Summary and Synthesis

There have only been a few weeks of class so far but I have learned so much about teaching already.  Dr. Reins has shown so many more ways than just the going over the material, worksheet, and test at the end of the unit way of teaching the students.  Teachers have such a wide range of options for showing students different methods of learning the material that they need to learn. I have found this out by just sitting in Math Methods class.  We do not go through a power point and take notes and then have a test over it.  Dr. Reins shows us in his own classroom that there are other ways to approach the material other than lecture.  It is great to see the higher order thinking in the classroom and it will help us as teacher impliment it in our classroom.

ELED 330

Before I started ELED 330, I was very naïve about how math should be taught. I was positive that the best way to teach math was: the teacher shows the students how to do a problem, then the teacher and the students do a problem together, then the students do problems alone. Consequently, this was the way I was taught math in elementary, junior high, high school, and even college. My approach to teaching mathematics has completely changed within the first three weeks of class. Teaching through problem solving is a great way to get students engaged in their learning and use mathematics in real life situations as opposed to learning one type of problem out of context. However, I am struggling to understand how a student who has no idea about the concept of addition or subtraction can learn it through a complex problem. Is it necessary to teach basic concepts prior to the big problem? The textbook says no. Also, what if a problem does not work out and the children do not reach the desired answer and/or method that the problem was designed to teach? Do we make another problem or go straight into teaching the concept? These are just a few questions I have so far as I learn a completely new way to teach math.

Summary and Synthesis

The biggest impact made so far in the class is that teachers must find ways to engage their students and get them to think for themselves. There are many different ways to go through the process of solving a problem. There is not one set way to do it – the students should use strategies that they know and be able to explain the way in which they have solved a problem. The activities and discussions that we have had in class support this. When doing the handshakes problem, digits needed, and triangle activity people used several different strategies to complete the task. We were able to explain our reasonings and the strategies varied. The hardest thing to do is to think about what we are doing and actually explain the process without skipping any of the steps. This is especially true when we are using formulas to solve problems. We are so used to just plugging in numbers to find an answer. We need to actually think about why we are using the numbers we do and why they give us the answer they do.

ELED 330

Before entering this class I did not realize the importance of teaching math through problem solving. My previous math classes consisted of taking notes, doing a few example problems, and then being tested on the material. There is nothing engaging about this method of teaching.Dr. Reins teaches in a unique way that allows us to answer our own questions. He also helps us build meaning for the concept presented. I never really realized what exactly a good problem or task was before this class. I figured any method of teaching that taught the concept was acceptable. Now I know a good problem or task must be engaging, must have a purpose, should be relevant to students, must have multiple routes, and must use good language. I am looking forward to learning more about this unique way of teaching math so I am able to implement this approach in my classroom someday.

Through these past couple of weeks I have learned to teach math from a very different viewpoint. When I was in elementary school I was taught using the traditional way. The instructor would explain the process, give the students a few examples, and expect the student to use the method given from the teacher. Students were not encouraged to find multiple routes to a solution like we are in class. Using the non traditional way of teaching like we are encouraged to do in Math Methods is actually very helpful. When we are allowed to share our strategies with other students and the class as a whole it enables everyone to see multiple routes, a student may find another route easier than the instructor's method. In class we have been provided with higher level thinking questions. With these questions we are ask ourselves, "What are we supposed to be teaching our students, or what are we teaching our students?" Recently, we have been going over the standards to make sure we are teaching by the standards. I also found this to be very helpful. I have really enjoyed this new hands on way of teaching math, it gets students excited about math, even those who struggle. Last Thursday, when we were given the worksheet with blank squares and we had to make as many triangles as we could, it allowed us to do our own thinking, it challenged us. This way of teaching math is different, but I could definitely get use to using it with my future classroom.

Summary and Synthesize

For the past few weeks of class, it has definitely been interesting for me. I haven’t been enthusiastic about math, and learning how to teach math wasn’t my idea of an exciting class. The newest style of teaching has me thinking otherwise now.

The Project Based Learning (PBL) approach has been very helpful. It provides me with a new way of teaching mathematics to my students. The approach specifies that the concepts being taught should be meaningful and relevant to the students. Students will no longer be learning math from solely from a textbook and a lecture style mode. Students will actually be exploring and coming up with their own thoughts and ideas on how to solve a math problem. By using PBL, I can teach my students math, how to understand its concepts, new ways of solving problems, cooperative learning, and to like math.

