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?

I was not exactly sure what to expect from this math course. I'm very used to learning math content and different approaches and methods to teach the concepts I learn, so I did expect to learn much about how I should be implimenting math instruction in the classroom. From what I've experienced so far in the course, I have realized I will be learning a very indepth approach to teaching math, and also realize I will need to be open to using different approaches, because we learn a lot about the methods that may be most appropriate for students. The instructor, in my eyes, has a very unique and new approach for teaching math in the classroom. The approach is almost nothing like what I've seen before, but seems as if it'd be very beneficial for math instruction in the classroom. The readings and assignments have been very indepth, and call for a great deal of analyzing, interpreting and using our pwn judgements and knowledge in order to work through different problems and methods. I have yet to learn a lot, but am constantly discussing with classmates about different ways to approach problems and material. I haven't learned a lot about how children are in the elementary classrooms and the types of math instruction being used currently, but I believe my knowledge in this area will become profound by the end of this course and I will be able to apply what I've learned to benfit students when giving math instruction.

Constructivism

Students are discovering and taking the role of the teacher, with the teacher guidance. Class is made fun with a safe learning environment and different activities. I tend to also think of it as constructing scaffolds or building up knowledge.

Ruthie

Summary and Synthesis

There have been a number of recent experiences in this class that I have learned a great deal of information from. To start, I have learned so much about standards. All the of other methods classes we have had have not gone into detail the way we have in the class, and I am so thankful that I have actually been able to explore the different standards, and determine what they actually mean. Picking apart the math standards has really taught me a lot about how I can teach different activities, and also it has shown me a variety of different resources I have as well. Another this class has taught me about is the learning process and how it is used in the math setting. I am so used to just getting answers, and this class has shown me that in order to truly understand the material, you must do some of the "figuring out" on your own. The activity we did with the algorithims really helped me see this. It was difficult at first to put everything into precise detail, but what I found in the end was that I really did have a better understanding on the topic.

Summary and Synthesis

The past week in class we worked on making our own algorithms and testing them. This was something that I had never experienced before. After looking at the different polygons and trying to decide how to find the area, it was interesting to put our thoughts and hypothesis into action with different polygons. It was also interesting to see how the formula works with the algorithms that we created. Our algorithms would only work with correctly inscribed triangles, whereas, the formula will work with any triangles whether correctly inscribed or not. I enjoyed getting to work with the numbers and formulas and algorithms in order to find the area of the triangle. I definitely used my prior knowledge of geometry to try and solve the algorithms and its problems before we were able to discuss it as a class. I learned that prior knowledge and deeper thinking and understanding are important in order for students to learn, comprehend, and apply what they learn to every day life.

Summary and Synthesis

In this first month of class, we have focused on problem solving and standards. I have learned so much in the first bunch of classes. I never understood how much goes into standards. I also didn’t understand how many different ways that standards could be taken by teachers or administrators. I now understand why standards are unpacked and have extra information presented to help you understand what the standards are really about. I never understood how state and national standards overlapped and was related. I have learned so much about the standards and I would like to explore other subjects’ standards as well and see if they relate as much as math does to national standards.

We have talked about problem solving quite a bit and have even used it in our classes. I have didn’t understand how big of a roll problem solving had in math until we learned about it in class. The steps of problem solving can really help you when you are trying to solve any problem. People use problem solving everyday but don’t really ever realize it. You are specializing and generalizing your thoughts and figuring out the problem you are working on. There has been so much we have covered in this first month and I have learned so much from it as well.

Summary and Synthesis-Blog #1

Summary and Synthesis - Summarize and synthesize of the impact of recent experiences, ideas, and/or issues encountered on the Tuesdays and Thursdays in class thus far from your perspective.

Last week in class when we were discussing algorithms I feel that I have gained a new understanding on fully comprehending a subject matter. When Dr. Reins had us come up with our own algorithm and test it our to see if it worked on all of the different polygons I feel that, that helped me become more independent when trying to figure out math problems. Now I feel that if I can teach that to my students I can help them to become better at math or any subject. They just need to sit down and take some time to fully understand the problem, figure out what they know and then decide what they need to do to figure out the answer to the problem.

Contructivism

What is Contructivism? Cuntructivism to me is a student learning approach that helps kids think deeper. What I mean by thinking deeper is that I think the students are resposible for their own learning through different class activites! Students will use prior knowledge and try and connect it to information they just learned!

constructivism

Constructivism is a student-based approach. It involves students in hands on activities rather than listening to the teacher lecture. The students are responsible for their own learning by discovery while the teacher is there to guide them if they need help. By doing this, it motivates the students to learn and make the content more meaningful. 

