not correct. I feel like all classrooms should be set up in this way and that it is very beneficial to students of all ages to experience the benefits of a CGI classroom.

New Insights

Learning about the CGI method for teaching younger students about addition/subtraction and multiplication/division has really helped me to see how we can teach math better starting with the earlier grades and moving up. What CGI has taught me, is that students know math and it is up to us as teachers to work with them on using their knowledge. When giving them a problem for them to work on, we don't say we are doing multiplication today, as that is going to scare some kids. Giving them a story problem that they can draw out or use manipulatives on isn't as scary. After taking about it in class, I got to see that CGI problems are used at St. Agnes here in Vermillion in the kindergarten classroom. They have a math journal that every week each student works on their problem. It isn't "we're learning this today" but a chance for them to work out something on their own without being scared of labeling the problem. And that may be part of the math problem now. With traditional math, we start each lesson by what we are doing for the day, which can scare students before even getting to the problems. It is already too hard for them, and they haven't even tried. We should move away from that, and that is what the reform method is teaching us.

Personal Concerns and Next Steps

As a future teacher I am concerned that I will not teach these concepts correctly to students. This is more about me coming out of my comfort zone, which I don’t mind doing depending on the situation. My main issue is how I will teach my students this method of math when other teachers are still teaching the students the old way, by using the textbook and by the students not solving the problems on their own. My thought is that if I am trying to teach students these concepts how am I to make sure that the students are taking them to next level and ensure that the teachers are also? I think that I will have to find teachers that are familiar with this method or even teachers that have not heard of it and to provide teachers background information on this type of math. I need to get other teachers buy in so that the students are able to expand on this way of thinking and are able to use it year after year. Maybe setting up a math group with other teachers so that we could work as a team in planning our lessons and helping the students scaffold on this learning. I think that this is a great method for students to use when it comes to math so that the students can find their own way of solving the problems which will help to retain the process better and actually take something away from math. Personally, I have gained a new perspective on math and wish that when I was a student that my teachers would have used this method, I think that maybe I would be more comfortable with math and would understand it more.

Personal Concerns and Next Steps

Going into this class was imtimidating to me as I have always struggled in this area. Growing up math has always been done the traditional way of coming up with the answer and everyone was taught the same and seemed to me it was a much easier. This class allows the student to think cognitively and bring their own knowledge and concepts into the classroom and connect that knowledge with mathematics. I know the emphasis is on what the student can do rather than what they can't do but seems to me doing it this way, there are so many different ways of coming up to one solution that it has become difficult to teach. I feel there are so many different understandings and concepts to teaching these methods and maybe it would be easier for the student who is struggling but I haven't quite grasped it all yet and certainly don't feel comfortable as of yet in teaching it. Sometimes the new ways are better and students feel more at ease learning what they are capable of, so as this class progresses, I intend to continue to have an open mind and do what is best for the students when I become a teacher.

CGI

The videos we watch in class about CGI teaching were helpful in understanding what a cognitively guided instruction classroom would be like. The presentations on addition/subtraction and multiplication/division were helpful. I now know how and why its important to create different types of problems for children. Its also important to make the problems relevant to the students lives. In a CGI classroom, children naturally use a model that suites their style to solve the problems with out the teacher's rote instruction. After students solve the problem, they communicate with the rest of the class on how they solved the problem, what tools they used, and their answer. A variety of methods will be discussed before the class moves on to another problem. CGI is a good instructional strategy that I plan to use in my classroom. It's important for a teacher to build on the child's knowledge and to meet them where they at and to take what they already know and push them to the next level of mathematics.

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.

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.

Blog #3

Throughout this course we have been studying many different ways to teach students about math, but the newest method is by Cognitively Guided Instruction or CGI. Through listening to two different LPU's on CGI, I have to admit that I am taking a liking to this method. I really like the fact that teachers are present various questions to students, and allowing students to find their own answers by using their own unique way. Students are able to pull from their background knowledge and previous experiences to find the answers on their own. When thinking about the CGI model, two questions form into my thoughts. First, how can I use the CGI model as a special educator. And with this question I believe that I can answer that myself. It's easy. Students of all varieties have previous experiences that can help them in their own way. The key, is being able to pull from those experiences that will actually apply to the task at hand. The problem for students with disabilities, is their ability to know how to take from their previous experiences. That is my job as a special educator to help those students work with what they already know, and then help them to manipulate what they know to find the answer, or maybe help them use an easier strategy. Then, that brings me to my second question. How do we help students using the CGI model when they don't get to the right answer. This was brought up during the video that we watched during class. In one of the clips, a little boy did not get the wrong answer when he used his method to solve the problem. The teacher then referred to another student who used a similar method, but got to the correct answer. I realize that it is not always important for students to know whether their answer was right or wrong and that sometimes it's more about the process. But, when students are using their own methods, and still not getting to the right answer, how do we teach students to use a better method, or what do we do to help those students who are struggling?

Personal Concerns

I will admit that I am a little worried about this new approach towards teaching. I have always been taught with a traditional approach, so I am worried that I will not be able to implement this new approach effectively. I think that with more time and practice, I will become more comfortable with this appraoch, but as of right now, I am not comfortable with it. Throughout this course and watching my fellow classmates presented their LPUs, I have learned various approaches and strategies that I will most definately use within my classroom. However, there are still some approaches that I do not understand. Therefore, if I plan to use these approaches, I know that I will need to do more research and practice these new methods before I could use them in the classroom. It is important that as a teacher you are comfortable with what you are teaching. If I do not feel comfortable with what I am teaching, students will be able to notice that and it might worry them and turn them away from math. I think the best approach towards this new way of teaching is to implement it a little bit at a time while still teaching in a more traditional approach...just until students become more comfortable.

