Questions and Answers

One of the questions that I find myself repeatedly contemplating is the effectiveness of technology in the classroom, especially a math classroom. I am from a very small town with limited resources, and technology used by my math teachers was limited to graphing calculators. Therefore, it is sometimes difficult for me to see the relavance of incorporating technology into my future classroom. I feel that technology often complicates material that I learned simply through my high school textbook, class lecture, examples/discussion, and maybe the use of a calculator. However, I understand that students in high schools today are used to a much greater amount of technology in the classroom and their daily functions as a whole. Therefore I also understand how teaching the students with the resources that they use on a daily basis is important. I feel that for technology to be incorporated effectively into the classroom, rather than complicating the subject matter, teachers must be very well-educated on the technology themselves, they must plan for a certain amount of time for their students to become accustomed to the technology, and they must have very specifically defined learning targets regarding the intended outcome of using the technology. While teachers should be well prepared for all lessons and instruction, I feel that this preparation is particularly critical when the teachers are incorporating technology that is also new to them as the teacher. Further, I feel the best use for technology is in discovery and exploration. There are many lessons in which lecture and examples/discussion cannot be replaced. However, leading into such lessons with a technology component that allows the students to explore their own ideas and/or create personal conjectures regarding the material is an excellent way to bring technological advancements into the classroom.

New Insights and Their Implications

I have really enjoyed the technology presentations this semester. I particularly liked the mathematical explorer presentation. It was a completely new program to me which made me a little more interested in learning about it. It seemed very advanced in the mathematics that it could perform for you, but took awhile to type in all the information. I am sure that this is something that just come with time as you use it more and more. Watching the video on lesson study one was great. It allowed us to all see how the lesson worked out in the classroom. And it has become aware to me that you could have created a perfect lesson and still would of had a hard time teaching it on that day. All the distractions with halloween made it hard to reflect on how well the intruction was prepared. I am hoping to make some better conclusions from lesson study number two and number three. Hopefully it will be easier to observe the students perspective and their grasp on the material.

Summary and Implications

I am in Lesson Study Two and in the third Technology presentation so I am feeling a little overwhelmed with the material now. I did not realize all the members of the lesson study group had to go through to prepare the lesson study lesson. I have a lot of respect for Group One's members because I am seeing how much time it is already going to take. I realize that both projects are coming up fast and it just shows that as a person who is preparing to be a teacher there is going to be times you are going to feel overwhelmed and not sure if you can get everything done or not. I know that this is good practice for when we get out to teach and will help us be more prepared so I am glad that we are doing both of these projects. It was exciting to see the girl I tutor that attends Elk Point-Jefferson pull on Geometry Sketchpad that her teacher had taught them a lesson on it today. It was a little sad that she was not exactly sure how to do it and that she could not explain to me how to do it, but I was excited to see a teacher using it and knowing what it is from class. I also think that watching the video and analyzing things will be greatly beneficial. I also feel like the more exposure we can get to a classroom will lessen the nerves once we become teachers. I do not think that the nerves will ever not be there, but I believe that it will help. I feel like the lesson study and technology presentation will be helpful as I continue my training. I also have realized that sometimes you have to be extremely flexible when you are a teacher. So, I feel like I am getting valuable knowledge from this class.

New Insights and Their Implications

In the creation of Lesson Study 1 a lot of time and thought went into the format of this lesson. At first, this long drawn out procedure was an experience that was hard to see the outcome and hard to see if it could even be used later on in our profession as a teacher. Once we actually presented our lesson to the classroom we saw an outcome that wasn't quite expected and definately a learning experience. We had many expectations coming into the lesson from the students and that could have been where we made a mistake. If we were to think of every aspect of each student in creating this lesson we maybe could have seen different reactions to it. Also, once we have our first year teaching job, we are going to be making many lesson plans from scratch. Yeah, we may not be able to have a group of people collaborating to put a lesson together, but after one teaches the lesson for the first time one can reflect on how it went and note changes that could happen to better the lesson. After years of doing this many well thought out lessons will be filed and for the different types of classes one has there will be at this point different options for lessons on that particular subject. So, out of this experience reflection after a lesson is taught and observed how students take in the lesson will be incorporated in my career as a teacher.

