New Insights and Their Implications (Blog #1)

This month I have learned a lot about how to teach mathematics. Going into this class I was unsure how to explain concepts to other students. I really enjoy how we are discussing with each other how to explain different concepts. Every student learns differently and by showing us all of the different ways we can solve problems we can keep this information in our notes so when we teach it to students we can show them that there are more than one way to solve a problem. I also learned that it is important to have a variety of questions to show examples of when teaching mathematics. As a teacher, I need to have students perform a multitude of easy, moderate, and difficult questions and also show them how to do some of each for examples. I also need to find different ways to get students to have hands-on learning when it comes to mathematics so they can perform trial and error for themselves without the aid of the teacher. The final thing I learned this month was that teachers need to give little help to students when they begin their work. We need to let them try things for themselves and not just give them the answer.

New Insight and their Implications

I am starting to gain new insight into the standards. I was not aware that one needs to take into consideration both the National and State standards when planning a lesson. So far with my education I have looked at the standards and written down every one that might pertain to the lesson plan. I see how this does an injustice with our students. It is better to pick a couple of standards, both from the state and national standards, to focus your lesson on. This way one can make sure that you have taught all standards required. Listing a bunch of standards, on a certain lesson, may lead you to believe that your already taught a standard but you have not.
I have new insight into realizing that I have not had math for a long time, and the old addage 'if you don't use it you will lose it' may be applicable. This class will help me learn and remember what I have already learned. I have noticed in the schools that they are teaching differently from when I was taught in school. My children are in 3rd, 5th, and 7th grades and their homework is a bit different than I remember. For example, my 5th grader is not allowed to line up math problems on top of each other for multiplication. There are at least two other ways they are learning to do multiplication. They use a table to solve the problem. I am anxious to learn these new ways both for teaching and helping my own children with their homework.

New Insights & Their Implications

Since this class has started, I have already gained many new insights in regards to teaching. I now understand how important it is for students to be able to think for themselves and engage in a learning process in which they are able to independently create solutions from the information and material given. As we have talked about numerous times in class, it is beneficial to students' learning if the teacher lets them struggle a little to figure out solutions instead of giving them the answers. This way, the students are more active learners and will take responsibility for their learning. We also discussed in class how it is extremely important to not only refer to state standards when planning lessons, but also consider national standards. It was made very clear in class how the state standards are very vague and may be missing vital components. The national standards are more detailed and help provide a better description of the learning that is expected to take place at each grade level. In other classes, we have not talked much about national standards, so it was very helpful that we covered this in class. These are some of the new insights that I have gained so far in class.

New Insights and Their Implications

Since the beginning of this class, the main idea that I have learned is how to teach math. Growing up I was taught math, but ALL my teachers taught me the same way. They would present the problem, do an example on the board, and make us do like 15 for practice. However, since being in the class I have come to understand there is another way to teach math. If more students were able to understand math, by struggling through math problems and using their own solutions then math would not be a scary subject like it is now.
Another insight I have really learned a lot about through this class is standards. Before coming to this class, I though of standards as state standards and that is the only information I NEED to worry about teaching. However, once again I was wrong. When I teach, I need to look at National as well as State standards. If I look at both, as well as APPLY both it will allow my students to score better on tests, and dig deeper into certain material, rather than of the idea of "a mile wide and an inch deep."
The last insight I have really learned from this class already is the wording and choosing standards. With the exanple we did in class, it allowed me to realize to choose one or two standards and teach those, rather than trying to teach seven different standards as one time. In addition, I need to research the meaning of the words in the standards and not just use my defination of them.
I have learned about myself that I am closed minded when it comes to math. I was always taught a certain way, that I assumed if I ever taught math that would be the right way to do it; however, I need to be more open to math and allow my students the opportunity to struggle, learn from others, as well as from the teacher.

New Insights and Their Implications

I have lerned many things from my peers and the instructor so far in this course. I have learned that there are a variety of ways to teach math, and no one way is the correct way. I have learned that you have to allow students (and yourself) to struggle in order to come to a solution to a problem, and to truly understand the concept. I have also learned that there are many ways to approach problems, and various ways (or ramps) to take when solving a problem to get to the correct solution. Some implications for teaching and learning mathematics are to allow the students (and yourself) time to figure out the problem independantly. The students and individual must struggle a bit if they are to understand the concept presented before them. Students must be allowed to test different ways of reaching a solution to a problem, as well as understand how they came to the solution. The same can be said for learning mathematics; you must concentrate, and struggle with problems before coming to a solution to further your understanding. Through this course, I have also learned a lot about myself and my own struggles with mathematics. I am not the best math student, but I find that talking with peers and asking questions about reaching solutions is a great way to learn because it allows me to understand the concept for myself, not just simply coming up with a correct answer. As the semester progresses, I hope to obtain more insight into the teaching and learning of mathematics.

