project based learning

I'm starting to get a better grasp on project-based learning. Now that we have taken the midterm and have seen a few more groups present, I'm starting to get used to the way this class is set up. I'm starting to appreciate the way we are learning the material, but it's still hard to bring down my level of thinking so I can see if from a child's perspective and that is something I definitely need to work on. However, I think this will be easier when I'm in a classroom and have my student's experience to base my instruction on. I can try to come up with different ways to do a problem and come up with ways that children would look at this problem but it's harder when you don't have an actual classroom to work with. Of course there are our peers but our college peers don't interact and don't do math like elementary children would. I've never had experience in an elementary math classroom, but those videos we watched today about CGI were helpful and fun to watch. I'm gaining an appreciation for math as this class is progressing, and I'm getting more out of this class than I have from others.

Blog 2

Though I am still struggling with the Project Based Learning in math, I also understand why it is so important that we allow our students to come up with their own conclusions as to why things are the way they are within the rules of mathematics.  Had I been taught this way, I probably would not have such an overwhelming fear of math as a subject.  Every time I attend this class, I am left wondering, 'Why has this method of teaching come around sooner?'  Though it is out of my comfort zone, being forced to look at the reasoning behind the rules and processes of mathematics has given me a deeper understanding of why math works the way it does.  I am slowly beginning to understand why it is important to move out of the comfort zone of worksheets and easy, fast teaching into a method of teaching math that will allow the students to not only perform the tasks, but really understand them. 

Summary and Synthesis

As the semester goes on we are continuning to learn problem-solving based learning. It has been very helpful to learn the different strategies Dr. Reins models to aid in our learning to teach math this way in the future. I also think it has been helpful to learn from the different student presentations we have had so far. It is beneficial for us to see how our peers are teaching this way of math as well. Although it seems frustrating at times, its important we learn this reform based math instruction so it will benefit our students in the future.

Blog #2

From my first post until now, much has changed. I am still strugging with the PBL method of teaching and how to learn from them. I feel that much of the freedom we are given leaves me feeling unguided in assignments and expectations. I feel that I would benefit greatly if were given more detail or guidance with our homework. I know that this is something that is proven to be alot more beneficial in teaching math, I am not sure that I will be ready to teach math in this way by next fall. I agree with all of the concerns that Molly addressed, and am wondering if there are any other resources for teaching PBL in math. It would be great to have more information on this since graduation is coming up very soon!

New Insights and Their Implications

I have learned so much in this class so far and I will definitely use this tips I have learned in the future. The groups that have presented gave great ideas for teaching math. For example, the LPU with the fractions was fun to listen to. It was fun to see different ways on how to teach fractions. Dot paper, pattern blocks, fraction bars, and rods can all be used to teach the same thing. I like the idea of using different techniques for one subject since every student learns differently. Also, the approach of project-based learning has been a good experience. I think students get more from the lesson if they aren't just handed the formulas and answers, and if they actually do the work of the process. By participating in project-based learning, I feel like I am becoming a better-informed teacher. If I actually participate in activities students will be doing, I get more of an idea of what it is like to teach it.

I have learned so much so far and have gained so much insight and I cannot wait to put it to use in the future!

LPU

So far in class these groups have presented their lesson plan for understanding, my group happened to be one of them. Our lesson focused on area formulas. When we first chose this topic we thought it would be a fairly easy lesson to create, but after we met with Dr. Reins our opinions quickly changed.
We could not figure out how to teach a lesson that would have our students coming up with the are formula themselves. We met several times and felt frustrated because letting students explore and find things on their own is a hard thing to do. In junior high we were taught formulas by copying them off the board and then taught which numbers get plugged where, so naturally we felt scared.
After another meeting with Dr. Reins we felt comfortable with our lesson, but were still unsure if our classmates would understand what we were asking them to do. The day of our presentation things went smoothly and we did just fine, but without our planning and preparation it would not have went as smoothly.
All in all I enjoyed our lesson. It was a great way to practice project based learning. I now know I am capable of teaching the "new" way and look forward to actually implementing it into my classroom some day.

