Summary and Synthesis

During class we have been talking about finding the area of any polygon on a geoboard and got to do some hands on activities for this concept. One activity we did was writing an algorithm that would work for any polygon that was made on a geoboard. In class some students talked about their different algorithms and showed the different ways this concept could be learned. After I got to see the different solutions I decided my algorithm needed some changes that would make it simpler. (I could take off a few of my steps. Ex: one of my steps was having a trapezoid, but the trapezoid would be divided into a triangle and rectangle). I think by allowing the students time to discuss their solutions in class, we learn a different view of the concepts and also gives a time to justify our answers.
The class also did a more hands on activity by cutting the triangle out of the rectangle and used string to make different shapes to see what would give more area. I believed the rectangle would have more area because of the length of it. I was wrong though, it was the circle.
I realize by having the students do different activities with one concept; they are getting a more in-depth learning. They are starting to realize why the different approaches work and see a variety of strategies to complete a task. We are not focused on memorizing one formula for a problem, we are allowed to explore and talk about our learning with others. I know in my elementary/high school that is how we learned math, memorized a formula and practiced it for the test. We never did look back at the formula once we got past the test. Now i find myself struggling with math classes in college, the educator show how but next explained why and had us make the connections.

New Insight and Their Implications

I have learned a lot already in this course about math issues as well as teaching in general. I have always thought of myself as being able to learn math concepts and understand them fairly easy, but I am struggling in this math course with the new way of learning these concepts. I didn’t ever think deeply about the way mathematics is taught in the school systems and how I was taught the different formulas. Now knowing how repetitious our math program is and how we never really understand the concepts behind what we are learning, I know I won’t be able to teach that way. I have become more insightful and already learned and retained information on many math formulas that I would have never been able to remember previously.
Taking this course has allowed me to really think about teaching to every child and how using different methods to teach the same concept can really benefit every student in the classroom. Having students memorize formulas without understanding why they are like that and how the formula is made hasn’t helped students retain the information learned. As a teacher, it is going to take a lot of time for me to look deep into the formulas and make lesson plans that teach this way. In the long run though, I will be teaching student’s information they will remember and hopefully reaching every student by teaching to all the different learning styles.

Personal Concerns and Next Steps

I am truly concerned with my ability to connect standards to lessons correctly. This is one of the most important things we as teachers have to do. I feel as though we have not been taught enough about this subject in previous classes. In Dr. Reins class we are talking about it, but I still feel like I am not able to go out into a classroom and start writting lessons with standards without wondering if I am doing it correctly. I hope that in this class we will talk about standards more and in more depth. This way we can feel comfortable using the standards in our lessons. The question that I am wondering about is why if these standards are so important how come we haven't talked about them in all subject areas. We have been required to look them up, but nobody has ever helped us learn the true meaning of them. I am going to work hard in Dr. Reins class by reading the material and taking notes in order to learn as much as I can about the standards and how to use them correctly. Hopefully this will help me feel more comfortable using these standards in the future.

New Insights & Implications

The most prominent new insight for me would have to be the fact that many mathematics problems can be solved using many different routes. In my previous math classes, we were taught formulas and specific ways of solving problems. However, this is not the best way to teach since every student thinks in a different way. Teaching this way merely forces students to use numbers in a certain way every time, go through the motions, and never really understand what they are doing or why they are doing it. When teaching, I now believe that the students should be allowed to come up with their own method of solving a problem by using the knowledge and understanding of certain concepts that they will hopefully gain through the teacher's guidance and activities. It will be a difficult task for me, since I was never forced to think deeply about mathematics before. I feel like I am starting over, but the more I am forced to think in this way in this math methods course, the more practice I will have, and eventually I will constantly be thinking in this way. When I start teaching, I will be learning right along with the students. But if I am learning mathematics in a different way with deeper understanding, I will know that my students should be as well.

Personal Concerns & Next Steps

My biggest personal concern for Math Methods is being able to completely grasp what is going on in class. I feel that since this is a different approach mathematics that what I have normally been taught, that I may not fully understand and grasp this new concept.

My solution to this problem, is to continue reading the book, doing my assignments, talking and visiting with Dr. Reins with concerns and problems I'm not understanding, and talking with classmates to better understand this concept.

So far I've liked this class and the approach it's taking and hope that I can turn my thoughts around so I can fully understand what's going on in class.

New Insights and Their Implications

Based on the mathematical instruction that I have had in my past schooling, I thought that the only way to succeed at math was to memorize as many formulas as possible and hope that I didn't forget them. However, it was very easy to forget these formulas because no one ever took the time to explain where the formula came from and why it worked to solve for the correct answer. Even in elementary school I remember memorizing charts and multiplication tables. In class I like that we work on the theory behind these formulas and processes so that we can better understand how to apply them and why they work. Math is definitely not my strongest subject and I think it would have been easier to understand if I was taught in a way that I could make connections and put reasoning behind what I was trying to do.

As a future teacher I look to teach math to my students in a different way than I was taught growing up. I think that by teaching students how and why something works they will be able to better understand the application and be able to retain the information. I can understand that it may be more difficult to teach in this way, especially since math is not my strongest subject, but I can still properly prepare for instruction and I believe that I can still accomplish teaching my students in this way. Students will be more motivated in mathematics if they are taught in a way that enables them to understand the "why" and the "how" and be able make connections from one concept to the next.

