New Insights and Their Implications

I think the biggest thing I've learned in this class is that the way I was taught math growing up is completely wrong! I always had a very traditional way of learning math; my teachers talked about the new concept for awhile, gave us a worksheet to do, and after enough lessons, tested us on it. There weren't many hands-on experiences provided to us students. When it came time to take a test, we just memorized the equations and answered the questions. After the test was done, pretty much everything we memorized was forgotten. That would probably explain why I'm not very good at math now.

I guess I never really knew that there was a different way to teach the information. But thanks to this class, my conceptions on teaching math are changing drastically! Although there are times I get frustrated in this class, I can honestly say I'm learning so much and actually retaining the information because we're doing hands-on activities and working on constructing our own knowledge. I really see the benefits of teaching math in this manor. I hope to be able to adopt this method in my own classroom. I think my students would really benefit from learning this way!

Personal Concerns and Next Steps

My convern in this class is a personal concern which I have struggled with a lot but even more so in this class. I understand the concepts and the materials you are presenting us but I have a hard time explaining it to other people sometimes and think it could be benefital to me how to explain the whys some more rather then just presenting the right kind of problems. To help students understand the right connections.

Personal Concerns and Next Steps

Some personal concerns that i have are that I am unable to think out side the box. I have always learned a certain way to mathematical formulas and how to problem solve. I was never really given opportunities to be challenged and find different solutions. Another concern of mine is that it is so hard for me to take tests and comprehend and make connections while studying that it could eventually hurt me in the long run. Some steps that i can take into account when i am studying is to try and make those connections to real life situtations, and maybe start studying a couple weeks before the text, rather than a couple days before. It is just very hard to study so far in ahead, when we are required to do some much homework in all of my other classes. I am not complaining, but sometimes school gets a little overwhelming and i seem to fall behind in all of my studies. Some other steps i can take in order to improve would be to give myself challenges and make my self solve problems using different strategies.

Summary & Synthesis

The impact of the recent experiences throughout the Tuesday and Thursday blogs have really opened up my eyes to thinking "outside" the box. Many math classes encountered today in elementary school have made way into the old thinking of how math is run. Through this math class I am in, I have had a tremendous impact on the fact that as teachers we need to guide our students into their own thinking and help them to model and demonstrate their prior knowledge in order to build upon their new experiences in math. The thinking in itself in these classes makes known that there are MANY different strategies and skills used to be able to solve ONE problem. This is effective to the classroom because it allows students to pick and choose and experiement with all in order to find out which problem-solving tactic works for them. This is a wonderful idea, because it focuses on the independent child, and their individual needs! The issues that are brought up in the classroom, with the research encountered through Japan and other countries of the region, look at math a completely different way. The U.S. lacks in math and needs certain progress. This class helps explore dicussions through models, student to student interaction, student to teacher interaction, geoboards and many manipulations that will help us to better understand the methods of teaching math.

New Insights and their Implications

I think that the most important thing that I learned during this first half of a semester is how to teach mathematics in a more reformed way by taking a constructivist approach. By looking that the TIMSS data, I learned that we do need to take a different approach in mathematical instruction in the United States. But knowing a change is necessary and knowing how to make that change are two different things. That is where the constructivist approach comes in. From what I have learned about constructivism during class and from the readings, I believe that this approach is a good step toward reformed mathematical instruction. By allowing students to construct their own knowledge we will be allowing them to again a deeper understanding of the concepts. Also, a classroom following the constructivist approach will have better focus and coherence. I feel that if I am able to implement a constructivist environment for my students to learn in, I will be doing my part in the reformation of mathematical instruction. I feel that the learning that takes place during a lesson built with a constructivist approach mirrors that type of learning we want our students to be having based on the results of the TIMSS study.

What does it mean to "Do Mathematics?"

