Summary and Synthesis

Eled 330 has had helped me to see a whole new perspective on the way to teach math. I didn’t think that it was wrong, nor did I necessarily think it was right, to teach math right out of the book; I am not sure of how I thought was the perfect way to teach math. Being in class over the last few Tuesdays and Thursdays, has brought some insight to me on how to teach math in the correct manner. I, as well of many of my classmates, grew up learning math right out of the book, rarely doing any activities that were not located in the book. If a student did not understand the math problem, then the class continued with math and the student could receive more assistance from the teacher at a later time; there were not multiple entry points for the diverse learners in the classroom. I never remember math dealing with a lot of problem solving either, more memorization than anything else. Now on the other hand, the correct way to teach math is to involve deeper level thinking that engages students, allows students to relate to the math problems brought to their attention, and has several different entry points for the diverse group of learners in the classroom. Students need to use a variety of strategies to come to a solution and the students should also be able to converse with his or her peers about the problem so they can see how their peers approached the same problem in a different way. The teacher should also not give the students the solution to a problem right away rather give the students time to work alone on the math problem, and then allow them to convene with neighbors. The correct way to teach math, that was just previously described, will take deeper level thinking from the teacher than I thought. Math has always been the easiest subject for me in school and I have always enjoyed it thoroughly, but recently in Eled 330 I have become frustrated because I am not used to the deeper level thinking that we are doing; I am upset that I was unprepared for this due to previous schooling. My hope is that if my students were to take this course, they would not get as frustrated as I did working on some of the math problems because I will have prepared them enough for different math problems that are thrown at them.

Summary and Synthesis

Over the past several classes, I have learned numerous things about teaching math. Before, I thought math was just taught by the traditional "here is a problem, here is how you solve it, now you do it on your own," type of way. Now I know that if I want to teach math in such a way that my students will benefit from it, I have to teach them different strategies to approach mathematics. The strategies that were taught in class were somewhat new to me. I have heard and used some of them when I was in high school math class. I had a teacher that was very great at helping students learn new strategies on how to solve a problem, but not necessarily give them the answers or routes in which they should take. Math takes skill and strategies and in order for students to understand mathematics completely, we, as teachers, have to help them get there. We have to help them develop the skills so that they can find a strategy that works for them. That doesn't mean that we give them the strategy to use, it means that we guide them in the right direction. We teach them the problem solving process which is to first understand the problem completely, then to devise a plan to solve the problem, next, carry out the plan you chose, and lastly, take a look back at the strategy used and the route taken to get the answer. Teaching students valuable strategies and skills will help them to be better at math, it will show them the importance on figuring out situations and problems without having someone to hold their hand.

Summary & Synthesis

During the past few weeks of class, I have come to realize that I need take a step back and re-evaluate how I am going to teach math within my future classroom. All I have ever known about ways to teach math is what I observed in elementary school and high school. The same approaches were used class after class and year after year: the teacher provides step-by-step examples and then assisgns an abundance of similar problems for students to practice. However, after the short time spent in this course, I now understand the importance of teaching students how to problem solve rather than just practice the steps that were shown to them. By doing so, students are able to make their own interpretations and use their own approaches and background knowledge when solving problems. As we discussed in class, when teaching problem solving skills, we, as teachers, need to have several goals in mind: we need to help students recognize when various strategies are appropriate and when to use them, and we need to help students become capable of inventing their own strategies and adapting existing strategies. In simplest terms, this means that we need to provide students with the skills they need to come up with their own ways to solve problems rather than telling them how they 'should' be solving the problems.

Summary and Synthesis

These first few weeks of class have made me look at the way I am going to teach math through a different viewpoint. I have learned that when teaching students how to problem solve teachers must almost take a step back and let the students teach themselves and each other. What I mean by this is that a teachers first inclination when teaching math is to show the students how to do a problem step by step and then have the students practice the skill taught. Instead what we as teachers need to do is to allow students to come up with their own ways to solve problems. By doing this students will be able to problem solve on their own without having to rely on a teacher on how they should solve problems. Also, when teaching problem solving, a teacher must allow students to discuss the routes that they took to solve the problem. Allowing students to discuss their routes with the rest of their classmates will show students that there isn't always just one way to solve a problem. I had never thought about allowing students to come up with their own way to solve a problem. I think that this is because as I went through primary and secondary schooling my teachers always used the method of showing me how to solve problems and then requiring me to practice those taught skills. However, from the class discussions these past few weeks it makes a lot more sense to me now to allow students to teach themselves different problem solving skills instead of repeating my problem solving skills.