Personal Concerns

I don't have too many concerns but there are a few. I'm nervous of teaching mathematics the 'new way' since the 'old way' is what I am comfortable with; it is also how I was taught and how I know the information that I do. I understand the importance of teaching students how to come up with strategies on their own and why it's important to let students explore mathematics so that they thoroughly understand the concepts. However, I'm not sure that switching to this new way is going to be easy and can be accomplished by the time I will be teaching. What are some ways that I can 'switch over' to the new way of teaching mathematics at a fast enough pace so that I can start right away when I have my own classroom? How can I teach my future students this new method when I myself, am not real comfortable with it?

Recently In Class

Recently in class we've been talking about fractions; addition, subtraction and a little bit about multiplying fractions. I found the last lesson that was taught in class to be rather interesting. A new concept of teaching fractions was brought about and I thought, "why didn't anyone show me that before?!"
The fraction table method that they showed us we new information for me and I was really impressed with it. It is defiantly something I would teach to my students. Not only does it show you the break down of the fraction and give you the least common multiple, but it also works other math skills like multiplication tables. I didn't expect to learn anything new with the lesson and I was pleasantly surprised when i did.

The house project we've been working in recently however hasn't been so plesent. My group was assigned the task of figuring out the area of the roof to figure out how many shingles would be needed. It took us quite awhile to figure out where to start and even longer to get a good idea of what the roof actually looked like. I'll admit i'm still struggling with this class and i'm worried about the midterm but I have to trust that there is a light at the end of the tunnel i'll eventually see.

Personal Concerns

After having been in class for a while, I have the concern of not liking this way of teaching. I understand the concept of it, and how it will be beneficial to students. But I think about how I was taught and how well I excelled in Math because of the way I was taught. I love Math and I will say that what I haven't had to use, I've lost, but I just don't know if I had been taught a different way, would the outcome have been the same. Would my love for Math still be there if I was taught the way we are talking about? In order to move forward with this, I am going to have to think through my past Math classes and how I could incorporate reform based teaching into it, so that the students who will learn from traditional teachings can learn right along with those that will learn better from reform based. This means extra thinking time for me, and in class I will need to focus on how I can use what I am learning in a different way.

New Insights

K-8 Math Methods is so much different from any other methods and/or math class I’ve ever taken. The approach is much different, which I appreciate. This class has showed me that I have a chance at being a decent math teacher—granted, it’s a very small chance, but a chance nonetheless. I have learned a lot from Dr. Reins, but I’ve learned even more from my fellow classmates. The LPU presentations have been very interesting, fact filled and entertaining, but I’ve picked up a lot more knowledge from our “talk time” in class. I am seated around a handful of great gals (and occasionally Adam and/or Kyle), we’re all very comfortable with each other and explaining ourselves and our ideas. So many of my math fears have subsided because of a one-on-one explanation from one of my peers, which is really something special.

New Insights and Implications

Through out this class I have realized I never really knew how to teach math.  I have had so many teachers who simply show us how to do a problem and have never explained why.  I feel like in order to really teach students math, we need to teach them how AND why we are doing problems the way we did.  When asked the question in class, "Have you ever learned how to do a mathematical problem, but were never taught why?' I thought to myself, YES!  I feel like every single math problem I have learned I don't know why that is the way we do things.  It makes me nervous to teach this way because if no one ever explained it to me, then how am I going to explain it to my students.  I have begun to think in an entirely different way of how I will be teaching math.  Students aren't going to be able to simply "get it" without proper explanation.  Now that I know this, I will have to work hard to figure out the best way to teach my students.  I don't want to be the teacher that makes students hate math.  I'm just happy I learned this before I start teaching, rather then later.

