New Insights and Their Implications

I think the best thing that I learned from this class is how to teach differently.  We learned from a study called TIMSS, which showed the United States that we are behind in our way of teaching that we need to do something different.  From this study we found that we need to teach like some of the other countries are teaching which is in a constructivist manner.  We also talked about why constructivism is important in the classroom.  We learned that students and everyone comes to know, with their knowledge.  Everyone needs to build off of there existing knowledge that we have processed.  If I can learn to teach in a constructivist manner then I will be helping future students. 

Personal Concerns and Next Steps

Some personal concerns for me is being able to teach math this way and do a good job at it. I do not always understand what we are talking about or how we figured out to do the problem. I think that this is because I never had to think outside the box when doing math and math has always been hard for me. I will continue to try and understand math, keep up with the readings and work through the problems and hopefully by the end of the class I will have a better grasp of things. I think that this is the best way at teaching math and hope that I will be able to successfully teach my students this way.

Summary and Synthesis

So far, this math class has taught me that teaching mathematics to students is no longer about memorization and following the steps exactly as outlined in the book. Because of studies done between countries, primarily focusing on Asian cultures and the U.S., math curriculums are being evaluated and revamped. Students are now learning in a more constructivist manner, including more hands on assignments and class discussions about problems. The math textbooks have changed in order to facilitate and encourage student learning. Unfortunately, I remember having textbooks with paragraphs of explanations about the problems which would show up later in the chapter; however, once I got to the problems, the time I spent reading was a waste because I could not figure out how to apply the book knowledge to the problems.

I have learned that much of what students gain from their school experience does not stick with them; students may also have their own preconceived notions which interfere with the correct information. This is why teaching math properly at a young age, and continuing with it all throughout their school years, is incredibly important.

Summary and Synthesis

All of the work and exploration we did with geometry and the area of shapes was really interesting. The way the learning was left to us was a good experience to have. We talk about constructivsm and student-centered classrooms in so many classes, but I have never been in one until this class. When studying for the midterm test, it was not like other classes where you go to the class notes and find definitions typed out. This class requires exploration which is honestly a new experience for me. It is a great experience though. As a teacher, I want to run my classroom similar to this because student retain information better when they have to work to find the answer and it's not just simply given to them. One more thing I want to sum up is that the midterm test was rewarding. I was expecting it to be difficult and to much, but because I studied and had learned in the class, I felt great after taking it. I hope my students can have a feeling like that. By working hard and really understanding a concept, assessments are intrinsically motivating.

Summary and Synthesis

I have learned interesting ideas from this math methods class. The most important part for me, is learning about the United States educational system. In class we have learned that the US is behind in mathematics when compared to other countries; yet, the US spends more money than these countries. I found it fascinating to learn why the US trails so many countries. Countries that are ahead of the US have a smaller focus (meaning they have fewer topics to cover) but the ideas they do teach have a higher degree of coherence (meaning the topics are linked together). The US tries to cover everything and the ideas have little coherence. Since the last blog, I have learned more ways to teach in a constructivism manner. I learned more about constructivism; it is a way that students construct their own knowledge about something. It is an inquiry and discovery manner of teaching and math learning. It was nice to have constructivism modeled for us in class. I liked the lessons and how they gave me examples of how to teach using problem solving. I have never been exposed to this much hands on math learning and I believe that this method of teaching is a ton better than the old method of teaching. I believe that if teachers adopt this method in the US, we will see improvement in our country's ranking in math comprehension. Since the last blog, I have become more of a believer in this new method math learning.

Summary and Synthesis

My perspective of this class has changed a lot over the semester. At the beginning I was really worried it was going to be extremely difficult, but now since I am somewhat comfortable with your method of teaching my perspective has become a lot more positive. I still do not know if I completely understand the philosophy of the teacher, but over the year I am coming to understand it more and more. After having the first test done makes me a lot more comfortable as well because I always stress out about the first test the most with a new teacher because I do not know what to expect.

Summary and Synthesis

Overall, I feel completely different about this class now than I felt after the first week of class. After the first week of class I felt as though this class was going to be extremely challenging and overwhelming. I no longer feel that way, however there are times where I struggle to complete assignments fully. I think that is the point...that is the best way to learn. At the beginning of the year I also felt as though the class website was too cluttered with information to provide much help to students, however I have adjusted to that as well and it proves to be an excellent resource.

