New Insights and their Implications

I have thoroughly enjoyed the first part of this semester. This is by far my favorite class because we are actually required to think critically about how we will be teaching our students. We have been learning that the best way to teach is to allow students to solve problems on their own and not to be the "almighty answer holder." The idea that students need to struggle to be able to gain a deep understanding of concepts is something that I have always felt to be true. I have always wondered however why more teachers don't actually apply this practice in their classroom. Its not easy to watch students struggle, but when its going to benefit them in the end it should be looked at as a positve. I can't wait to learn more about how to challenge students in their learning as the semester progresses.

New insights and their implications

So far this math class is not like any class I've every had before. I have learned that math should not be taught the way we have all expierenced it. Never before have I been a student in a math class that did not involve examples on the board and then many many problems out of the textbook for practice. I have learned that in order for students to truly understand math and its concepts they must struggle and have some challenge. I have come to understand that there is a difference between struggling to find an answer and being given a worksheet and having no idea where to start. As teachers we must elp students to help themselves learn by letting them struggle, but not so much that they become discouraged and begin to hate math. I am looking forward to the rest of this class and learning how to make teaching math better than we ever expierenced as students.

Blog #1-New insights and their implications

Throughout class so far this semester, I have gained a lot of new insights towards the field of mathematics. I think the biggest thing I have learned so far is in teaching math to students. Growing up, I had the traditional math teacher that did two or three examples on the board and assigned problems 1-25 to give us practice. My senior year of math was a joke because we did accelerated math on the computer where we would print out our assignments and have to figure it out. When we asked for help often times our teacher did not even know how to do the problem. Where this story is going is that I have learned through our ELED 330 course, that math should be a class where students can use their own path of thinking to come up with the right answer. Students don’t need the magical formula to get them to the right answer. I have always looked at math as being a problem with one right solution and one right path to get there. Through the handshake problem, I came to the understanding that one problem can be done any number of ways to still come up with the same answer. Additionally, the handshake problem showed me that students can benefit from sharing their strategies with their peers. I had not even thought of doing the handshake problem the way that some of my classmates had done. Overall, I have gained a lot of insight about teaching math in these first few weeks. I now know that my students need to be challenged and that it is okay for them to struggle, the value of sharing strategies, and some problem solving tools, such as George Polya’s problem solving strategies, that may benefit my students. I am looking forward to the rest of the semester and what information I will learn that will help me in teaching my future students mathematics.

New Insights & Their Implications

Today in class we talked about the NCTM standards and the state standards. I thought that this was helpful because I think one of the hardest things about teaching is connecting the standards to the lessons. Breaking down the standards today really showed me that it does take practice to understand what the standards mean. I think it was also very interesting how vague the state standards were compared to the national standards. I always thought that the state standards were the easiest to understand but now my opinion has changed. I think the national standards were much easier to use since they were more specific. The focal point that was shown in class was also a great resource because it was even more specific then the national standards. Using those three resources will be very helpful when choosing standards in the future.

New Insights and Their Implications

From only being in this class for three weeks, I have already learned some very important points for teaching and learning math. I have learned that students need to struggle in order to succeed. If the teacher is too helpful to the students they may never fully understand the process needed to solve the problem they are faced with. Students want the teacher to tell them if they are doing a problem right, but the teacher should not give them a definite yes or no answer, but ask them, "are you doing it right?" Students need to think about the steps they are taking and ask themselves why they are making the decisions they are to find the answer. This will help them catch their own mistakes and make their learning more meaningful. Teachers need to model good problem solving skills by showing their own thought process aloud to the students, this will help them to think about their own thinking. From the scale factor activity I did struggle quite a bit, but after working and discussing with my group members we were able to talk out and contemplate what we thought we needed to do. This really helped better my understanding. Having the shapes in front of me was also helpful because we were able to work hands-on and strategize with them. I have also learned about choosing the right standards for my lessons and thinking deeply about what each standard is really aiming at for the students to learn.

New Insights and Their Implications

The last two weeks we have been working with the area activity and the national and state standards. Although the activity itself proved to a little challenging at times it addressed so many styles of learning. The table that we used showed the pattern that was emerging and asked to produce a generalization of what the equation for area would be. For people who can visualize something in their head this works well. For others who actually need to see a physical representation we were able to use the geometry shapes as well as the website online. I also liked how the activity could have an extension into another, such as having your students design a house from the scale drawing much like an architect would. Having a real world connection would help some kids find a purpose to what they are doing. We also focused on the standards. The SD standards seem to be plentiful yet vague at the same time. In a way it could give a teacher the leeway to be inventive with the standard. The national standards were not as long but they seemd to to more effectively state what was expected. I know that we need to adhere to our state standards, but by using the national standards and doing activities with strong content wouldn't we also be using the state standards? I think that as long as children are given the tools to solve problems and think creatively they will do well on standardized tests even if not every single state standard was met, but the national ones were.

New Insights and Their Implications

In class we have looked at math in a completely different way than I have previously looked at it. I have struggled with math for as long as I can remember. Math is not an easy subject for me. With the block activity that we did in class, I found it incredibly difficult to follow through with the activity. After having discussed the assignment in class, I am coming to a better understanding of it. Having the students work with their limited command of the material to find their own answers and solutions is an interesting concept. The activity helped me to understand what the students go through in the process of learning a new concept in a problem-based learning situation. The activity also helped me to have a better understanding of the concept. I am looking forward to using a problem-based learning environment in mathematics when I am a teacher. I think it will provide the students an opportunity to think through their problems without directing their approach.