Constructivism

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?

I came into this class thinking it would be another methods class where we learn mostly content and little method. What I got on the first day of class was therefore surprising. We are spending some of our time on content, but only in the respect of how we should have our students complete the same tasks that we are completing.

This class was definately new and interesting. We are never given the answer but challenged to figure it out. While this can be hard and frustrating in the end it is worth it because we have found the answer and made, hopefully, a lasting connection. In doing this, I realize how important it is not only for my students to understand the material, but also for them to make a connection with whatever we are learning. While students can complete assignments if they are simply given an explanation and then handed a worksheet, they will most likely not retain that information.

Summary and Synthesis

Our first month of this class has focused on required testing, problem solving, and the standards that we run our curriculum by. It seems like we have learned so much in such a short time. I never realized how much problem solving plays a part in solving math problems but it definitely makes sense when I look at it now. It really helps that we have been using the steps of problem solving in class when doing activities such as the area of polygons and Fenced In. It is one of those things that you know you are organizing thoughts and doing things in a sequence in your head but unless you sit down and think about it you don't realize that you are specializing or generalizing.
The standards have been mentioned in a lot of my methods classes but I never understood the layout and how the state and national standards parallel each other until this class. It really makes it a lot easier to use the standards when planning lessons when you know how to find resources such as the Unpacked Standards or use of the Curriculum Focus Points guide. It makes me anxious to learn if other content areas have supplementary materials such as these. I have noticed on the SD Content Standards page that each area has unpacked standards but I haven't had time to explore these yet.
Although we have talked about quite a few topics already this semester they all relate to each other which helps my understanding of the content. The standards guide everything that should be taught and problem solving is used in every aspect of doing math. I have thought a lot about how I approached math before compared to now when we look in depth at problems and why we solve them the way we do. I feel more confident in my solutions when I know how I arrived at my answer and can easily justify it.

Constructivism

I have been introduced to Constructivism in previous classes and I know that is is a type of learning. Students who use constructivism take new information and link it to prior knowledge or something they have already experienced.

Constructivism

What i know about constructivism is all based on a learning theory I was introduced to in a previous class. What I know is that constructivism is based on Piagets theory and involves prior knowledge and making connections based on prior knowledge.

New Insights and Their Implications- Blog #1

We have only had about 5 class periods of math, but I have learned so much in just a few short weeks. Not only have I learned about a new way of teaching math, but I also have a new sense of how to learn math myself. I have had a fear of math, and a fear of teaching math, yet slowly but surely that fear is disappearing. The new way of teaching math, through problem solving, makes math more understandable, and it also gives it a better sense of purpose to learning mat. I can remember when learning math I would continue to ask myself, “Why do I need this?” and saying “I’m never going to use this”. I hear that from a lot of students when talking about math, and that is really too bad. I also think teaching math through problem solving helps students to become better problem solvers in other areas of their schooling and their lives, such as when reading books or building projects in shop class. I really like the use of having students think about problems and come up with ways to solve that problem, before talking about how to do the problem. I think that this helps students to activate their brains and dig down deep to find an answer. I am looking forward to learning more about this new (to me any way) teaching style and also look forward to using it in my classroom!

Constructivism

What is constructivism?  Constructivism to me is creating meaning from my own knowledge or viewpoint.  Taking what I learn from my environment and making sense of it.  I also feel constructivism could be part of a learning theory or theories, but I am not sure what theory it would fit.

Deanna Smith

Preconceptions of Constructivism

Lauren Swann
ELED 330
Session 1
1-17-08

What is constructivism? When I think of the word constructivism, my brain reflects back to the days of my earlier ELED classes, and the one thing that I am confident about is that constructivism is a learning theory. Also, I believe that it is an approach that is more student based and hands-on type learning. In addition, I feel that constructivism allows for students to make connections between themselves and real life experiences.

What is constructivism?

Summary and Synthesis

When learning about fractions, i thought that there was only one or two ways to learn about them but i was definately wrong. After this class it really has shown me especially in the area of fractions that there are numberous ways to teach it using pattern blocks, fraction bars, caesianaire rods, etc.... I think that being a visual learner I would have understood fractions better given these objects unlike what i did have to work with when i was in elementary school. This made me realize just some of the options that i have to help me teach my students about fractions.

New Insights and Their Implications

I never knew about all the different steps when learning about measurement. It was interesting for me to learn about the six different steps and how the students really should be learning about measurement, not just be given the tools and use them right away. It made me reimence about my education, and all i remember is using the ruler and calculators and not really understanding why. I think that sometimes this would be more work for the teachers to make sure that the lessons include these steps but i think that its work the students education to let them fully explore these math concepts. It makes me also think that maybe if i would have learned somethings this way my view towards math would be better, and i would feel more confident in this area.

