Summary and Synthesis

This class is really starting to open my eyes about how to teach my future students, and how not to teach. When we were learning about multiplication and division of fractions just recently in class, I learned many new ways to teach my students including activities that I never thought about before. Just because I learned best by writing fractions out on paper, doesn't mean that my students will learn that way, so it was nice to learn about various ways to teach my students.

New Insights and Implications

I found this class to be a little confusing when we first started the semester. I was unaware of how to teach or learn math in the different methods that had been brought up in class. As the semester goes on, it is becoming easier to understand this new form of teaching and learning. I also feel that the LPU projects are going to be another way that we can learn how to teach different areas of math. Having our peers teach us is also a great way to learn.

Summary and Synthesis

I like the idea of having us as a class teaching some of the topics to each other and then having Mr. Reins add in his perspective and then teaching us at the end of the class period. I actually did learn a lot Tuesday from getting information from the group that presented. And then we get to use the items that Mr. Reins uses in his lessons too. For instance the group was able to incorporate in the fraction bars and pattern blocks. This makes learning and knowing how to teach a topic easier.

New Insights and Implications

For me, this class is about learning new techniques and strategies to teach elementary math to students. I feel that I know, generally, how to do math problems, but I lack the strategies on how to TEACH it. That is where I get a lot of insight through this class. For example, a new insight I have learned recently in this class has to do with the use of manipulatives. I have learned that by allowing students to use tangible objects to better understand problems, you are allowing them to work more indepth with the problem and allowing them to see the problem from a different angle. By doing that, they are more likely to remember it. I will use this idea throughout my classroom because I have learned in this class that it is important to have a higher level of thinking in math and it is important to teach my students to value that higher level of thinking.

New Insights and Implications

I enjoy learning new ways to teach mathematics to my future students. When I was an elementary student, I don’t remember learning the way that Dr. Reins has taught us. My teacher just gave us the algorithm and had us practice it. By not learning through manipulatives, it makes it hard for me to understand how to do everything, but when I finally grasp the concept, I know I will be able to teach my students different ways. Also it is necessary for a teacher to know why we use a certain algorithm. This way he or she can teach their students and they will truly understand.

New Insights and Implications

Math Methods has been much different then any course I have taken up to this point. It has encouraged me to think way beyond the knowledge I have learned in the past. I feel the class is very difficult because in many cases I am having to relearn the math as well as how to teach it in great detail to new learners. I do wish that this course could be two semesters long instead of just one so that not so much information would have to be crammed into one semester. Math has always been my most troubling subject. I feel that if my teachers in elementary school had thought me the reasonings behind math then maybe math would have been a more positive experience. I hope that with Math Methods I will learn ways to better teach math and help my future students learn math. My goal is to help students understand and enjoy math. I would like to take my negative experiences in math and build on them to help my students have a more swuccessful learning experience in math throughout school.

New Insights and Their Implications

Learning why we do things and not just how to do them have made me realize the importance of doing math for understanding not just product. Fractions have always been one of those confusing topics but seeing why I flip the reciprocal helps me better understand the concepts and now know why I should teach students not to pass the test but understand the topic. I also have developed a liking for project learning and how learning can be greater from that than just lecture listening.

New Insights and Implications

I'm really excited to be able to have all these new ways of doing different problems under my belt. This class is still difficult for me to understand everything that's going on, but I find I'm understanding the new concepts better and better as time goes on. It's great to be able to find all these new ways for math related problems that I can share with my students. With every child learning differently, these concepts are going to be very useful in my future classroom.

Summary and Synthesis

This math course has been different then ones I've taken in the past. Over the semester, we have learned the reasoning and processes behind math concepts. Instead of learning how to do math concepts, we are learning why we do the problems and how to make connections. Dr. Reins has used a variety of methods to help us learn about connection and how to help students make connections. If, we as, educators don't know the process behind math problems, we can't help our students to discover them or make connections. With the help of manipulatives, students can see concrete models of the problems they are doing. Instead of teaching students an algorithm, we should be using activities that allow students to discover it on their own.This semester has helped me to discover just how important it is to understand the "why" in the math problems we are doing. Knowing these things is important so we can help our students deepen their understanding of math concepts.

New Insights and Their Implications

I never thought I would actually learn an easier method in math when I was in college that I was not previously aware of. I thought my ELED teachers did an okay job teaching me math as a child (although I was never very good at it). Now I'm wondering: is the reason I wasn't very good at math because my teachers were taking the wrong approaches to teaching me? I have always struggled with math, but while doing the area exercises a "light bulb" came on in my head - and I suddenly understood the concepts of finding the area for ANY figure. I never knew the trick of boxing out the figure, then finding the area of the boxed figure, then the area of either the figure or the empty space around the figure to come up with a total area. Although it seems like more work than just plugging in a formula, it seems to make a lot more sense. I also realized WHY area formulas are written how they are. After breaking down the figure to find smaller figures that I was familiar with finding the area of, it made creating a formula and figuring out the area of any figure simple. I wish my math teachers would have provided me with those types of examples when I was in school - I think it would have made my experiences with math much more enjoyable.

After realizing how much of a difference learning a new method now, as a senior in college, can make on my math career - I can now see the importance of explaining the why you do a math problem the way you do to students, not just giving them the way to solve a problem. Having an insight of why you're doing the formulas and problems the way you are truly helps create a much deeper understanding of math that sticks with you; it is much more effective than just memorizing formulas and plugging in numbers to get answers.

Summary and Synthesis

In yesterday's class we learn how to show our process on dividing fractions. I can easily divide fractions given a problem and using the method that the group showed in class. When it comes to teaching students how to divide fractions I am not sure I was aware how to show the process to students. After their lesson, I had some ideas and realized that this may be helpful to me in a special ed classroom. I like how Dr. Reins shows us the manipulatives during his lesson and can give us different ways to teach different concepts. I am going to have to show my students how to get to the answer or break the problem for them to understand it. Especially in a resource room I am going to need as many ideas as I can get because not everyone learns or understands the same way. The class is fairly fast paced and it is still sometimes difficult for me to grasp the concepts right away, but after some extra time I begin to understand more fully what exactly the processes are.

Personal Concerns and Next Steps

Each teacher has a different learning style, and it is always hard to get used to all the different ones. I think this class is completely different than how we have been taught math in the past, which is what makes it hard. When we are learning a new concept in this class I feel I understand it, but as we go more in depth I find myself becoming confused as to the process of how we came to get the numbers or formula we do. I think it is just different than simply memorizing formulas and problems like I have done in the past. The next step would just be to keep trying and working hard! If I do not understand something the best way to fix this is to go in for help and asking questions. Hopefully if I keep applying myself and putting in effort in our activities, the connections will be made!