Summary and Synthesis

In class we have continued learning how to incorporate problem-based learning into our elementary classrooms. I have realized exactly how much work this type of teaching will be. It is going to be a challenge but I have also learned that there are resources out there to help you. Also, you can use other teachers and the students themselves to help generate ideas. Throughout the classes, our classmates have done a wonderful job explaining a couple math concepts using this style of teaching. Using their lesson plan, the students will have a better chance at understanding the concept fully and not just go through the motions because the teacher told them it was the correct way.

LPU

After having completed the LPU this past Tuesday I have concluded that it is very important to understand the concept being taught. When we began planning this LPU my group members and were not sure we knew exactly what we were going to be educating you all on. We were taught fractions one way but here we were expected to look at it in a different light. Once my group members and I started practicing and doing what was read from the book and notes we come to an understanding of how to teach this concept in a new way that now made sense to all of us.I found the table method to be something so simple that I never would have thought to use it. I feel that the table method will be very helpful to my peers and me when we are teaching our own students. The fraction bars for me were the hardest to grasp and that is why it is always important to have more then one way of showing students how to do something. Using a semi-concrete model as well as manipulatives can result in great success from students. One thing that I found most valuable from the LPU was that you need to remember that you are older and have had the information already built upon and these students you are teaching are starting from where you are starting. Keeping an open mind and allowing for constructive criticism will better your teaching in the years to come.

New Insights and Their Implications

This class has given me many tools I now would feel comfortable using while teaching math in the K-8 setting. The most useful tool I have accrued is a completely new style of teaching and a more effective style based on projects and higher level thinker. I have already begun experimenting with some of the new insights I have gained in an internship experience where I am working with two students who are struggling with math. I often find myself explaining how a mathematical property works and alternative routes can be used to find the solution. However, when I am working with them on their homework it is always a worksheet or a set of problem from the textbook. This concerns me because I am sure there are students who are passing the assignments and do not require addition help but are in fact missing the entire concept. These students will doubtfully struggle when more challenging mathematical problems are given to them, maybe years from now. The most helpful and probably most recent insight I have been exposed to is to make sure the students understand the how’s and the whys instead of learning rules without reason.

New Insights and Their Implications

After being in this class for 6 weeks, I have realized that even though this method of teaching math is more difficult it is much more meaningful to the students.  Teaching math this way allows students to find and discover formulas and answers on their own, which makes learning more meaningful to them.  I grew up with the teachers just giving me the formula and then I would just plug in the numbers to make it work.  I am in my last year of college and I am just finding out the reason/purpose for certain formulas.  I think that by giving students the chance to discover and learn these things on their own when they are still young will allow for that information to stay with them.  This will also allow them to grow and be more confident in mathematics.  I think that as long as our students are being challeneged but are not frustrated, students will be more confident in mathematics and will perform better. 

Blog #2

New Insights and Implications

I will admit, as interested about learning this new of math as I was at the beginning of the semester, there was still a part of me that was very nervous about it as well. I was unsure of whether or not I would be able to fully comprehend it. However, though I have struggled along the way, I have begun to discover that I am starting to grasp it (at least for the geometry part). It was very interesting to see how geometric understanding builds throughout the grade levels, and thus how we can build off their prior knowledge to help them discover new concepts of mathematics. From one of our beginning activities where we took a rectangle and transcribed a triangle into it to actually developing a formula for the area of a triangle, I was able to see how this way of "discovering" math is accomplished, and accomplished well. Another example was through developing multiple formulas for determining the area of a polygon to being able to take the idea further to apply it to a real-life situation - determining the amount of shingles it would take to cover Mr. Reins roof. Through this activity I was able to discover how we help students take the mathematical concepts they are developing and go beyond it to other areas and know how to do it. That was something I had quite a bit of difficulty doing in my math classes, so being able to help students achieve this is one reason why I will be very happy to use this math method in my future classroom.
A final new insight I have gained in the past few weeks is how difficult this will truly be to implement. I know that we discussed it, however, one never truly grasps it until he or she sees it done. From watching the groups present, I have been impressed by what they have done, and I have come to discover just how much effort it will take to teach in this style. However, I have also learned how important and beneficial it will be as well. So, I hope that I will continue to progress in my understanding of the method as the semester continues on, and that I will become confident in using it in my own classroom.

