Blog Four: Questions and Answers

My question is: How do we as new teachers keep ourselves from falling back on the "old way" of teaching math?
I think there are many ways to confront this problem. Some of these could be:
-Never be afraid to try something new
-Learn from the students
-Collaborate with other teachers
-Learn from other teachers
-Never be afraid to ask for help

Blog Three: Summary and Synthesis

I think the Cognitively Guided Instruction that we have just learned has been the most beneficial part of this class. I wish we would have spent more time in class on it. I think this class has helped me understand how children think about math and also that there are many ways that children think about math. This math class has also helped me understand some math things that I previously did not understand completely. Now it is up to me to put my knowledge from this class into motion in the future.

Questions and Answers

Questions and Answers - Questions raised as a result of the experiences and include your personal thoughts as to a solution/answer to your question. (These could be inquisitive questions, musings, wonderment questions, or future research questions.)

After finishing the first half of the course, I have some questions. One question I have is about the tests. I did not do nearly as well as I thought I would on the 2nd test, and I am wondering what all is taken into consideration when grading them? After the 2nd test, I thought I would do much better than I did, and was very disappointed when I saw my score. My views on teaching mathematics are certainly going to be different than the instructors at this point as I am still a student myself, and I found a lot of the questions to be rather open to interpretation. I also question what else is taken into consideration for grading in this class? I know it may sound as if I am only concerned with grades, but when you are this close to the finish line, it would be extremely disappointing to take a class over and delay graduation. Some solutions I could find to these problems would be to take into consideration the students response to the test questions, and realize that they may be viewing the question froma different point than the instructor, and to put yourself in the students shoes to understand their rationale. I would also hope that the small in class assignments are taken into consideration while grading, though I don't know if they can make up for the lost points on the test. Anyway, these are my questions and answers for now, and I'm sure I'll have many more as the semester goes on.

Summary & Synthesis

I feel that now we are actually getting into what we will be using in teaching Math to elementary school students. I feel this way because, in my opinion, what we have been doing since the begining of this class is just being students... not becoming teachers. I know that CGI is being used in classrooms now, so why not teach us future teachers this instead of Math Concetps all over again? I am glad that we finally were able to view our exams, as I felt a little more prepaired for the final that was just days after. I really hope that the next class we have is more beneficial to becoming a teacher.

Personal Concerns & Thoughts

I feel much better about this class after I saw my first exam score. I did much better then I thought I would and I'm very proud of myself since I have been struggling a little in this class. Now I'm worried about the exam we just took, so I can't wait to see how I did. I look forward to the next part of this class and I also look forward to working on the LPU assignment with my group. I guess what I've learned through this class is to never give up and keep on trying.

synthesis

This last bit of class has been really interesting. I like that we are finally getting into the specific ways to teach more difficult concepts like multiplication and fractions. I'm not very good at articulating mathematical processes or explaining how they work so the strategies that we worked on in class were a little bit tricky for me to figure out but they really helped me to grasp how to explain the concept. CGI is also something that I really liked learning about. It makes so much sense for students to figure out and present their strategies to the class!

Concerns and Thoughts

This class was frustrating. However it feels like one of the few classes that I'm learning something that's relevant and useful. I was a little worried about the tests but we got to fill out and use the study guides. Even though this class was frustrating I couldn't really imagine it being any other way.

Personal Concerns and thoughts

I really do not have any concerns, I was worried about how I did on the first exam but after viewing the test I did better than I thought I had. I really enjoyed the CGI method and feel that I have a good grasp on that and that it will be a very useful method to use in the classroom.

Personal Concerns and thoughts

As you know, the students in the class and myself have learned math differently than we should teach our students. I think that this is going to be something that I struggle with as a teacher, because I am used to "here is the equation, now plug in the the correct numbers and get the answer." Now, we are learning to teach math, to actually have our students learn math instead of memorize an equation for the test, I think it's great, but I am very nervous for when I get out into the field and trying to 'actually' teach math.

Summary and Synthesis

From what we've discussed in class, the CGI model for instruction seems like it would be extremely beneficial to students' progression through learning. Allowing students to work with multiple strategies will help them decide which method will work best for them. In doing so, the students are able to choose the strategy which makes the most sense to them and helps them better understand the concept. Another important part of the CGI model is to give students opportunities to share their strategies with their peers. This allows students to learn from one another and to gain deeper understandings. These two aspects of the CGI model are very important in providing successful learning experiences for all students. Because this model for instruction is being practiced more often, I think it is very important that we were introduced to it. Hopefully, we will all be able to successfully implement this model into our future instruction as teachers.

Summary and Synthesis

Over the past few weeks of class I have really actually enjoyed this different type of learning that is being presented in this classroom. As I stated before in my first blog, I was slightly unsure of how this new way of teaching being done by Dr. Reins was going to go. Now after experiencing it first hand and realized just how much this has worked for me I have now rethought my teaching method for mathematics. By allowing students to struggle just the right amount with the information it allows them to feel a sense of accomplishment when they do finally figure out the answer. It makes it that much more worth the time and effort when you had to work at it rather than to just be given the formula and plug the numbers in. In addition to that, I have also enjoyed learning abou the CGI method and how that helps students as well. By giving the students a problem and allowing them to figure out the answer in their own unique way and then letting them share their answer with the class, it also helps students take pride in their learning and whent that happens it creates a much better learning atmosphere as a whole. In the end, I am definitely stepping out of the box and allowing my self to see a whole different side of teaching and am truly enjoying it.

