Working as a group of five, I felt that our group did a wonderful job, and we were very successful in the classroom. Picking a topic may have been what took our group the longest, but after we were set on the idea of our project, the planning went very smooth, and in a matter of a couple of days, we were ready to go into the classroom. It was the first time that any of us had formally been in the classroom to actually teach a lesson, so trying to get everything perfect may have been our only pit fall. We all realized after the lesson that there were many aspects of teaching that may sometimes have to fall into place. I say that because students are unpredictable, if someone has a great idea, then the discussion may shift to a new idea, or if students are really not into the concept at hand. These were a couple of things that we as a group could see happening with normal lessons. With our CTL lesson, all the students were eager to get started, they all paid attention to the directions and were quick to raise their hand if there were any questions, because they wanted to succeed in the task. This made the lesson go very smoothly. The students had been working on concepts that we were using, so thought it was neat to see those ideas actually being used. We tried to keep the activity as open to change as possible, and that may have helped when the students actually started the lesson. As a group, we were able to monitor the students, and see the different ways the groups of students were constructing their project. I felt that was a major success, but I do feel this may have been because of having five of us, we were able to keep a close eye on the groups, and make sure they were on the right track. One of the most important aspects about CTL is the concrete knowledge that the students gain by actually applying what they have learned. We even had a student say that she would recognize and remember similar triangles when she took her SAT's because she had something to relate the concept to, and didn't just have to remember it for a test. Also, many of the students said that this lesson was the best class they had ever had, because they actually came up with their own ideas of how to construct their project, and all we did was supervise and give helpful ideas. I have to say that throughout the past several weeks, with everything we have learned and used involving CTL, I feel there is no better teaching method in the classroom, especially with mathematics. CTL is the most integrated teaching method, which actually involves the students in every aspect of the learning process. I have really enjoyed learning about CTL, and I also hope to use it as much as possible when I have my own classroom. One thing I have learned with CTL is flexibility. CTL is very open and versatile, there are so many ways to use CTL, it can be used at any point in a lesson, or at any focus on a concept. It also breaks the pressure on the teacher of planning notes and homework every day of the year, which in turn, helps the students to stay better focused and not get into a grind with note taking and homework. Students can actually have fun learning. That to me is the most important aspect to teaching high school kids, they have to have fun at some point in order to really pay attention, and enjoy what they are doing. If not, they lose focus, and remember only short term any concepts or ideas they my have been taught. One question that I have about CTL, is an area that I have been confused in for a while. When and how do we use CTL in the classroom? I know it sounds crazy and it's really not that simple, but I know sometimes I think of when to use CTL when planning a lesson, and I wouldn't want to start an CTL activity early on, or wait too late when the material may become elementary to the students. That's why my answer to that may be around having guidelines of CTL, that actually teach the teacher the best time to incorporate a CTL lesson into the present lesson. I feel that the more teachers not only know about CTL, but understand it as well, the more they will be willing to use it. This class is a good example. I will learn about CTL, and some small scale concepts of when to use it, but what about when I am in my own classroom. For our project, we went to Clarke County High School on February 12, 2001 to Mr. Dan HunterŐs ninth grade algebra class. For our contextual algebra lesson, we first did an experiment called the Ball Dropping Experiment to introduce how to find the "perfect" tennis ball and seeing how the start height was related to the bounce height. Our second experiment, the Fence Problem, was done completely on GeometerŐs Sketchpad (GSP) to illustrate the largest area of a pen. Throughout conducting the experiment, I learned several lessons about teaching contextually. The students really seemed to enjoy the Ball Dropping Experiment and were able to make several good conjectures of the relationship between the start height and the bounce height. The students were very active during the experiment and had many questions to ask us. We were able to describe to them the importance of a ball having the "perfect" bounce because many of them play sports and are very interested n that subject. All of the students understood what it was like to, for instance, play tennis with a flat ball and the effect that it has on the outcome of the match. I believe that this experiment went very well and the students thoroughly enjoyed the interaction and overall experience. The lesson that I learned from this experiment was basically that students not only enjoy, but they understand the experiment when it applies to their reallife activities. On the other hand, I believe that the Fence Problem did not go as well. The students were not familiar with GSP and had a very hard time following the