Personal Concerns and Next Steps

This class has been great in showing me a new style of teaching that I have never seen before. I do have some concerns with it though.  The Project Based Learning is very new to me so I am not completely comfortable with it quite yet.  My concern is that there is only a month and a half left in the semester and I don't know if I will feel comfortable enough to use this type of teaching in my classroom when I am student teaching.  One way that I am going to try and solve this is look at the book that is provided for the class.  My group has been preparing to present our lesson next week and when we have been preparing, it has made me realize that the book has a lot of great activities to use for all grade levels.  Another concern that I have is that I do not really love this style of teaching.  I have always been a "math person".  After taking this course, it has made me look at the subject area in a different way.  The way that I am going to try and solve this concern is to be open-minded. I know that every student is not like me and does not like the "old way" of doing math.  The "new way" of math may work for some students and teachers need to accomodate for every student that is in their classroom.

project based learning

I'm starting to get a better grasp on project-based learning. Now that we have taken the midterm and have seen a few more groups present, I'm starting to get used to the way this class is set up. I'm starting to appreciate the way we are learning the material, but it's still hard to bring down my level of thinking so I can see if from a child's perspective and that is something I definitely need to work on. However, I think this will be easier when I'm in a classroom and have my student's experience to base my instruction on. I can try to come up with different ways to do a problem and come up with ways that children would look at this problem but it's harder when you don't have an actual classroom to work with. Of course there are our peers but our college peers don't interact and don't do math like elementary children would. I've never had experience in an elementary math classroom, but those videos we watched today about CGI were helpful and fun to watch. I'm gaining an appreciation for math as this class is progressing, and I'm getting more out of this class than I have from others.

Blog 2

Though I am still struggling with the Project Based Learning in math, I also understand why it is so important that we allow our students to come up with their own conclusions as to why things are the way they are within the rules of mathematics.  Had I been taught this way, I probably would not have such an overwhelming fear of math as a subject.  Every time I attend this class, I am left wondering, 'Why has this method of teaching come around sooner?'  Though it is out of my comfort zone, being forced to look at the reasoning behind the rules and processes of mathematics has given me a deeper understanding of why math works the way it does.  I am slowly beginning to understand why it is important to move out of the comfort zone of worksheets and easy, fast teaching into a method of teaching math that will allow the students to not only perform the tasks, but really understand them. 

Summary and Synthesis

As the semester goes on we are continuning to learn problem-solving based learning. It has been very helpful to learn the different strategies Dr. Reins models to aid in our learning to teach math this way in the future. I also think it has been helpful to learn from the different student presentations we have had so far. It is beneficial for us to see how our peers are teaching this way of math as well. Although it seems frustrating at times, its important we learn this reform based math instruction so it will benefit our students in the future.

Blog #2

From my first post until now, much has changed. I am still strugging with the PBL method of teaching and how to learn from them. I feel that much of the freedom we are given leaves me feeling unguided in assignments and expectations. I feel that I would benefit greatly if were given more detail or guidance with our homework. I know that this is something that is proven to be alot more beneficial in teaching math, I am not sure that I will be ready to teach math in this way by next fall. I agree with all of the concerns that Molly addressed, and am wondering if there are any other resources for teaching PBL in math. It would be great to have more information on this since graduation is coming up very soon!

New Insights and Their Implications

I have learned so much in this class so far and I will definitely use this tips I have learned in the future. The groups that have presented gave great ideas for teaching math. For example, the LPU with the fractions was fun to listen to. It was fun to see different ways on how to teach fractions. Dot paper, pattern blocks, fraction bars, and rods can all be used to teach the same thing. I like the idea of using different techniques for one subject since every student learns differently. Also, the approach of project-based learning has been a good experience. I think students get more from the lesson if they aren't just handed the formulas and answers, and if they actually do the work of the process. By participating in project-based learning, I feel like I am becoming a better-informed teacher. If I actually participate in activities students will be doing, I get more of an idea of what it is like to teach it.

I have learned so much so far and have gained so much insight and I cannot wait to put it to use in the future!

LPU

So far in class these groups have presented their lesson plan for understanding, my group happened to be one of them. Our lesson focused on area formulas. When we first chose this topic we thought it would be a fairly easy lesson to create, but after we met with Dr. Reins our opinions quickly changed.
We could not figure out how to teach a lesson that would have our students coming up with the are formula themselves. We met several times and felt frustrated because letting students explore and find things on their own is a hard thing to do. In junior high we were taught formulas by copying them off the board and then taught which numbers get plugged where, so naturally we felt scared.
After another meeting with Dr. Reins we felt comfortable with our lesson, but were still unsure if our classmates would understand what we were asking them to do. The day of our presentation things went smoothly and we did just fine, but without our planning and preparation it would not have went as smoothly.
All in all I enjoyed our lesson. It was a great way to practice project based learning. I now know I am capable of teaching the "new" way and look forward to actually implementing it into my classroom some day.

Personal Concerns

I don't have too many concerns but there are a few. I'm nervous of teaching mathematics the 'new way' since the 'old way' is what I am comfortable with; it is also how I was taught and how I know the information that I do. I understand the importance of teaching students how to come up with strategies on their own and why it's important to let students explore mathematics so that they thoroughly understand the concepts. However, I'm not sure that switching to this new way is going to be easy and can be accomplished by the time I will be teaching. What are some ways that I can 'switch over' to the new way of teaching mathematics at a fast enough pace so that I can start right away when I have my own classroom? How can I teach my future students this new method when I myself, am not real comfortable with it?

Recently In Class

Recently in class we've been talking about fractions; addition, subtraction and a little bit about multiplying fractions. I found the last lesson that was taught in class to be rather interesting. A new concept of teaching fractions was brought about and I thought, "why didn't anyone show me that before?!"
The fraction table method that they showed us we new information for me and I was really impressed with it. It is defiantly something I would teach to my students. Not only does it show you the break down of the fraction and give you the least common multiple, but it also works other math skills like multiplication tables. I didn't expect to learn anything new with the lesson and I was pleasantly surprised when i did.

The house project we've been working in recently however hasn't been so plesent. My group was assigned the task of figuring out the area of the roof to figure out how many shingles would be needed. It took us quite awhile to figure out where to start and even longer to get a good idea of what the roof actually looked like. I'll admit i'm still struggling with this class and i'm worried about the midterm but I have to trust that there is a light at the end of the tunnel i'll eventually see.