Doing mathematics means that you are involved in the science of pattern and order (pg 13).  You are always exploring different ways to solve math problems.  You have to look at multiple angles of the problem to see if it is the correct way to solve it.  The old way of doing mathematics is “listen, copy, memorize, and drill” (pg14).  This is one way to do mathematics however the new way is more efficient and helps you learn why you get an answer not just, this is the formula, solve the problem.  The new way to do math is to have the students think of the problems and formulas and start from the beginning.  When you are doing this the students actually remember the process more and understands why something is the way it is.  This is doing mathematics because you are looking at the science of pattern and order.    

What does it mean to "do mathematics"?

When students are doing math they are engaging in the science of pattern and order. The students are exploring and explaining different ways that they used to come up with the answer to the problem. They are making sense of and figuring out the problem. The environment also has to be one where math is not threatening and every student is respected for their ideas.

What does it mean to "do mathematics?"

According to Van De Walle, "doing mathematics" means that students are engaging in the science of pattern and order, and doing mathematics is effortful and often takes alot of time (13). I think that in order to be able to"do mathematics" children should be actively involve in the process of understanding how the problem works, how they can connect it to their lives, and how they can solve the problem in not just way but in maybe several ways. We are taught in school that there is only one way to do a problem, but in all reality there could be several ways to solve the problem and get a probable solution. "Doing mathematics" also means that it shouldn't always be easy, we should be able to dig into it and struggle a little bit. According to Van De Walle there are many verbs we can correlate to "doing mathematics." For example, we can correlate explore, investigate, conjecture, solve, justify, etc (13). When students are engaged in these verbs it is very impossible for them to be passive learners or observers (13).

What does it mean to "do" mathematics?

Please add your comments to this question raised by chapter 2 of Van de Walle. Comment directly to this post about what it means to be involved in "doing mathematics."

What does it mean to "do mathematics?"

Doing mathematics means that one is actively engaged in solving problems. While doing mathematics, one is looking for patterns and order to come up with the answer. When doing mathematics, one is not just following rote procedures that were previously taught by a teacher. By doing mathematics, one is able to understand why they got the answer or why a formula found works in the given situation.

Personal Concerns

Since coming to college math has not been the easiest thing for me, I never used to have a problem with it, it was always a subject that I understood. However, I believe the teaching styles have changed since I have come to college, that they assume we as students know more than we do. So far this class has been easier to follow then most math classes I have taken in college. I believe it is the style of teaching used in the classroom, it is broken down and you give us a way to find the answer ourselves. It makes learning more enjoyable and less stressful.

Personal Concerns and Next Steps

I, honestly, have been a little worried about this class because it's math. In the past, I have never been given a good reason to enjoy math. I've always struggled with some mathematical aspects, so, I have grown to actually dislike math. However, I am doing my best to have a positive outlook for this class. I'm trying my best not to judge this class based on other math classes that I've taken. I have to say that, so far, I am very interested in this math methods class! I am very anxious to learn much more about how to teach my future students. I look forward to learning many different methods of teaching my future students.

Personal Concerns and Next Steps

This class has offered a lot of valuable information. Perhaps almost too much, but I think that is the point. I can definitely see myself using some of the resources, such as the National Library of Virtual Manipulatives. Also, I enjoy the projects because they are not as belittling as other class’ projects, such as coloring and gluing. I also appreciate having the standards being related to what we are doing within the class, mostly so we know how to start choosing them on our own as we will have to do this very soon. I just worry that in the future I will have trouble finding projects and assignments that accurately fit all of the standards. However, having more experienced teachers and good resources will be a great help.
[andrea]

Personal Concerns and Next Steps

Currently my only concerns in the class are figuring out where to find each piece of information and apply it to my learning and future. With all of my other methods courses and classes being on D2L, everything is new to me and is taking time to get used to. I find myself in class trying to pay attention and figure out where everything that was covered was recovered at, however, when I return home to review the information, I find myself confused as to what was read and where to click into. The class has been both informative and stressful. I feel that since we only meet twice a week, there is a lot of information being covered in class each meeting. Some of the information that we began class with, always has the potential to slip my mind by the time I walk out of the door.

