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