Summary and Synthesis

I was really impressed with our book we have been looking at and using in class lately. We have been talking about (CGI) or the teaching techniques of Cognitively Guided Instruction. I really enjoyed watching the videos because they gave you a first hand look at how this teaching technique is used in a classroom. I also believe that asking a question to the whole class and allowing them to work to come up with an answer is great. It is important in my eyes that they come together and discuss what they did to figure out the question as group. This was also demonstrated in the video. By allowing students to use a variety of manipulatives to aid in their solving students will come up with unique ways of discovering the answer. This technique helps students learn the material more in depth rather than just memorization. Watching these videos helps me see how I can use this teaching technique in my future classroom.

New Insights and Their Implications

I never new until this class all the different methods of teaching fractions. I was very impressed with all the different techniques that the other students in the class came up with. Dr. Reins was very helpful in opening up my mind to new ideas for teaching fractions. It is difficult to think about new ways when you were only taught one. To me it just seemed easier using the ways I knew until I tried some of the techniques everyone else came up with. It was nice being able to use the fraction bars, pattern blocks, and Cuisenaire rods because they are all helpful methods to help students see the fractions and to do the math problems. I was able to use these things to discover new ways for solving problems. It is important to know that children learn different than eachother and using several methods to solve a problem will help all the children succeed. I will make sure that I use these different techniques when teaching fractions in my future classroom. I will also keep an open mind to new ideas of solving problems. I will also allow my students a chance to discover new ways to solve problems.

Summary and Synthesis

These last weeks we have been learning about fractions. We have been using the (CGI) Cognitvely Guided Instruction book. I like this book because it shows very good insites to teaching math. I also liked watching the videos that came in the book. I agree with how the teachers had many different manipulatives that kids could use to solve the math problems. I like how they let the children solve the math problems their way instead of just giving them one way. I also liked how she had them teach the class how they solved it. I am still amazed by how many ways there are to teach fractions. I really like this about them because it could be easier for a student in a way...but it could be harder for a student to do it that way....so there are numerous ways you could teach the students in order for them to understand the problems.

Summary and Synthesis

I did not realize until the last couple weeks of class how many different ways we as teachers can teach fractions. I can honestly say that I still struggle with adding, subtracting, multiplying, and dividing fractions. It seems as though every time I am presented with these I am having to be retaught each and every time. It is good that there are so many different ways that we can teach this and make each student understand. Using the fraction bars, pattern blocks, or Cuisenaire rods are all helpful methods to help students see the fractions and to do the math problems with. I am not sure if we had these when I was learning this in school, but I can definately see how helpful they are now. You know, Math is my worst subject. The reason is becuase no one can ever tell me why we do the things we do in math. I was always just told, "That's the way it is! I have a really hard time when things are not explained to me or if I can't see it or physically do it. I think that these manipulatives are great learning tools becuase students can actually see why and how. Working with partners has also been a learning experience. Watching how other groups members solved the probems compared to my style was interesting. It showed that not every students will go about the problem the same way.
There are many methods that can help students learn about fractions. Teachers and students will actually have to work together to come up with methods and teaching strategies for the best learning to occur.

New Insights and Their Implications

These past few weeks in class we have been introduced to methods of how to teach students about addition and subtraction and multiplication and division. Dr. Reins has recently introduced the Cognitively Guided Instruction (CGI) to us. Although this method is fairly new to us, the basis of the approach is to use concrete materials, such as fraction bars, pattern blocks, or other manipulatives, to help students see or "act" out the problems. I think this method is a wonderful way for students to get a visual of what is happening during an addition, subtraction, multiplication, or division process. The CGI approach is a great way for students to figure things out on their own also. They have manipulatives to use to demonstrate 4 + 2 or 7 x 4. All students have different ways of thinking, and by giving them blocks, a time line, or fraction bars, they are able to show their process of thinking. This can be beneficial to the teacher so that he/she can see how their students learn best. Another point I would like to make about CGI is that the teacher should have all the students model how they arrived at a solution and their way of thinking. The teacher should be there to guide and instruct the students, and also encourage them.

New Insights and Their Implications

I have a great experience because I work at a daycare in Sioux Falls and while taking these methods courses this is helping me to apply and understand what is being taught to us in class. During study time, I get to work with students on their math skills so as we talk in class I am able to think about the students that I am working with and help them apply the strategies. I see them trying to apply what they have learned from teachers and are unable to correctly use what has been taught to them as well. I feel that for experienced teachers, changing their way of teaching must be difficult, however as a new teacher I will be able to help students construct their own understandings as this will only benefit them.