Personal Concerns and Next Steps

Personal Concerns and Next Steps
-We are currently rounding out our third week of classes and I feel like this class has already given me a run for my money. I have been given more information in this class the last couple weeks than any of my other courses thus far. I am concerned because I feel like I sit in class and pay attention as much as possible, but yet the information is going in one ear and out the other. I feel like during lectures we don’t get down to the nitty gritty and that’s what I need to feel comfortable with what is important and what is just additional information or resources. I want to be able to listen during lecture and have it all click instantly, but there is just so much information. During class I am finding it hard to pinpoint the important facts to store away into memory. My solution to my problems is to study alot and read the chapters once and maybe even two or three times to understand the materials presented. It looks like I’m going to need to adjust my way of learning and adapt to this new and challenging course.

Personal Concerns and Next Step

I believe that class has been going well so far. I am pretty good at understanding math if I have a little time to look at it. I have encountered both good math instructors and instructors that were so bad that I had to help teach the class. I believe that this class can better prepare me for teaching than the old way of just showing it for memorization and then forgetting about it. I do not have any concerns at the moment. Just enjoying myself. It is amazing that in our world today we have only now come to really look at the standards and how to do things better than we did before.
Adam Jastram

Personal Concerns and Next Steps

The main concern I have with the math class is that I have not been taught to enjoy or like math. I am also not very good at math, so it makes it really hard in this class. The math teachers that I have encountered throughout my math history always just showed me how to do what needed to be done in class. The teachers also just gave me answers a lot of the time instead of explaining to me how to think logically through the problems. Though this class is taught with totally different methods that I am not used to, I believe that I will be able to learn more about math and really enjoy it. Through this class, I think I will be able to think more about math logically and use reason. Also in this class, I plan on really trying to understand math rather than just getting by.

Personal Steps and Next Steps

I have really liked this class so far and it has been very interesting to me. I have already learned a lot more in these few weeks than I have in other math classes on how to teach math. I know that this is a new way of learning and a teaching way that most of us have not been exposed to at the university. It is a bit difficult for me but not too hard that I am not learning. I just wish we maybe had more time to discover things like we have been but also have more time to talk about things and go over the right answer. I like that were are going over the standards because in all the method classes we are needing to look at them more and more and most teachers just expect us to know how to find the right one. In this class we are going more in depth with what to really look for in standards. I have always liked math, maybe have not been that good in teaching it, so I am looking forward to being able to know how to teach it better and to help other people understand it better also. How do you change the standards for special need students? This is one question that I am interested to learn more about in the last couple of weeks. I know that each student is different in their own way and am excited to learn more about fitting the concepts, the individual, the standards and the new way of teaching all together.

Personal Concerns and Next Steps

A concern I have within teaching math, as well as other content areas is the standards. If I am teaching a third grade class math, science, social studies, and language arts, there are a large number of standards I will need to be aware of and make sure I am meeting. This past Thursday in class (Sept. 18) helped me realize that it really is not to difficult. The standards, both state and national, are easy to find, and for the most part, easy to look through. I found the assignment to find the 7th grade math standards for the activity we did in class to not be very difficult. The standard websites have links to go directly to the grade and directly to the strand. Finding the 7th grade standards in geometry and measurement just took a few minutes of reading. Though I am realizing it's easier then I initially thought, I want to find a way in which I can make sure I am effectively finding all standards for every content. I also want to learn a way in which I can sort the standards myself in order to have easier access.

Summary and Synthesis

I have enjoyed learning more about math and can not wait until we talk about the CGI program, or at least I hope we talk about the CGI program. These last couple of weeks we have been talking about the process of problem solving, scale factors, and both the NCTM goals and expectations and the state standards. One of the first things that we did was the handshake problem. This was interesting because we were asked to write down what we were thinking while trying to solve the problem. For me it was harder to figure out why I was doing what I was doing because it seemed to be so automatic for me. I immediately started to solve it by using diagrams but could not tell you why I decided to you this strategy to solve the problem. I also appreciated the activity on similar shapes. This was great because we had the opportunity to work in groups and we also had to try many different things to find out how to enlarge the shape by a scale factor of both 2 and 3. I hope that we continue to do hands on activities that we could also do with are classes when we begin to teach. I have always believed that hands on learning is a great way to teach and learn different things.