Personal Concerns and Next Steps

Throughout this course, I have looked at math differently. I have learned that just giving students the answers and equations is not going to do anything for them except help with their memorization. With the CGI model we have been learning about, it is important to allow students to create their own strategy on how to get to the problem, which is a great idea. However, I am worried that I will not give students enough time to develop their own strategies or I will give them too much time, and it will make us fall behind. If we fall behind, then we will not be ready to take standardized testing. Another concern I have is that by the time I get students in my class, other teachers will have taught them the same way I have been taught, which is memorization, and then I will spend the whole year trying to get them to develop their own strategies. Which will make students frustrated because it is nothing they are used too. In addition, after they leave my class how can I know for sure that they will continue to use CGI.

New Insights & Their Implications

I have never really thought about developing specific types of addition, subtraction, multiplication, and division problems, but I now see why this is necessary. Although we confront problems with more abstract thinking, students who are just learning math really do perform specific strategies based on the problem type. Being able to create each problem type will help me challenge my students to take risks and try new strategies.

Throughout the class, we have learned a lot about developing a relational understanding in mathematics. Although I have learned the relational understanding of fractions and other concepts in this class, I feel that I only have an instrumental understanding of many math concepts we have not discussed. I may know exactly what to do when confronted with a math problem, but have no idea why. I plan to develop in my students a relational understanding of mathematics so they don't end up confused about why they are performing operations like me.

New Insights and Implications

Over the past few weeks, I have learned a lot about fractions. Coming into this class, I did not like to do anything with fractions. I wasn't good at adding or subtracting them and hated doing it. Now, after learning about models and manipulatives, I understand the process of equivalent fractions and adding and subtracting fractions. I learned a lot about how to compare fractions and teach my students how to add, subtract, multiply, divide, and compare fractions.

Summary & Synthesis

I am really excited about what we have been recently learning about in this class. We are finally seeing what we can do to incorporate techniques in the classroom. The CGI model will probably be something I will eventually use because I would like to be a math teacher some day. I like the ways we are learning about the CGI model and seeing how we can incorporate it into the classroom. We are in a way being students during this process but this is good because we will actually be teaching this concept someday in the future.

Questions and Answers - Blog 3

Throughout the last few weeks of instruction, I have learned how Cognitively Guided Instruction can greatly benefit student's learning. I have several questions about CGI. How do teachers use CGI in their classroom and plan for timely instruction? I understand that teachers will plan lessons that allow students to develop their own strategies to solve problems, but how to they do this in a timely manner. I am having a hard time understanding how teachers plan their weekly or monthly lessons using CGI since the teacher will not know how long it will take for the students to develop an understanding of the concept. How do educators teach the important concepts that students need to know for standardized testing? How do you encouage students to use their own strategies and methods for solving problems in a timely manner? I know that it is important for students to use their own strategies for solving problems, but in order for students to be successful on standardized tests, students must be able to solve problems efficiently. How do teachers use CGI and encourage students to seek their own answers efficiently?

Summary and Synthesis # 3

I have enjoyed learning about CGI, and I can see how this helps the students. I can see how having students use their own knowledge of problem solving to tackle a problem. This is a much better way to allow students to obtain deep understanding of the process that they will go through to solve fractions. I know that a lot of students struggle with math, and hopefully with this type of teaching, it will become clearer for these students.

I was a bit skeptical about the first half of this class. I truly thought that what was being taught was for older students. That was, until I went to my 3rd grader's conferences on Monday. They are going to start working with rhombuses, trapezoids, right triangles, obtuse angles, and parallelograms. So for those that think that they are not going to be teaching this stuff in the earlier grades, you will be. On that note I will keep the information from the first half of this class for my student teaching and beyond.

Summary and Synthesis #3

I have found this unit on CGI to be quite interesting. For most of my progression through education, my teachers have taught me one method of doing a task or a problem and I was just supposed to accept that as being the only method. Having students experiment and work through the problems using their own strategies is a great idea! Having the students share their strategies with one another foster class interactions and it can also be a learning experience for students. One student may not understand a topic and by listening to another student's strategy may begin to understand the concept. As we have discussed in class, learning stops when the answer is revealed. Students can utilize their different strategies to new situations as well and not just to that particular type of problem.

New Insights and Their Implications

Throughout the past few weeks (since our first test), I feel I have learned a lot about teaching math to students. Not only did I learn and now understand certain concepts about adding, subtracting, multiplying, and dividing fractions, but I also learned how to use models to represent them. Never before had I been taught how to use models to show my thinking. I understood the instrumental part of math but not always the relational part that really explains why and how we do things in math. I understand why we multiply fractions the way we do because of the multiplication bar method. I now feel I can teach this concept to students without questioning myself on how/why we do the instrumental parts of math.

I learned the importance of teaching fraction concepts to students through the CGI model. I think it's a great way to have students use their previous knowledge to construct their own learning. It gives more responsibility to the students and has them figure out how/why they perform a mathematical process instead of the teacher just telling them 'this is how we solve this.' Especially in the last few weeks, I feel I have learned a great deal that I will take with me to my own classroom.