Personal Concerns

After having been in class for a while, I have the concern of not liking this way of teaching. I understand the concept of it, and how it will be beneficial to students. But I think about how I was taught and how well I excelled in Math because of the way I was taught. I love Math and I will say that what I haven't had to use, I've lost, but I just don't know if I had been taught a different way, would the outcome have been the same. Would my love for Math still be there if I was taught the way we are talking about? In order to move forward with this, I am going to have to think through my past Math classes and how I could incorporate reform based teaching into it, so that the students who will learn from traditional teachings can learn right along with those that will learn better from reform based. This means extra thinking time for me, and in class I will need to focus on how I can use what I am learning in a different way.

New Insights

K-8 Math Methods is so much different from any other methods and/or math class I’ve ever taken. The approach is much different, which I appreciate. This class has showed me that I have a chance at being a decent math teacher—granted, it’s a very small chance, but a chance nonetheless. I have learned a lot from Dr. Reins, but I’ve learned even more from my fellow classmates. The LPU presentations have been very interesting, fact filled and entertaining, but I’ve picked up a lot more knowledge from our “talk time” in class. I am seated around a handful of great gals (and occasionally Adam and/or Kyle), we’re all very comfortable with each other and explaining ourselves and our ideas. So many of my math fears have subsided because of a one-on-one explanation from one of my peers, which is really something special.

New Insights and Implications

Through out this class I have realized I never really knew how to teach math.  I have had so many teachers who simply show us how to do a problem and have never explained why.  I feel like in order to really teach students math, we need to teach them how AND why we are doing problems the way we did.  When asked the question in class, "Have you ever learned how to do a mathematical problem, but were never taught why?' I thought to myself, YES!  I feel like every single math problem I have learned I don't know why that is the way we do things.  It makes me nervous to teach this way because if no one ever explained it to me, then how am I going to explain it to my students.  I have begun to think in an entirely different way of how I will be teaching math.  Students aren't going to be able to simply "get it" without proper explanation.  Now that I know this, I will have to work hard to figure out the best way to teach my students.  I don't want to be the teacher that makes students hate math.  I'm just happy I learned this before I start teaching, rather then later.

Summary and Synthesis

In class we have continued learning how to incorporate problem-based learning into our elementary classrooms. I have realized exactly how much work this type of teaching will be. It is going to be a challenge but I have also learned that there are resources out there to help you. Also, you can use other teachers and the students themselves to help generate ideas. Throughout the classes, our classmates have done a wonderful job explaining a couple math concepts using this style of teaching. Using their lesson plan, the students will have a better chance at understanding the concept fully and not just go through the motions because the teacher told them it was the correct way.

LPU

After having completed the LPU this past Tuesday I have concluded that it is very important to understand the concept being taught. When we began planning this LPU my group members and were not sure we knew exactly what we were going to be educating you all on. We were taught fractions one way but here we were expected to look at it in a different light. Once my group members and I started practicing and doing what was read from the book and notes we come to an understanding of how to teach this concept in a new way that now made sense to all of us.I found the table method to be something so simple that I never would have thought to use it. I feel that the table method will be very helpful to my peers and me when we are teaching our own students. The fraction bars for me were the hardest to grasp and that is why it is always important to have more then one way of showing students how to do something. Using a semi-concrete model as well as manipulatives can result in great success from students. One thing that I found most valuable from the LPU was that you need to remember that you are older and have had the information already built upon and these students you are teaching are starting from where you are starting. Keeping an open mind and allowing for constructive criticism will better your teaching in the years to come.

New Insights and Their Implications

This class has given me many tools I now would feel comfortable using while teaching math in the K-8 setting. The most useful tool I have accrued is a completely new style of teaching and a more effective style based on projects and higher level thinker. I have already begun experimenting with some of the new insights I have gained in an internship experience where I am working with two students who are struggling with math. I often find myself explaining how a mathematical property works and alternative routes can be used to find the solution. However, when I am working with them on their homework it is always a worksheet or a set of problem from the textbook. This concerns me because I am sure there are students who are passing the assignments and do not require addition help but are in fact missing the entire concept. These students will doubtfully struggle when more challenging mathematical problems are given to them, maybe years from now. The most helpful and probably most recent insight I have been exposed to is to make sure the students understand the how’s and the whys instead of learning rules without reason.

New Insights and Their Implications

After being in this class for 6 weeks, I have realized that even though this method of teaching math is more difficult it is much more meaningful to the students.  Teaching math this way allows students to find and discover formulas and answers on their own, which makes learning more meaningful to them.  I grew up with the teachers just giving me the formula and then I would just plug in the numbers to make it work.  I am in my last year of college and I am just finding out the reason/purpose for certain formulas.  I think that by giving students the chance to discover and learn these things on their own when they are still young will allow for that information to stay with them.  This will also allow them to grow and be more confident in mathematics.  I think that as long as our students are being challeneged but are not frustrated, students will be more confident in mathematics and will perform better. 

Blog #2

New Insights and Implications

I will admit, as interested about learning this new of math as I was at the beginning of the semester, there was still a part of me that was very nervous about it as well. I was unsure of whether or not I would be able to fully comprehend it. However, though I have struggled along the way, I have begun to discover that I am starting to grasp it (at least for the geometry part). It was very interesting to see how geometric understanding builds throughout the grade levels, and thus how we can build off their prior knowledge to help them discover new concepts of mathematics. From one of our beginning activities where we took a rectangle and transcribed a triangle into it to actually developing a formula for the area of a triangle, I was able to see how this way of "discovering" math is accomplished, and accomplished well. Another example was through developing multiple formulas for determining the area of a polygon to being able to take the idea further to apply it to a real-life situation - determining the amount of shingles it would take to cover Mr. Reins roof. Through this activity I was able to discover how we help students take the mathematical concepts they are developing and go beyond it to other areas and know how to do it. That was something I had quite a bit of difficulty doing in my math classes, so being able to help students achieve this is one reason why I will be very happy to use this math method in my future classroom.
A final new insight I have gained in the past few weeks is how difficult this will truly be to implement. I know that we discussed it, however, one never truly grasps it until he or she sees it done. From watching the groups present, I have been impressed by what they have done, and I have come to discover just how much effort it will take to teach in this style. However, I have also learned how important and beneficial it will be as well. So, I hope that I will continue to progress in my understanding of the method as the semester continues on, and that I will become confident in using it in my own classroom.