New Insights and their Implications

These past couple of weeks I have been thinking a lot about how I am going to teach math in my own classroom. This has never been something that I have worried or even really thought about because I have always been fairly good at math. However, I have become fairly concerned about being able to teach math in a way that will get students to think about math on a deeper level rather than me showing the students how do something and then they just practice what I showed them. This new insight implicates to me that I am going to have to look at math in a deeper way myself. I think that this class has shown me that there are several ways to express and teach math on a deeper level. However, I do feel that once I do get out into the classroom that I am going to have to continuously be conscious of how I am teaching math and if my students are really learning the concept of a problem or if they are just learning how to do the problem. I may struggle with making sure my students are always learning on a deeper level, mostly because I was never taught to see math on a deeper level, but I think that if I constantly think about how I am teaching a math concept and constantly ask myself "what are the students learning," then I think over time I will be able to consistently teach math on a deeper level.

New Insights and Their Implications

Throughout these past couple of months I have found a new appreciation for teaching elementary math. I have never experienced a teaching style such as reform based math, until Dr. Reins. I learned that students have to use their higher order thinking skills to solve problems, which comes a lot easier when using manipulatives, such as the ones we've used in class. I've also learned it is more difficult from the teacher's perspective of planning, I feel this is the reason so many teachers use the traditional style of teaching (worksheets, handouts, etc) because it is so much easier. However, this is also why our students aren't meeting national standards. When doing the LPU I learned that I want to teach according to the reform based math strategies, I want my students to have to think and solve the problem themselves, instead of knowing they can get the answer from me. This style of teaching is somewhat frightening and difficult, but I want to learn more about it so my future students and myself can benefit.

New Insights and Their Implications

Throughout these past couple of months that I've been in this class, I have experienced math in a way that I would have never thought of before. I have learned that math should not be so procedural in that a teacher gives the student a formula and tells the student to plug in the numbers because he/she said so. Math should be about students finding those procedures out for themselves and learning why they need to be used. I have learned that my understanding of math is definitely instrumental instead of relational. I have always been showed how to do a problem, then been told to complete different problems like the one shown on my own. I never knew the relational understanding or the what to do and why's of math. By teaching students why they are using a certain formula or why they are going about a problem in a certain way, the student can obtain a better grasp of a mathematical concept. I have learned that we must teach in a way that the student can learn cognitively. We must first start with what the student already knows and build upon that. I think the LPUs are a great way for us to try and begin teaching in the way that we have recently been learning about. Although it may be difficult for us at first, I understand why it is important that we learn how to teach our future students in a way that they will have a relational understanding of mathematics.

New Insights and Their Implications

I think the biggest learning experience in this class so far was the LPU. It made me realize just how effective project based learning is. Its easy for a teacher to have a student memorize a formula, plug the numbers in and solve it. From this experience I learned how much more effective teaching can be if hands-on manipulative's are used and if you let students discover answers on their own, compared to just telling them answers. However, it did make me realize just how hard it is to teach from this perspective. No teacher I have had up until this point has ever taught like this. It is definitely a learning experience. I am looking forward to learning more about this new way of teaching.

New Insights and Their Implications

After six weeks of this class, I have been shown a much different perspective of learning math than I ever have before. I have always learned by a certain route or formula to use for finding the answer to something. I was only shown a small glimpse as to why it was done that way, only shown how to do something. This class has really felt like I am back in elementary. The way in which project based learning works really challenges my traditional thoughts. I feel as if I am relearning all of the material over again. However, I am actually seeing why some formulas are used the way they are in math. The implications I have learned is that it is much more beneficial to the students to see the the why in a math problem before they learn the how. Otherwise, they are just doing something just do it without an idea of why.