Summary and Synthesis

Lately, we have been discussing a lot about lesson study one. I really believe it was a success. I was able to think about the lesson and teaching methods in alternative ways. There were aspects I would have never thought about it if I was going to create this lesson myself. I was given the aspect of analyzing student questions and teacher questions. I did not realize how many questions are asked within a single lesson. Our group has been working hard on our technology presentation. I have also been researching for lesson study 2 and 3. Overall, the duscussions we have been having about lesson studies have benefited me the most lately. I have been able to take different view points on how to design lessons. Therefore, this class has improved my teaching methods and strategies

Personal Conerns and Next Steps

Through out this course, I have been concerned with the work load and expectations. Thankfully, I have managed to help my group with the lesson study and my technology group prepare for the Fathom presentation. Now my concerns are focused on the last question and the other lesson studies. I guess I feel that the next two lesson studies are at a disadvantage due to the fact that time is limited and our resourses are spread between many other courses. However, while these limitations will make it more difficult, however, the values of these were well worth the effort. This leaves me with the hope that the other groups will recieve the same opportunities.

New Insights and Their Implications

After observing and watching the video of the first groups lesson plan, I am more aware of how students might view lessons and how reviewing a lesson on video would help with future lessons. Being able to be in the classroom observing how students worked with the technology was my job for the lesson study. I was able to see how the students were responding to the lesson also. I was particularly interested in how the students would did not seem to be forth coming with answers to questions that Brittany would ask. I think that in most cases students will be hesitant to answer questions in a situation where it is new to them or if somebody that they are not used to teaches them. The students for the most part were actively engaged through out the lesson, however they did not seem to have the confidence or as stated earlier were just shy about the situation. Reviewing the video of the lesson is also something that I think is very important. You can reflect on your teaching after you give a lesson but if you watch the video of your lesson you can point out specific examples and ideas you might fix or improve on for next time. I think that lesson study is an effective way of improving your lessons and teaching.

New Insights and Their Implications

Watching the first lesson study group really gave me insight into the real classroom. It was different to watch the classroom from that angle and really investigate the behaviors of the students. I have done both my paraprofessional and internships, and taught lessons during each other experiences. However, while teaching those lessons, I never really had the opportunity to see how the students reacted to me as a teacher and to each other. Observation of the classroom teacher is something that I have done for both experiences, however being a new teacher really changes the way that the students interact in the classroom. It was a great lesson study and was very well planned. Execution for the group was difficult but they had a great deal of challenges stacked against them given the time that the lesson was given. Regardless, I walked away from that experience with a better understanding of the classroom setting then I had ever had, and gained insight into how my lesson study group should approach teaching our lesson.

New Insights and Their Implications

From the first lesson presented at the high school, I learned that student participation is not always very good. I thought that the group presented a lot of interesting and engaging questions and information, but sometimes the class did not respond with the enthusiasm that I expected (and was hoping to see). This makes teaching more difficult because it is essential to plan for a motivation that does not get the anticipated results. I have also learned, particularly from the Fathom presentation, that the classroom experience is continually changing. It seems it has changed more from when I went to high school to the present than between my parents' days in high school and my days there. I understand that I am biased and that this statement is arguable. This seems to have happened because of all the technology. I was a big fan of writing on the white (and even chalk) boards. However, as in my observation of the lesson study at the high school, I know that I have to account for different learning styles and try to get students engaged in learning. Therefore, the new technology may be my opportunity to do so. I have encountered many effective teachers, and I hope to teach using a blend of the best methods and styles that they have collectively used.