Blog #3: Questions

A few questions that I have: I think CGI is a really great addition to mathematics but, I feel like it's only appropriate for lower elementary. My question is, how would you use CGI in upper elementary, or even middle school mathematics? Can you? Another question I have deals with the syllabus. It talks about "wikispace," which is something I am VERY unfamiliar with so...what is it? Also, aside from online manipulatives, which we already have looked at, what are some other pertinent technologies that should be incorporated into a math class?

Blog # 3 Questions and Answers

For my third blog, I decided to ask some questions. A few questions that I have is how are teachers implementing the CGI model into instruction? How do teachers use technology in a math classroom? I have talked with my aunt, who works at a middle school in Sioux Falls, and we were talking about how math instruction has changed throughout the years and how it is totally different. She told me that how they teach math is fun for the students to engage in. I understand that using the geometric shapes on the internet and using the camera deal to display group activities on the board are being used but my question is how else is technology being used?

Blog # 3

Questions and Answers...
What is Wiki space? How will using this website benefit us as students who are becoming educators in the near future? Do a lot of teachers use this technique/ method? And do they generally enjoy it? Just trying to get a heads up on the lesson.

New Insights and their Implications-Blog #3

I have never loved math, but have always gotten through it with help from others. I can relate to using CGI because hearing how somebody else does a problem has almost always helped me. As a result, I will use cognitively guided instruction in my classroom because I know the benefits of using it. Additionally, I learned there are even books that use CGI that teachers can include in their classroom libraries. I think students can really benefit from trying to solve the problem on their own, using their own processes, and sharing their ideas and strategies with one another. As a future teacher, I would like to be able to see how math is taught using CGI. I do like the idea of CGI, but I have one concern with using it, which is the time. As a teacher, we have to cover so many topics for students to be able to do on the standardized tests, so letting them discover the answers and develop the formulas on their own takes a lot of time. I am just curious how teachers use CGI but still cover the entire curriculum. Overall, I think CGI is a good thing, I just don’t know how it works out in an actual classroom with all the content there is to be taught.

Personal Concerns and Next Steps

Throughout my entire education, I have always struggled with certain aspects of math. Geometry was one part of math that I have always done well in. However, when the questions about why we use the area formulas came up, I had no idea how to even think of a reason. This class has taught be a lot about what is behind the basic fundamentals we were all taught to memorize. I worry, though, that I am not fully aware of how to teach such ideas because it is still so new to me.

The CGI model that we have been talking about is a great tool to keep in mind and to think about when it comes to teaching math. I look forward to seeing all of the different and creative strategies my future students can come up with when solving problems.

synthesis

This last bit of class has been really interesting. I like that we are finally getting into the specific ways to teach more difficult concepts like multiplication and fractions. I'm not very good at articulating mathematical processes or explaining how they work so the strategies that we worked on in class were a little bit tricky for me to figure out but they really helped me to grasp how to explain the concept. CGI is also something that I really liked learning about.

Summary and Synthesis- Blog 3

Since the midterm we have been talking about CGI (Cognitively Guided Instruction). I personally have never seen or been introduced to this instruction before. After learning and watching videos over it, it makes sense. Why would you tell the students the answers before they begin? Why should there only be one way to solve a problem? There shouldn't. Having the students explain how they got the answer to the questions to each other, is more beneficial to them. They are talking with their thinking and mind which can relate better to their peers. Telling the students how to do a problem limits their learning. The model you teach may not make sense to them, but the way their peer does it, does! I am glad that we went over this and I will definitely use this in my classroom. It's a great way for teachers to understand the student's mathematical thinking.

Personal Concerns and Next Steps- #3

Throughout this course my main concern has been that I am afraid that I am not going to be a successful teacher of mathematics. This is not because I feel that the class isn’t teaching me enough, but I am worried that my own personal fears about math are holding me back from reaching my potential. I think this is due to the new way in which we are taught mathematics in this class. I have struggled with math through my entire educational career and this new way of learning has definitely showed me how I have somewhat developed learned helplessness over the years from my school years prior to college. My past teachers did not challenge me to find solutions on my own and when I asked for help they would basically give me the answer and I still had no idea how I got that answer, and sadly, I was satisfied with that way of learning. This class has made me realize what I need to work on in order to break my learned helplessness habit in math. If I do not fully understand the concepts (or even if I do) we are working on in class I go back through the material after class and try to make sense of it. I have started using the online manipulatives and they have really helped me to understand why we add and subtract fractions the way we do and different ways that it can be done. I feel like by going over the information and using different materials I am re-learning the math facts, which is very helpful to me. Reading the textbook assignments has also been helpful to me. I am beginning to feel like I can be successful at math and I need to continue pushing myself to make sure that I understand and think about what I am doing and why I am doing it when it comes to solving mathematics problems. I am thankful for this new way of thinking about mathematics because I feel that my struggle will help me to better understand and relate to my future students who are struggling

Blog 3- New Insights and their Implications

One thing I am learning from my peers is collaboration. Sometimes, I might know how to do a math problem and get stuck in the same spot and they might be able to help me with that. Peers have different insights on things and can help me. I am usually one that likes to do things on my own and definitely not work in groups. I know I can count on myself to get things done and partners are not also accountable. But, this semester so far has showed me working in groups can be very beneficial to the learning experience and deeper the learning to a new level.