instructions with such little GSP knowledge. We ended up just letting them watch Natalie on the overhead, but I am still not sure if they really understood the lesson. This lesson definitely had a lot of context in it and the students were able to recognize that, but were simply burdened by having no previous GSP experience. We were a little more successful by drawing pictures on the board and allowing the students to interact in helping us find the largest area using the formula of the perimeter and area that they already know and by using trial and error. The lesson that I learned from this experiment is to make sure that the students are familiar with the tools that you are using. I also learned some other teaching lessons that do not necessarily apply to CTL. One huge lesson that I learned was that the students do not understand our mathematical language. We must remember to lower down to their level of thinking when trying to explain things. This was, I believe one of biggest problems. The students would hear one big, unfamiliar word come out of our mouths and begin to be totally lost. Another simple lesson is just to be patient. When you ask a question to the class, you need to wait a few seconds in order to give them time to answer. Silent moments are not that bad. A final lesson that I learned was that it was pretty easy to get rid of the butterflies that I had before we began our lesson. As soon as I got a few words out, it was easy as pie! From where I am standing right now, contextual teaching and learning has several important aspects. Even though I do not believe that everything in mathematics can be taught contextually, I do believe that contextual teaching should be used as frequently as possible. Students enjoy doing classroom activities and seem to be ore interested in the mathematics when it applies to their everyday life. I think that contextual teaching is very effective in the classroom. I guess my only question about contextual teaching and learning is: can it be applied to all aspects of mathematics? Do you recommend using it in every single lesson that is taught, and is that possible? CTL Reflection Our CTL project on February 12th was quite an interesting experience! Because this was the first opportunity that any of us had to actually go out into the schools and perform an activity, I believed that we all learned a lot from it. Our group, consisting of Natalie, Raju, Doris, Lindsay and I, visited Dan Hunter's 9th grade Algebra I class for the last period of the day, which ran from 1:58 to 3:30 p.m. As a group, we had the class look at applications of linear and quadratic equations with two activities known as the Ball Drop and the Biggest Fence Problem. The first activity was more of a handson investigation, where the students were split up into groups of five and were required to perform an experiment where they dropped a ball from a certain height and measured the height of its first bounce. The students seemed to enjoy this particular activity because it gave them a chance to go outside of the classroom, talk, and work together. Then, we had them come back inside of the classroom in order to discuss the results of their experiments. They were able to use Excel on individual laptops in order to graph the data they got from the experiment. For the second activity, we explained to the class that they were required to build a fence with a maximum area for their dog, using one side of their house as part of the enclosure. The only restriction was that they were given only 100 feet of fencing. We began by discussing some ideas that they may have about how to make a maximum area out of the fencing, drew some examples on the white board of possible fences, and also drew some extremes, where one side of the fence was much longer than the other. Next, we attempted to teach them GSP to create a fence and be able to see what happens to the area when you vary the length of one of the sides. We concluded by discussing the graph that would be created when we actually plotted some points, and then tied the two activities together. Some of the overall success were that the students really seemed to enjoy the problems that we gave them, most likely because we discussed topics that were probably more applicable topics than most of the problems that they are given on a regular basis. Although it was the last period of the day, the students seemed to be thinking about most of the questions that we posed, and they were also well behaved for the most part. We were able to see the point where the students realized that the graph for the dog pen actually looked familiar, since their homework the previous night was to graph quadratic equations. Some of the aspects of our project that we had ideas about improving were that it was too difficult to learn GSP in such a short period of time. If we were able to perform a much simpler task on GSP, I believe that they would have understood the exercise better and could have been less confused and rushed as well. Also, we thought that much of the language that we used made them confused, which was probably due to the fact that they hadn't used many of those terms before in a mathematics class. I think that we needed to remember that we were teaching 9th graders and not seniors or college students. Also, I believe that with more experience, we will be able to create lesson plans where we would actually be aware of the amount of time that a given activity requires. Finally, I think that we may be uncertain (or at least I am) on how to have the students be more responsive to our questions in class. From where I stand right now, I believe that it is very important for students to be able to relate to the mathematics that they learn in the classroom and be able to connect it to their own lives, so basically, relating