New Insights and Their Implications

This last month I have gotten a better understanding of shapes and how they relate to each other. I have had past experiences using Tangrams but haven't really analyzed and classified shapes into groups by their properties. I am not good at identifying shapes by name but the class discussions have helped me understand why shapes fall in the category that they do. The book also talks about using Tangrams and other manipulatives for discovering shapes and their properties.
Usually when it comes to math if I don't understand a problem the first time I see it, I am never going to get it. In my College Algebra class I relied on a friend who is a math minor to explain things to me, so I definitely agree that peer tutoring is a great way for students to learn from each other. In this class it has been fairly easy for me to understand the concepts and even if I don't completely get it right away, after I see a few examples and work it on my own it becomes a lot clearer. I just have to have time to think about it and see why it makes sense.
I was unfamiliar with the van Heile levels but I can definitely see how the concepts that take place in the first two levels are essential for students in the elementary grades. The book also gave some great examples to demonstrate students' learning. Overall, I feel that I am getting a lot out of this class because although I am familiar with the concepts we discuss such as area and problem solving, it is being presented in a new way that really gives meaning to why I use certain strategies when solving problems.

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.

Math in and of itself has never been extremely hard for me. I have always taken for granted that I had a formula that led me to an answer. This class has challenged my view of mathematics. I no longer just randomly apply a formula and spit out an answer. I think about the different things we have done in class. For instance when we found how the area of a triangle connects to the area of a rectangle or how we found different ways to find an area formula for different trapezoids and the algorithm to back it up. While these things were not necessarily difficult, they challenged me to look beyond what I have been taught and look how they connect in my own world. While this may be sad to say, I had never realize the connection between the area of a rectangle and triangle. I was never taught how to or expected to prove my algorithms or answers.

Today in class we were working on fractions. While we did not get far into the lesson, I am already doing things that I would never have thought to do before. While I am still somewhat confused with why we were doing some of things we were doing, I made a better connection with fractions that will hopefully help me understand what my students will have to go through to understand what they are doing. While I am still confused I already know more than just rote procedures!!!

Questions and Answers

I am going to admit that sometimes this class scares me. I never know what to expect and I'm the type of person who likes to be prepared. Does anyone else feel this way? I sometimes feel like the material we cover is going way over my head and then sometimes I feel like I GET IT (which is exciting because that doesn't happen often for me in math).

I have a lot of questions about how using the constructivist approach to teaching math would work in a classroom. Wouldn't all teachers have to use this approach and implement it K-12? What happens when a student has been taught traditionally using the rote approach and then is thrown into a completely different learning environment? Won't it take time and effort out of learning time to get students to adjust? My little brother (1st grader) transferred to Austin Elementary half way through the school year last year. The way math was being taught at Austin was entirely through problem solving. He had never experienced this before and I remember my Mom finding the whole process pointless. My little brother struggled with this transition. This brings me back to one of my prior questions. What happens when students move from a constructivist approach to traditional and vice versa?

Look at me. I have never really learned in this matter. I agree with Lauren when she was talking about just wanting answer or a formula. I think when we are so used to things being "concrete" and without explanation it is truly hard to step outside and see the big picture. Math has always been a struggle for me. I am terrified of messing some student up because of my lack of math knowledge. The other day I was reading either chapter 20 or 21 and I realized I didn't know that you are supposed to count the spaces in between marks on a ruler not the actual marks. How I am supposed to teach students the right way when obviously don't know the right way?

I guess it is good that I am questioning my level of knowledge because it makes me aware of my short falls and where I can improve. I think that will make me a better teacher because I will be forced to keep learning more and more. Perhaps that is the problem with some teachers. Some are so sure of their own knowledge and are never willing to question themselves to grow as educator. I don't think a person can ever know all the answers and once that person thinks they have all the answers they should stop teaching.

Sorry this kind of went all over the place!

Summary and Synthesis

First, I have very poor feelings towards math in general. To only further my negativity, I felt unprepared as a future educator upon completion of Math Concepts I and II (my overall understanding and knowledge gained from those classes would probably be expressed in negative numbers so to speak). So, coming into this class, I expected a wrap-up/review of Math Concepts I and II. Although, that wrap-up is NOT what I have found. I have found that as future math educators, we are learning ways to teach math in which we, ourselves, have never been taught. The term "rote" has come up in many class discussions. I believe that for the majority of us, this has been the way we were taught. We were to memorize information and then, we would later forget it. This does not go to say that all of us were taught this way, but I do feel that a large amount of us feel this way. Upon stating this, I do recognize that it is our job as future educators to teach our students math in new and exciting ways. My only question--this corresponds to a blog written by Lauren (Questions and Answers) in which she wondered about the ability to "bust out of the traditional way of learning"--is how do we actually do it? Lauren said what is on my mind too...This is truly something that I am struggling with. I know we need to be better teachers not only for ourselves, but for our students.
I do believe that improvement does begin with classes like this where we begin by breaking down standards and understanding each part. From here we can begin to understand what we need to teach. Next, the activities that we have participated in and out of class has challenged us to think in different ways and to improve upon our own knowledge of various concepts.
Overall, I find this course and the material challenging. I look forward to the continual discovery of the various ways to teach mathematics.