New Insights and their Implications

These past couple of weeks I have been thinking a lot about how I am going to teach math in my own classroom. This has never been something that I have worried or even really thought about because I have always been fairly good at math. However, I have become fairly concerned about being able to teach math in a way that will get students to think about math on a deeper level rather than me showing the students how do something and then they just practice what I showed them. This new insight implicates to me that I am going to have to look at math in a deeper way myself. I think that this class has shown me that there are several ways to express and teach math on a deeper level. However, I do feel that once I do get out into the classroom that I am going to have to continuously be conscious of how I am teaching math and if my students are really learning the concept of a problem or if they are just learning how to do the problem. I may struggle with making sure my students are always learning on a deeper level, mostly because I was never taught to see math on a deeper level, but I think that if I constantly think about how I am teaching a math concept and constantly ask myself "what are the students learning," then I think over time I will be able to consistently teach math on a deeper level.

New Insights and Their Implications

Throughout these past couple of months I have found a new appreciation for teaching elementary math. I have never experienced a teaching style such as reform based math, until Dr. Reins. I learned that students have to use their higher order thinking skills to solve problems, which comes a lot easier when using manipulatives, such as the ones we've used in class. I've also learned it is more difficult from the teacher's perspective of planning, I feel this is the reason so many teachers use the traditional style of teaching (worksheets, handouts, etc) because it is so much easier. However, this is also why our students aren't meeting national standards. When doing the LPU I learned that I want to teach according to the reform based math strategies, I want my students to have to think and solve the problem themselves, instead of knowing they can get the answer from me. This style of teaching is somewhat frightening and difficult, but I want to learn more about it so my future students and myself can benefit.

New Insights and Their Implications

Throughout these past couple of months that I've been in this class, I have experienced math in a way that I would have never thought of before. I have learned that math should not be so procedural in that a teacher gives the student a formula and tells the student to plug in the numbers because he/she said so. Math should be about students finding those procedures out for themselves and learning why they need to be used. I have learned that my understanding of math is definitely instrumental instead of relational. I have always been showed how to do a problem, then been told to complete different problems like the one shown on my own. I never knew the relational understanding or the what to do and why's of math. By teaching students why they are using a certain formula or why they are going about a problem in a certain way, the student can obtain a better grasp of a mathematical concept. I have learned that we must teach in a way that the student can learn cognitively. We must first start with what the student already knows and build upon that. I think the LPUs are a great way for us to try and begin teaching in the way that we have recently been learning about. Although it may be difficult for us at first, I understand why it is important that we learn how to teach our future students in a way that they will have a relational understanding of mathematics.

New Insights and Their Implications

I think the biggest learning experience in this class so far was the LPU. It made me realize just how effective project based learning is. Its easy for a teacher to have a student memorize a formula, plug the numbers in and solve it. From this experience I learned how much more effective teaching can be if hands-on manipulative's are used and if you let students discover answers on their own, compared to just telling them answers. However, it did make me realize just how hard it is to teach from this perspective. No teacher I have had up until this point has ever taught like this. It is definitely a learning experience. I am looking forward to learning more about this new way of teaching.

New Insights and Their Implications

After six weeks of this class, I have been shown a much different perspective of learning math than I ever have before. I have always learned by a certain route or formula to use for finding the answer to something. I was only shown a small glimpse as to why it was done that way, only shown how to do something. This class has really felt like I am back in elementary. The way in which project based learning works really challenges my traditional thoughts. I feel as if I am relearning all of the material over again. However, I am actually seeing why some formulas are used the way they are in math. The implications I have learned is that it is much more beneficial to the students to see the the why in a math problem before they learn the how. Otherwise, they are just doing something just do it without an idea of why.

New Insights and their Implications

I think that the LPU's have been a very productive part of this class for me. They have shown me that there are many different approaches to teaching mathematics and they also show me how parts of math are learned through the eyes of a child. I have also learned much from the readings and my instructor about all of the ways you can approach teaching mathematics. The readings fit our class lectures very well and serve as a great supplement to the course.

New Insights and Their Complications

Since the last blog, I have learned many different insights through my classmates LPU's. They have showed me the importance of doing project based learning in lessons, and the struggles and complications that go along with them.

My classmates have all done a great job with their LPU's and have set the standard on how a project based learning lesson should go. I have learned that allowing the students to do a project with prior knowledge that they do have engages their mind and makes them think about previous ideas they have learned about. Once the previous knowledge is brought to their attention, adding a new idea with a project allows the student the chance to figure out the problems themselves. I have also learned to allow the students to answer their own questions and to figure ideas out for themselves otherwise they will always depend on you to help them.

Doing project based learning lessons has also shown me there are many complications that go along with it too. It takes along time to be comfortable with the teaching style of project based learning and it won't be an easy task. It is important to start a lesson a week or more prior to when you want to do it. That way you can think about the background ideas and a specific project and outcome you want the students to have. It is also important to remember that teaching in a new style will be a complication at first, but the more you do it the more comfortable you will become with it.

New Insights and Their Implications

This class has been very instrumental to me helping me better understand the teaching methods of K-8 students. I believe the main understanding I have so far is the tools required to instruct a math centered class. I have found out that there are many different approaches to incorporate into the teaching process. Once these approaches are taught, students then will have the ability to use the skills, knowledge, and the learning resources to understand the concept taught. I believe the primary goal of this course is to prepare us future educators to be effective and engage news ways to instruct. I believe teaching math to elementary students is significant for establishing a firm foundation for success. Making it fun and interesting will help us as the students progresses to the upper grade levels. Understanding it early is so important so there isn't a struggle as they approach high school.

In addition, I have learned that putting students in situations which they have to apply what they are learning to personal experiences and situations helps to reinforce the concepts of math and gives them a much better understanding of this subject. I struggled in math in my elementary years as well as high school and with these new concepts I am learning, I am confident that I can teach my students effective learning techniques.