content and context. Also, I really believe that the handson and cooperative learning is important, because in the real world, most likely when people have a question, they are allowed to ask others questions and get feedback from peers. The handson learning enables students to be more involved with the material and stay interested for the duration of the class. Finally, one new question I would have about CTL is: how do you find a balance between getting all of the required material taught in the classroom and still keep the students interested and having fun with the mathematics as well? This project was very interesting and informative; I am excited that we had this wonderful opportunity! I worked with Julie Terry, Amy Terry, and Kristin Thomas. We chose an Applied Algebra class at Apalachee High School, taught by Patti Ayers. We were unsure what Applied Algebra was when we picked the class but the teacher explained to us that these students were at risk of dropping out of school. The class had 17 students with many basketball players. We found out the students were learning how to add, multiply, and reduce fractions. Therefore, we wanted our CTL teaching project to relate to fractions. We set a date with Ms. Ayers and were told we had 45 minutes of instruction time. We were worried about the time but were thankful for the opportunity. After talking to the teacher and gathering the information we needed we discussed what we wanted to do for our CTL project. We wanted to involve the community and at the same time teach fractions. In addition, we had to take into account that we could not over challenge these students or they would turn away from our CTL teaching project. Therefore, we adopted a basketball free throw experiment with fractions. The students were divided up into four groups. Each member of the group was given the same amount of free throws. Each group was asked to make a fraction that resembled the amount of free throws made with the amount of free throws attempted. After, each group completed their group fraction we brought all the groups together and discussed the fractions and posted each groups fraction on the board. We then asked the groups to get back into their group and find a fraction that represented the entire class in free throws made with free throws attempted. In addition, we asked each group to reduce their fraction and put their fraction in decimal form. After each group completed their assignment we brought the class together and discussed how to find the fraction and a common denominator. Then we discussed finding decimal representations of the fractions. The CTL teaching project went great. I enjoyed working with the students and the students said they enjoyed our project. Our timing was perfect; in fact when we started planning the project we were worried that we would not have enough time. However, we finished exactly 45 minutes after we started the project. Also, our project worked out nicely because we could work with the students in small groups. The students enjoyed the basketball free throw activity and could relate it nicely with fractions. The students were challenged when they had to find a common denominator of the four fractions of the class. However, they were not over challenged and did not become disgusted. They worked on the fraction in their group and we helped when we were asked. Therefore, I feel the CTL project was a success. The one aspect of the project that I would like to improve is I would like to use the gym or a basketball court for the experiment. The balls that the students were throwing would bounce out of the laundry basket at times. Therefore, I could eliminate this problem with the use of a basketball court. I do not feel that there is an aspect of the project that I am uncertain about improving. I feel CTl is important because teachers take the time to relate real world experiences with teaching. In addition, CTL is important because students can see that mathematics relates to their community and their interests. For example, most of the students we taught had an interest in basketball. The students learned through our CTL project what percentages mean in free throws and how fractions can look different but are the same number. Also, the students could relate fractions to decimal representations, which is how free throw statistics are published. I feel that students learn more through these types of experiences. My question about CTL, is how can you convince the administration of a school that you need to implement different teaching strategies other than the traditional lecture, quiet, teaching methods? I feel administrators are not going to agree with many of the aspects of CTL. For example, taking students out of the classroom and into another part of the building for a learning experience. Also, students are louder when experimenting and working in groups. Therefore, administrators are going to think that the learning experience is a playtime. Thus, how do you convince them that CTL is important? I worked in a group with Rebecca Parker and Melanie Sauer. We taught Dan HunterŐs ninth grade algebra class at Clarke Central High School. The lesson was to create different types of distance v. time graphs using a CBL motion detector connected to a TI83 calculator connected to an overhead projector. We gave each student a packet with 4 pages of questions. Before beginning the actual activity, Rebecca and I reviewed linear graphs with the class as well as the concept of slope of linear functions. The first page of the worksheet we worked as a class. Then, the class was divided up into 4 groups by the color of the wrapper of their ReeseŐs peanut butter cups. The students would hypothesize as to the answers to each question in their groups. After the groups had talked about a