One thing I have learned from Dr. Reins is mostly all students are being told the answers. I never thought of that being wrong until I realized the amount of education I have missed out on and the many things that I do not remember from grade school or high school. I am learning that each student must struggle a little to endure learning and further knowledge. I know how I want to teach to better my student's future and help them live in a society that is always changing. Who knows when someone will need to use the area formula or be able to cut a pizza in 12 slices. But, if they remember the information the task will be very easy.

I'm glad I'm learning a new way of teaching and cannot wait to implement the learning into my teaching style.

Personal Concerns & Next Steps

In the beginning, I didn't think this class was going to be that bad. Math definitely isn't my strongest subject area but if I try hard I can usally do pretty good. I did not realize how challenging this class was going to be. I'm so used to the cut and dry math where you just memorize formulas/equations, so this form of math is very new and challenging to me. I thought the midterm exam was frustrating because I felt as though I didn't know how to do a lot of it and found myself guessing. I guess I should put those feelings aside since it's over and try to work harder for the next one.

Personal Concerns and Next Steps

I thought that our midterm exam was actually a fun exam to take and work through. It made me think in a different way and I actually got “to do” math instead of worksheets – which is what I enjoy. Math has always been my favorite subject and I hope to teach it someday. This class is starting to help me make connections and show what the important aspects and concerns of math education are. I am starting to think about teaching from the starting point instead of showing students a formula or equation and telling them “this is the way you solve this problem. If you do it this way then you will get the answer right.” I’m looking forward to learning more and walking into the classroom with a different mindset each day.

Personal Concern and Insight

Usually math is not a problem for me. I can understand how to solve problems, but once I solve them I usually just put the equation or the solution out of my mind. That is my concern for the class because this class is something that I am not used to, in this class we have actually learn the problem which is difficult but will help me in the future. After the mid-term I am feeling even more uneasy about this class. I don't think that I did well on the exam but am hoping that I start understanding the material and doing well at it. Time is something that I feel hurt me on the exam, I felt rushed and don't think I completed the test to the best of my ability because I knew I was running out of time, but will set up a time to finish the exam.

Blog Two: Personal Concerns & Next Steps

The number one concern on my mind right now is the midterm test. I am slow when it comes to taking tests, especially math tests, and this one definitely required more than the allotted time. So therefore I am hoping that there will be a time during which I can finish the test. I felt I was adequately prepared for the test, I just did not have the amount of time necessary for me to complete it. Other than that, I do not have many more concerns. The math class is an eye-opener. Though just today I sat in on a freshman/8th grade algebra one class and it was still being taught in the way that I had learned math. The teacher is only in his second year of teaching too, so it makes me wonder when this whole math thing will switch over/gradually change/whatever. Anywho, moral of the story is that I am concerned about the test. I feel my next steps for the next test would not change much just maybe more aware of the time. Which would help if there was a clock in the room.

Personal Concerns and New Insight

At the beginning of the year, I was not worried about this math class because math has always came easy to me. I expected this class to be like any other methods type course and expected to learn how to teach math. After the year has progressed, I feel like this class has nothing to do with math and has more to do with the thinking process in general. Sure, we are thinking about math but it involves thinking more outside teh box. I know I have learned information but I feel more confused and shambled after class. The quizzes are not a highlight of the class. I understand that they are designed to think outside of the box but I feel they are to confusing for ELED teachers. For example, I believe it was quiz 3 when not one person in the class correctly answered the first question on a quiz. I have not talked with one person in the class who has got a 100% on a quiz. The midterm is another topic that makes me want to pull my hair out. One hour and fifteen minutes was enough time for only TWO people finish the test. The proctor was not aware of allowing additional time to complete the test therefor in the last ten minutes I struggled to fill in the answers on the test and not have any blank. I feel the midterm was very unorganized. I am trying my best to stay positive about the course and I am sure it can only get better.

New Insights and Their Implications/Personal Concerns

Like it was stated in the beginning of class, this class has become frustrating. Both good and bad. Good because I believe you must struggle with a concept in order to make the connection to the learning that is taking place. I also think that it is important for us as teachers to understand the "why" behind math, if we don't understand how can we teach our students? However there have been some bad frustrations. I am never exactly sure what is going on in class, what topic we are specifically covering, or even what homework is being assigned, and even when homework is assigned I am never sure what exactly is being expected of me. I also never know if what I did for my homework or answers that I have given in class are correct or on the right path. I think that sometimes some feedback is good. I know there are multiple ways to get to the answer of a problem but I would like it if maybe you would show us some of your methods, or how you came to an answer...or if we are going in the right direction.

On the other hand I have learned some useful information. I have learned the importance of being able to show "why". I think as children it is not an obvious question, usually younger children will accept that you do things just because that's how you do it, especially if they aren't taught why. In my job I teach adults who are trying to get their GED or just improve their skills. I have realized that these older students really want to know why we do the things we do in math, and from this class I have gone out of my way to help them see "why" we do what we do in math. I think that it really helps them grasp the concept. I have actually used the fraction bars that we made in class with one of my students to explain equivalent fractions, and it worked pretty well.

