Personal Concerns and Next steps

I am HORRIBLE when it comes to any math! specially Geometry! working on the polygons is terrifying to me. As a future teacher it scares me to even think about not being able to help the students with math. English is my second language and when I was force to change my mathematical knowledge to English was difficult because i had not learned the right vocabulary. I hope this class can help me catch up with the math vocabulary and understand ways that math can be solved and hopefully math will be easier for me to understand and to teach.

Summary and Synthesis

So far this semester's Tuesday and Thursday classes have opened my eyes to a different way of teaching. One thing I have always wondered about was how am I going to teach math to my students so that they are able to understand it in a better way than I was. This class has given me a new way of thinking and has produced me with some new ideas about teaching math. For instance working on one quality problem with extensions can help a student become more confident in their math skills. The trick is to make sure the task is meeting a standard and is at the appropriate level for the students. Another thing I have learned is that the teacher needs to stay out of the way of students learning. Students learn by making mistakes and as a future teacher I will try to balance the line between encouragement and support and taking over. I remember reading some article where the teacher taught his entire class by asking questions like; what shape is this? and how would you find the area? Asking questions helps students make meaningful connections to them that will develop into quality math skills. The recent experiences I have had in this class has encouraged me to become a more quality teacher and I am excited to see what else I will learn.

Summary and Synthesis

In class so far this semester, we have been exploring geometry and new ways to discover how to scale shapes to a larger size, find the area of a triangle with out the formula and making observations about triangles. I would have never thought about teaching math in the way we are learning to problem solve and determine and justify answers with out the answer given to the students. Students get to work through the problem with out a formula. I think that it is a good way to get students problem solving and remembering how to do math problems.

New Steps and Personal Concerns

To be blunt, I am terrible at Math, and I always have been. I think a big part of my problem has been, I have never had a "good" math teacher. Teachers have always lectured, lectured, lectured. And expected, me as the student, to understand what they are saying, without providing that extra help and explanation. My personal concerns for the future are that I will struggle when comes to Math. I don't want my students to struggle as I do, and I want them to feel comfortable enough were they can ask questions, without feeling like they will be looked down upon because of their confusion. This class however is helping me to conquer my fear of math, by giving me specific and help skills that can be used in a classroom. I hope to feel more comfortable with the word "MATH" and everything that comes with it by the end of this course.

summary and synthesis

Summary and Synthesis – This class is one of my favorites. I like how we actually get to participate in hands on activities as we are taught to teach. In all my other classes we are simply talked at and told to use these techniques in our classroom but we never get to see them implemented. One issue I have, which is probably just because I like to know things, is how we are given problems but not provided the answers, even after several weeks of working on it. I find it frustrating and a bit discouraging but I know that it is also because I am not used to this way of teaching. I learned a lot. One thing is the names of the strategies that are used and also different ways to ‘attack’ a problem. I also learned that as we are going out into the school the standards are all going to be changing over to the core standards rather than state standards. I have learned that I speak too quietly and am always unsure of my answer, therefore causing me to not get involved very often with the conversation in class. I am one of those people who is afraid of being wrong.

New Insights and Their Implications

I have learned from my peers what it would be like for my student working with their peers in a classroom. One person has the simple easy solution and then we begin to feed off of that and understand the more complex parts of the math problem. I feel like I am always looking for the simple easy solution and it takes more time for me to remember how I solved problems like this back in Elementary/Middle School. Through the methods class I have learned that there is more than one way to find a solution to every problem. A student can use manipulatives, models, drawings, and many other ways to see a problem visually and solve it. As a teacher we can find a way to extend every problem for further learning or gifted students in the classroom. I feel like I have learned many great new strategies for problem solving that I will one day implement in my classroom. I will give the students time to work and struggle on the problems instead of just giving the answers or working through the problems right away.