Summary and Synthesis

My experiences with class so far this semester, have been meaningful but at times frustrating. I feel the material we cover is somewhat difficult, but the way we participate and investigate various activities helps me understand the content. To find what is expected of me for this class, I realize looking at the session notes is the most beneficial. Taking the test on Tuesday also helped me understand that the session notes are the only way of obtaining what is expected of me to know and retain. I now know how and what to do before each class period to be fully prepared each day for discussion.

Summary and Synthesis

My experiences with the class have been all right. I find that the worksheets and the hand outs really do help me study and understand the content better. I have conquered my fear of the chop strategy, and I have found that scale factor is a weakness. Some of the experiences have been frustrating, because some of the topics covered are still difficult to handle. The directions are sometimes hard to follow, but a question is never turned down in class. I feel as thought the questions asked and answered really have helped in my understanding at times. The most important thing for me to remember is that thinking outside the box is OK, and to take risks is important when teaching and learning math.

Summary and Synthesis

To be honest at the start of this class I was very skeptical about the methods that Dr. R was teaching us. I wondered to myself how would I ever be able to teach in a manner that I had never learned myself? Throughout the course of these past weeks though, I have started to come around to the idea of it. I have been learning things that I already knew how to do, but did not know why I was doing them or why they worked the way they did! Essentially, I have always had an instrumental understanding of math and now I am beginning to (slowly) have a more conceptual understanding of math. Already I can see the benefits to this type of teaching. I hope with this new attitude I will have a more positive outlook and learn even more from this class.

Summary and Synthesis

I have learned a lot of information so far this semester in math methods. I have learned a variety of new ways to present and teach material to students. I have learned what constructivism is and how to teach in a constructivist manner. It is important to have children learn to solve things on their own without the equation or formula given to them. Students can explore the problem first to try to develop the formula on their own. When students work this way it gives them a better understanding of how to solve the problem, how the formula works, and how they acheived the answer that they got. By working this way, students are making meaning out of what they are doing. Teachers need to make sure to use the students prior knowledge and to connect that to what the students are learning. We have learned different ways in which to teach scale factor to students. We have also learned different ways to approach problem solving and ways to help students solve problems in multiple ways. Right now we are learning about different polygons and finding the area on them. I have learned a couple of different ways to find the area of a polygon; such as, Pick's Thereom, chuncking the interior, and chunking the exterior area of the polygon. We are also learning the different formulas for the polygons. This class has required to think on my own and to use my prior knowledge to connect to new ideas.

Summary and Synthesis

I have learned so many new and interesting concepts this semester through math methods, such as constructivism. I have learned that it is important to be a constructivist teacher when teaching math because students need to learn how to do mathematics on their own. They need support and guidance also, but helping them to actually do mathematics is the best thing for them. When students learn new concepts on their own they make meaning out of it and learn much better. Using prior knowledge to help construct new knowledge is extremely important and can be used to help students develop new ways of thinking about math. Constructivism is just one of the many different concepts that I have learned this semester. Another concept that I have dealt with is finding areas of different shapes and polygons. I have used my own prior knowledge to help me with finding area formulas and coming up with algorithms for areas of polygons. Pick's Theorum is just one of a few methods that I learned for finding the area of a polygon. I found it to be very useful and easy to use. Throughout this class, I have been required to think on my own and find answers to questions that I did not know before. This entire course is based in constructivism and it truly does help in the learning process.

Summary and Synthesis

Since my last blog, I have remebered and discovered new methods in finding area of shapes and what the definition of shapes are. The definition of a polygon is one of the first things that I learned by doing looking at different shapes and figuring out if they were polygons are not. I also learned different methods in figuring out the area of any polygon. One formula I learned was Pick's theorem which as a pattern toit when drawing shapes on a geoboard. There were also other qualifications for quadileterals and rectangles that I had to remember since grade school. Many of my textbooks had defined a rectangle but they defined it in a way that it was so broad and it could be another shapes definition. I think it is important to define shapes well enough so students understand exactly the characteristics of that shape and what makes that shape unique compared to the other shapes.

Summary and Synthesis

I have learned from my instructor that I am not bad at math but was taught math with all of the wrong techniques. I now realize that I should have been taught math through a constructivist manner. I was always taught math content in a broad and general way. It seemed as though I had to hurry and memorize formulas, definitions, procedures, etc. the fastest way possible just so I could keep up with material my teachers would be teaching. I now know that children need to build upon their prior knowledge in meaningful ways in order for them to gain a deeper understanding of the information that is presented to them. I also now realize that I need to implement constructivism into my own teaching style if I want my students to really and retain most of the material that is presented to them. Implications of learning and teaching mathematics is that it can have some very difficult. This is why it is important for teachers to understand how children learn best.

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