Blog #3 Summary and synthesis

At this point of the year near the end of classes i have looked back over what we have done in class and what i am able to take away from the class and apply into my own future classroom. I believe the biggest piece of information i have gained and will use is not to teach students the regular procedural knowledge they are use to getting. Instead i want to do activities that lead them in the direction that the proceedural steps were developed to do. The students will then be able to see where the "steps" came from and why we do them and why the work. To me this offers kids the chance to understand math instead of just being able to do the tricks they have been taught. Even though i dont plan on teaching math i think this lesson is applicable to a lot of different subjects that i do plan on teaching.

Math LPU

Ali and I taught our LPU a few weeks ago and it was a very good experience. Ali and I prepared for a long time when putting this lesson together. We struggled with the overall concept and trying to figure out a way to teach it to the class. Once we figured out how to solve the problem using our method we were able to continue on with the actual lesson. Teaching in front of the class was completely different than we expected. Since we struggled with the concept as much as we did, we thought for sure that everyone else in the class would struggle but they did not. This made for teaching the lesson less diffcult than what we thought and had prepared for. If I were to teach the lesson again, I would make sure that I had many more challenging examples for the class.

Blog 3

Personal Concerns and Next Steps:

Teaching our LPU for the class was a huge eye opener. Brooke and I prepared for a long time to teach the lesson, practiced for multiple groups of people, and had a rough outline of what exactly we were going to do. However, standing in front of the class was a totally different story. Our presentation did not go exactly how we planned, but it was enough for us to understand exactly what reform based teaching is all about. Since I am not used to it, I felt awkward standing in front of the classroom waiting for my classmates to come up with solutions and answer my questions. It is definitely a different feel that takes lots of practice, experience, and time to master. I think more time to practice this type of teaching would be beneficial, but now I know what all goes into planning and preparing this type of lesson. I think I will practice designing curriculum using a majority of this type of teaching because it is obviously beneficial and in the long run, it saves a lot of time for students and leaves extra time to learn more and in depth material.

Blog 3

Summary and Synthesis

Since the previous blog and even throughout this entire course, I believe that I have learned a lot of valuable information. I also feel that I will be able to take what I am learning to help me to be a better math educator. I feel that I have seen approaches that I would have never been aware of without this class. The day that sticks out the most to me is the day that we watched the videos on Cognitively Guided Instruction. I used to view math to be so constructed and there is only specific ways to solving a problem. I loved how each of the videos showed how the students came up with their own solutions to problems. By allowing for students to solve problems in their own way gives them the opportunity to open their minds and use their own steps in solving. I also like how they showed the way they got to their answers. Everything was very visual and hands on and it also can help other students who are struggling so that maybe they can see a way that another student did something and they too will understand in that way. After seeing and learning about CGI I know that I will definitely be using it in my classroom and I know now how much it allows for children to grow in the understanding of mathematics.

Blog 3

I'm really glad that we're moving to talking about diverse learners, because like what was mentioned in class, our lesson plans have had "phony" modifications. We simply just make them up, and don't even know for sure whether it would actually work for a student in this situation. Even if we did find a modification for a child with a specific learning disability, it doesn't necessarily work for another child who might have the exact same disability. I'm really glad that between these two math classes we don't have to write a lot of lessons, we just develop a deeper understanding about how to do so. I really think that it is important to develop this way of thinking, because then we automatically start to think about these concepts on a deeper level.
I also think it's important to realize how we learn, visually, with manipulative, or whatever it may be, and also acknowledge all the other learning styles as well. This way, when we are formulating the concepts into lesson, and thinking about how we are teaching, we look at how everyone learns in the classroom, and not just a specific group.
When I reflect on this class, I realize how my thinking about mathematical concepts has changed, and I wonder why I never thought this way before. Why didn't my elementary teachers teach me this way? It makes more sense, and there is better understanding when kids learn this way. I really have a positive outlook on math, and if I were offered a job teaching math, I honestly would not hesitate to take it.

