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

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

Summary and Synthesis

Personal Concerns and Next Steps

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

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

Summary and Synthesis

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

-Brianna

Summary and Synthesis

Since my last blog I have learned alot about our new math methods and we should teach them to our future students. I have also learned alot about the different kinds of math standards that we are expected to tie into our curriculum. It is a little confusing with all the standards, and i should tie them all into my curriculum. How do i decide whether or not to use the National, State, or the NCTM's standards. I am very focused on my future and all of these standards are a little imtimidating. It is very helpful though to talk about standards and how to appropriately use them.

We also have been talking about similar shapes. I am going to be honest with you, I was so lost at first, but once figured out the concept of similar shapes the concept was fairly easy to understand. If we were to increase the scale factor by 2, all we would have to do is multiply the variable by 2 squared. The activity that we did in class would be very helpful to use in our classrooms. They are given situations, in which they are able to solve and discover their answers. They are also given a chance to explore and investigate their answers, so hopefully this learning process would eventually go into their long term memory and later in life they can make connections through this activity.

New Insights and Their Implications

What I found out most interesting thus far in our classes, was the fact that the United States is lacking in Mathematics. As such a diverse and advanced nation, it makes me think where we are leading our students in the future. Although, in our class, we are learning about the methods it takes to solve these problems that the United States are facing. For instance, the amount of time the United States has for each problem, compared to Hong Kong or China who take 15 to 20 minutes in just ONE problem. In the United States, we compare with just one to two minutes PER problem. We are learning more about the thinking and discussing part of math right now and how each child needs to investigate more deeply or how we as teachers can help provide a deeper understanding for that specific child.
What I also learned was that we should not only be looking at the South Dakota Standards of Math for our students, but we also need to be looking at the NCTM's standards. By looking at both of these types of standards, we will be teaching better and our students will be learning more math in depth. The NCTM's standards take an in depth look at what our students need to be learning for each standard. This is very informative in the fact that it outlines specific cases and examples of what we SHOULD be teaching our students and is detailed in the account of what each specific standard means. These two standards put together a more detailed look at what needs to be taught and a not so vague look at what each one is presented to be.
All of these insights have implications. They are all implicating that as pre-teachers we need to take a better approach at teaching mathematics in our classrooms. This class will help better our knowledge and teach us methods and strategies of math so that we are able to be the best teachers for our students!

Summary and Synthesis

In Tuesday's class we discussed area, perimeter, and scale factor. At first I thought the activity we did was really confusing but once my group started discussing it, I started to understand it and that made me really excited! I know I learned this information when I was younger but I must have completely forgot about it because at first I didn't have a clue what we were talking about. We discussed that if there are two similar objects and we increase the scale factor of the original object by two then the new area for the larger object is original area times two squared. If we increase the scale factor by 3, the new area is original area times three squared. Therefore, we found that the general rule for area in terms of scale factor is Area x's scale factor squared. I thought the way we did this activity was really beneficial to us students. It was a great hands-on experience; we got to actually use different manipulatives and create the new areas with the shapes. I think this is a much better way of learning the information than just reading about it in a textbook!

New Insights and Their Implications

From the few class meetings we have had, I have learned a lot. From my instructor I am learned more about the constructivist approach, which I did not know very much about. I have also learned about the TIMMS study. I think this did a great job of opening my eyes and realizing how to change some teaching habits that may be to familiar. One such habit is that of trying to teach too many different things. I as a teacher need to spend more time on one topic until it is fully understood. I also have learned about the the National and State standards, from both the text and the instructor. These are extremely important to understand because of their high importance in the classroom and because of NCLB. I have also learned about how to use SENTEO quizzes in the classroom. This tool and technology seems like a great thing to use in the classroom regarding not only Math, but other content areas. I also loved the Virtual Manipulatives. These are great for lots of activities and do a great job of involving the students and using a visual to teach the lesson for students.

One of the main things we have been focusing on in class is regarding how to incorporate the standards and use them in an activity. I think this is important because there are certain things that need to be taught and certain activities students are going to enjoy. It is important for activities to be engaging and fun, yet still possess the necessary information that is taught to students. This class has taught me, already, lots of things regarding teaching practices. I think that if I continue to use the standards, think creatively, and be passionate about my teaching, that I could create a very conducive environment to learn in.