New Insights and Their Implications

After completing the LPU unit I realized how much time it can take to prepare information that you are not comfortable with. I realized that you need to plan and prepare in advance and give yourself plenty of time. It is best to start at least two weeks prior to your presentation date. I found it very interesting to see how different my peers and I grasp concepts about different topics in math. Some people definitely have a knack for math and others struggle at it like me. It is great to be presented with new techniques that can help a person come to solve a problem. I really enjoyed the lesson from the group I was in on fractions and using the table method. I found the table method to be something so simple that I never would have thought to use it. I feel that the table method will be very helpful to my peers and me when we are teaching our own students. I also enjoyed using the fraction bars but was not completely comfortable in using them because I had never used anything like them before. I learned that you can over think things and need to open up your mind to think about new ways of doing things, there may always be other ways to come about a solution. This is a method that we as college students should have been learning since the second year of college. By learning this method we are better able to help our students understand, enjoy, and build on math. Students should begin learning this method in preschool and should continue while they are pursuing their education. I think that this method of teaching is great and is one that we as students should have learned in school and I look forward to taking the practices from this class into my classroom.

New Insights and Their Implications

After another month of class; I feel like I have learned so much more from my peers, teacher and readings. I have watched my peers construct their own lesson plans that use the new method of teaching math that we have been learning about. By observing these lessons, I have learned that this kind of teaching is not always going to be easy for us as teachers to come up with, but it is what our future elementary students deserve and what is best for them. I really enjoyed the lessons on fractions. Before this I did not know how to teach fractions, but from the lessons, I got all kinds of ideas running through my mind.
During this course, I have learned a lot about myself as a teacher. I have learned that I am going to have all kinds of students that are all going to learn in different ways. With that being said, I have learned that I am going to have to be prepared to teach topics many different ways so I can help each of my students get a good grip on math. I really like that students can use hands-on activities to get a better understanding, I don't remember ever using hands-on activities for math. I'm really glad that I am getting a chance to make all of these discoveries in this class.

Summary and Synthesis

In class, we have continued to learn about the different approaches students can take to understand problems. The instructor has continued to push us to teach in a new way that does not just involve giving students a formula and telling them how to use it. We have learned not to just tell students how to solve a problem, but to allow them to explore and maybe find their own solutions. I find it very difficult at different times to learn this way and I think that most of the class would agree with me. Some of my classmates have given lessons to the rest of the class using the method of teaching that we are learning about. I have learned a lot from seeing how they taught and approached the lesson. It has made me think about how I am going to teach my lessons when I am a teacher. Sometimes in class, I find it difficult to understand concepts because they are new to me and I was taught and learned the concepts in a completely different way. In class, we have been challenged to understand why we do certain steps to figure out math problems and to not just know what to do. I am starting to understand why I do something, instead of just knowing what steps to take to arrive at an answer. Students can understand more of what they are doing if they learn it by trying different methods and not just following the teacher's steps or solutions.

Questions and Answers

Over the last month and a half, I have really started to consider how I am going to incorporate what i am learning in this class to my future classroom. Prior to taking this class, I didn't really have any anxiety about teaching math because it is a subject I have always loved and understood very well. I am now questioning how well I understand math. As the instructor continues to ask us questions, I continue to question how I am going to take the necessary steps to make sure that I incorporate this way of teaching into my classroom. As the instructor talks, the first question that comes to my mind is how am I going to have time to incorporate this way of teaching into my classroom? I am beginning to understand why I must teach this way, but with the pressures of teaching the material students need to know to perform well on standardized tests, how can I justify to everyone the need for teaching students so that they fully understand the material? I understand, but parents and administrators that have not had the opportunity to take this class may not agree with or understand my reasoning. This presents me with a huge problem. Working with parents can be extremely intimidating, so I feel it is very important that I do the research to make sure that I am prepared to answer all the questions that parents may ask me. I also feel that in order to be an effective teacher, I will need to put the time and effort into making sure that I know this material and can effectively help all my students to learn and understand the material.
As a future educator, I know the importance of making proper lesson plans and doing my "homework" to make sure that I understand the material I am going to expect my students to learn. My first few years of teaching this way may be very difficult, but by knowing that my students deserve to understand this material, I will strive to teach this material effectively, even if not every person understands why I just can't teach formulas to my students without them fully understanding what that formula represents. This method may take a little longer than just writing a formula on the board and giving students a worksheet with twenty questions on it that use that formula, but my students will greatly benefit from actually understanding each formula and why they use it to figure a specific thing out.

New Insights and Their Implications

When preparing for our LPU, I struggled to break away from the traditional approaches of teaching. Because this approach is all I have ever known, I found it hard to switch my thinking towards teaching through problem solving. This new approach of teaching takes time and practice, which has become widely apparent after our LPU presentation and after watching other groups present their material. It becomes hard to teach material to others that you are uncomfortable with yourself. After presenting our material, I realized just how important problem based approaches are. Instead of providing the steps or formulas for solving problems, it is important to provide students with the skills to find their own approaches to solving problems. Although I think this approach of teaching is important, I also think that it is important to introduce small portions of this approach with traditional approaches so students do not get overwhelmed. This approach takes time and if students are introduced to it all at one, they may get discouraged and not put forth necessary effort because of that discouragement. Once students feel more comfortable with this approach, I think they will have a better outlook on math. This is exactly what has happened to me over the last couple of weeks. I have always
struggled to understand math and this course is no exception. However, after preparing for our LPU and learning different approaches towards solving problems, I am now starting to make sense of everything. I am starting to grasp what is being taught and I feel more positive about teaching with this approach.

New Insights and Their Implications

I have learned alot from my peers, instructor, and the readings. This class has opened new doors to me in the ways of teaching math and how students learn from different approaches. It is important to let students discover a new formula on their own, instead of giving them the formula, telling them what to fill in, and saying "this is how it is done." I was taught that way and I have learned that it is definitely hard to break that habit and learn in a new way. My peers, instructor, and the readings have shown me that there is more than one way that we can teach students mathematics and every student learns differently. My peers have taught me about the different ways to learn through the LPU's. They have given us some great hands-on materials and activities that can help us learn different concepts in math.