The math activities that we have done in class have shown me what kinds of math problems I am supposed to be giving my students. I like the cooperative learning aspect of it all, and that solving the problem does not necessarily take a formula. That there are multiple ways, multiple entry points, to solve the problem.

New Insights and Their Implications

Though this class, I have started to think about teaching math to elementary students in a new way. No longer the traditional, show the students a couple examples and then assign them some problems, but rather, provide the students with higher level questions and have them use problem solving to solve the questions. This will help the students understand the mathematics and to critically think about what they are doing. This will be a challenge because of the different mindset that will be needed to teach math this way and also because of the time that it will take to find quality questions for the students, but I believe that it is worth a shot to try and teach this way because of the added benefits that it provides for the students. Also, if all else fails, you can still resort back to the traditional way of teaching math, but I feel that we owe it to our students to try and provide them the knowledge and skills to help them out in the future as much as possible.

Blog #1

In the past I was use to walking into a math class ready to take notes on different formulas and methods that my homework assignment would require me to use. This however, is not the experience I have had thus far in Math Methods. Dr. Reins is challenging us as both as students and teachers to embrace the new ways of math. This "new" way of thinking about math is all about letting students discover and share their findings with the class. Teachers are thought more as helpful racecourses, hint givers, and modelers. Students are encouraged to problem solve and use their prior knowledge to solve and figure out the problems instead of watching a teacher do a problem and then turn around and do a few by themselves. This way of teaching I feel will be beneficial to students of all ages and will hopefully increase their mathematical abilities.

Blog #1

I think what surprises me the most about teaching math in the "non-traditional" is not only having to create new ways to get the students to problem solve, but to also connect the teachings to standards. I had always thought that connecting the standards to what was to be taught in class would be easy, because the standards are to be measurable. But I was very wrong. It is clear that the South Dakota standards need to be revisited and revised. They are general, broad, and hard to know exactly what is supposed to be taught in class. In class we were able to compare the standards from 4 different locations, and they all pretty much said the same thing, except for the South Dakota standards. It was almost like you had to read between the lines to fully understand what you needed to teach. My group looked at the Common Core Standards and we found them to be clear, concise, and easy to understand. It was clear, after reading them, which standard we were meeting. If we, as teachers, are to meet all of these standards, then it is important for us to know exactly what we need to be teaching.

Blog #1

Every experience I have had with learning math so far has led me to believe that math is taught and or learned through a number of example problems to learn the process/rule followed by numerous practice problems to be completed as an assignment so you could work on the process even more. I thought that this class, eled 330, would be set up the same way as any other math class I have taken. But, I was wrong. So far this class has taught me to view math in a completely different way. It is important for students to solve their own problems and learn by making mistakes. Teachers should not just give students answers. We should help guide them through problem solving and help them work through their mistakes on their own. I think this course will help me develop good techniques to use in the future when teaching math. So far, in the first few this class has helped me open my eyes to a new and even better way of approaching math.

Summary and Synthesis

I grew up with math being taught the traditional way.  You were given a problem or formula, you were shown how to use it, and then you practiced.  It really didn't require a deep level of thinking.  After being in this class for a few weeks, I have realized that there is a much better way to teach math.  I will admit it is challenging but students will have a better understanding of math.  I have always been intimidated by math because I have never really understood it.  This method of teaching math allows students to make their own connections and use the prior knowledge that they have.  I think that is the most important because the connections are more meaningful because the students made them themselves.  Also with this method, students aren't just memorizing formulas to pass a test and then forgetting them as soon as the test is over.  Students will be able to perform better in math.

Summary and Synthesis

I love this new way of looking at math from a problem solving point of view. My past experiences have made me very uncomfortable with math, as well as having very little confidence in this area. I feel as though I am understanding so much more by putting the problem solving aspect first. I was pretty apprehensive about coming into this class unsure of how we would be taught to teach our students. I can say that I am pleasantly surprised to see such a holistic approach our class is experiencing. I can see the benefits to being taught with a problem solving approach rather than learn, memorize, practice, and dump. I'm glad to see that the results of this method of teaching have good long and short term effects.