New Insights and Their Implications

I have learned a lot of new information in class already. It is hard to take in everything that we have learned. It seems like there is so much information in such little time. One thing that I learned today in class is the difference between the state content standards and the NCTM standards. The NCTM standards have a lot of detail compared to other standards that are too vague. It was interesting to look at the NCTM standards because they have a goal and expectations. Another thing that I liked about the site is that they list activities that can be used in classrooms. There are links that you can click on to learn more about the activity. I have also learned a variety of things from other members of the class. It is always interesting to learn the different ways in which students learn math. Teaching has changed a lot from when we used to be in elementary school. It may be difficult to learn the new styles of teaching and to be able to use them in my classroom because I will be so used to learning from the old ways.

New Insights and Their Implications

I learned from todays lecture about the SD content standards and National Math Standards. These standards are the important to include in every lesson plan to make sure students are learning not falling behind according to NCLB. I learned today that most teachers focus only on the state standards. I cannot see how they can focus on just that because those standards are so broad. Any activity or assignment could fit under a number of the standards. I think teachers need to focus on the National Standards as well. These standards are much more specific and certian activities can align with these standards. The activity we did in class with the shapes fit under the National Standards and the National Standards were much easier to figure out how the activity relates to each expectation of each standard because the standards were so specific. I thought it was interesting that the National Standards were much more specific than the State Standards because previously I thought the State Standards were more specific.

New Insights and Their Implications

So far in this math class I have learned a lot of new ideas. The idea that has made the biggest impact on me is the use of problem solving to teach math. This method of teaching is entirely new to me. However, it makes a lot of sense, even though right now it is hard to learn because I have never been subjected to it. All the research findings in countries all over the world have shown what an impact teaching using problem solving has on students; it surprises me that the United States hasn't adopted more of the techniques of other countries and is still using most of the old methods of teaching. Also, I had never thought about how, in math classes, the teachers try to cover everything. It makes sense to me now why I struggled so much with math: I barely had time to learn the material before the teacher switched to another topic. I have forgotten so much from my math classes because we never spent enough time on any one subject. By using problem solving to teach mathematics to students, students will be so much more likely to understand the material and remember it, in part because they were involved with the material and had a chance to make connections with it. In math, depth is more important than breadth.

Personal Concern and Next Steps

Thus far, I have found the class quite interesting. However, I do have a couple of concerns. The first one is that the terminology is going to go straight over my head and I am going to be lost all semester. Everything seems so particular, for example from today’s class there are expectations, standards, and focal points. They all so sound so similar to me. My problem solving strategy for this though is quite simple, I need to spend more time focusing on figuring out the differences and if I still do not understand them then I need to talk to someone else and get some extra help. My other concern is that I won’t understand the new style of teaching since I grew up learning the old style mathematics. The only solution I see for this is to simply try as hard as I can and just try to adjust my thinking in a different manner and hopefully learn from the modeling that goes on during the class period. Overall, my concerns are not huge, but I still need to address them soon.
*Amanda

Constructivism

I think of Constructivism as Student Directed instruction. Concepts that keep gaining more discussion on. The students are engaged and keep discussions going and getting to the depper meaning of ideas.

Constructivism

Constructivism is building knowledge by using prior knowledge. Through constructivism, students learn new information by building upon their prior knowledge. A classroom that uses constructivism is student centered. A student centered classroom consists of hands-on projects, group work, field trips, etc.

Constructivism

When I think of Constructivism, I think of a building on to prior knowledge. Students learn by connecting new information with what they already know. A teacher who runs a Constructivist classroom tends to focus on student centered instruction. The classroom is hands-on and deals with a lot of group work. Constructivist teaching actively involves students. They are adding on to what they already know.

Jessica Murphy

What is constructivism?

Please comment to this post (by clicking on the "comments" link below), do not start a new post. Write your initial feelings as to what constructivism is to you. Do not ask anyone, look up anything, or read your colleague's comments. It is important that these are YOUR preconceived notions of what constructivism is to you!

Personal Concerns and Next Steps

You may blog about genuine personal concerns created as a result of the experiences in this course.

These last few weeks of class we have been listening to different peers present about different topics. We have mostly followed a progression from beginning number sense to learning about different probabilites. While everyone has done an excellent job at their presentations, I still feel like I do not have a full understanding of the different topics. I tried my hardest to follow what they were saying and complete the different activities. I would have liked a little more. I'm not exactly sure what, but something could be changed. At times everything felt very disorganized. We also nine times out of ten ran out of class time for further clarification.