Summarize

I think that because the Elementary Classroom is becoming way more diverse than it has been in the past it is absolutely essential for Math teachers to use a method of teaching that will allow every single student the opportunity and support they need to learn math along with every other subject they are learning in school. I think that the content in this class, although at time frustrating, is worth learning and will be very beneficial in each of our future classrooms. I think that it is absolutely important that every single student feels like they can learn in their classroom. When students feel like they are given opportunities to learn and feel comfortable with the support they are given they will succeed not only in the classroom but also in other areas of their lives.

Summarize

It is very important to discuss the concept of teaching diverse learners because this population is increasing in our schools. Students are now being diagnosed more often than before with ADD, ADHD, etc. and these are the types of students that we will have to make modifications and implications in our lesson plans for so all students can be successful in the setting we provide. When i was in school i cannot recall any situations where my teachers made implications for other students in the classroom and i think that is why so many students were falling behind. If students are well trained on how to make implications to their lesson plans it will be beneficial for not only the students but the teachers as well. Personally, if i would of had teachers that would have meet my needs better i think i would have a better feeling about my education, in elementary school i was the girl that never wanted to go to school. It got so bad that my counselor had to come to my house and pick me up for school because i had no motivation to get up and go. I think if my teachers would have helped me more and would have made modifications, i could have understanded the material being taught and i wouldnt have had such negative feelings towards school. I know that as a teacher i will be accomodating to all students needs, it may be difficult but there are tools, professional development opportunities, and other teachers that can help you learn how to meet all students needs. Overall i enjoyed talking about this topic, i just wish we would get more opportunities to see students with problems/issues/ and struggles in the classroom so we would know how to implement all of the modifications we add to our lesson plans.

Blog 3

Now that we are moving into the topic of Diverse Learners, I am starting to see how CGI is a tool for reaching all learners. Similar to the fact that some students do not benefit to an inclusive environment, some students will still not benefit from the CGI method. However, it is a great way to provide students with access to multiple ways of approaching a problem and the opportunity to get insight into the student's thinking process for solving the problem. When working with Diverse Learners it is important to remember that they shouldn't be regarded in any different way than other students in your classroom. All students deserve your respect and 100% of your effort towards helping them achieve academic goals. It is also important to note that you should be working towards helping students achieve the same goals as other students with accommodations, rather than giving them simplified goals or modifications.

Blog 2 Summarize

After working with reformed based mathematics for a couple of weeks i am starting to get the hang of it and i am starting to feel like i critically think about math more than i did before. Previously to some of these classes i knew math problems and some of the basic reasons why they work but for the most part i never really cared to take a deeper look and really ask why it works. Writing the formulas for area of different shapes was interesting because we were able to look at a shape, define its constant properties, and from those properties devise a formula to find its area. From this deeper understanding of the material i now know why the formula is the way it is. I had a teacher in high school do the same thing with the quadratic formula by starting with a generic problem it would be used for and taking it step by step to reach the formula itself. All of these steps can be used to deepen the students understanding of why the math is the way it is.

Blog #1 Insight/Implacation

In the first couple of weeks in this class i have already started to view math education in a different way. I think having students develop and struggle with the concepts they are learning before just giving them the formulas that go along with them is a great idea. Students will learn faster and retain more knowledge if they have a deeper understanding of the material they are covering than compared to being given the formulas and told to use them because they work. Even though i don't plan on teaching math this idea can be translated into any other subject that i can teach. As a good teacher i have to make sure the students make the material their own and fully understand it instead of just memorizing, regurgitating, and forgeting it.