This class has taught me a lot about myself as a learner. I have kind of always thought of myself as a hands-on learner, but I never thought this way of learning could work in math. I was just so used to the teacher giving me a formula and telling me what to do with it. This class has shown me new ways that I can teach math that is more meaningful and beneficial to my students. Some students might benefit from getting the answer right away, but others will benefit from understanding the steps and processes that it takes to arrive at the answer.

New Insights and Their Implications

I have learned a lot about elementary school students from my peers, instructor, and the readings.  This class has given me such a big insight into other ways of teaching and how many students learn from different approaches besides getting the formula and practicing the formula.  It has taught me so much about how giving the formulas, working on the formulas, and giving the answers is not always the way to do the problem, althought that might be how I was taught.   I have learned about the fact that there are many ways that we can teach students and some students learn differently than others.  My peers have taught me about the many ways that students can learn through the many methods that they use in their LPUs.  The readings showed me the many ways and methods that teachers can use to teach elementary students.


This class has taught me a lot about myself.  I never thought of myself as an "instructional based" learner.  I have always thought that this is the way that everyone learns and there is no other method to teaching.  By going through this class, I have found out that there will be other ways that I can teach and it is not just the cut and dry way of teaching.  Their implications to teaching and learning mathematics are that students have different ways of thinking.  For one student, a paper and pencil test might be the best way for them to learn but other students might be better with a more complex way of thinking that does not give them the answer right away.

New Insights and Their Implications

This math course is definitely much different than any other math class I have ever taken. I am learning new perspectives on math concepts that I was once very confident that I understood. When we do example problems in class or go over homework problems I am surprised to see strategies that I never considered from my peers. It is surprising because I always thought everyone basically thought through problems the same way and took very similar routes to achieving those results. My previous belief has certainly been disproven. It is important to work with partners and in groups because it encourages students to share ideas and learn new methods for solving problems. Other math classes I have been in, both high school and college, were focused on individual work and involved little or no group work. However, there would not have been much reason for group work because all we would have done is take turns plugging numbers into a formula. Not a lot of higher thinking or reasoning involved.

Before the first day of Math Methods I was pretty sure that the class was going to be a hybrid of Math Concepts I and II with the addition of students teaching lessons. Clearly, I was mistaken. The instructor is introducing mathematical concepts that I know how to solve and then poses questions about these concepts that are foreign to me. This causes me to, basically, relearn these math concepts in a way that I actually understand the “why” questions of solving a problem. For example: why do we use pie to find the area of a circle or why do we flip the second fraction and multiply while dividing fractions? These are items that I have to reevaluate in order to ensure that my students, and me, know why they are solving a problem the way that they are. I do not want to teach students just to plug numbers into a formula without understanding how the formula was derived. I am developing a much deeper understanding for geometry and fractions and I hope to be able to pass my knowledge on to my future students through this new method of math teaching.

Personal Concerns and Next Steps

The thing that I am most concerned about is how to do I switch the way I was taught how to do math; to how should I teach it? In all my math classes the teachers have always been there and helped me out if I was struggling. I know that everybody went through this same experience. I think I can speak for a lot of my peers. That this is going to be very hard to adapt to this new way. There are many times that I am frustrated with the material. Or when I am trying to figure out the homework and I just don’t get it. When you have been doing it in a certain way for so many years, it is hard to change your thinking and try a new approach. But, how can I make this switch? Not missing class, paying attention to the lecture notes, readings, and projects. This is very important that I understand how to teach in this way for my students. I don’t want to fall back on what my old teachers did. I want to learn this new way of teaching, it’s just going to be a struggle at times.

New Insights

After preparing, creating, and presenting my LPU lesson, I have discovered that teaching using the new reform based mathematics is VERY difficult. It is really hard to pose questions for students, without helping them along the way. It is in my nature to want to guide the students as they create their own understanding, instead of letting them struggle and find their own answers. During the preparation of the the LPU, it seemed really easy to teach in the new way, but when it came to actually teaching it to the class, it was very difficult.

My LPU was about introducing the concept of fractions. It is hard to introduce a concept to students who have no previous background, and get them to form their own connections, and create their own understanding. It was definitely a challenge, to say the least. However, all students have a background about fractions, they just don't know it, until it is presented in a way in which they can form their own connections. All students understanding the concept of a whole, and that there are parts to each whole. They just may not understand that a part of a whole is called a fraction.

If I were to redo the lesson plan, there are a few things that I would change in the presentation aspect of it. I still believe that my prep-work is sufficient, it was just a lot harder to present it than I had original thought. Reform based mathematics is still a new concept to me, but at least now I can say that I've done it and could do it again.

New Sights and Their Implications

So far in this course, I have learned a lot from not only the instructor, but also my peers. Each class period that there is a new group presenting, allows for one more time to see a different perspective on how to attack one of the many themes in mathematics. I have learned from my peers, how to show students to work through a problem without ever really thinking about the fact that they are doing math. The more times a teacher allows for his or her students to work in groups discovering a solution to a problem, the more success students will experience in learning taking place. On top of that, teachers need to always make sure to have different tools for the students to work with so they are receiving the hands on activities that are pertinent to learning. The more you, as a teacher, can deviate away from the fact that you are doing math work in the classroom during math, the better the outcome of learning is for the students. As a teacher, you do not need to always tell your students what they have to do in an activity or what knowledge they will gain from the activity, instead let the students explore and discover for themselves what knowledge they have gained from them partaking in the activity assigned.

The instructor has taught me all of those things mentioned above and more. If you want your students to gain the knowledge that you want them to; engage them in their prior knowledge. Teachers need to help students realize that they are familiar with the information presented to them; they just need to go back and retrieve that prior knowledge. Another important characteristic to teaching math that I have learned from my instructor is to always allow more room for work. If a student does not understand the material, make the material due a certain day, go over the material in class, and then collect the assignment the following day. If students are stuck and don’t know what to do after seeing the results to their solutions, allow them to come in and spend more time working with you on their homework; teachers need to always have a open door policy when it comes to their students.