Blog #1

     At the beginning of the course I felt like we would be taking another typical methods class, but now that we have started I see that we are learning much more.  I started off thinking that teaching math was as simple as teaching the students how to solve a problem and having them practice.  Now I know that there is a process involved.  I really learned a lot from the discussion we had on problem solving.  Now that we mentioned metacognition, it makes sense to motivate students to be more conscious of how they are working on solving problems.  I have never really thought about knowing how I know which steps to use, but now that I think about it there is a lot more of a process involved.  Looking at the ten strategies, they make sense! I never thought about using them as strategies to solving problems, but now that I think about it, I have used almost every single strategy in one way or another.  Now that I am conscious of the strategies I use to solve problems, I can use my knowledge to model/assist my students on how to use the 10 strategies to problem solving.
     Another thing I have learned is how to teach students without giving away the answers.  It's important to have the students work through problems on their own and get their own answer.  When students ask for help it's easy to just show them how to do the problem and give them the answer.  By working on the problems in class, I learned how to guide the students and have them figure everything out independently.  I have always been a huge math fan but it makes me nervous to teach students who don't like math.  With this class I'm already feeling more comfortable with teaching my students.

Summary and Synthesis

The past few weeks in Math Methods we have focused on the improving students math skills by concentrating on the development of critical thinking skills, meta cognitive thinking, and National Content Standards. Critical thinking skills are important to develop, this skill forces the student to use prior knowledge to solve problems. Problem solving is a key component of critical thinking and George Polya's four steps to problem solving could be used as a model for students struggling with problem solving skills. If students are able to think about the way they think and improve their meta cognitive thinking problem solving and overall math skills can be enhanced.
As a future teacher it is important I understand the standards I and my students will be assessed on. Standards are put in place to make sure students are achieving at similar rates. The new Common Core Standards are valuable to teachers because they are well written and each teacher will now be preparing their lessons based on the same set of standards. As we saw on the first day it is important the United States improves math skills at an early age. The national standards put in place are more detailed and make it easier for teacher to prepare lessons that fit the standards and improve student learning.

Summary and Synthesis

I grew up doing a completely different way of math compared to what I have learned recently. During the past couple weeks in Eled 330, I have realized that math can be learned through a different approach with problem solving. Instead of the teacher standing in front demonstrating a few examples and then assigning a book assignment, now the teacher immerses the students in math. The students learn for themselves what math is all about. Problem solving is an enriching activity where the teacher chooses appropriate problems and stands back to let the students figure out their own mistakes, instead of holding their hands and guiding them the whole way. I learned that there are certain qualities that make a good problem or task good; multiple entry point problems are ideal since students can attack the problem starting at different levels and problems that are meaningful will help the students connect to the problem more, resulting in a more positive math experience. Learning these qualities will help me in the future when teaching math because I will be aware of what type of problems my students will need. During the past couple weeks, I also learned there are different problem solving steps and strategies that need to be used in this new way of teaching. By learning these steps and strategies, I am understanding how children learn and the different techniques they will use to find the answer. Through hands-on activities in class, these techniques have been demonstrated and I will be sure to utilize hands-on activities in my classroom as well. Even though we have been in this course for too long, I have learned so much and I will be sure to utilize this quality information in my future!

Summary and Synthesis

Due to my recent experiences with math, I came into this class with a pretty good feeling about math. I would much rather to math homework than write papers, however, the way we've been learning about math in class for the last couple weeks is different from the way I grew up learning math. In high school, we did math worksheets and problems out of the book just like we talk about not doing with children now. Dr. Reins has really opened my eyes to the new strategies of problem solving and how new teachers need to reform the way math is taught in the classroom. I'm looking forward to the challenge of teaching math in this new light. However, I'm the type of person who has always been good at math but have always had a hard time explaining my answers to my classmates. I'm thankful that Dr. Reins is taking a new approach with us before we go out into the classroom. It's important for students to use the problem solving tools that we've been talking about so they can use the concepts of math in real life. It's important for children to see how math can fit into their everyday life. It's also helpful that he is introducing more than just the state standards in the classroom. In most of our other classes, we just have to align with state standards which in a few years will be of no help if I decide to teach somewhere other than South Dakota. After comparing SD Standards to The Common Core Standards, I can see why it's important to look at both sets. The Common Core standards are much more precise and easy to follow. They use specific terms instead of analyze, understand, identify, etc. I'm looking forward to learning new methods of teaching math throughout the semester.