Blog 2

Going into this class i definitely had my worries and issues with Math and teaching Math. I always thought that I am horrible at Math so how the heck am I going to teach Math. After being in this class for the past two months I have gained a better understanding of reformed based teaching so that I can teach more effectively and efficiently. I think that I am starting to understand what it means to actually teach math rather than just teaching operations and formulas. I think that I have a better understanding of some math concepts since being in this class. I like the fact that we break things down into smaller parts so that we can understand each part before we work on the whole. It makes me feel like I really understand the content rather than just getting lucky or plugging numbers into formulas. And by really understanding it I will be able to better teach it in my future classroom.

Blog 2

Teaching reformed mathematics is legit. At first I was worried that my previous knowledge with formulas was going to get in the way of accommodating to this new approach but everyday I am getting a little more confident in understanding the materials. I now understand that learning mathematic formulas are only the tip of the iceburg; you must be able to experience the frustrations and attempts by trial and error individuals went through in order to achieve a formula. We went over some decent examples but I do agree with everyone else that we need more... and perhaps an opportunity to observe this style of instruction in a real classroom setting. Other then that my only concerns with teaching mathematics is the time it is going to take to develop a meaningful mathematics curriculum that is going to motivate the students on both intrinsic and extrinsic levels. This is going to have to be a collaborative effort among educators; exposing children at an early age so they can develop personal meaning and problem solving persistence with mathematics. This way we can defeat the number one statement with students in math class,
"I don't know how to do this."

Blog 2

While many aspects of this class are difficult because of the new and necessary way of thinking, I find it to be exciting all at the same time. It is refreshing to find myself in a classroom learning something I've never considered possible, yet seeing that it is not only possible, but incredibly vital. Professor Reins has driven his point home (in my mind) as to WHY classroom teachers need to present new knowledge to students in this way. The struggle I have up to this point is believing in myself, knowing that I struggle with this challenging subject, as well as believing that I am capable of teaching students in such a thorough and intellectual way. I will continue to do what I can in this class to successfully transform my thinking into that of a confident and prepared instructor - ready to change the way mathematics is presented. I believe in Reform Based Mathematics because I feel strongly that, had I been taught math in this way, I would be much more skilled, confident, and prepared to teach it to others.

Blog 2

So for in math concepts I have started to understand the importance of teaching mathematics through a different approach and I also understand the purpose of the material thus far. I do see the meaning and effectiveness of reformed-based teaching in mathematics, but I struggle with the application of this. Although we have observed this method and will have a chance to demonstrate with our own lessons I feel that we need more experiences seeing other teachers in the classroom setting apply this method to mathematics. The observing of Dr. Reins has helps me to see the importance of teaching the actual concept rather than teaching a formula with symbols and numbers that become more memorized than understood. But if I had one suggestion it would be more observation time in a mathematics classroom. I will say that at times the homework and class activities put me at a blank wall, where I just don’t know what to do. I feel that working with classmates on these assignments definitely helps and it is very beneficial because we learn from one another. I am excited and interested to see how the lessons go and can’t wait to prepare my own.

blog 2

Up to this point, I have found myself struggling to learn math with a new approach. I do see the meaning and effectiveness of the reform-based approach Dr. Reins has been using in class, however I find myself becoming frustrated quite frequently. I think it is extremely important that we are learning this new approach to teaching in order to make learning content, particularly math, important to our future students. In this math course I have learned new things about old concepts that I have been learning about throughout my education. Mainly, I have learned the focus and meaning behind many formulas, such as area. The part that becomes frustrating for me is learning a new method in a manner that becomes tedious, especially when I know the simple way to find the answer that is much shorter. I believe this frustration is from working backwards, had I been taught the meaning behind the formulas in the first place I feel this process would make much more sense to me know. With that being said, this helps me to see the importance of teaching the actual concept rather than teaching a formula with symbols and numbers that become more memorized than understood. Another frustration I have is not necessarily with this class, but with the education program at USD in general. I feel that I should have been taught how to teach this way from the beginning, rather than having this one class my senior year showing me this approach to teaching. I will try my hardest to teach this way in my classroom because I do see the importance, however I feel that other professors should be introducing this approach as well so that we, as future teachers, are more prepared and comfortable.