Throughout this course I have learned a lot about myself not only as a learner, but as a future teacher. As a learner, I have learned that I do not learn well when teachers tell me instructions of how to complete a task, rather than write the directions on the board. I need those instructions in front of me in order for me to get the most out of my learning. Due to this discovery, I have decided as a teacher to always have my directions written out so my students are not confused about what is asked of them. I have also learned about myself as a learner that I need to have materials and tools in front of me while I learn to help me discover for myself the answer to the problem. As a teacher I have discovered that having tools that students can physically move/touch for themselves, with help them discover the answer at a far better pace rather than just working with paper and a pencil. One final thing that I have learned so far as a learner, is that I work best in small groups. If I am in large group learning, I feel like I am not getting as much out of the instruction because the group is so large. When groups are smaller it is easier to put your two cents in and also collaborate with your peers. As a teacher, I will allow for a substantial amount of time for students’ to work on problems and also collaborate with peers. It is my belief that it is better to work with others because then you can see the thought processes that they went through to come to the solution; it gives you more perspectives on how to solve a problem!

Blog #1- Questions and Answers

During the first part of this class, I have had several questions come up for me in regards to my future as a teacher.  The first question I have is how to keep working toward teaching a deeper form of mathematics?  I am afraid that I will become complacent as I teach math because I do not enjoy it to a large extent.  I am also wondering how it is possible to keep your job in a school and fight for this type of reform in the subject of math.  My last question is in regards to being able to ask good questions and assist my students in justifying their answers without always telling them the solution.

Personal Concerns and Next Steps

One of the biggest concerns that I have as of now in the class is how I'm going to switch from how I was taught math, to how I should teach math. All of my experiences in math involved the teacher showing us how to solve the type of problem and then setting us loose on worksheets or assigned problems from the book. So for me (and I'm sure almost everyone else in the class) math has just seemed like a grind, figure out how to do the next twenty problems and then shut your mind off and do them. So because of this, as I was growing up math just seemed like a punishment and something I gained no deeper understanding of. So how can I go from being the student of math I was, to being the teacher of math I want to be? The obvious ones are go to class, pay attention in class, and do the readings. Another way would be to start looking now and compiling a large number of problems that are good at teaching problem solving. That way when the time comes and I'm in a classroom I will be able to call on these problems to give to the students instead of falling back on what my old teachers did and give out worksheet after worksheet and let them grind through it.

BLOG #1: personal concerns & next steps

Math intimidates me to no end. I cannot pin-point the origination of my math insecurities to any particular event, but have felt this way for as long as my memory serves me. As a student, I have always struggled with the subject-- when reading mathematical text I am forced to re-read chapters (sometimes 2+ times) for comprehension, mathematical problems frustrate me and memorizing equations gives me a tummy ache. Because of the listed reasons and many more, I am scared to be an elementary teacher, and have set my sights on middle school--I can honestly say that I want to teach middle school because in middle school teachers have one specific subject. I am THAT scared of dealing with the subject on a daily basis and teaching young students math.
My main personal concern is that I wouldn't be able to teach the students properly, thus creating more people with math phobia's, therefore ruining their academic careers and futures as bankers, scientists and coupon collectors.
I have come to understand that I need to get over this. For instance, during class I try my hardest to stay on task-- listening to lecture and taking part in the discussions and activities (this is gut wrenching for me, just so you know). I have looked through the text and read the assigned chapters in hopes of having a better understanding of the topic and teaching the topic. I have looked through my mom's teacher's text (5th grade mcmillian) to attempt to find comfort and a flow. These are the steps I have taken in the past 3 weeks. I believe I am on the right path, and with continued effort I should find myself more comfortable with the subject of math and the idea of teaching it.

Summary and Synthesis

Math has always been one of my favorite subjects, but mostly because it was something that I easily learned. Each year when new information was added to what we learned from last year, I was ready to accept it. But going without math for a while has made me rusty, and then taking this class where we are learning a totally new idea from what we have known is also a little scary. So far I have yet to fully feel comfortable in class with this new idea. I understand what we are doing and why, but to me that isn't the way I learn best, so I have yet to get excited for each classs. By not teaching the tradition math teaching, I think more students will have a better time with math. I will have to work to get myself out of the traditional mindset in order to really understand what we have been learning about with problem solving, and working to teach students ways for them to find the answer, not just my answer.

Summary

I have never been big on math because I didn't have any outstanding math teachers in high school. Since I've been in college I've opened up to the subject a little bit because I realized how exciting and rewarding it is when you finally figure out a challenging math problem. I can't say I was extremely excited to take this class but each time we have class I see how beneficial this class is going to be to me as an educator. Most math classes I have taken focus on how to do the math, not how to show a student how to do the math. I feel like I am already learning how to teach math, rather then just how to do it myself. I feel like I am going to learn a lot of essentials for teaching throughout this class this semester and I'm looking forward to feeling very confident in my ability to teach math at the end of the semester.

Summary

Having to take another math class was frustrating to say the least. I am a person who loves and enjoys math, but do not feel as though I had learned what I was supposed to learn from my previous math courses. I had no idea what to expect from this math class, but am starting to realize why we are required to take it. We are learning about an entirely new approach to teaching math. It amazes me that after all these years, we are just now starting to teach upcoming teachers this new approach. Instead of holding our students hands while giving them every answer to every problem, we are going to allow the students to find answers and make connections on their own. This new approach is a sort of self-discovery approach in which children will hopefully learn and apply new material more successfully in the classroom as well as real world situations. I find it frustrating when we are not given the answers to problems in class, but that is due to past experiences of being hand-fed answers to math problems. Although this course will be challenging, I know that in order to make a change in our education system, we must learn this material now so that we can begin to teach future students in a more successful way.

I must admit I haven't been thrilled about not receiving all the answers to the problems and at times i've disliked not having someone hold my hand and walk me through things, but i'm beginging to understand the importance of teaching math this way. It's been tough but after seeing those statistics during one of our first class periods I understand just how important it is for us to start doing things differently. It's obvious that the old way of teaching math isn't working for us and for my future students and myself i'm going to work hard to understand how to better teach mathematics.
Math has never been my favorite subject (as i'm sure some of you agree) so i wasn't looking forward to taking this class, however, after getting started I see that i'm already learning a valuable new way to better teach a subject i previously felt extremely uncomfortable with. I
still don't think I'm anywhere near being ready to teach my own math class but i'm confident that this class will help prepare me for when i do.