Summary and Synthesis

These past few weeks have really opened my mind to a new way of teaching math. I will admit, once I entered middle school, math quickly became a subject that I was not confident in at all. That lack of confidence also made me a little nervous to take is this class, too. I've come to realize though, mostly through this class, that the main reason behind my shaky feelings is because math has been primarily a memorization task. We were given a formula, then we repeatedly practiced computing it. However, this class has shown me that math is a process of discovery; of questioning and developing an understanding of core mathematical principles that we can relate to. It has caused me to open my eyes and see that there is a lot more to math than I previously thought. The activities that we have done in class have been very interesting. They have made it evident that we do not need to be clinging to the formulas and procedures that the teachers give us, but that we can create the answers on our own with guidance from them instead. Therefore, I am very interested to see how this semester will progress. I am excited to learn this new match teaching style (even though it will probably be a struggle along the way), and most importantly, I am interested to use this method with my future students.

BLOG #1 SUMMARY AND SYNTHESIS

BLOG #1 SUMMARY AND SYNTHESIS

Since the beginning of this course I have learned how important math is to students and how important it is to be a teacher that focuses on challenges that allow the students to expand their way of thinking. I for one am terrible and uncomfortable with math and hope that this course will allow me to become more familiar and comfortable with the subject so that I am can be a positive teacher in all subjects, especially math. The classes that we have had really have made me think more into math. I have had to think deeper into problems in this class than other math classes because before I could get assistance from the teacher but with this class Dr. Reins has really pushed for us to apply ourselves more and to put more effort into solving the problem without giving us the answers. I have learned that as a successful teacher you need to listen to your students and allow them all to explain how they may have come upon an answer so that everyone in the class has an open mind and can see different perspectives. You must also listen to your students and give them feedback without making them feel stupid or completely wrong about answering questions. I think it is great that we are allowed to work in groups with our peers, this for one allows me (who is completely uncomfortable with math) to listen to others ideas and to see how they solved the problems. This course really makes you open your mind, dig deeper, and apply yourself to every problem and every solution. I plan to take away ideas from this course and to apply them to my future teaching. I really think that George Polya’s steps to problem solving, the ten problem solving strategies, and the process of mathematical inquiry will all help me to apply myself more to math and help my future students. One thing that I am terrible about is giving the answers and not helping the child to find it themselves. I have this issue with my sixth grade daughter; I try to help her solve and end up solving myself and am unsure how I can change my habits? I think that having a chart like Dr. Reins said he had will help me in helping my future students to apply themselves more to the problems. I am hoping that after this class I am more comfortable with math and will teach it appropriately to my students.
Maria Love

Summary and Synthesis

ELED 330 has given me a different insight on helping a student understand and utilize the different methods of math. My philosophy is understanding math from the beginning or early years helps the student to to have a better understanding as he or she goes along. Understanding numbers and the relationships between numbers will help as the student progresses on to algebra. Developing a good foundation requires the understanding and in addition, practicing those methods will help also. Through my experience in math classes, I have learned there are more then one way to solve a problem and the way the instructor teaches his or her way may not be the easiest way for the student. Allowing the student to have multiple ways of solving a problem and taking the task on himself, gives a better hands-on understanding of solving the problem, working independently and developing additional skills and strategies. If a student falls behind in their elementary years without any additional guidance, math only gets harder and the student will not be able to understand and proceed with his or her peers.
The Teaching Problem Solving criteria we touched on was beneficial to me because of the breakdown taught on solving a problem or situation. Thinking logically, reasoning, and understanding the concept, and organizing that part of thinking will help to enable the resolution of the problem. Symbols, charts, and graphs can also deepen their understanding of the concept of math and sometimes visual representation is a key to their understanding. Having multiple strategies to solve a variety of problems enhances the student's ability and to reflect on his or her past experience of problem solving techniques and helps to choose what works best in solving a problem or task.

New Insights and Their Implications

In this course so far, I have learned more about teaching mathematics to young children. The textbook has emphasized on teaching through problem solving. This means not just giving the students a formula and telling them what numbers to plug into it. Instead, the students try their own methods or strategies for solving problems. The instructor has also stressed this and how students can greatly help one another and think of different methods for figuring out or solving the same problem. I also have new insights on how students can help one another. I never really thought of how when students use different strategies from one another to figure a problem out, it could greatly benefit other students to hear about the different methods. Students can learn many different things from each other that can help them understand problems more. Teaching through problem solving might be difficult at first or at different times. My classmates have also mentioned how this way of teaching is different from what they are used to. I have also learned through class, that we all do not solve problems out exactly the same way. I have a new insight on how children learn math and plugging in numbers into a formula might not always be the best way for them to learn something. Over the past couple of weeks, I have learned some new ways for teaching math. It can always be helpful for students to learn from one another and listen to what each other has to say. It is helpful for students to try things out on their own and not always just follow a teacher's way of doing something or solving a problem. This might help them in the future with solving and understanding mathematics.