Using the constructivist approach to teaching seems very important in this class. For me to feel comfortable teaching somewhat in a constructivist approach, I need to feel comfortable with the materials presented in the classroom. I know I am going to have a variety of students and that I am going to have to present a variety of levels to a topic. I will have to review materials and hope that they sink in. I almost feel that there was too much material and not enough time.

Personal Concerns and Next Steps

Now that we are starting the last week of classes this semester, I find myself looking back at the semester. My views on math have changed along with how I will teach math. Especially after conducting the clinical interview, I feel that my views on teaching math have changed. I never realized how huge a process it is. I always thought it was a bunch of memorization. It was either you got it or didn't. I would like to conduct some sort of clinical interview on my students someday. I think it would be very beneficial for teachers to do this with their students. I sure wish one of my elementary teachers would have done a clinical interview. I wouldn't have struggled so much with math my whole life had one teacher realized the way I was thinking about math was wrong or needed clarification!
After teaching a lesson to our class, I have also realized how hard it is! You really have to know your stuff. How can you effectively teach without knowing the material. That scares me. I'm scared I won't be able to teach math in a way that my students will truly understand and comprehend. I know it will take a few years to get into my groove of teaching math and other subjects. But what about those poor students who get those first years of teaching?

Personal Concerns and Next Steps

I have had a lot of thoughts about class today (we talked about the Equity Principle) and I just wanted to talk a little about that topic. It very clear to me that much of what we do in teaching is better "said that done" and one has lots of ideas about what should be fixed or what should be done, but when it comes down to it, it's really hard to implement. I find this to be a struggle within my heart and my head because I have a true passion for helping students get to their full potential. I was watching a program last night about a district in Washington, D.C. and they were talking to a principle in this district that said if he could he would fire over half of his staff. I found this to be very interesting and he said his main reason is because they don’t set high standards for the students (they teach in an impoverish neighborhood) and they don’t believe the students can achieve high. To me that was very upsetting those teachers think and believe that way. In that case maybe it would be a good idea for him to fire them. It is important for people would WANT to help students and who CARE about students and take this seriously to be teachers. It really bothers me to see people who could careless TRYING to become teachers and passing some how... I think it would save our school districts a lot of headache and stress if we weeded out the teachers who don’t actually care about the students and being a good teacher. Teaching is a life changing experience and by that I mean we have the ability to change lives. We can all recall a time when we have had a "bad" teacher and it scars us or helps us, but either way it affects us. I just want everyone to stop and seriously think about why we want to be teachers and do what it takes to be the best that we can be, not only for ourselves but for our soon to be students also.

New Insights & Their Implications

I want to talk about Cognitively Guided Instruction and how much I love it. My internship teacher used this approach with her first graders. So I have seen it modeled several times. When she first asked me about it I was very unfamiliar with it and felt so behind. Little did I know that I would learn about it soon.  The principal asked my field based supervisor to go toa a training workshop and teach it to the other staff in the school. I remember one day she got a substitute and I observed her teaching math to other classes other than her own using the CGI approach.  I watched her use CGI with her students and demonstrate it for other teachers but never really understood until this class. What I particularly like about this approach is how students have a choice for which strategy they want to use in solving the problem. I also like how they can choose to use or not to use manipulatives. What I really like about this program is how all the students come together at the end and a select few will share how they worked through the problem. It helps us as teachers know their understanding of the content and helps kids think of other ways work. One thing that I loved is that my teacher used Math Journals. She would print off a story problem for each child and they would glue them in their notebook. These stories were made fun by using different the names of her students.  She would then ask them to write in marker because she wanted to see their thinking and that it was okay to make mistakes. I would never have thought of that! It is a great idea! I feel so fortunate to have been able to learn about this approach in class and to be able to see it in action. I know that a lot of teachers out there are now just learning how to implement CGI. As future teachers we will be able to go into the schools with the training already under our belts! This is something that we are going to need to know because Math will most likely not be taught the traditional old way. More and more schools are adopting this approach. 