New Insights and their implications

I feel as though I have already learned new teaching methods in this class. I have learned from the teacher, my peers, the textbook, and our online resources that we have been using. A lot of these concepts and methods that we have been learning are new to me. Alot has changed since I first began learning math. It seems like when I learned math I was taught one way to do it and then we just practiced that method using a multiple of different numbers. We never had to explain why we did what we did or how we got our answer. It was simply just two plus two equal four. The only manipulatives we used were little counting blocks. We didn't have manipulatives for triangles, fractions, etc. Through the new methods that I have been learning in this class, I have learned how to reflect on the math problems and how to explain why were are doing the steps we are doing. I am learning how to explain myself in the mathematical problems that I conduct as well as figuring out alternative ways to do problems. One problem can be expanded up on so much and that can definitely help students understand math much better. By reflecting on problems and explaining problems, students, as well as myself, can better understand the problem and be able to apply that method to other stituations and/or concepts. With a stronger understanding, students will gain much more confidence in their learning. They will want to reflect on their problems and they will become excited when they figure out new problems. I already experienced that within this class. When we were using different shapes to make a hectagon for example, it was exciting to achieve the correct scale factor. I want to implicate a lot of excitement and hands-on learning in my classroom. I want my students to be confident and motivated to learn! I am excited to gain even more ideas from this class and learn more methods that I can implicate into my own classroom someday.

New Insights and Their Implications

I have learned that there are many different ways to teach subjects. Students are going to learn in many different ways, but if we can get students to actively engage in the activities, learning, and classroom discussion than there might be a greater chance that the information will be learned more effectively. I believe this is the case with what we are doing in Math this semester. It is a new way to attack math and one, at least for me, that is very new and uncomfortable. I loved my math teacher and I loved most of my math classes in high school. But seeing this approach to teaching/learning I wonder if I would have enjoyed Geometry rather then dreading it. Like I said above I really thought this new methods was uncomfortable and to be honest I thought it was wasting my time. But I would say the day we went over the manipulative assignment it all changed for me. I began to see the reason and the positive effects of this teaching method. So I guess now i am ready to learn how to effectively teach this way.

Questions and Answers

I wonder if my oldest daughter would feel better about the subject of math if she had an instructor that had engaged her in problem solving?
The process of learning through problem solving that we have experienced in class so far this semester has made it very clear to me why my oldest daughter hates math. Math for her was a struggle because she constantly felt that she was failing by making errors. If she had an experience where she could have applied the knowledge she had (background knowledge) and engaged in a problem solving process where mistakes were supported she may have learned to love math. This way of teaching and engaging students with math makes math a subject that is directly related to their lives and not just something that they either excel at or fail at. The use of math in our daily lives is overlooked in most math classes which makes the learning really not relevant to the students. It is my hope that by taking this class and striving to teach math in an engaging and problem solving way that students like my daughter will not leave my class hating math, but instead feel confident and successful.

New Insights and their Implications

I have learned many thing already in K-8 Math Methods. I learned from my peers, teacher and the book that there are many ideas and concepts dealing withmethods that were new to me. I learned to tackle a problem with many different ways to solve that same problem. We can use the multiple ways to check our work as well. I have learned that a good problem will have many entering points for different learning levels the students may have. I have learned that math can be more fun and interesting instead of cut and dry, question and answer. I have learned how to help my students when they begin trying to solve new problems. I have learned that students do not always need to know the answers, but we as teachers, should help foster the confidence in our students to want to try to solve a problem, with thinking and discussion. The students should be praised for any connections they try to make, instead of being afraid to fail. I have learned about the content standards and aligning my lessons with these standards. I hope to learn even more strategies to use in my own classroom to help my students to become more confident in their problem solving.

Personal concerns and next step

The person concerns i have always had with teaching math is that i will not be able to teach it effectively because I as a student have always struggled in that subject. I hope that i am able to learn many concepts and ideas to help math strugglers like myself and I become confident in my math teaching. The next step is make sure that i develop great ideas and concepts so that i can become an effective math teacher, this class will defiantly help me become more confident in teaching math. My next step will also to make sure i am engaged in the activities so i can effectively understand that so i can teach them someday.

Personal Concerns and Next Steps

I have never been very good in math. I have also had to struggle through my math courses. I have tried everything to be good at math. This class has offered me new insights into understanding math. I think this course would have been very helpful to take before Math Concepts because this course has helped me understand math better than those courses did. I worry as a teacher that I will not be able to teach my students math very well but this course is helping me learn very valuable techniques. I cannot say that this class has made all my fears go away but I'm hoping later on in the course I will learn to be more confident in my math skills.