New Insights and their Implications

I think that the LPU's have been a very productive part of this class for me. They have shown me that there are many different approaches to teaching mathematics and they also show me how parts of math are learned through the eyes of a child. I have also learned much from the readings and my instructor about all of the ways you can approach teaching mathematics. The readings fit our class lectures very well and serve as a great supplement to the course.

New Insights and Their Complications

Since the last blog, I have learned many different insights through my classmates LPU's. They have showed me the importance of doing project based learning in lessons, and the struggles and complications that go along with them.

My classmates have all done a great job with their LPU's and have set the standard on how a project based learning lesson should go. I have learned that allowing the students to do a project with prior knowledge that they do have engages their mind and makes them think about previous ideas they have learned about. Once the previous knowledge is brought to their attention, adding a new idea with a project allows the student the chance to figure out the problems themselves. I have also learned to allow the students to answer their own questions and to figure ideas out for themselves otherwise they will always depend on you to help them.

Doing project based learning lessons has also shown me there are many complications that go along with it too. It takes along time to be comfortable with the teaching style of project based learning and it won't be an easy task. It is important to start a lesson a week or more prior to when you want to do it. That way you can think about the background ideas and a specific project and outcome you want the students to have. It is also important to remember that teaching in a new style will be a complication at first, but the more you do it the more comfortable you will become with it.

New Insights and Their Implications

This class has been very instrumental to me helping me better understand the teaching methods of K-8 students. I believe the main understanding I have so far is the tools required to instruct a math centered class. I have found out that there are many different approaches to incorporate into the teaching process. Once these approaches are taught, students then will have the ability to use the skills, knowledge, and the learning resources to understand the concept taught. I believe the primary goal of this course is to prepare us future educators to be effective and engage news ways to instruct. I believe teaching math to elementary students is significant for establishing a firm foundation for success. Making it fun and interesting will help us as the students progresses to the upper grade levels. Understanding it early is so important so there isn't a struggle as they approach high school.

In addition, I have learned that putting students in situations which they have to apply what they are learning to personal experiences and situations helps to reinforce the concepts of math and gives them a much better understanding of this subject. I struggled in math in my elementary years as well as high school and with these new concepts I am learning, I am confident that I can teach my students effective learning techniques.

New Insights and Their Implications

After completing the LPU unit I realized how much time it can take to prepare information that you are not comfortable with. I realized that you need to plan and prepare in advance and give yourself plenty of time. It is best to start at least two weeks prior to your presentation date. I found it very interesting to see how different my peers and I grasp concepts about different topics in math. Some people definitely have a knack for math and others struggle at it like me. It is great to be presented with new techniques that can help a person come to solve a problem. I really enjoyed the lesson from the group I was in on fractions and using the table method. I found the table method to be something so simple that I never would have thought to use it. I feel that the table method will be very helpful to my peers and me when we are teaching our own students. I also enjoyed using the fraction bars but was not completely comfortable in using them because I had never used anything like them before. I learned that you can over think things and need to open up your mind to think about new ways of doing things, there may always be other ways to come about a solution. This is a method that we as college students should have been learning since the second year of college. By learning this method we are better able to help our students understand, enjoy, and build on math. Students should begin learning this method in preschool and should continue while they are pursuing their education. I think that this method of teaching is great and is one that we as students should have learned in school and I look forward to taking the practices from this class into my classroom.

New Insights and Their Implications

After another month of class; I feel like I have learned so much more from my peers, teacher and readings. I have watched my peers construct their own lesson plans that use the new method of teaching math that we have been learning about. By observing these lessons, I have learned that this kind of teaching is not always going to be easy for us as teachers to come up with, but it is what our future elementary students deserve and what is best for them. I really enjoyed the lessons on fractions. Before this I did not know how to teach fractions, but from the lessons, I got all kinds of ideas running through my mind.
During this course, I have learned a lot about myself as a teacher. I have learned that I am going to have all kinds of students that are all going to learn in different ways. With that being said, I have learned that I am going to have to be prepared to teach topics many different ways so I can help each of my students get a good grip on math. I really like that students can use hands-on activities to get a better understanding, I don't remember ever using hands-on activities for math. I'm really glad that I am getting a chance to make all of these discoveries in this class.