Summary and Synthesis

When I learned that I had to take another Math class, I, quite honestly, was not excited. I was expecting to walk into the classroom on the first day and watch our teacher show us examples of math problems, while we students sit there and try to understand what the teacher is actually doing. However, in ELED 330 I have learned how to present math to my future students. Dr. Reins has modeled to us how to teach math in a problem solving manner. Problem solving is key in mathematics; and in our class we have discussed how there is a process to problem solving. By teaching our students this process and by modeling it, our future students will soon be able to solve their own problems, and this doesn't just include math problems. As a teacher, we learn what types of students we have and we give them strategies to use that best fit the individual student. In Math Methods, we are challenged to figure out problems by using the strategy that we find most appropriate, and by following George Palya's four step guide to problem solving. I enjoy this class and look forward to learning more.

New Insights and Their Implications

So far this is a very challenging course. I have never been a fan of math, and I am trying my hardest to learn math in this new approach. I am not very good at thinking outside of the box. There are times in class where I am completely lost and struggeling to make sense of the lecture and projects. I can see the importance of this class by observing Dr. Reins. I understand how important it is for students to be able to think for themselves and engage in the learning process in which they can create solutions by themselves, by using the material and information given. I can see now, that the teacher needs to help them think, but not walk them through the problem step by step and give them the answer. I have learned so much new material, in this short amount of time. In reading the book, there is so much information, that it can be overwhelming at times. But, it is material that we need to know. I know that this class is going to be tought; I just need to gain as much of the material as I possilby can. So I can be a successful teacher for my students.

Summarize and Synthesis

Math is the one subject where I have the least bit of confidence in teaching. Since the class has started I can tell my confidence level is rising just a little bit. It was very helpful to know that I am not the only one who is not completely comfortable in teaching math yet.
There is so much to learn about teaching Math. One issue we talked about in class that effected me was how the South Dakota Math standards are written out. The other day when we completed the activity with standards, I was shocked at how unclear they were. As a teacher I would find it to be difficult to write and carry out a lesson plan following those particular standards. I am happy to learn there are other standards out there that South Dakota is looking at to adopt.

Summary and Synthesis

There have only been a few weeks of class so far but I have learned so much about teaching already.  Dr. Reins has shown so many more ways than just the going over the material, worksheet, and test at the end of the unit way of teaching the students.  Teachers have such a wide range of options for showing students different methods of learning the material that they need to learn. I have found this out by just sitting in Math Methods class.  We do not go through a power point and take notes and then have a test over it.  Dr. Reins shows us in his own classroom that there are other ways to approach the material other than lecture.  It is great to see the higher order thinking in the classroom and it will help us as teacher impliment it in our classroom.

ELED 330

Before I started ELED 330, I was very naïve about how math should be taught. I was positive that the best way to teach math was: the teacher shows the students how to do a problem, then the teacher and the students do a problem together, then the students do problems alone. Consequently, this was the way I was taught math in elementary, junior high, high school, and even college. My approach to teaching mathematics has completely changed within the first three weeks of class. Teaching through problem solving is a great way to get students engaged in their learning and use mathematics in real life situations as opposed to learning one type of problem out of context. However, I am struggling to understand how a student who has no idea about the concept of addition or subtraction can learn it through a complex problem. Is it necessary to teach basic concepts prior to the big problem? The textbook says no. Also, what if a problem does not work out and the children do not reach the desired answer and/or method that the problem was designed to teach? Do we make another problem or go straight into teaching the concept? These are just a few questions I have so far as I learn a completely new way to teach math.

Summary and Synthesis

The biggest impact made so far in the class is that teachers must find ways to engage their students and get them to think for themselves. There are many different ways to go through the process of solving a problem. There is not one set way to do it – the students should use strategies that they know and be able to explain the way in which they have solved a problem. The activities and discussions that we have had in class support this. When doing the handshakes problem, digits needed, and triangle activity people used several different strategies to complete the task. We were able to explain our reasonings and the strategies varied. The hardest thing to do is to think about what we are doing and actually explain the process without skipping any of the steps. This is especially true when we are using formulas to solve problems. We are so used to just plugging in numbers to find an answer. We need to actually think about why we are using the numbers we do and why they give us the answer they do.

ELED 330

Before entering this class I did not realize the importance of teaching math through problem solving. My previous math classes consisted of taking notes, doing a few example problems, and then being tested on the material. There is nothing engaging about this method of teaching.Dr. Reins teaches in a unique way that allows us to answer our own questions. He also helps us build meaning for the concept presented. I never really realized what exactly a good problem or task was before this class. I figured any method of teaching that taught the concept was acceptable. Now I know a good problem or task must be engaging, must have a purpose, should be relevant to students, must have multiple routes, and must use good language. I am looking forward to learning more about this unique way of teaching math so I am able to implement this approach in my classroom someday.

Through these past couple of weeks I have learned to teach math from a very different viewpoint. When I was in elementary school I was taught using the traditional way. The instructor would explain the process, give the students a few examples, and expect the student to use the method given from the teacher. Students were not encouraged to find multiple routes to a solution like we are in class. Using the non traditional way of teaching like we are encouraged to do in Math Methods is actually very helpful. When we are allowed to share our strategies with other students and the class as a whole it enables everyone to see multiple routes, a student may find another route easier than the instructor's method. In class we have been provided with higher level thinking questions. With these questions we are ask ourselves, "What are we supposed to be teaching our students, or what are we teaching our students?" Recently, we have been going over the standards to make sure we are teaching by the standards. I also found this to be very helpful. I have really enjoyed this new hands on way of teaching math, it gets students excited about math, even those who struggle. Last Thursday, when we were given the worksheet with blank squares and we had to make as many triangles as we could, it allowed us to do our own thinking, it challenged us. This way of teaching math is different, but I could definitely get use to using it with my future classroom.