New Insights and Their Implications

Today in class we were to discuss the state and national standards that we located in response to our scale, area, and perimeter activity. After breaking down the wording of the state standards I found it quite interesting that we really did not have a standard specifically for that activity. I found this to be quite disappointing because I learned greatly from that activity, but would not have used it in my classroom due to the fact that a standard did not dictate that I should teach it. It was interesting to see just how many different paths could be taken when deciphering the standards. The wording was so vague that it was difficult to pinpoint what the focus of the standard was supposed to be. Standards are the basics in teaching and if we cannot decipher their meanings now, then what does this mean for our future students?

New Insights and Their Implications

Teaching and learning math is way more than I thought it was. I have learned a lot about problem solving and how it should be taught in the classroom. Students need to be able to brainstorm the problem and create different ways of coming up with one solution. It is clear to me that not every student is going to learn in the same way so by having students communicate the different ways they found a solution to a problem, it might help other students understand the concept. Also, after talking about the South Dakota standards today, it made me think about what I am doing when I am picking standards. I feel that I will analyze the standard more after this class period as well as look at the National Standards and Curriculum Focal Points.

New Insights and Thier Implications

Doing the scale factor activity really thaught me alot about where I am in my mathematical education. I understood alot more concepts when I talked about it with my peers and with other groups. It is important to rach out to other peers when you are struggliung and sometimes this is not asy for me to do because I like to do things on my own. I also learned that I understand concepts but am unable to express them verbally. I can do it on paper but when I tried to help my classmates I was unsuccessful. This has taught me to remmeber that while being a teacher it is not always best to have studnets working independantly. It is important to let studnets converse and figure things out together because they might be better able to help one another.

New Insights and Their Implications

I couldn't believe that the State Standards and the National Standards are so different from each other. This was the first time that I have looked at the National Standards so I was very shocked at how the State really don't make sense when you read the National ones. I believe that now after seeing the National ones that every teacher should take a look at these before creating a lesson. You do however have to still make your lessons match the State standards. This was a very important class for me.

New Insights and Their Implications

Today in class we discussed the NCTM standards compared to the state standards. I was shocked to see how the state standards are so vague compared to the national ones. I had never looked at the national ones before. In every class we use the state standards for all subjects so I had never thought to look at the national ones. It is a big eye opener to see that it is much better for the students to look at the national ones and then at the state standards. The national standards are easier to look at and tell what the standard is. It tells you exactly what you need to do. There is no reading into it, guessing or thinking maybe this is what it means like with the state standards. I think that it would be so much better as a teacher to use the national standards. The national standards say exactly what you need to have the students learn. This would make it so much easier to find activities that fit the standard! I know that I will have to look at state standards and plan lessons around them but the national standards will help me also. I can look at them first and then look at the state standards to pick my standards that work best

New Insights and Their Implications

South Dakota state standards have been the focus of so many of my methods courses here at the U. We, as students becoming teachers, are told that we have to follow the state standards in each content area because that is what our state's main high-stakes tests cover. Choosing state standards has been almost a kind of guessing game in many of my classes. You know the activity that you want to do and you go through the state standards and cherry-pick the ones that "sound good" or the ones that you think the activity touches on. It takes quite a while! It is hard to find standards sometimes because, as we talked about in class today, they are written in such vague terms. I was not there when the standards were written, so how do I know what exactly they mean?

Today we discussed the benefits of using national standards and curriculum focal points to help in the process of choosing certain standards that apply to an activity, or to find an activity that applies to the standards. Honestly, I very rarely have looked at the national standards for most content areas when making lesson plans for other courses. It astounded me how much easier it was to pick one or two of the state standards after looking at the NCTM document and at the curriculum focal points. It will be extremely helpful in the future to be able to look at all of these documents when choosing standards for lessons.

New Insights and Their Implications

Today in class we talked about standards. I was shocked to look at South Dakota's state standards and compare them to the national standards. From the scaling activity we did in class, we found specific detailed national standards that supported our activity, but when we looked at the state standards, it was very difficult to find one that matched and if we did it had to be stretched out or further explained. By looking at these standards, it made me realize that there is more to be covered then just what the state of South Dakota is asking. This was a great activity and I believe it would be very beneficial to students in upper middle school, but when looking at the South Dakota state standards, I am not sure this activity would have fit in. It was a very good discussion in class, and interesting to hear what other students had to say. If I was a teacher in South Dakota, I would probably not have done this activity because the state standards are to be met, and that's what the students will be tested on. Also learning from the scale activity, it was a great way to work with our peers. We had the actual blocks and had to design the shapes. It was very interactive, even though it was frustrating at times, but we learn from each other. After the activity was done, the scale factors were then explained. At first I was a little confused, but after today I have a better idea on how to explain and figuring out how to enlarge the scale factors to find area and perimeter.

Personal Concerns and Next Steps

My personal concern is if I'm going to meet all the requirements for my students by providing them enough activities, meeting the standards and knowing the subject matter to its entirety. I have not done my intership so with this class it seems like becoming a teacher is a lot harder than it looks like. I know one way to solve this fear is to go through my intership and practicum and see if my fears change. Math is not a strong point so maybe I could go to a math camp or practice math more often or volunteer in a classroom to gain my knowledge. I had never seen the Smartboard technology and I had no idea there was National Standards that need to be met until taking this course. By going to my classes, I can converse with my peers about technology and ideas they have.