New Insights and Their Implications

I have learned a nimber of things in this class. I think that it has been helpful to see different ways that we can teach the students. I really enjoyed the CGI approach. This approach has really made me think about the different ways I can teach in my own classroom.
I really liked how the CGI approach allows the children to work on their own ways to solve problems. I think this makes this task more interesting to the children, rather than just having the answer told to them. I also liked how they can share their ideas, so they can see what else may work, and also that there may be a better way to solve it than what they had done.
It was interesting to see the videos about this approach. This helped me to see a real example of this, making it more understandable and usable than just reading the text. I was also given the opportunity to see this approach used in a real classroom in my internship. The children really seemed to enjoy using this in their classroom, and using the children's names in the problems really got them interested in the problems. The children also were able to keep these problems in a journal, so they can look back at the old problems and explore other ways to solve problems. I think that this will be something that I can use in my own classroom that the children can carry on with them as they continue through their schooling.

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?
First, I just want to say that I feel that I have a new appreciation towards math in general. I really had a "math fear" for a very long time and this class has helped tear away at that fear. I can't say I love math, nor can I say I love learning about it quite yet, but I think in time I will eventually feel that way. I can say for certain that I have an amazing group of classmates. They have all made me feel like I was part of the group and I feel comfortable speaking out in front of the class because they have made me feel like what I have to say is important. In the past that would have been hard for me to do. So I want to thank you all for that. Also, I have learned so much from all of you and everyday I keep on learning more. Dr. Reins has taught me to become a very deep thinker. I have never had to think so much on a math problem in my entire life before. I like his way of teaching and I think he does a remarkable job doing so. Finally, I hope that I can someday teach in a way that my students will be able to not only know and do a formula to get an answer, but have a deep understanding on the significance of that formula. Plus, I hope that my students will be excited to learn math and that they don't develop a "math fear" like me.

Questions and Answers

Questions and Answers - Questions raised as a result of the experiences and your personal thoughts on a solution/answer to your question. (These could be inquisitive questions, musings, wonderment questions, or future research questions.)
My partner and I have been continually working on our LPU. One question that has come up is how detailed does the lesson script actually get? We have looked at previous LPU's and there is a wide-range. Some students described almost everything and others kept the script concise. How in-depth should they truly be?
I know what I DO NOT want as an answer for this question (ex) "It should be however long you think it should be or take."). The reason being is that this kind of answer will not help me. I am confused by how much actually should be typed into this section of the LPU or what main characteristics this section needs to have. Does anyone have any solutions or suggestions from they have already done on their LPU or are planning to do? Let me know! Thanks!-Kristin

New Insights and Their Implications

During this class we have worked with different types of manipulatives that I have not been in contact with before. I remember working with rods but not the many different types that we have encountered in class: Cuisenaire rods, pattern blocks, etc. I have learned that it is important to provide many different options for students to be able to learn fractions. I do not have fond memories of learning fractions when in elementary school myself but now I think that it would be easier if students were presented with the many different manipulatives and strategies to find the solution to fraction problems.
Reading the blue CGI book has also presented many different ideas to work with in the classroom. I never knew that the CGI program even existed before reading the book. I never realized that problems needed to be categorized even within the category of the type of problem, for example addition having the different types. From reading the book I now know that it is important to have a variety of different problem types and structures. Also, the foundations of a CGI program are things that I would like to be able to incorporate into a math class that I may have in the future. Through this method I believe students would learn best. It would definitely have been better than some of the math classes that I have had.

Summary & Synthesis

During the last month we have been talking about fraction concepts, which is definitely not my favorite subject but I feel I have learned a lot through the class activities. I think many children don't like dealing with fractions because of the way they were taught and they don't have the relational understanding as to why it must be done the way it is. This class has shown me a variety of ways to learn and understand fractions, yet our schools are all teaching in the same manner, it doesn't make much sense to me. I really liked using the pattern blocks and cuisenaire rods to complete those worksheets because I could see how the problems made sense instead of just completing the problem in the way I was taught. I think many students enjoy working with manipulatives but teachers need to ensure that that is not the only way students can solve problems, they need to reach the symbolic stage of working. I was a little confused when using the dot paper to solve fraction problems but I can see how it may be beneficial for some students.
I really like the blue CGI book that we are reading because although I have used these types of problems and can teach it, I didn't realize that each strategy has a name. The error patterns book that we did some problems out of was also really neat and gives some great ideas for helping struggling students. It seems like the past month we have been doing a lot more hands-on activities that could easily be used in the classroom and I feel like I get a better understanding of the concepts by doing these activities.

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?

While we have begun our foray into writing the lesson plan for understanding, I have learned a lot about myself. This lesson is very difficult for me to write because I want to fall back into my comfort zone and the way I have always been taught. In writing this lesson, I know it is more beneficial to my students and their learning to use the approach that we have learned thus far in class. While old habits die hard, new and improved ideas are popping out of my head. I am using and adapting the ways that I was taught into my new way of thinking.