Summary and Synthesis

Lesson Study 1 was an eye opening and beneficial experience for me. Our group spent numerous hours on preparing the lesson, however I learned that no matter how prepared or well planed the lesson is not every student is going to partake in the lesson. Motivating the students is a crucial part of teaching, either it being intrinsic or extrinsic motivation. Students have to want to learn the material! I want to become a successful educator and these in class experiences are very important to becoming the teacher I want to become. I can get my college degree in education and still not be fully prepared for becoming a great teacher, experience in the classroom and working with students is important. I strongly believe that the Lesson Study experiences are great opportunities for us. We get to work on lessons that we will eventually teach and get the first hand experience in teaching them. From my Lesson Study 1 experience I also realized how much work it is to develop a unique and intriguing lesson. Teachers do not have the time to develop all their lessons to this extent. I think it was a great opportunity to present a teacher with a different type of lesson that they can use in the future.

Summary and Synthesis

Teaching Lesson Study 1 was a really good experience for me. One thing I learned from this experience is how important it is to motivate students. During the lesson about 1/3 of the class were not very interested in the lesson and spent a lot of time talking. I've realized that some students need a lot of motivation in mathematics, even when doing a technology based activity, which I would think would be something different and fun. Another thing I learned from teaching the lesson study is that sometimes you will ask a question and students will not answer. After teaching this lesson I now know what it feels like to stand at the front of a classroom and hear nothing coming back at you. There was a lot of talking going on during the activity, but when it came time to reflect on what they had learned, the students were all of a sudden very quiet. It was difficult to get the students to share their answers to the activity and to answer my questions. I think that had I known the students it might have been more comfortable for them to answer my questions and I also could have called on specific students. I think the most important thing I learned from this experience is that some things you can only learn from experience. This makes me look forward to student teaching next semester when I will definitely be learning a lot more from teaching experiences.

Summary and Synthesis

I really enjoyed the information on motivating students. I have heard about how to motivate students in other classes, but I think the more it is reinforced the better prepared I will be when I get to have my own classroom and students to motivate. I really liked the different motivational strategies that was presented in class. I think that I will be able to apply them when I am teaching. I also liked the instructional strategies that were covered because it gives me as a teacher several different ideas and things to try. I realize that if one way is not working then I can switch and try something different.

Personal concerns and next steps

The main concern that I have and have had from the start is that at the end of the semester, I still will not be prepared to take control of a mathematics classroom. I am a physical education major with a math minor so my content knowledge, I feel is not the same as that of mathematics major. This also means that I will not be able to have my student teaching in the mathematics classroom so I will have to make all of my lesson plans on my own with my content knowledge. I hope that one of the next steps that we can take is to find resources and helpful parts to add to lessons for geometry and algebra and other courses that one finds in a secondary mathematics classroom.

Summary and Synthesis

I believe it is getting harder and harder for students to become motivated in the math classroom. I know from my experiences in the classroom, most students (not all) portray a strong negative attitude to having to learn math. Mostly because they are not sure why they have to know many of the certain concepts portrayed in mathematics. I've heard this plenty of times even when I was in high school, "I'm never going to use this, so why do I need to learn it?" or even just the negative attitude to math in general. That is why I found the ten techniques to motivate students, we went over in class, very interesting and useful. It may be hard to find motivators for every math lesson, but for the lessons you do it can make the lesson that much more memorable. I think the summary of all the ten techniques is to relate mathematics with real life situations that pertain to the majority of the students in your classroom. Once a student has something they can relate to, it can potentially open their mind to what the lesson may have to offer them.

New Insight and their Implications

Working with geometry sketchpad, our group found that it is a little hard to work with. We wanted to do certain things and found out that we were unable to do them the way we wanted to. So we needed to find new ways to get the same result. It made us think about how we should teach using geometry sketchpad. We had to cut different material out of our lesson to make our lesson more understandable and workable. Some of the aspects of geometry sketchpad is really very beneficial but other aspects are flawed. Like many programs with computers their are many other ways to get the result you want out of it. Which sometimes makes it a little more difficult to work with. When you come upon difficulties with the program you are working with you need to try to simplify your strategy with that program. So one of the easiest methods is to cut your loses, meaning cut steps out. Geometry sketchpad, as a group, is a great program to use but it could be more user friendly. Many tools could be added in sketchpad that could make the program a lot more workable/usable.