Summary and Synthesis

In class, we have continued to learn about the different approaches students can take to understand problems. The instructor has continued to push us to teach in a new way that does not just involve giving students a formula and telling them how to use it. We have learned not to just tell students how to solve a problem, but to allow them to explore and maybe find their own solutions. I find it very difficult at different times to learn this way and I think that most of the class would agree with me. Some of my classmates have given lessons to the rest of the class using the method of teaching that we are learning about. I have learned a lot from seeing how they taught and approached the lesson. It has made me think about how I am going to teach my lessons when I am a teacher. Sometimes in class, I find it difficult to understand concepts because they are new to me and I was taught and learned the concepts in a completely different way. In class, we have been challenged to understand why we do certain steps to figure out math problems and to not just know what to do. I am starting to understand why I do something, instead of just knowing what steps to take to arrive at an answer. Students can understand more of what they are doing if they learn it by trying different methods and not just following the teacher's steps or solutions.

Questions and Answers

Over the last month and a half, I have really started to consider how I am going to incorporate what i am learning in this class to my future classroom. Prior to taking this class, I didn't really have any anxiety about teaching math because it is a subject I have always loved and understood very well. I am now questioning how well I understand math. As the instructor continues to ask us questions, I continue to question how I am going to take the necessary steps to make sure that I incorporate this way of teaching into my classroom. As the instructor talks, the first question that comes to my mind is how am I going to have time to incorporate this way of teaching into my classroom? I am beginning to understand why I must teach this way, but with the pressures of teaching the material students need to know to perform well on standardized tests, how can I justify to everyone the need for teaching students so that they fully understand the material? I understand, but parents and administrators that have not had the opportunity to take this class may not agree with or understand my reasoning. This presents me with a huge problem. Working with parents can be extremely intimidating, so I feel it is very important that I do the research to make sure that I am prepared to answer all the questions that parents may ask me. I also feel that in order to be an effective teacher, I will need to put the time and effort into making sure that I know this material and can effectively help all my students to learn and understand the material.
As a future educator, I know the importance of making proper lesson plans and doing my "homework" to make sure that I understand the material I am going to expect my students to learn. My first few years of teaching this way may be very difficult, but by knowing that my students deserve to understand this material, I will strive to teach this material effectively, even if not every person understands why I just can't teach formulas to my students without them fully understanding what that formula represents. This method may take a little longer than just writing a formula on the board and giving students a worksheet with twenty questions on it that use that formula, but my students will greatly benefit from actually understanding each formula and why they use it to figure a specific thing out.

New Insights and Their Implications

When preparing for our LPU, I struggled to break away from the traditional approaches of teaching. Because this approach is all I have ever known, I found it hard to switch my thinking towards teaching through problem solving. This new approach of teaching takes time and practice, which has become widely apparent after our LPU presentation and after watching other groups present their material. It becomes hard to teach material to others that you are uncomfortable with yourself. After presenting our material, I realized just how important problem based approaches are. Instead of providing the steps or formulas for solving problems, it is important to provide students with the skills to find their own approaches to solving problems. Although I think this approach of teaching is important, I also think that it is important to introduce small portions of this approach with traditional approaches so students do not get overwhelmed. This approach takes time and if students are introduced to it all at one, they may get discouraged and not put forth necessary effort because of that discouragement. Once students feel more comfortable with this approach, I think they will have a better outlook on math. This is exactly what has happened to me over the last couple of weeks. I have always
struggled to understand math and this course is no exception. However, after preparing for our LPU and learning different approaches towards solving problems, I am now starting to make sense of everything. I am starting to grasp what is being taught and I feel more positive about teaching with this approach.