Summary and Synthesis

In class, we discussed perimeter and area. I thought I had a good idea of how to do them, but I realized that was all I knew...HOW, not WHY. I thought it was interesting what results we got when we were given string and used it to find the perimeter/circumference of different shapes. I always thought the square would be larger than the circle, but instead it was the other way around. I thought this was a great way to demonstrate this fact to students rather than just stating the fact that it is. I think learning this will help my students to understand the concept more than just performing the problem "because I said so"

I also thought it was interesting learning about the algorithms and using the geoboards. By forcing myself to come up with an algorithm, I am more likely to understand it than to just perform it. I liked how we could compare algorithms, so we could see how everyone else solved the problems and how different they all were.

Personal Concerns and Next Steps

I too do not know if I should put this under this heading or under questions and answers, but i feel that this is more of a concern than a question. When we were at Ponca Park we talked as a class about standards. We talked about the differences in state and national and then we also pulled apart the stands so that we could understand what they actually meant. Now in math class we are learning how to understand the language. My concern is that we are pretty far in our careers of becoming teachers, and we all know that we have written many many lesson plans for other classes. Why is it now that we are learning how to read and understand the standards? I am now asking myself if I have connected all the lesson plans to the right standards. I feel that this is something that should be done in a earlier class. Maybe education foundations? what do you think??
Megan

New Insights and Their Implications

I learned by finding the area of a triangle and polygons that there is more than one way to come up with the same answer. Instead of plunging numbers into an equation. I can exactly see that you can make difficult concepts easier by using hands-on activities. If students can visually see how a concept works it makes the concept easier to understand and most students will remember it. This activity reinforced my belief that hands-on activity is a great way to teach math. I knew that hands-on activities were great with lower elementary students but this activity showed me that hands-on acrtivities are also a great way to teach hard concepts to older students.

Insights and Implications

Insights and Implications- Learning math in school has always been receiving the formula and finding the correct answer. I never really knew why we learned formulas or how math was used in the real world. This course has shown me that students need to understand the "how" and "why" of math. Students need to be allowed to get into groups and find different ways of getting answers. I have also learned that students can not be scared to give wrong answers because they can lead students in a different direction towards a solution. As a teacher I need to teach deeper into the concept instead of teaching a lot of concepts. I am finding out that math is about finding ways to solve problems and understanding how math concepts are used in the real world.

While learning about area, we got the opportunity to use cut-out shapes, find the areas of polygons on a geo-board, and use string to have a deeper understanding of the concept. I want my students to learn math by finding the answers through exploration. Students can use past experiences, peers, and models to explore different roads towards solutions of problems. Being able to find solutions on their own, students will have an increased motivation and positive attitude towards math.

New Insights and Their Implications

Math has never been my favorite subject, it is fun when you understand it, however as I got to higher grades, and more difficult topics it seemed that my understanding dwindled (as did my interest level). I think that the reason why I have difficulty with math is that I never had a good basis to grow as a student. This class has taught me the importance of teaching math in a way different from how we were taught. Students need to be taught WHY we do the formulas WHY we do in math. On Thursday (Sept, 27), this really became evident to me because students need to know why they are using the formula for the area of a triangle. In my education, my teachers stopped at just telling us the formula. I think these insights mean that I need to teach math differently from how I learned. I want my math class to investigate math, and make sense of mathematics rather than telling them how to do it. Math has become too much of an independent study that is only taught through completing assignments solely from a textbook. Learning math, I think, should be more broad and a group effort (at times). At first I think that this takes more effort and is time consuming, but it builds a core understanding of math which makes the more complex/difficult problems easier to complete.

Summary and Synthesis

This semester, thus far, has been very informative and eye opening. We have explored many different topics in the short period of time we have had. We began with the topic of constructivism and what we thought it meant. Different meanings were investigated along with the history and the true meaning of constructivism. After the thorough study of constructivism, we were introduced to problem solving and the different methods involved in teaching a student. I found it interesting that as a pre-service teacher, I myself have never questioned as to why certain mathematical problems are approached the way they are. I have always been taught what to do but never knew why (regarding mathematical processes). Following problem solving we took a field trip as a class to Ponca Park. Integration, concept mapping, and standards were the focus of this trip. Unfortunately, the weather did not cooperate with this experience and we were inside for most of the day. I think if the weather had cooperated, the experience would have been more fulfilling than it was. After the Ponca Park experience, and currently, we have been working on geometry and all that it has to offer. Dr. Reins has given us different theories, articles, and methods to all look at to help benefit our learning in becoming a teacher. Overall, this class is helping me to explore different ways of thinking and essentially benefiting me by opening my mind up to several methods and approaches in teaching mathematics at an elementary grade level.

Summary and Synthesis

Last week we focused on finding the areas of triangles and polygons. In the past, I have always encountered short lessons on the area of triangles. The teacher simply gives the formula, shows how to "plug" numbers into it, and then gives an assignment over it. I have never spent so much time discussing and digging deep into the formula itself. I feel like I now fully undertand not just how to use the formula A=1/2Bh, but what it actually means. I like how we took time and did several different activities that helped us uncover the formula's actual purpose.

I also think it has been helpful to discuss problems with our peers. I think everyone has different views on things and it is very helpful to hear the way others solve problems. If I can look at a problem and be able to identify several different paths to the same solution, it will be easier for me to make sense of the problem. Talking with others helps me to become aware of other possible strategies I would not have thought of on my own.