Summary and Synthesis

After only attending a few weeks of class I have to realize that I really need to step back and look at how I view mathematics. When I was taught math it was always copy the definitions from the book, do practice problems in class, assign homework problems, do the homework problems, and correct them in class the next day to get a grade. Due to the way I was taught math I have become very uneasy about teaching and knowing how to properly teach math because I do not want to make my class suffer from a regular math schedule such as I did for many years. Since I opened our textbook and started reading I have found some great ways to look at math and how to integrate it into other areas in school. I have learned that teaching problem solving in mathematical activities and only telling the students what is necessary to understand the problem and allow them to mull the situation is truly a great way to help them grow in knowledge. I have grow so use to always getting the correct answer to a math problem that I will have to say it has taken a class or two to understand that always being given the right answer as soon as class starts is not a very productive way of accessing the students high level of thinking. I am now able to start to understand the way of Reins teaching and making us mull the problem and then discuss it out loud.

New Insights and Their Implications

Over the last couple of weeks, I have really considered what I know about teaching math to young children. As I get closer to graduating, I am now carefully considering how prepared I am to teach. Mathematics has always been a topic I have enjoyed, but I know many people who strongly dislike math. I do not want to be a teacher who makes her students dislike math. Throughout this class so far, I have learned some valuable tools for helping my future students to succeed. I have learned that it is so important to present problems in different ways and that what seems to make sense for one student may be confusing and seem impossible for another student. I have learned from my peers that we all learn in different ways and how sometimes peers can do a better job of teaching one another that a teacher can. In the shaking hands activity, a peer explained it in a way that was so much easier for me to understand than the way I had figured it out. Having this knowledge about how all students will learn a little differently will greatly impact my future classroom and teaching abilities. The instructor has really made me start to understand the importance of math standards and how I will need to carefully consider the best ways I can meet these standards with the lessons and activities I choose to teach my students with. I have learned that it is important that I challenge my students appropriately.

Summary & Synthesis

In the short time that we have had class, I have learned a lot about the way to present math to students. Often times math is a subject that scares students away, because they are afraid to get the wrong answer or what others might think of them. This class so far has showed me that I need to look at how I will teach students in a whole different perspective. If I encourage them to learn and to what to find a way to get the answer themselves, they won't feel the discouragement of not understanding a formula. I have learned that teaching math shouldn't be a "here is a formula, plug in the numbers, here is the right answer" method, it should encourage students to find their own way of getting the answer and sharing their method with other people. Students need to learn math by doing math, and solving problems themselves. As a teacher, I have learned that I will need to step back and let the student work on their own. If asked for help, I should ask the student to explain themselves and give hints on how to become unstuck, but I shouldn't give the student my way of figuring out the problem. This class so far has taught me that communication in math is huge, and if a student can explain how and why they got an answer or did a problem they will fully understand it better. I have learned to integrate communication into math to help students talk the problem out. This class has also taught me so far that the problems and standards I use in a class is very important to the outcome. So often "formula" problems are used to meet general standards. I have realized that it is important to give deeper thinking problems to the students to meet more specific standards that will help the students in the long run and in many different subject areas.

Summary & Synthesis

The first couple of weeks in class has given me a whole new perspective on how to teach math. I have learned that it is important to back up and give students the chance to solve problems on their own. Teaching math, for most people, means introducing a problem and showing students how to solve it in a step-by-step process. Instead, I have learned that as teachers we need to allow students to work through a problem in a way that works best for them and come up with a solution on their own. Students will learn how to solve problems on their own without relying on a teacher telling them what to do. It is also important for the teacher to allow students time to discuss their problem-solving processes. Discussion gives students the chance to reflect back on their work as well as share their findings with other students. When sharing with others, students will see that there is more than one way to arrive at a solution. I never really thought about this approach to teaching, because I remember learning math the way that the teacher taught it to us--the way she wanted us to learn it. The last few weeks of discussion has really opened my eyes to a method that I would have never thought to use.