Questions and Answers

Something that I am continually wondering while taking education classes that inform us about technology methods for teaching students is whether or not that technology is really getting the point across to students. I come from the small town school where the technology that we had in the classroom consisted of an overhead projector and a graphing calculator. And believe it or not, that was almost too much for me to handle. I still to this day am illiterate when it comes to computing problems on a graphing calculator and using the graphing options that we learned about in school. It makes me wonder if with all of the new technology that we are introducing to these students, are they really understanding what the concept is and why we are teaching it? Or are they just going through the motions and learning how to use cool, new technology?
After investigating that question with the technology presentation that we gave on Geometer's Sketchpad, I think it can be a little of both. I also believe that there is a balance between the two, learning the concept or learning to use the technology, that can go one way or the other depending upon how the instructor uses those tools. I believe technology is a great thing, and there are more and more students who are learning concept because of it, but what happens when we replace the paper and pencil with a computer screen and mouse? Are we creating a great way to learn or depriving our students of basic knowledge?
Again I think those questions rely heavily on how that technology is used, and I hope to be the teacher who conveys the message that learning the concept is the main objective and technology components supplement my lessons.
Just some things I have been thinking about.......

Summary and Synthesis

It was never difficult for me to be motivated about mathematics because I have always enjoyed it. However, currently I am doing my internship in an alternative learning center and have realized how difficult it can be to motivate students that either do not like math or struggle with it. It is a reoccurring battle day to day for these students to complete their assignments. I frequently hear from them, “I hate math” or “I’m never going to use this, it’s a waste of my time.” When we started discussing motivation in class I found the information very interesting and useful. I believe that as a future teacher I need to find situations that use the math being taught in my courses and relate it to the student’s life. There are many applications out there but if they are not relevant to a student’s perspective at their time and place in life it will not intrigue them enough to learn the material. When I become a teacher it will be one of my main goals to show students where they will use these processes in the “real world” which will hopefully intern motivate them to master the material.

Personal Concerns and Next Steps

After teaching the lesson with Geometry Sketchpad, two concerns came up for me regarding my teaching abilities. First, I am having a hard time trying to find the correct pace when giving the lesson. I feel as if sometimes I am talking to fast and other times I feel like I am going to slow. When you are only given a few times to present lessons, you really don't have that feeling of being comfortable. I think the more opportunities you have to present lessons, the better idea you will have for how to pace yourself and you will be more comfortable. Second, I feel like I didn't a full grasp of how to use Geometry Sketchpad. I felt out of place talking about the software because it didn't seem like it was doing what I wanted it. It showed up in the lesson when the angles were off by hundredths. I just feel that I need to have a deep understanding of how to use the software or the material at hand. In most cases I have the knowledge of the material, but I just didn't grasp the software as much I thought needed. I think that having more time with Geometry Sketchpad would have allowed me to feel better about what I was teaching and more comfortable in general.

New Insights and their Implications

To be completely honest, I am finding this course difficult. This being said, I am very happy to be enrolled in it. I know that I have forgotten a lot of what I learned back in High School (I graduated in 2001, so I am working with a little more time removed than many of my peers). Some of the terminology that we are revisiting has been beneficial. I am happy to rediscover some of the interesting pieces of knowledge that I have put in the back of my mind and, at the same time, learn to use technology with math. I came to this class prepared for a math teacher to write on a white board in front of the class. I like the new applications that are available and how harmless just "playing" with them can be. I have a feeling that I will be doing a lot of that before presenting my first lesson to my future class.