Personal Concerns and Next Steps

The reason I chose this to blog about was as a result of the recent test I just took. My main concern is that I did not finish it! I really wanted to do well on it, so I took my time, and the time got away from me! I hope that I will be able to finish the questions I did not get to. Another concern I have deals with actually teaching mathematics in the classroom. Wednesday of this week I participated in project Coyote in which I helped teach in a first grade class and a third grade class for the day with fellow classmates. It was a great experience, but it did kind of worry me about actually teaching in my own classroom someday, and because math is by far my least favorite subject, I hope that as I go through this course, I will be shown examples of an effective way to teach elementary level students in ways that they understand. Other than those two, I have no concerns and have found this course to be very helpful, and I know that as it goes on, I will continue to learn new things and carry that information with me into my own classroom.

Personal Concerns and Next Steps

The test we had last class period was an eye opener. Although we were able to use notes I felt that I did pretty horrible on it. It gave me a starting point for the next test however and what I will need to do to better prepare myself for it. Overall this class has been way different than any I have had and I see how this will prepare me for teaching math to students.

Personal Concerns and Next Steps

Lately, I have been thinking about how I was taught mathematics throughout school and how it is different from what we are learning now. I have always known the cut and dry math-- you memorize a definition or a formula and use it without questioning "Why?" I think it will be very hard for me to change how I think about and do mathematics in order to teach it differently. I wonder if I will be able to learn math in a constructivist fashion despite the ways I have been taught. It will take a lot of work!

Also, I am very concerned about that midterm! Ouch! I had completed my study guide and studied and studied! I read the book, read the modules, read my study guide... rinsed and repeated! And still, I didn't get close to finishing. I have always been one who takes a long time on math tests, because math is not my strong subject I like to think things through very, very thoroughly. I don't even know what I could do differently next time. I studied everything as best as I could and still had trouble. Although this experience was difficult for me, it made me realize that every student, even in college, has different strengths and weaknesses. It is important to work with these students so that they don't fret and stress over something so much that it impacts their performance on any kind of assessment.

--P.S. I don't know how the time-stamp works... I know for my K-8 Sci. Methods blog, it shows up as 12 hours or something later than when I post. I don't know how to change my timezone on this thing! Sorry!

Personal Concerns and Next Steps

I am wondering how I will be able to teach mathematics to my students in a way that they will be able to understand the how and why of the problems. I am wondering this because I am not sure I know the hows and whys. I believe that I am learning more and more with this class. I have learned how to find ways to understand the standards I am going to teach. I believe that I am learning how to think through problems in a way that I can deliver my thinking to my students. But waht I am struggling with is the whole process of how can I link the mathematics I am teaching to real life... why do we need to do mathematics and what purpose does it have in real life. Maybe the answers will revela themselves when I am planning the lessons for my classes. Maybe I need to take one problem at a time and think about one thing at a time.

Personal Concerns and Next Steps

This last month of class has been fantastic. I really enjoy this class because it challenges my way of thinking in a good way. I know that most of my peers do not really like having official tests and whatnot but I thoroughly enjoyed the test that we took on Tuesday. I don't find myself being challenged to think critically often enough in my other classes so I like the constructivist structure of this class. Having to actually work through the process of creating proofs, developing formulas, etc. is great for keepin us on our toes as far as what we know but also helps us to understand what our students will be going through. On the first day of class we were told that we would most definitely be frustrated throughout the course of this class and after browsing everyone's blogs I am starting to see that coming through.

New Insights and Their Implications

Throughout this class, I have begun to understand proofs because I have to break apart a picture and find the proof for myself. In high school, everytime my teacher would say we are doing proofs, I became nervous because I did not understand how to do them; however, when I had to find a formula for a parallogram, I was more confident because I found the formula using everything I knew. Another new insight I have gained from my peers are different ways of solving mathematics. When we were given the Pick's Theorum worksheet, it was amazing to understand how many different routes people took to solve the problems. It allows me to understand that not all students in my classroom are going to learn the same way I did, and it is important to allow them to experience different routes to solving a problem. Lastly, I have learned how to make my own definitions and not rely on the definitions in the book. It is so easy to look in the book, find a definition, and write it down; however, I understand and know the definition better if I write it myself.

Personal Concerns and Next Steps

Coming into this class, I was very excited to learn how to teach math. I love math; however, now that I am further into this class, I am very concerned about teaching it to students so that they actually learn. Never have I struggled in math until this class. Having to explain myself and my thoughts with detailed information is completely different than I have done in any other math class. While completing this class, I need to keep in mind the fact that I will struggle, but struggling is what makes me learn. I need to remember to be more patient and not turn to my classmates for help right away.

Blog #2: Personal Concerns and Next Steps

This class as a whole has definitely been completely different than any other of my classes. The only concern I slightly have with this class is the midterm that we just took on Tuesday. I understand completely that with us getting behind and with Dr. Reins having to miss this week of class that no matter when we chose to do our midterm it was going to be slightly unorganized. Going into the test, I wasnt nervous at all however, when I sat down and received the test and it was 10 pages long and I only had a hour and fifteen minutes to complete it, I definitely went into panic mode. It was also hard because this was the first test we have taken in this class so as students we didnt know what to expect from Dr. Reins and once we did get the test we couldnt ask any questions. I just felt kind of helpless in a small way. It also was slightly frustrating that only ONE person actually completed the test before time was officially up. Perhaps we can discuss the test more fully once Dr. Reins gets back and maybe get a chance to make some corrections for bonus points? Either way, this is definitely a learning experience for me personally.