February Blog

I can understand all of the purposes of the material we have covered so far in this course. I just feel like now we need opportunities to apply what we have learned. I do wish we had more experiences where we obesrve a math classroom and see how these new methods of instruction that we are learnign about are being applied. The activities just seem frustating at times but that is only because I have never worked well with Geometry. However, I feel like these methods we learned in the past month make more sense to me than any of the 20-some formulas I have been taught in the past! I am interested to see how the lessons go an dhow difficult creating the lesson will be when the time comes closer. I agree with Ali R., more practice with this material is definately needed! If I had any suggestions, it would be to have more opportunities to observe and practice math instruction.

Blog #2

New Findings and New Implications

Throughout the semester, I've gone back and forth from completely struggling with some of the concepts to feeling confident in my math abilities. However, after getting acclimated to the CGI approach used in this class, I feel myself a little more confident with each passing day in class. Inititally, I was frustrated with the fact that I just didn't understand what was going on. However, it is very reassuring now that I understand the approach and am now beginning to think "outside the box". I also firmly believe in the use of manipulatives in teaching. Being a highly visual learner, myself, I find that the use of manipulatives is extremely beneficial in helping to bridge the gap for students. So, throughout the course of this class I've found that using a different approach to instruction and using manipulatives are two very successful ways for students to understand mathematical concepts. I look forward to what the rest of this class and semester has to offer.

New Insights and Implications

I am finally starting to see the importance of reform-based teaching. I realized that all of these concepts we are developing, I had no idea why they were in place before. I learned that in elementary school I just went through the motions to arrive at the right answer without even understanding why I did what I did. Now, I can hardly remember how to do any of that anyways. I think I still have a lot of practicing left to do before I could actually implement this into my classroom, but I do know now that this is a style I would prefer to teach. The critical thinking skills required for this course are the skills that I have always lacked. Being able to think critically in math would also lead to the ability to think this way in other subjects. I do hope that watching my classmates teach their LPU's to the class helps me feel more comfortable teaching this in my own future classroom.

Blog 2

I can honestly say that math was never a huge struggle when I was in grade school. There were always some weak spots of mine, but overall I usually did very well in math. However, most of my teachers were teaching it in the "traditional" I show you the problem and formula, then I do a worksheet. I have struggled through some of the activities in class because my prior knowledge has built a wall that is tough to get over. But, I have really come to like the word develop, and having students develop problems and ideas rather than giving worksheets with numerous problems. As I think about this, I wonder why all of us in the cohort had to sit through two semesters of Math Concepts and learn formulas, and do massive amounts of problems, and we cannot even remember them now, much less when we get into the classroom. I really like the way class is set up, and how it is developing our math skills and theories. I really hope to use this way of teaching in my future classroom. It will take time to develop, but it will eventually happen, and students will be much better critical thinkers too!

Blog # 2

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?

Since our last blog, I have become more confident in my ability to understand mathematical concepts. I have always felt that the pieces that make up mathematics are beyond my comprehension and too complex for my understanding. I have come to find that through class activities, I am actually enjoying finding out how easy it can be to understand where formulas come from and how in-depth looks at common math misconceptions can actually create a fuller understanding of the subject. I feel like I am learning how math works from the bottom up and not just what needs to be done to get the answer. Because of this new understanding, I feel that if I can understand what is going on I can teach it to someone else. I am slowly gaining the confidence to try new things in mathematical learning without the fear of having the wrong answer.

Blog 2

As we move through the semester I am finding that this class is getting easier. I have a better understanding of your expectations and what we need to gain out of this course. I have gain new knowledge about how formulas are made and how to solve problems without using the formula. It helps me when we use manipulative in class while we are working on examples. I believe that manipulative would help students better learn the concept of math if they were used more in the classroom. This class has me completely engaged and I look forward to learning more throughout the rest of the semester.