Questions and Answers

In the recent reading of Chapter 3, the final section addresses literacy in mathematics. After reading this section a couple of questions came to mind. (1) How do you make time for reading and writing in a mathematics classroom? It seems there is already so much to do and so little time. (2) How do you motivate students to read and write in math classrooms? I can see students complaining a lot about having to read and write in a math class.
In response to the first question I have regarding the time issue, my solution would be to integrate reading to the homework assignment, as suggested by the textbook, yet this would make the homework assignments even longer for the students who may not have enough time to complete all the assignment if reading was a part of it. So, in this case I would make sure I allowed ample time in class for students to get a start on the homework, including the reading, and maybe even finish it. As far as writing goes, having daily student logs or journals I think would take a lot of time for students to write every day and for me as the teacher to grade them. However, I think it would be beneficial to know what students are thinking about the material. To cut down on the time problem, I think I would have the students write in their journals only once a week, which would still allow me to gain insight from the students’ writings. Also, I could incorporate one problem including writing on tests which allow students to express mathematical concepts in their own words.
The answer to my second question seems a little harder. I think having students read books or short stories about mathematicians or mathematical concepts could interest them if the stories pertain to their lives. Reading a story that uses mathematics could engage students and motivate them to become interested in the topic being presented by the story. Finding these stories may be difficult, however. Motivating students to write may also prove difficult. Writing as part of an exam would provide external motivation since it is part of a grade, but promoting internal motivation for writing may be more difficult. The weekly student journals may be internally motivating for some students because the journals allow them to express their thoughts about mathematics without having to say them out loud. Also, the book’s suggestion for connecting the mathematical significance with a particular newspaper article may be motivating for students.
Both questions I have posed after reading this chapter have allowed me to think about how I might use reading and writing my mathematics classroom. The answers I have come up with so far may work, but they might not. I think every teacher needs to try different ways to include literacy in the mathematics classroom and see what works best for them. It may be one of those things you fail at first, but over time discover something that works in your classroom.

New Insights and Their Implications

One of the biggest things I have learned from the instructor is that it is easy to forget content from high school. It has been so long since any of us have had that level of mathematics, that it is easy to forget certain terms and definitions. I also learned that questions will arise as you are teaching that will be hard to answer. I really like the questions that are on Dr. Reins's website. They are questions that students often ask that I think would be difficult to answer on the spot. It will be a great resource for me and all of us when we get our MQFC questions and responses turned in. I believe it will make me better prepared for my first years of teaching. Some simple things that I have learned from my peers are ideas for different lessons. I enjoy hearing responses from my classmates on different ways you could teach a unit or lesson. Often times I find it hard to think of different ways to teach a lesson, so hearing input from my peers opens my mind up.

New Insights and their Implications

One of the most influential insights I've gotten from my peers and the instructor of this course is the importance of setting specific overarching goals and long-term development goals in the classroom. I believe that if a person asked teachers whether they have long-term development goals for their students, a majority of math teachers would agree. However, I'm guessing a good portion of these teachers may have an idea of the long-term development they are trying to instill in their students, but many have not actually set specific goals in this area. I've learned through discussion with my peers and the instructor that actually putting overarching goals and long-term development goals on paper makes the accomplishment of such goals more realistic. For instance, a teacher may have set a long-term development goal for students to develop self-motivation for learning mathematics. This is a very difficult goal to accomplish. However, I've learned that by setting this goal in a classroom and continually acknowledging this goal, the teacher will make the most progress in developing self-motivation amongst students in the classroom. Though the goal may seem unattainable, acknowledging it and specifically reflecting on the goal are the first steps to it's achievement.

New Insights and Their Implications

One of the main things that I learned from this class so far is the actual lay out of problem solving and how to get people to think in that mode. I think that this will help me get my students to think through the problems with out step by step assistance.
The algebra tiles are also something that I have been introduced to through this class. While I am not quite as skilled with the tiles as I hope to soon be, I can clearly see how they are a valuable tool that can be used to reach many more learning styles. I hope that I will be able to learn many more such methods to apply to my classroom.

New Insights and Their Implications

I have already learned a lot in this class so far and look forward to learning more. I learned how important a part technology will play as I continue on in my education and as I start teaching. Technology is something that is always changing and so it is very important to understand and be able to use it or at least be exposed to all the different technolgy products that are available. I also learned a new way to explore the lesson of completing the square. This lesson study example gave me a whole new perspective and outlook on a technique that I was taught to just memorize and to use. I think explaining it this way helps me understand the basic concept better and will give me a couple of different ways to approach teaching this technique so that hopefully all of my students will understand this technique one way or the other.