New Insights and Their Implications

This course has already helped me to gain a deeper understanding of what a successful math curriculum should look like. I have learned new knowledge from my peers, the instructor, and the readings in the book. From my peers, I have learned that there are a number of ways to comprehend and solve a problem. I have learned new strategies for which I can use to answer a problem. Through the group work in I have learned that everyone begins the solving of a math problem in a different way. In other words, there is not a right or wrong way to understanding and solving a problem. Math has multiple routes for which students can take and also multiple solutions. From the instructor I have learned that there are four types of methods for solving a math problem which include: George Polya's four steps to problem solving, drawing a diagram, solving a simpler problem, managing your point of view, constructing a table or chart, and the process for mathematical inquiry. In order for our students to be successful problem solvers, we must show and discuss with them these multiple routes for which they can chose from when working to solve a problem. They need to develop a sense of confidence in their math skills. If we are unable to help them develop the confidence at a young age, math will only become more difficult for them. I have learned from the class that teachers in the United States need to try a different approach to their instruction of math. Teachers should not just give students the answer right away. They should give students time to reflect and work with others around them before simply giving them the correct answer. Students need to develop stronger critical thinking skills not just for math purposes but for all subject areas. I believe that the process of specialization is a key building block for helping students understand math. Specialization is simply starting with a random problems and moving to more organized problems or in other words systematically changing the problem to make it more complex. Students again need to gain confidence in their math skills. We should allow them with the opportunity to get up and front of their peers and work out a problem and congratulate them even if they do not get the right answer. We should first discuss what they were doing right before criticizing what they are doing wrong. Overall, I believe this class will help me to be a stronger and more confident teacher of math.

New Insights and their Implications

There are many things I have learned from my peers, the instructor, and the readings about elementary school students and the teaching and learning of mathematics. From my peers, I have learned some different ways students may think about problem solving other than the ways I thought they would. Through small group and whole group discussion, I have learned other ways, routes, and strategies to problem solving that elementary students are going to use. I have also learned that I will not always be able to know or guess what routes students are going to take to solve problems since there is no direct route to problem solving. Students are going to use their own experiences and past knowledge to find a strategy that works best for them. As a teacher, I need to be flexible and let them explore these strategies. Through discovery, students will be able to build on their own schema's and become better problem solvers over time. From the instructor I have learned that it is best to have students explore and justify their answers through using multiple strategies. Mathematics is not about teaching students the way to arrive at the answer through a set of processes but rather have the students discover for themselves how to arrive at an answer. Mathematics teaching has changed dramatically this way since I was in elementary school. Teaching mathematics today is about facilitating students on how to develop problem solving skills and have students use their metacognition to think about what they are thinking about. Problems should be open ended in that they should have more than one solution, they should draw on the student's mathematical knowledge, they should address Common Core Standards, and they should be presented in realistic/authentic context. From the reading, I have learned that teachers are lacking focus and coherence while students are lacking reasoning and sense making. As future teachers, we must instill that students are able to draw conclusions on the basis of evidence and have the ability to develop understanding by connecting it with prior knowledge. I have also learned the many tools that can be used such as George Polya's steps to problem solving, ten problem solving strategies, and processes of mathematical inquiry. By learning these new strategies, as a future teacher I plan to implement them into my classroom so my students can feel better about approaching and solving mathematical problems.

February 4th by 5pm.

Summary and Synthesis: So far throughout the semester, I have learned a lot about math and me. This subject is the one I am nervous about teaching in the future, because of my own personal struggles. This has been apparent in some of the activities we have done thus far such as the scale factor, area, and perimeter chart and questions. I understood everything sooner or later, however I do not want this to happen in my future classroom. As a teacher I should know what I am teaching and understand in order to teach them from the beginning. It just makes me nervous. I hope by the end of this course my thoughts about math and teaching it will have turned.