Personal Concerns and Next Steps

I have never experienced math in the way that this class requires. In the past, teachers just gave us the formulas and we memorized them. Knowing why to use the formula seemed irrelevant, as teachers didn't encourage this inquiry and we were given the formula, anyway. I've never had to struggle quite as much in any other class as I have in this one. When I don't understand information or can't find solutions, I tend to get frustrated, sometimes to the point that I just want to give up. What I need to remember is that by struggling, I am finding the solution for myself, thus learning in a more valuable way. Also, I need to have more patience during this process. These are some things that I need to keep in mind in regards to this class.

Personal Concerns and Next Steps

I have always been pretty good in math. I have never struggled with any concepts about math, that is until know. I have been pretty frustrated in this class. It has been may years since I have been in math class, and I have only been taught formulas. I was never taught to use different ways to approach a problem. Nor was I ever taught to question a formula. I do understand how this type of thinking may help other students, who do not get the formulas, or why that formula works, to solve problems. I have children that are in 3rd, 5th, and 7th grade, and they are changing to this type of teaching for math. This class has helped me to explain somethings to my kids. This has helped me understand somethings, by explaining it to them. However, I do feel left in the dark on some items. I am hopeful that one day it will just click, and everything will be put in place. Until that happens I will continue to struggle to understand these concepts.

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.

personal concerns...

Throughout this semester so far there have been different ways to think and understand this subject. I get frustrated pretty easy when I don't fully understand something and I have been on a rollercoaster of frustration and confusion. I try to cope with all the new learning strategies and fit them into everyday situations. This class is definitely different than any other math class previously taken. It is good to accept a challenge and work at it, but when I continue to try and don't grasp a concept, I get frustrated with myself and find myself stopping at what i'm doing and coming back to it to make sense or just leave it all together. I need to be a little more patient and look outside the box to find the answers, sometimes this is difficult for me.

New Insights and Their Implications - Blog #2

Throughout the last month of class, I have learned many valuable lessons. I believe the module and lesson on geoboards and area of a polygon were the most beneficial activities. I found it challenging to try to formulate different methods for solving the area of a polygon. During this activity, I learned how to cooperate with peers in order to solve more of the difficult problem. When we brought the worksheets back to the classroom, I realized how students could use several different methods to solve an area of various polygons. Even though I was able to view the different methods/strategies my colleagues and the professor used to solve the same problems, I understood my method best.
After completing this specific activity, readings, and modules, I realized that students can learn how to solve problems in various ways. I will use this information and carry it into my future teaching. I believe it is important to allow students the opportunity to show their method/strategy for solving a problem. In addition, I realized that I learned best by using my own method to solve these problems. I have concluded that students will learn best by using their own methods to solve problems. In my future teaching, I will give students problems and ask each student to come up with a method of solving. Even though I struggled through this activity, I believe I learned much more. In conclusion, I believe students will learn a concept more thoroughly if they apply their own ideas to finding the solution.

Personal Concerns and Next Steps- Blog 2

Math has always been extremely difficult for me and this class is a challenge too. It is difficult to look at math in a different way when I have been doing math one way for so long especially when I struggle with the way I was taught. I do believe that teachers who struggle with a concept and then finally understand it are going to be able to teach the students well. I think that teachers who struggle will teach the concepts to the students well and be able to help them with their problems. I know that it will take more than just this class to understand this type of math especially when I still have problems understanding the old way to do math.

Personal Concerns and Next Steps

This semester I have gained a lot of new insights and ways to understand math in a completely new way. I have been challenged, confused and frusturated a lot this semester because I am being taught to think about math in a totally different way than I have ever been taught. It is diffucult to try and learn something in a completely new way. I know what it feels like to be a student learning a brand new concept. The concepts that have been introduced are important but are still hard to look at in a new way.

Personal Concerns and Next Steps -Blog2

I have always enjoyed doing math and being in math class. This class has definitely been a different view on math and challenging me in different ways. I really like the activities we have been doing in class. Like finding the formulas of a trapezoid and parallelogram by breaking down the shape into simpler shapes. I have never thought of doing it this way before. I have always just memorized formulas and never knew where they came from. Looking at in a different way was very challenging for me, but it made sense. I also liked using the chop strategy for finding polygons. I have never thought of surrounding it with a rectangle and decomposing shapes from it. I really like all the new ideas that we have been learning in class.

Blog # 2--Summary and Synthesis

We have been talking about finding the area of polygons. I find this topic interesting and hard to understand. I did not learn this in grade school and never used a geoboard until now. With listening to other student methods and knowing there is more then one way to solve the problem, makes it more understandable. I also find it interesting that there is only one true written down formula known as Pick's theroem and by reading the modules and class discussion, no one knows his thinking that made him come up with the formula. Pick's theroem works wonders and anyone can find the area of a polygon on a geoboard really fast. I am learning that there is not just one way to solve a problem and students can help each other. The teacher does not need to provide the answer, but look at the student's method of solving the problem.

New Insights and Implications

Since this class started I've learned several things in regards to concepts about math education. I've always viewed math as a very dry subject with only one right answer; when in fact there are several ways to approach one problem. It's important to encourage students to come up with a solution in their own way rather than paving the path for them. When doing this we teach students problem solving skills. We also talked about the importance of using the right math standards for both state and national. We also learned about what standards mean and how to analyze each standard and put an appropriate assignment with each standard.