Summary and Synthesis

This semester I have found it very interesting learning all the ways to integrate technology. As a future educator I will definitely try to use some of these techniques as they are available to me. I have really enjoyed learning about the four steps to problem solving and the process of problem solving. It is something that I find very interesting because I tend to do problem solving in a very round about way. I often time don't achieve the answer through the best or easier way possible, but eventually get there. It was fun to learn about the processes and see how all the steps related to myself. Lastly, I have liked learning about the algebra tiles. This was something I had never seen before and I have struggled using them. However, it is something that I think I could get used to and it is a very good visual/hands on learning activity. I can see students benefiting from using the tiles and would like to use them someday in my own classrooms.

Summary and Synthesis

So far this semester, I have been very interested in this course. I really appreciate all we are learning about different technology options to enhance our students learning and the appropriate amount and time for incorporating technology into lesson plans. I am also really looking forward to the lesson study portion of the class. It is something that I, as well as a majority of the class, have not had previous experience participating in. I think it is going to be a wonderful way to gain insight on students' learning styles and how to create good, interactive lesson plans. The interactive aspects of lesson plans is very important, and I really like that we are learning a more active approach to teaching/learning mathematics. I feel that a majority of my education throughout high school was very textbook, lecture, and solving problems with pen and paper, so learning more effective and interesting methods of teaching math has been very beneficial to me. While I understand that every style of instruction has its own place in the classroom and the redundant practice of certain problems with equations may be necessary, I really enjoy learning to take a broader view of problem solving and learning to find similarities between various, seemingly different, types of problems. Finally, this course has already taught me alot about problem solving in general. I have always considered myself pretty good at solving math problems, but I had never given any thought to the actual process I was taking myself through in solving the problems. To really teach problem solving to students, I feel I need to reflect more often on my own problem solving strategies and the actual process I am using to solve the problem and learn.

Summary and Synthesis

So far in the our SEED 418 class, I have been gaining a lot of new knowledge. The biggest area that struck my attention was the problem solving section. I always knew how a went through the process to problem solve but I never really have been asked how I could explain my students how to correctly problem solve. This idea was very time consuming for me, it took a lot of thought and reasoning. Also, in this class I have enjoyed the way we are learning the lessons with a hands on approach. The other day when we did the lesson study, I thought to myself how difficult it may have been to grasp the completing the square steps if we weren't given the pieces to follow along with. I am a very hands on and visual learner, so theses methods have enhanced my learning thus far. Lastly, I am very excited to do the lesson studies. The input that each other will receive from the experience will last forever. The lesson study is going to make me think about each lesson in a much different way due to the opportunity for each group member to have insight on how they would perform a task. Overall, class has gone very well for me thus far.

Summary and Synthesis

Effective teaching comes from adapting to new styles, technology, and new generation of kids. Being able to communicate with your students is one of the first ways of learning how to teach. As a teacher you need to keep involved in learning new styles and understanding how kids think and learn. I learned that using technology in your class can be real fun and fun for your students. As a teacher you need to make learning fun and interesting so that they want to learn. Making learning fun and easy will make your job as a teacher real easy. Students that are unmotivated and uninterested in a topic will have a difficult time with learning. The key is to find out what motivates students and how to get them interested. Using technology can be a fun and very beneficial way to help students learn.

Summary and Synthesis

Effective teaching involves constantly reviewing and developing further knowledge. I learned in completing the square how many steps are part of the process and how easy it is to overlook some information that may seem elementary to us, the potential teachers, but may be crucial to the new learner. An effective teacher must let the students ponder and even struggle a little with the new concepts before offering a solution. I also greatly appreciate the present technology such as the Smart Board. Technology was not a part of my high school mathematics, but it is great to have it present and at our fingers for this classroom.