Kami and I are working together to create a lesson for the order of operations. I distinctly remember my teacher writing the order on the board, making us copy it, and then telling us we had to memorize it. We were to use what we memorized (Please Excuse My Dear Aunt Sally) to complete different problems in assignments and test now and in the future. She never explained why we had to use them and why specifically in that order. It was just something we were expected to know. In our lesson, we have realized that we need to let students discover the order (Thanks Dr. Reins) on their own and also the importance of knowing why they have to do it. We have looked into a variety of sources and our just now discovering the why's. Hopefully our students will not have to wait ten or more years to discover this.

Summary and Synthesis

So, I found myself pushing outside of my confort zone and attempting to use and look for ways to incorporate construvism within my teaching philosophy. Working with my partner on the LPU, I have found myself working hard and trying to use this approach. It does take a lot more time, however, as a student I found that learning this way is effective. Each day in class when are taught using this approach the concepts sort of stick in my head. Even taking the Praxis, I used some of the information we learned. I know how to find the area of different objects because I learned the process of developing the formula instead of just memorizing the formula! I found that part of the exam to be less stressful because the way I view math and math problems has changed.
I also find myself applying this approach in science. With all the reflecting we do with reading and daily activities, I can see the transfer of teaching this way into science also. I'm not exactly sure how to apply this to other content areas but its cool to see how it can be used in science too. As much as I complain and whine, I know this class will have a big impact on my teaching ability, strategies, and overall philosophy.

Questions and Answers

My partner and I have been working on our lpu and it has raised a few questions.  First, do teachers really have to write lesson plans that are like our lpu assignment?  Do teachers mostly get their lessons out of the teachers’ manual and follow that or do they write their own lesson plans?  The past few days we have been working on our lpu and it seems me a teacher should take ideas out of the teachers’ manuals, but have the main ideas and activities be their own.  It maybe difficult and time consuming to write lesson plans as multifaceted as we are, but I feel the students will get a lot out of our lesson plan. 

As I have been looking through 5^th grade teachers’ manuals I have noticed that there are worksheets for different leveled math students.  My question is when handing out a worksheet for homework do you give each student a different worksheet, one that has questions that fits the level they are at, or do you give everyone the same worksheet.  I don’t ever remember not having the same worksheet as my classmates when I was in grade school. 

Deanna

            

Questions and Answers!

I am interning in Yankton, SD in the Special Education room and find the view point of this class and the view point of the SPED classroom to be clashing. We are learning how to be constructists teachers, in which we help students obtain knowledge, in Math Concepts. In the SPED classroom they do direct instruction where the answers are practically handed to them on a silver platter. My question is can the constructivist way of teaching be modified for SPED students or do I need to stick with direct instruction? I comtimplated this idea for awhile and even talked with my intern instructor at Yankton Middle School. She told me that most SPED students do not have the patient's or background knowledge to be able to use the constructivst way of teaching. She than preceeded to metion that if they had been started out learning in that way they probably would be able to now, but since direct instruction is the easiest and only way they have been shown than introducing something like that now would only be a set back. It makes me sad that these students are being pushed along and forced to memorize information just of pass the standarize testing. Anyway, I kind of would like you thoughts on this!

Ruthie

Summary and Synthesize

Over the past month, I have really come to understand what I need to do in order to teach math effectively. First of all, it can be said the the majority of us in this class (not all, but a lot) came into this class with strong dislike of math. I myself have always disliked math and struggled with many concepts. What this class has taught me thus far is that students can NOT continue to come out of math instruction feeling this way. We as educators need to adapt to the new methods of math instruction that we are being taught and implement them into our classrooms even if we are planning on teaching lower grades. The traditional mathmatics approaches that we have been taught are not effective and we (myself included) are all the perfect example of this. I now understand why I struggle with some math concepts, because I was just given a concept and I memorized how to do it (or at least that's what I want to think). I enjoy learning new ways to teach different concepts, and have taught myself to keep an open mind with learning new techniques. I have finally come to terms with the idea that teaching math traditionally is not going to work. I will be cheating my students. The things we have learned about fractions has really helped me with the idea of not teaching traditionally. I honestly can say that I have never thought about fractions this way, and I hope that I will continue to see ways to teach students the right way.