Summary & Synthesis

Over the last month, I have learned a few important teaching strategies for teaching math. These ways of teaching were not how I was taught, so they seem somewhat exciting and somewhat scary at the same time. I have always enjoyed math and like figuring out why and how math works. The last month has challenged my math skills in a very different way. For the first time, I found myself struggling with math in a different way than I'd ever struggled with math before. I now somewhat understand how we're suppose to teach math to students; letting them struggle to come up with an answer. However, it's hard for me to completely grasp since I was taught math so differently. Over the last month, I have gotten frustrated with assignments and readings because it's forcing me to think about math in a completely different way. However, I still love math and am extremely excited to apply these teaching methods to my own math classroom.

Summary and Synthesis

On Wednesday, October 14, 2009, our class went to Beresford Elementary for Operation Coyote. While at Beresford, I taught not only one math lesson but two math lessons. The first math lesson was in first grade and we introduced the number line and worked on addition and subtraction. The second math lesson was in third grade and we worked on the number 5 times tables. At first, I struggled with the thought of teaching a math lesson without adequate preparation time, but once I started teaching the first lesson (in first grade), I become confident in how I was presenting the information. Later in the afternoon during my second lesson (in third grade), we taught a lesson about the number 5 times table. We gave the students a problem of the day and had them work on. Then, we had the students talk about the answers they got. Most of the students had the correct answer but some had different ways of getting the answers. We had the students talk about the different ways in which they found the answers and told them that just because you had a different way of getting the answer, does not mean your way is the only way. I found experience to be a great connection to what I am learning in this class, math methods. When I was doing math in elementary, there was one way to do a problem and that was it. When this type of instruction is introduced to students, more students will "get" math problems.

New Insights and Their Implications-Blog #2

Throughout class this month, I have learned a lot of new things about teaching students math. However, the one thing that sticks in my mind and that I found extremely interesting was breaking a shape into other shapes. For instance, it was really interesting when we found the formula for the trapezoid by breaking the trapezoid into two triangles and a square. I had never looked at shapes in that way. I had no idea that I could develop a formula on my own and didn’t believe I could until that assignment. I also found it helpful to use tangrams to see how shapes can be composed and decomposed. Overall, I learned a lot about teaching math to students and am looking forward to learning how to teach the more difficult concepts that students struggle with in the upcoming classes.

blog #2: Personal Concerns

This class is definitely unlike any other math class that I have had. Although I have gotten frustrated with this class a few times, I have learned a lot too. For example, when we did the taking apart area formulas, I struggled with this concept a little at first (proofs). Now that I can see where the formulas are coming from it will definitely help me to teach the formulas to my studnets. Going through my previous education years, I definitely just memorized formulas, but actually being able to produce the formula even if I can't remember it is a huge benefit. I just hope that as the class goes on I keep reconstructing my previous notions.

Summary and Synthesis

Throughout this course, I have altered my thinking about what constitutes best practice for teaching mathematics. Like many of my classmates, I have been challenged by this course to think in new ways and make sense of ideas without taking shortcuts. Each concept we have experienced in this course has been linked and built upon other concepts, which are all part of a "bigger picture." Teaching math is not about drilling isolated concepts and formulas to students, which are impossible to remember or understand, but is about allowing students to construct their own ideas and create a conceptual understanding about why they are carrying out procedures. Like Bridgette mentioned, I also learned the benefits of cooperative learning. In the past, working with others has usually been considered a form of cheating. From this class, I have been able to see how everyone benefits from sharing their thinking and justifying their own ideas, which strengthens each student's individually constructed understanding.

New insights and their implications

Through this math class so far I have learned a lot about how kids should learn math and how I learn math. I really like this class because I am learning math in a way that is like I have never learned before. I have always been someone who struggled to learn and memorize formulas and then know how to use them in a situation or problem becuase I did not understand them. This class is teaching me math the way I should have learned it, and is showing me how to teach kids math so they actually understand what they are learning. I have learned that students are not actually learning anything when they memorize formulas, but learn much more when they understand why and how to solve a problem rather than just memorizing solutions. I have also seen through this class how tough it may be to change the way math is taught, but in my classroom I will be able to help students learn math in a different and most likely a more effective way.

Summary and Synthesis- Blog #2

This Math Methods course has definitely caused me to think about teaching math in a new light. I have been struggling with quite a few of the concepts that we are learning, and this may be because I am used to math teachers in the past walking me and my class through all the steps that need to be taken to complete a problem. In this class we are learning through accessing our prior knowledge and using critical thinking skills to solve problems without the instructor as the facilitator. I had a hard time with finding the area's of the shapes on the geoboard, and after I asked for help I am much more confident with the concept. I have learned that I need to think outside the box and focus on what I need to be doing to solve the problem in front of me and not get overwhelmed, because that is when I run into trouble. This new way of teaching and learning has been a stuggle for me but I am able to see the positive effects that will result. If students are finding their own methods for problems and going through the entire thought processes, like we are in this class, they will be more likely to retain that information and make their learning more meaningful. This class is a struggle for me but each day I am learning in new ways and I am hoping that it will have positive effects on my future teaching of mathematics.