Summary and Synthesis-So far in the semester, I feel like that we are learning quite a bit, with good teaching practices and technology used in the classroom. The things that we have been shown with the whiteboard and systems that we can use to show math problems are things that I would definitely use in future teaching experiences if the resources were available. In addition to what we are learning by using technology, the idea of lesson study is a great idea for every school. Being able to reflect on the practices that we use on a daily basis is only going to benefit our teaching and the students' learning as long as there is useful feedback on the lesson and how it can be improved. Hopefully all schools with adapt this practice, even if it is only introduced as a teacher workshop about how students learn best.

Questions and Answers

I believe that integrating technology is very critical for mathematics education. When I was in high school there was not much technology in my math courses. So when we discussed this topic during class I expected to talk about the usage of graphing calculators. It blew me away when I found out how much math technology there is. With all the possibilities one would think integrating technology into the classroom would be simple. However, funding is a major problem. Some schools do not have enough money to buy recent textbooks let alone computer programs or calculators for students to be using. I think a solution towards this problem could be the use of smart boards. Smart boards have numerous math tools that would aid teachers in their lessons and students in their mastery of the material. These boards allow students to interact with math instead of solely being lectured over it. Smart boards are expensive but schools can purchase one that can be used in every classroom no matter the subject. I still have many concerns with how to integrate technology into a math course, but I now know how to get started.

New Insights and Their Implications

So far I have been introduced to a couple of new insights to this course which will give me the opportunity to practice them my next field experience. One of these insights was being able to see the use of the SmartBoard, which has broadened my technology world immensely. Most of my generation (I think anyways) has not had to much of a variety of technology in their Math classes in high school. I know growing up in my small school, teachers were limited with their technology resources. And sometimes if they used technology it seemed as though it was forced. (like we said in class) I believe that being able to use technology most effectively would help my students better understand the material. So far seeing the SmartBoard's different options has shown me several different ways to incorporate technology in my future classroom. I look forward to being introduced to other resources of technology in this course in order to analyze where they could potentially be used or which piece of technology would be more effective.

Questions and Answers

After reading the articles on Lesson Study in Japan, I became curious about how this might work in the United States. From the articles it seems that this is very successful in the elementary classes and middle school classes. There were no articles about how this might work in the high school setting. This is what my question was then, How would lesson study work in the United States? First, I believe that this would work in the high school in the United States, however, I think it might take some work to get students to buy into this type of delivery. High school students might be used to a traditional style of teaching and not accept lesson study. I think that if a school were to start students in Kindergarten and continue to teach lesson study through out their school time, lesson study would be successful. I am sure that it would work with out applying something like this, but a great opportunity to research is there for someone.

New Insights and Their Implications

This class has provided me with new insights about technology and how it can be used in a mathematics classroom. Before this course my knowledge about technology use in a mathematics classroom consisted of the use of calculators and possibly PowerPoint and Excel. The class discussions and the readings have broadened my view of technology in the mathematics classroom. I now realize how useful a SmartBoard can be for everyday instruction and that there are several software programs that can be useful in math education. The one thing I will continue to work on though experience and practice is how to best use technology in my classroom so that my students will benefit from the technology. I believe technology is a great exploration tool and can help students grasp difficult topics by presenting the material in a new way.
I've also learned that teaching just mathematics procedures without letting the students discover ideas for themselves is sometimes detrimental. I, myself, do not remember learning the "completing the square" method in high school most likely because I just memorized the process presented by the teacher and then quickly forgot it after not using the process regularly. After the lesson on completing the square, I think I have a better grasp on the subject and will never forget the process. I believe that using a visual representation and being able to discover the pattern first before the teacher gave it to me allowed me to really understand what it means to complete the square. After this experience I think that when designing lessons it is important to let students discover math concepts on their own so that they can gain a greater understanding of the material and will appreciate the problem solving processes and strategies used to arrive at the solution. I hope our future work with lesson study will help me to see exactly how and when to allow students to discover mathematical concepts on their own.
The new insights I've learned both about technology and student discovery have given me new tools in creating a better learning environment for my future students.