New Insights and Their Implications

Prior to this class I had never really seen myself teaching mathematics. If I were put in the position to teach Math I would have taught it the only way I knew how, the way I was taught. However my views have already drastically changed. I have learned about the deficiencies that we as the United States face when compared to other countries. I think that the problem solving approach is a very practical way that I can teach Math effectively. When we began discussing the problem solving approach and how much more time it takes and the amount of time the problems take i had serious doubts. I personally thought that this was going to be a discussion about how we SHOULD teach that was not practical whatsoever. I have been enrolled in classes in which we have been told how to teach but there is no way that we can teach that way and meet goals and standards that have been set forth. It seems now that I am confident that i can use an approach that can increase student learning as well as meet state and national standards.

Personal Concerns and Next Step

So far the class is really interesting to me, and I have learned quite a bit about how math is taught and how it should be, but I do not feel as though some things are gone into depth as much as I like. I know that letting the students explore how they think and what their methods are are important, but at the same time I need to worry about the standards. I feel it is a bit over whelming knowing that there is a new style of teaching, but the standards have stayed the same. Knowing the standards is not going to make students better learners, or even meeting them. However, I think that teaching is about the students and what they can do and pushing them to a new level of learning. The standards are important, but as far as students with disabilities are concerned how do they fit in the learning process?
I think that the standards are important, but implementing them in a way that makes learning fun and meaningful for the students is the challenge and I would love to learn more about different ways to do this. Students should be the center of our teaching process and fitting the standards into that process sometimes seems to be a challenge because they are so unclear.

New Insights and Their Implications

So far I have learned that our Math scores here in the United States are quite poor when compared to a country such as Japan. I have also learned that the United States does not devote more than five minutes to any one math problem. When we look at a country like Japan and find out that they spend fifteen or more minutes on just one problem, we begin to see why the United States might not be scoring well on these tests. I have learned quite a lot of information in Math Methods these last few class sessions, but this is the one bit of information that really got me to listen. Seeing how poor the United States scores on these tests makes me realize that it is more important than ever to be looking for different ways of teaching math to students. We need to start letting the students find ways of coming up with the answers for themselves, rather than just telling them how to arrive at an answer. Obviously, Japan is doing something different and the United States needs to step up and start doing the same. We need to incorporate more actual thinking into mathematics, rather than using the traditional, here's the problem, here's how you do it, and here's the answer technique. If we as teachers don't start changing things, then our students and the United States will suffer the consequences.

New Insights and Their Implications

Attending class these past couple weeks have been a great learning experience for me, because I now know more about the many ways to teach mathematics to students. I was very impacted by the data that was shown to us about how the United States differs from many other countries when it comes to mathematics. I have always felt that we as a country have high expectations for our teachers and education is put on a pedestal which creates a well rounded learning environment for students. After learning about the statistics I have a new outlook on mathematics instruction. All students learn in a number of ways, especially when it comes to mathematics. We as teachers need to be knowledgeable on the content area so we know how to reach our students. This class so far has prepared me for many types of situations that I may encounter as a teacher, and I look forward to learning more about how to teach students about the many aspects of mathematics.

New Insights and Their Implications

I have already learned a lot of new information pertaining to the concepts of mathematics, but the piece(s) of information that captured my attention the most so far in class were the test results. I have always considered the US to be on top and be successful when it comes to comparing us to other countries, but that was not the case when it came to the test scores. Not only were our test scores lower, they were extremely lower in some cases. This was an eye-opener and pure evidence that we need to step it up and start bringing some fresh, new ideas to the classroom instead of the boring traditional teaching styles. I strongly believe that we need to let students understand the different approaches to solving math problems and encourage them to explore different approaches. Students should also be rewarded for showing creativity and developing or experienmenting with new learning styles. I feel students also need to absorb more of the information by going more into depth on the material they are learning. As a future teacher, I want to do more than just simply demonstate the problem and then send homework home with the students. Taking a fresh new approach and a step further into the learning material will make a difference in how the students learn and retain the information!