Blog 2

Personal Concerns and Next Steps

Math has always been a struggle for me. I have found myself very confused numerous times in class. Since math is something that I am not very good at, it is hard learning new strategies and thinking outside of the box and thinking differently from what I am used to. Although sometimes I feel very lost, I feel that I am slowly making progress in my math skills. I really like how many examples we do in class and the different ways we can find answers to things. This really helps me to understand the concepts we are learning because I can see through the examples how to do things. I also like how we are to develop our own formulas or problems. Although it is a challenge, it really gets me thinking. By doing examples in class and creating our own problems has allowed me to make progress and I hope we can continue to do these things in class because I feel like I have really benefited from it. I also feel like the past couple weeks I have started to catch on a little bit more and I hope to continue on this path.

Summary and Synthesis

Since my last blog, CGI is started to make more sense. In the beginning, activities we would do in class using the CGI approach would be very frustrating and I would have to struggle through them. Now that I am starting to understand the approach I can see how the activities are suppose to benefit the student and to see what they would see when completing the assignment. Since we already know the information that we are seeking to find in the activities, it can make it more frustrating. When students are approaching the activities with less prior knowledge though, you can see how the activities are building on their knowledge and helping them create the new concepts. While I still would not use CGI for all activities in the classroom, I understand more now that while it may be frustrating at first for the students, it is beneficial as well.

Personal Concerns and Questions

As the semester greatly speeds by, I cannot help but to notice the strength of enlightenment of this course. Growing up, mathematics was never my an academic advantage of mine. I found that efforts were greatly asserted to make the standard expectation. As I find myself taking Math Methods, it makes me feel very reassured that I can pursue a career and grow as an educator. If it was up to me, I would suggest that Math Methods was a course that was advised to be taken before the Math Concepts for Teachers courses. The reasoning is that those preliminary courses have a heavy emphasis on direct application much like every math class I have ever taken. Math Methods instills multiple strategies and perspectives that embraces the subject matter comprehension as opposed to presenting information and having students regurgitate the material. Other math classes can instill great anxiety merely because of the sensation of being left behind in understanding while the class moves on to the next topic. I believe that I would have succeeded immensely in college mathematics if I had taken this course before Math Concepts. I would like to see a shift in the school's advising so future students would not face the anxiety they felt in high school. Keep up the excellent work Professor Reins.

New Insights and their Implications

We have just been talking about factions and talking about how to bridge the gap between modeling manipulatives and use of regular assessments through instruction. I have clearly been able to understand when using correct manipulatives can help students “bridge the gap” of understanding a concept and applying the concept to homework assignments. Students that are able to see how and why we do this certain math problem like having a common denominator, have a clear understanding of the concept and will be able to retain the knowledge more. The use of manipulatives should be used religiously in a classroom for children to see a concept and correlate why we do this math concept this way. I also see where math manipulatives can be a hindrance in the classroom, like just having a manipulative for a time waster and not really relaying important concepts to the students building foundations for math concepts. I also really like the use of the pattern blocks as fraction pieces. I think students could really retain the knowledge a lot better when they can see and touch the fraction of the whole of an object.

Questions and Answers

Throughout this class i have definately realized the importance of teaching your students using the "new" method of teaching, but it does not seem that easy from a teachers perspective. So my question would be...How do we as teachers not allow ourselves to fall back into the "old" methods of teaching?
Some of the answers that i can come up with are...
- Think of the positive influence that you are having on your students. I can say that i have had horrible math teachers in my past and i think this is truly why i dislike this subject so much. So if you, as a teacher, think of the positives for your students it should help you not fall back to the old way of teaching.
- Do your preperation in advance so you are not rusing to finish your lesson before class. If you do not have your materials and instruction already planned it is more likely that you are going to fall back to the old method of teaching math.
-Learn to think outside of the box. You as a teacher, need to be improving your teaching everday and if you allow yourself to use the new method of teaching you will be learning something new along with the students everday.
- Always keep in mind that you are not the only one learning this new method of teaching. Those of us that are going to be joining the workforce probably have a few more experiences that are fresh in our minds because we have just graduated and we have just learned this new material. You can always use other teachers as a reference, if you feel that someone else is more knowledgable about this topic, dont be afraid to collaborate and learn from one another.

Overall I think I have learned a lot of information in the first part of this class, I definately do not want to fall back into the old way of teaching math because I am a first hand example of how the old method of teaching math did not work. I have never liked math simply because of how I was taught math.