New Insights and Implications

I have always enjoyed math and can't wait to teach my future students the subject. Before taking this math methods class, I have never thought about the little details that go along with teaching math. I have come to realize, more now than ever before, that teaching math may be more difficult than it seems. The scale factor activity made me learn a lot about how to teach students in a way so that they are learning for themselves. In addition, linking the standards to the scale factor activity was a great way for us students to analyze each standard to see how they fit or didn't fit into the activity. I feel like this class will truly teach us how to help our students learn math instead of just doing math. So far in the few weeks we have had class, I have learned what not to do and what to do in terms of teaching math to students.

Summary and Synthesis

Throughout the beginning of this course, I have learned to view mathematics through a different eye. By participating in classroom discussions, group work, and small group assignments, I understand that teachers need to instruct students on problem solving, not the actual problem itself. I now believe that teachers should work harder on developing students who are unique and individualistic thinkers. In addition, teachers should allow their students to make conjectures about mathematical problems in order to better understand their mathematical thought process.
When we completed the scale factor activity, I realized how difficult it must be for some students when they do not understand a certain math concept. During the activity, I became frustrated with certain drawings and equations, but I was able to work through the problem with the help of my peers. I believe this was one of the best ways for me to understand this difficult concept. As a future teacher, I believe we should all students to collaborate with other students to better understand each other's thinking as well as their own.

New Insights

Over the past few weeks we have spent some time going over our area and perimeter with scale factors worksheet and I have seen a completely different style of teaching that I personally haven't seen or experienced first hand. Instead of running to our rescue right as we have a question or perhaps start to veer off the path to the correct answer, Dr. Reins lets us stray from the correct path and allows us to struggle to work our way back to the right path. This is something that for some students may be discouraging, however it has helped me tremendously. I have never been scared to ask questions however through this new way of teaching, it has allowed me to first think about the question, where I need to go and then from there I begin to work backwards almost to try to fit the two pieces together. For the students who get frustrated or discouraged easily, a small hint every once in a while may help build their confidence and slowly from there give them less and less help. Overall, I have found that although this method of teaching is quite difficult to get used to at the beginning, the rewards at the end are completely worth it.

New insights and implications

Last week we did an activity which involved area, perimeter, as well as scale factor. All of these terms were familiar to me, but as the activity progressed, it became more difficult. I found that it was beneficial to work together and talk in a group to come up with a solution to the problem. Talking with peers helps because, for me, it is sometimes easier to understand their point of view rather than the instructors; however, when you the instructor explained in more throughly, it was easier to understand and your graphic organizers helped as well. I learned that sometimes when things don't come as easy, I should try to talk to peers inside and outside the classroom. This week, we also discussed standards and the several kinds (state, national, and focal points). It was interesting because the focal points seamed to be very specific in which I think standards should be measured. I learned from my peers and instructor how to look at standards as well as determine if how certain standard (s) fits a certain activity.

New Insights & Their Implications

Throughout the first few weeks of class, I have altered my thinking of what makes good mathematical teaching. As typical of many of my peers, I learned math in the basic way of being told the correct way to approach a problem and then completing a number of similar problems. We learned in class that there are multiple entry points for every math problem, and one strategy should not be considered superior over others. By showing students that there is only one correct or best way to approach a problem, we as teachers may be boosting the confidence of one set of students, but we will also be discouraging other students who puts lots of effort into their work. I love Math because it challenges me to think critically and look at problems from multiple perspectives, but I know all my students will not have the same opinion. It is my duty to learn and understand how to use all different strategies of approaching problems. This knowledge will enable me to reach all my students at their current level of mathematical understanding and encourage them to apply strategies that work best for them. In addition, I also find it interesting that Jolley requires their teachers to be accountable for reaching each of the state standards at least three times. Even though we learned state standards are not as reliable as national standards, I think this is a great idea. When teachers address a standard one time, they may not reach every student. By being accountable for all standards and reaching each standard several times, teachers increase their chances of having all students meet the standards.

New Insights and Their Implications

After having a few weeks of this class, I have realized that teaching math is harder than it looks! I have always enjoyed math, so I assumed that teaching it would come somewhat easy for me. However, I've learned that applying mathematical concepts is more important that always getting the right answer. It's more about the process than the answer. This class is forcing me to think about math from a different perspective; my students'. In order to teach students, I must understand where they are at, how they are thinking, and what strategies they struggle with. Understanding how my students interpret math will make it easier for me to teach them skills like problem solving. Students will benefit more from struggling to learn the process more than they will if I just gave them the answers. I'm excited to learn more about teaching mathematical strategies to students.

New Insights

There have been several new insights this semester that I find useful and interesting. The last couple class sessions we have been talking about the state, national and focal point standards that guide math curriculum. Before this class I never realized that they were more standards to follow or use as a guide beside the state standards. I find it very helpful and useful knowing that there are more standards out there to use besides the one for your state.
This class has also opened my eyes into a new way of teaching math that I never considered before. Growing up in all of my math classes we did a lot of worksheets with examples on the board to teach the process. As a student, I remember that if I struggled I could look to my teacher for help. I can't say that they would just give me the answer, so I do believe that they used some of the similar teaching techniques in which we are being taught in class.
Solving problems can have a lot of different steps to take and I have also learned how to approach teaching story problems. I believe it all begins with the approach in which a teacher delievers to his/her students.