Summary and Synthesis

Class has been very in depth and enjoy the challenge. I feel like this is the only actual methods class where we are learning how to teach the subject at hand. My other classes I feel are just full of busy work and that I am not increasing or building my knowledge at all. It is kind of like I am just be assessed all the time with all the projects and busy work; but when I come to Math Methods I learn so much. Standards are very important and appreciate the fact that we spent so much time on them. I thought the group project, where we were to break down a standard, really helped me because when I am teaching I will be able to use that tool with other standards. The way the quizes are set up are very helpful because they direct me as to what I need to look more at. The first day of class where you showed us how bad our scores are compared to other countries really woke me up. We have always been raised to believe that the United States is the best place in the world. It helps me reach and strive to learn to be the best teacher I can be.

Ruthie Need

New Insights and Their Implications

Coming into this class I was not excited because every math class I take is a struggle.  After 5 weeks of class I can honestly say I am enjoying this math class.  Every math class previous to this there was only one method taught and that was to the discretion of the instructor.  In eled 330, I have enjoyed learning multiple methods to solving problems.  Up until last week, I did not feel comfortable enough to explain area to someone.  I have now acquired enough understanding of the concepts of area that I could help someone else who is struggling.  

I have learned that their is a lot to take in during the class period. There are days I have to go back and reflect on what was covered 2 or 3 times to understand the meaning of the material Dr. Reins has covered in class.  The difference between this math class and other math classes is that after 2 or 3 times reviewing the material I am grasping the concepts.  That has been exciting for me!

Deanna Smith

New Insights & Their Implications...

What have I learned about the teaching/learning of math from ELED 330? 1) This class should be a 400 level course, bc it’s so deep. 2) Even though I’ve had to take over 3 years of Math, nothing has prepared me for teaching math to any age of students. 3) A constructivism vs. traditional method of teaching.

In past math courses, I will not lie, I have done whatever I could to simply stay afloat. Yes, I got that great grade to pass and move on to the next course, but obviously none of that helped, in that ELED 330 is completely different. Every Tue/Thur, my brain gets heavier and heavier with more things to process, and every Tue/Thur, I get more and more apprehensive when thinking about teaching math to students-even future KINDERGARTEN kids…I am still pondering the constructivism vs. traditional method of teaching; I feel both have their place and maybe a balance of the two would be best for Mrs. Tia’s future classroom.

So, what are the implications of my new insights? Well, first of all, thank goodness I’m in the semester before my student teaching, as I have a lot to glean, and secondly, maybe instead of focusing on why/how math can be difficult, I could focus on what I can do to teach math in a creative and fun environment…

Questions and Answers

Hey everyone,

I guess I have been wondering if I can ever bust out of the traditional way of learning. I have been wrapped up in it for so long, I feel as though I only know how to do it that one way. I know that I want to teach constructively, but I am still struggling with ways on how to do it. For example, I have been working on the Pick’s Theorem problem and I am trying my best to figure it out on my own, without help from peers or looking it up, but inside I am screaming for a solution, a formula, an answer!
I am thinking about how it is so easy to get an answer when you are learning traditionally because the teachers just give you the answer, but in the end, am I even learning? Now, when I don’t have a formula to work with, I actually have to look and search for the answer by myself and without help. It is hard and in the back of my head I am asking myself, is the traditional way of learning really that bad? I know the answer to that question. I know that learning constructively is the only way to actually learn. What I am trying to say is that it is extremely tough to go from one way of learning to a total opposite way of learning. I am trying to adapt, I know it will take time. I just want to know how everyone else is feeling. Am I the only one who is struggling trying to transition into this new type of learning? Does anyone else feel like at times they even miss the traditional type of learning? I am just curious…


Lauren

New Insights & Their Implications

When I first entered the classroom I was terrified. I always thought I was horrible with math concepts and never had much interest in it. I always viewed it as my worst subject and was terrified of that simple word "Math". Little did I know that in just a few weeks I would start to form a passion for math. Yes, I said it...I guess I do like math after all. I believe what changed my mind the most was how the information has been delivered. I have always been taught math the traditional way much like what we are seeing today. With this new approach of constructivism and testing it out, I think it is something that I really enjoy. Yes, the homework and activities have been quite challenging and involve a great deal of analytical thinking to work through problems. This is what helped me to understand and never forget the content. Before we did the area of polygons activity, I would have never been able to tell anyone how to get the answer...right off the top of my head. After working through the problems I figured it out and I found it fun to find each answer. After spending an hour of much analyzing, I know that I will never fail to find the area of a polygon. It is honestly something that I will never forget! I know that it is due to having to figure out how to solve the problem on my own and now I can recall those steps. I would love to teach in a constructivist approach. I know this will be challenging to do and I will need lots of resources, support, and time. I feel this is the best approach for students to learn. I learned so much and want the same for my students. I am now going to challenge myself to think in more of a constrivist way from here on out. 

New Insights and Their Implications

After the first week of class I was beginning to wonder what I was getting into with this course. I have never felt like I was very good at math and was worried about this class before we even started, by the end of the first week I was a little confused over what was going on. Not only is this course different from any math class I have ever taken it is also different from any of the methods courses I am taking right now. In this course I am learning more on how to teach students and being shown a technique that will help students in any future class that I may have understand math better than if I just gave them answers, which is how I was taught.

Even though I have never felt that math was a strong suit I have never struggled as much as I am now. I am beginning to realize that since this is such a new idea and approach to math that it is going to take me a little while to fully comprehend what is happening. If I keep an open mind and be willing to struggle with the concepts, like Pick’s Theorem, then I think that I will have a great knowledge base to start teaching with. This course will help me provide instruction that will benefit students.

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.