New Insights and Their Implications

I have learned alot from my peers, instructor, and the readings. This class has opened new doors to me in the ways of teaching math and how students learn from different approaches. It is important to let students discover a new formula on their own, instead of giving them the formula, telling them what to fill in, and saying "this is how it is done." I was taught that way and I have learned that it is definitely hard to break that habit and learn in a new way. My peers, instructor, and the readings have shown me that there is more than one way that we can teach students mathematics and every student learns differently. My peers have taught me about the different ways to learn through the LPU's. They have given us some great hands-on materials and activities that can help us learn different concepts in math.

This class has taught me a lot about myself as a learner. I have kind of always thought of myself as a hands-on learner, but I never thought this way of learning could work in math. I was just so used to the teacher giving me a formula and telling me what to do with it. This class has shown me new ways that I can teach math that is more meaningful and beneficial to my students. Some students might benefit from getting the answer right away, but others will benefit from understanding the steps and processes that it takes to arrive at the answer.

New Insights and Their Implications

I have learned a lot about elementary school students from my peers, instructor, and the readings.  This class has given me such a big insight into other ways of teaching and how many students learn from different approaches besides getting the formula and practicing the formula.  It has taught me so much about how giving the formulas, working on the formulas, and giving the answers is not always the way to do the problem, althought that might be how I was taught.   I have learned about the fact that there are many ways that we can teach students and some students learn differently than others.  My peers have taught me about the many ways that students can learn through the many methods that they use in their LPUs.  The readings showed me the many ways and methods that teachers can use to teach elementary students.


This class has taught me a lot about myself.  I never thought of myself as an "instructional based" learner.  I have always thought that this is the way that everyone learns and there is no other method to teaching.  By going through this class, I have found out that there will be other ways that I can teach and it is not just the cut and dry way of teaching.  Their implications to teaching and learning mathematics are that students have different ways of thinking.  For one student, a paper and pencil test might be the best way for them to learn but other students might be better with a more complex way of thinking that does not give them the answer right away.

New Insights and Their Implications

This math course is definitely much different than any other math class I have ever taken. I am learning new perspectives on math concepts that I was once very confident that I understood. When we do example problems in class or go over homework problems I am surprised to see strategies that I never considered from my peers. It is surprising because I always thought everyone basically thought through problems the same way and took very similar routes to achieving those results. My previous belief has certainly been disproven. It is important to work with partners and in groups because it encourages students to share ideas and learn new methods for solving problems. Other math classes I have been in, both high school and college, were focused on individual work and involved little or no group work. However, there would not have been much reason for group work because all we would have done is take turns plugging numbers into a formula. Not a lot of higher thinking or reasoning involved.

Before the first day of Math Methods I was pretty sure that the class was going to be a hybrid of Math Concepts I and II with the addition of students teaching lessons. Clearly, I was mistaken. The instructor is introducing mathematical concepts that I know how to solve and then poses questions about these concepts that are foreign to me. This causes me to, basically, relearn these math concepts in a way that I actually understand the “why” questions of solving a problem. For example: why do we use pie to find the area of a circle or why do we flip the second fraction and multiply while dividing fractions? These are items that I have to reevaluate in order to ensure that my students, and me, know why they are solving a problem the way that they are. I do not want to teach students just to plug numbers into a formula without understanding how the formula was derived. I am developing a much deeper understanding for geometry and fractions and I hope to be able to pass my knowledge on to my future students through this new method of math teaching.