New Insights and Their Implications

From both the article and classroom discussions, I have learned that there is a completely different way of teaching math that is not seen in the typical classroom. Mathematics is more than just being told the formula, plugging in random numbers, and finding the answer. Mathematics is being able to discover and understand the problem and investigating different ways the problem can be solved. Through allowing the student to work through the problem on their own, they are able to see the components that make up the problem and understand the solution and how they found it. A way that teachers can develop lessons to ensure that their students are understanding mathematics is by teaching it in a constructivist way. Constructivism in the classroom can be seen by: being child centered, teachers are acting as guides for student learning, students are working with real world problems, communication is open between student and teacher, students are building previous knowledge, and students are actively working through the problems. When students are given a real life problem to solve and the teacher helps guide the student by using open communication, instead of telling, students are able to truly learn the answers on their own. Constructivism is a theory that dates back hundreds of years ago and is now starting to be recognized as a method for teaching mathematics. In fact, the NCTM Mathematical Standards are designed around this theory. After having the discussions, reading the article, and actually seeing what constructivism looks like in the classroom, I hope to be able to provide my future students with the opportunity of actually being able to explore a math problem instead of being trapped to using the textbook and falling into the same routines of so many teachers. I want my future students to be able to completely understand the problems that are presented and know how to solve them.

Personal Concerns and Next Steps

Math has always been my weakest subject. Every math class I have ever taken, has always been a struggle for me. It always took a little extra time and a little extra explaining for me to understand. Because of this, I am concerned about teaching math in my own classroom. I know how a lot of those children feel when the math concept just doesn't click. The only problem is, is that I'm not sure if I could be of much help. I am so used to and stuck in the traditional ways of teaching math that its going to be hard to change my ways. I am excited for this class to teach me new and more significant ways to teach math. So far, it has been difficult for me in grasping this different concept in teaching math. I know that the way I learned math originally cannot be the way I teach math in the future. It is up to me to make sure that my students are given significant mathematical tasks and that I provide a lot of opportunities for my students to succeed in math. Changing the ways we teach math is going to be difficult but necessary. I want my students to feel confident in math, unlike I ever did. This is probably one of the most important classes I will take here at USD and with every one's concerns on math scores, it is up to me to do my best in this class and get the most out of it. I hope I can take a lot out of this class and apply it to my own classroom.

Summary and Synthesis

Recent experiences that have impacted me through my math course on Tuesdays and Thursdays include, new ways of thinking when teaching and learning, new ideas to think about when planning for lessons and tests, and new ways to encourage students to learn. Over the past couple Tuesdays and Thursdays I have learned about what teachers and students are currently lacking such as, teachers are lacking focus and coherence when teaching students, and students are lacking the skills of reasoning and sense making. I have learned that it is vital for students to be able to make sense of what they are learning and be able to give reasoning on why they did a problem the way they did and how they come up with the solution. In the past and recent years, teachers have been failing in teaching students how to make sense of mathematics and how to provide reasoning for their thoughts. Teachers are also lacking when it comes to focusing on the number of math topics covered. Other countries teach fewer content areas and cover them in a deeper manner. I believe, after being in this class, that here in the United States, we do the opposite. Rather than teaching our students what they need to know now and for the future, we teach our students what is in a textbook and then move on. This does not allow students to develop a deeper level of thinking. We need to focus more on certain skills that will help our students succeed now and in the future. I have also learned through this course that mathematics needs to be learned through hands-on activities that use manipulatives and the problems need to be relateable for students. The students can learn math so much easier and can understand different processes better if they have manipulatives to look, touch, and use. This allows students to use their hands and their brains and discover many different routes to solving problems as well as, helping them be able to explain their reasoning for what they did. I have also learned about the 5 strands of math and the 4 processes of math and how to help my students be successful for each one. The impacts these experiences have had on my will affect the way I teach math to my future students. I will not teach right out of a textbook and I will allow my students to focus their attention on a realistic problem for as long as it takes for them to all understand it and be able to explain what they did and why. I will also make math more exciting for students by allowing them to be creative, work in groups, and us manipulatives. Through my experiences in this course, I truly feel that I will be an excellent math teacher for my future students.

-Danyel