New Insights and Their Implications

Over the past few weeks, we have learned many aspects about math. The block activity stands out the most for me and I feel I learned a lot during those two days and trying to solve the problem. The activity helped me develop problem solving skills and really think about how I was thinking. I was shocked when we tied this activity to the standards. It fits multiple standards but only pieces of each standard. When we broke down the standards, I found it very interesting how you need to really look into the wording of the standards to get the real meaning out of them. I think it is crazy how much money is spent to revise the standards when we already know in two years they are going to change.

New Insights and Their Implications

This class has been quite an eye-opener so far. I thought this class was going to be fairly simple because math has always been one of my better subjects but I have come to find that this class is more than math concepts. Instead of simply finding an answer and moving on, I've learned to take a step back and think about the why's and how's. For instance, the activity we did with the shapes seemed very simple, until we discussed it in class. I never noticed a pattern with our data at all until the class discussion. Even then, it wasn't about finding the pattern, it was why and how this pattern existed that was important. It's not always about the right answers but the methods and strategies used to get that answer. Also, I've learned that the content standards used for mathematics in South Dakota are not very well written. The discussion we had the other day about state and national standards was pretty interesting. I never really thought about standards in that much detail - always took them for what they were. I have really learned to consider both standards in order to give my students a more thorough education.

The past few weeks in the class has been something I have not experienced before. I usually do very well in classes, I normally understand concepts and complete them to the best of my ability. I have never have a major struggle with any school work, until this class. I am used to just looking for the answer and then once I get the answer I could truly care less about how I got the answer, as long as I got the credit for the right work and right answer. This class has turned that all upside down for me, which I feel is something that all students should experience. The way you teach math is the way that math should be taught, I am actually building on my knowledge instead of just "floating" through the class with the correct finished product. In the past few weeks I have really been testing my knowledge with a different way of thinking, even though it is extremely frustrating that it does not just come to me, I feel that I will benefit from this class. While sitting in class I try to think of ways to teach like you, as in to really get my students thinking, not just saying "here is the answer."

New Insights and Their Implications

Through this class I have a better understanding of the standards, state and national. I had thought I did understand them and what they ment, but after this week I am shocked as to how much I do not know. When we looked at the activity and tried to find standards that would fit with the activity, I thought I had done alright. As a class, we looked at other standards and talked about them. This was wonderful, as I got to hear what other studetns were thinking when they chose the ones they did. With the implications standards being what they are, I am supprised that they are so vague in their attempt to let the teacher know what to teach. I now know that I need to look at the national standards with the state standards to produce quality lessons that my studetns can learn from. What I need to do now is to take this new found information and apply it to all my classes.

Blog One: Insights & Implications

I have already learned a lot in this class about how to teach math and how students learn. First off I have learned that giving students time to solve problems themselves is the best way for them to learn. Like my peers in class I too was taught math in the manner of here's the problem, here's how to do it, now practice by doing a worksheet filled with problems. Even though I may have been able to learn math this way, not every student thinks the same way as their neighbor. I have also learned a lot already this semester about the standards. It is now quite clear to me that the state standards are much different from the national standards. It is interesting that the state standards are so vague. I had never realized that to be so until we spent time picking them apart in class last Thursday. What I hope to continue learning in this class is how to connect the standards to my teaching successfully. Successfully to me means that a lesson is one that the students were able to relate to, connect prior knowledge to, and understand.

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.

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.

Constructivism

Constructivism is where a student builds on prior knowledge to create their own ways to solve any problems and establishes their own learning styles.

What is Constructivism?

Please copy-paste your response to this question in a comment to this post. Do not start a new post. Thank you.

New Insights and Their Implications

New Insights and Their Implications - What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?

During the past month in class I was amazed on the many different tools that can be used to help students learn fractions. I really enjoyed learning how to incorporate models into the classroom as well as experimenting with them myself. I thought the interactive sites on the web were outstanding and look forward to using them in the near future. I have always enjoyed fractions, but I do realize they may be difficult for some to understand so with the help of what we have learned in class as well as the models I believe I can now more effectively teach fractions. I look forward to learning more about math during the last month of class and can't wait to adapt this information to my own classroom.

Question and Answer

When we started the section on fractions I knew I was going to have problems understanding this topic because it has always been something that i have struggled with. As we went through the weeks about discussing fractions and learning more about them a lot of my questions were answered. The first question that i had was, how am I suppose to teach about a subject that I am not comfortable with. The solution I have come to is I will use my resources. Dr. Reins has pointed out a couple websites that I can use as resources to help my future students understand fractions. I will also use my book as a reference because they have many good ideas that I can use in my class room. The second question that I had was, what other models are our there that I can use to teach fractions to my students. This question was answered when as a class we were introduced to fraction bars, pattern blocks, dot paper, cuisenaire rods, and the cake pan method. I quickly caught on how to use each of the models and I will be using them in my classroom as well to help further my students understanding for adding/subtracting fractions and multiplying/dividing fractions. After the lessons on teaching fractions the only question that I still have is with all of the methods that we have been learning about is there one we should start with first or is it OK to start with any and then cover them all eventually? I feel that I would want to start with the one that know the best so I can give the students a foundation and then branch of in showing them all the other methods.

Summary

I enjoyed learning how to use all the manipulatives we used in class and the different ways that they can be used to teach. I liked learning why we do the steps we do to solve math solutions instead of a rote method of trying to memorize. I enjoyed watching the CGI video in class, it was good to see an example of how it is supposed to work in the classroom environment. I think the CGI method could be very beneficial for students as long as the teacher can guide the lesson and engage the students in the activity.