Personal Concerns and Next Steps

The thing that I am most concerned about is how to do I switch the way I was taught how to do math; to how should I teach it? In all my math classes the teachers have always been there and helped me out if I was struggling. I know that everybody went through this same experience. I think I can speak for a lot of my peers. That this is going to be very hard to adapt to this new way. There are many times that I am frustrated with the material. Or when I am trying to figure out the homework and I just don’t get it. When you have been doing it in a certain way for so many years, it is hard to change your thinking and try a new approach. But, how can I make this switch? Not missing class, paying attention to the lecture notes, readings, and projects. This is very important that I understand how to teach in this way for my students. I don’t want to fall back on what my old teachers did. I want to learn this new way of teaching, it’s just going to be a struggle at times.

New Insights

After preparing, creating, and presenting my LPU lesson, I have discovered that teaching using the new reform based mathematics is VERY difficult. It is really hard to pose questions for students, without helping them along the way. It is in my nature to want to guide the students as they create their own understanding, instead of letting them struggle and find their own answers. During the preparation of the the LPU, it seemed really easy to teach in the new way, but when it came to actually teaching it to the class, it was very difficult.

My LPU was about introducing the concept of fractions. It is hard to introduce a concept to students who have no previous background, and get them to form their own connections, and create their own understanding. It was definitely a challenge, to say the least. However, all students have a background about fractions, they just don't know it, until it is presented in a way in which they can form their own connections. All students understanding the concept of a whole, and that there are parts to each whole. They just may not understand that a part of a whole is called a fraction.

If I were to redo the lesson plan, there are a few things that I would change in the presentation aspect of it. I still believe that my prep-work is sufficient, it was just a lot harder to present it than I had original thought. Reform based mathematics is still a new concept to me, but at least now I can say that I've done it and could do it again.

New Sights and Their Implications

So far in this course, I have learned a lot from not only the instructor, but also my peers. Each class period that there is a new group presenting, allows for one more time to see a different perspective on how to attack one of the many themes in mathematics. I have learned from my peers, how to show students to work through a problem without ever really thinking about the fact that they are doing math. The more times a teacher allows for his or her students to work in groups discovering a solution to a problem, the more success students will experience in learning taking place. On top of that, teachers need to always make sure to have different tools for the students to work with so they are receiving the hands on activities that are pertinent to learning. The more you, as a teacher, can deviate away from the fact that you are doing math work in the classroom during math, the better the outcome of learning is for the students. As a teacher, you do not need to always tell your students what they have to do in an activity or what knowledge they will gain from the activity, instead let the students explore and discover for themselves what knowledge they have gained from them partaking in the activity assigned.

The instructor has taught me all of those things mentioned above and more. If you want your students to gain the knowledge that you want them to; engage them in their prior knowledge. Teachers need to help students realize that they are familiar with the information presented to them; they just need to go back and retrieve that prior knowledge. Another important characteristic to teaching math that I have learned from my instructor is to always allow more room for work. If a student does not understand the material, make the material due a certain day, go over the material in class, and then collect the assignment the following day. If students are stuck and don’t know what to do after seeing the results to their solutions, allow them to come in and spend more time working with you on their homework; teachers need to always have a open door policy when it comes to their students.

Throughout this course I have learned a lot about myself not only as a learner, but as a future teacher. As a learner, I have learned that I do not learn well when teachers tell me instructions of how to complete a task, rather than write the directions on the board. I need those instructions in front of me in order for me to get the most out of my learning. Due to this discovery, I have decided as a teacher to always have my directions written out so my students are not confused about what is asked of them. I have also learned about myself as a learner that I need to have materials and tools in front of me while I learn to help me discover for myself the answer to the problem. As a teacher I have discovered that having tools that students can physically move/touch for themselves, with help them discover the answer at a far better pace rather than just working with paper and a pencil. One final thing that I have learned so far as a learner, is that I work best in small groups. If I am in large group learning, I feel like I am not getting as much out of the instruction because the group is so large. When groups are smaller it is easier to put your two cents in and also collaborate with your peers. As a teacher, I will allow for a substantial amount of time for students’ to work on problems and also collaborate with peers. It is my belief that it is better to work with others because then you can see the thought processes that they went through to come to the solution; it gives you more perspectives on how to solve a problem!