New Insights and their Implications

Before this class I knew that the US as a country needed to help and improve our school systems, but I did not realize that we needed as mush help and improvement like we do. Barely touching base on something in math or another subject then trying to move on (expecially when you have to build on it) is hard to accomplish and that is probably one of the reasons we such low test scores and improvement in our classrooms compared to some of the other countries. We need to be diving into deeper meaning in our content. Instead of assigning a lot of problems to a student we should only do a few and pick them apart more than try more problems to review and make sure we have the concept down. Instead of doing a chapter a day we should focus on a chapter a week and make sure the transition from one to the other is clear.

So far in math class I have learned a lot.  I have noticed that I really need to keep up on my work, because I think it would be very easy to fall behind.  I have never been all that good in math class, but maybe this new way that you are going to be teaching us will help me understand things a little better.  I am also kind of confused about that standards I should be using, there are the State and National standards, however you said that one was better then the other.  I want to be the best teacher I can be and I want my future students to have the best education from me.  My goal in this class is to find the best way for them to learn.  

We have been taught about shapes, which was a really fun, but confusing activity.  I did get the hang of it when you explained the activity about scale factors to the class.  One of the examples that I will remember is that, if you have a scale factor of 2 and multiply the variable by 2 squared you get the new area.  When I am reading about all of these concepts in the book it is hard to understand, I am glad that we have a class where there is hands on activities to help me learn better.  I have also learned about many different studies that show how the United States is really far behind from the rest of the world in out test scores.  I think this class will be a challenging but fun class to be in.  

Summary and Synthesis

Personal Concerns and Next Steps

A combination of two topics discussed in class creates an area of concern for me when I think about implementing them in a classroom situation. These two topics are the need for reform in the way we teach math and standards. I have always been a little nervous thinking about how I am going to make sure I cover all the required standards in all the subject areas and make sure that my students are proficient in them. Our class discussion about standards has not made this nervousness any better. I have learned that on top of the state standards, I also have to look at the national standards to make sure I am also covering them. Then we have to add in the fact that the method of teaching math that I am most familiar with through my experience as a student is not the most effective and I will have to learn a new method. So now I am thinking not only do I have to concentrate on meeting the standards, I also have to come up with a new way to teach those standards.

This seems like it could really be a hard thing to do, but I know that it is very important to do it. Thus, I really want to work hard so that I can successfully teach all the state and national standards in an effective method of teaching. I am hoping that the remainder of the class will be able to really help me gain some reformed methods of teaching math as well as help me ease my nervousness with the standards. I also know that I will have to be thinking of ways that I can really organize myself so that I can find a way to effectively monitor the standards that I have covered and the ones that I still need to work on.

Summary and Synthesis

I have felt pretty good about class so far. I am noticing that there is a lot of things about math that I need to touch up on before I try to teach it in the schools. I have never been very good at math and it is a little overwhelming to have so much information at once. I think that this class is going to be good for me because I need to start to understand some more content as well as some effective strategies for helping my students who may struggle with math as I did. I keep thinking that I want to find a way that I can make math better for my students than it was for me. I always dreaded math class and I want my students to feel that they understand what is going on and I hope they can always be open about sharing ideas and suggestions. In all math classes I have had, I have felt that I shoudn't say what I think because I don't want to be wrong. I always thought of math as a right or wrong subject, but I am learning that there isn't always just one right way to solve a problem. Just because the teacher shows one way to solve a problem, that doesn't mean that there isn't another way to solve the same problem to get the same answer. I feel that I have already learned some valuable things in class and I am looking forward to what will come in the future.

-Brianna