My biggest concern is that students will not be able to correctly construct their understanding. Will my teaching help them or hinder them?

New Insights and Thier Implication

I have a great experience becuase I am doing my SPED intern this semester while taking these methods courses and this helps me apply and understand what is being taught to us in class. In the resource room that I am in I work with a group of students on their math skills so as we talk in class I am able to think about the students that I work with and the strategies they apply to thier math. I see that many times they are taught how to do it (a process) and not given the chance to brainstorm on their own. I do wonder with this group of remedial math students if they would be able to constuct thier own understanding with out any guidance. But I do see them try to apply what they have learned from teachers and are unable to correctly use what has been taught to them. It is hard for experienced teachers to change the way they teach but as a new teacher I will help students construct thier own understanding so that they can benefit on thier own. My concern is, as I stated before that these students will not be able to construct the correct understanding. So am I hurting the students more than I am helping them?

Summary and Synthesis

During the past few days we have been discussing the teahing techniques of Cognitively Guided Instruction (CGI). I enjoyed viewing the videos shown in class demonstrating this model of teaching. I agree with asking a question, and allowing students to discover a solution on their own, coming back as a whole group and having the students explain their rationale for their answer. Allowing students to use a variety of manipulatives for their discoveries is helpful. Peer teaching can be helpful for those students in need of additional practice. Many students are taught knowledge and never fully comprehend the why of the problem, manybe the teachers don't fully understand the why, Who knows. Understanding the CGI model and seeing it demonstrated will allow me to let my students to explore and demonstrate on their own.

Summary and Synthesis

In the past few class we have been working on CGI. It is a teaching strategy to helps students learn in a different way. I feel that this is a wonderful way to guide students' learning. I think that by teaching this way students will be more motivated in math class and also have a better attitude when it comes to math. However, I do think that when teaching math, a teacher must also used a instruction strategy at some point. There is such a variety of students in the classroom, and some learn best with CGI where others need more direction. Another reason why you can not just teach in a CGI approach is because the standardized test that are required do not allow students to use anything other than their fingers, so students can not rely on manipulatives. It think that it is important for students to have some CGI in the classroom though because it helps students to understand the WHY of math. When they have discovered this they can move in to the instructional understanding of math so that they can do well on the standardized tests.

New Insights and Their Implications + Question

We are now reading the CGI book, which has given me new insight to students' learning of math as well as the teacher's role. Cognitively guided instruction, to me, means that the teacher allows the students to explore ways of solving problems, choose a method that works for them, and explain how they used that method to reach a solution. The book focuses on addition, subtraction, multiplication, and division, giving a variety of examples of word problems that can be used to help students understand each. The CGI book states, “It is when children decide upon a strategy to represent a mathematical situation and implement that strategy that problem solving takes place.” I have now realized that students can develop their own understanding through the use of good problem-solving questions, manipulatives, and other tools. The teacher guides the process by giving appropriate problems and asking the students questions about their thinking and how the problems were solved. Reflecting on their strategies helps students improve their understanding as well as value the thinking of their peers.
As also stated in the book, "Gradually, children come to recognize that their thinking is important, and they come to value the process of doing mathematics." We have been learning from the beginning of this class that students should "do mathematics," and learning about CGI has helped me to verify this in my own thinking. And just as Dr. Reins told us, that we won’t get the class at first but will eventually…I finally have that understanding. My philosophy of teaching mathematics has therefore changed. I will now create a classroom environment that supports doing mathematics, encourages communication, and allows students to actively explore strategies on their own and develop their own understanding so that they can form connections and value their learning. I do wonder, however, why we did not begin the class with the CGI book?? I think the class would have made more sense to me from the beginning if we would have started out learning about cognitively guided instruction.

Summary and Synthesis

The most recent work we have been doing in class with the fraction bars, pattern blocks and cuisenaire rods has really helped to shape my new understanding of mathematics using fractions. I have always been fairly decent when dealing with fractions, but until this class have never thought about common demoninators in this way. Using the manipulatives we have been using really helps focus my attention on why to use a certain denominator. As mentioned in class, I always just used factors of the two denominators to find the least common multiple. That way is probably alot faster, but does not show how or why you got the LCM. Using these manipulatives makes it clear to see how important it will be to use them with my students in the future. By having them explore fractions using them, they are able to get a visual picture of what a specific fraction means. I think this will help them to be successful at mathematics with fractions.