Summary and Synthesis

I actually liked this last unit on fractions. I liked that we were able to work with different manipulatives like the pie pieces and fraction bars. Most of what I know (with Math) is due to rote style learning. I like that this last unit gave us different ways to teach fractions. I agree that teachers need to start showing their students how to develop an understanding of "why" to do things, rather than just doing things without a reason and just off of memorization. I believe that students will have a better chance of understanding and remembering different mathematical rules and operations if they understand why they are doing what they are doing. I liked learning about the CGI program as well and it was nice to watch the video to see the classroom with that learning approach. I think that it is important to give students many options when solving problems and I thought this unit did a great job of showing us future teachers how to achieve that goal in our own classrooms!

Summary and Synthesis

We have been learning about addition and subtraction problem types. I have never heard of join, separate, part-part whole or compare.I think this is an interesting way to look at problems. It took me awhile to understand the differences of and what each one meant. These four are different structures of a problem and they describe the way a number sentence will be written. This is good for teachers because they know where to start when giving their students addition and subtraction problems. The teacher will also know what types of problems to give to the students and also what types of problems the student struggles with.

Summary and Synthesis

During the last month we have discussed the different ways students can use manipulatives to help them solve addition, subtraction, multiplication, and division of fractions. This is a very important skill for students to have, because it requires the students to think about fractions without just looking at number and memorizing steps used to solve for the solutions. I thought it was very beneficial to have multiple manipulatives, especially the Cuisenaire Rods online. It is a known fact that students have a hard time learning fractions and I agree that building the skills using manipulatives in the beginning will help the students with the skills they need when solving fractions throughout their education.

Summary and Synthesis

This last unit over fractions introduced me to new ways to teach math. There are many different manipulatives available to help make math more hands on and gets students involved. I learned that manipulatives that are not labeled are better when teaching fractions because they can be used to represent different whole units. I really wouldnt have thought about that unless it was brought to my attention. We have also been discussing how a CGI classroom is set up and how it runs. I think this is really interesting because I know personally I like directions and clear and concise explanations, however according to this method of teaching it is all about student exploration and figuring things out on your own. In some ways I agree with this and in others I dont think that it is right. I think that to an extent students need to be taught basic skills and concpets about math and then five them problems to solve on their own. Personally I am not a birg fan of the whole exploration technique because I am HORRIBLE with math concepts and why they work and how you do things. I like steps and directions... but I guess that is something I will have to come to appreciate!

Questions and Answers

One question I had at the beginning of this unit was, how can I teach students about fractions so they have a relational understanding of the process? It was obvious to me that I only had a conceptual understanding of most processes and did not understand WHY we follow certain steps to solve a fraction problem. As a student, I do not remember ever using the manipulatives as extensively as we have in this class to understand the fraction concepts. As a future teacher, I now understand the importance of using those manipulatives and following certain steps to develop the concept of fractions in my future classroom. While I know the steps are not a foolproof manual that will give the students immediate and complete understanding, I realize that the steps can be used as a guide to get students thinking and building on their own ideas about fractions.

Questions and Answers

As our ELED 330 class went into the fractions unit, I had many questions about fractions because of my background with adding, multiplying, dividing, and subtracting fractions. When I learned fractions in grade school, I don’t remember using so many models. It’s refreshing to know that when I teach fractions, that I will be able to provide and use many different types of models in my classroom. Also, I have a clearer view of the different methods that can be used in helping solve fraction problems dealing with addition, subtraction, multiplication, and division. My question at the beginning of this unit was, what method should be taught to help children learn more about fractions? I now know that the students should have the opportunity to look at a problem first and find their own methods. Since I want to teach elementary, a good way to let children explore their own methods in fraction problems would be through literature.

Throughout my time in K-8 Math Methods, I have learned a ton of valuable information when it comes to the teaching of mathematics. Looking back, I can say that when i first entered this course, I was scared to death. I had very little confidence my my mathematic abilities. However, I have definitely seen a change in my confidence over the last three months. I am no longer doubting myself when it comes experimenting with different mathematic concepts. My understanding and confidence in the area of math has definitely increased. However, I still have one question. How well will I transfer this new understanding for teaching math into the classroom? When I think about this question, I think about incorporating these new learning experiences into the classroom while trying to meet state standards, preparing my students for state mandated testing, and more. However, as I mentioned above, when i first entered this class, I was scared. Yet over time, my confidence in mathematics grew. I believe the same process will happen when it comes to incorporating these teaching strategies in the classroom. Over time, my confidence in the teaching of mathematics education will increase as I gain experience in the incorporation of these strategies.

Questions and Answers

Many of the questions that I have had have been answered throughout the last couple of class periods. I had always wondered what types of tools are appropriate when instructing students and trying to help them understand a concept. After talking about addition, subtraction, multiplication, and division models and processes, I understand now that there are so many ways to teach these applications. My question still unanswered, is how do you choose which model or method do you teach first? I know no matter what that when I choose method, I'm going to have to teach a different student a different method because not every student will understand the same way, but how do you know which model will be the most successfull within your classroom. This is my only remaining question, otherwise I feel that I have a good understanding of the various ways in which to teach these processes.