question, we would come back together as a class and one student (a different student every time) would perform the motion in front of the CBL to get the desired graph. The studentŐs group would coach him while he moved in front of the CBL. I feel that this activity was a huge success. Even Mr. Hunter was impressed with how well the class went. The students were very interested in the whole activity. I think one thing that excited the students so much was that they got to move around and be active. I also noticed a lot of competition between groups to get the graph perfect on the right try. I was glad to see, though, that the students within a group were not demeaning each other; they worked together very well as a team. The students got the graphs right the first time on every question. I was amazed at how much the class understood about linear graphs and the concept of distance v. time graphs. Each student picked up on the concept very quickly. The action and competition involved in the lesson also helped to keep the studentsŐ attention. There were hardly any students who dazed off or lost all attention. I did notice two or three students who wouldnŐt participate when their groups were discussing the question at hand. They wouldnŐt even have their packet on the right page. I would walk over to these kids and ask them what they thought the answer to the problem was. The student would usually get the answer right, he just didnŐt look like he knew what was going on. I donŐt think I would improve anything about the actual project. If I was actually teaching the class on a fulltime basis, I think I would expand the project to take a deeper look at speedŐs effect on a distance v. time graph. Especially with students who have taken calculus, I could focus on the fact that velocity is the derivative of distance. This probably would take another class period, but it would be well worth it. I think contextual teaching and learning is very important in education, especially math. Students remember things and understand things better if they have an actual context to associate them with. Even when looking at the different types of graphs included in the lesson, the students could create a reallife situation that would produce a graph like the one at hand. For instance, the class was given a graph that looked like an inverse quadratic function. The students actually were able to decide at which point on the graph the person walking from his house to the park encountered a hill. I was stunned at how well the students understood how a hill would affect the distance v. time graph. Several students even were able to explain it to the rest of the class. With a deeper understanding of any topic at hand, a person is much more likely to remember the information in the future. I see how important contextual teaching and learning is in a math class. However, sometimes I think it could be a reach to find a contextual situation for EVERY math topic. Sometimes it seems better just to teach the information straight forward. Is contextual teaching always the best method? Reflection on our CTL Activity: Fractions Our CTL assignment gave us many opportunities to plan and participate in teaching a lesson that was very beneficial for the students. Upon planning our project, we had to make sure we were developing a lesson that was adequate for the studentsŐ abilities, and that fit into the time frame of the class. Also, we had to ensure that our lesson plan was a contextual learning experience for the students we were teaching. Because we had to do all of these things, we now have experience in developing CTL lessons for our classes in the future. Many of the students complained about the supplies we had for them to implement our project. For example, we had clothesbaskets and Styrofoam balls for them to use. The balls always kept "jumping out" of the baskets when the students threw them. Therefore, it would be nice to get materials that did not frustrate the students so much. Maybe being able to use the gym and real basketball courts would be nice. Also, I would like to bring the class more into an overall discussion. Because the time frame was so little, our class did not get to connect ideas as a whole. Everyone was given equal opportunity within their group, but as far as a whole class, I think every student getting to hear the ideas of each group would have been good to enhance the learning experience from the activity. I believe contextual teaching and learning is pertinent in a classroom. I remember many times when I was in school when my fellow students kept on saying, "When are we ever going to need this?" Contextual teaching and learning helps show students when they are going to need the things they are learning, especially with the subject of math. Math is a very abstract idea that requires a lot of formal thinking. For students who are not quite to that level of thinking yet, being able to relate what they are learning to concrete aspects in the world, can motivate the students while learning. A question I would write about contextual teaching and learning is: "How do we, as teachers, implement contextual teaching and learning into the classroom more, and still have time to adhere to the state curriculum requirements?" All of our students seemed to have really enjoyed our activity because their interests seemed to be kept throughout. I am glad we had the opportunity to go into the classroom and apply what we are learning. Last Wednesday Rebecca, Kristen, and I went to Dan HunterŐs ninth grade algebra class to teach them a contextualized lesson about slope. As the class came into the room, they each took a piece of colored candy. Then we put them into four groups based on the color of the candy they had. There were four groups with about 56 students in each. Dan told us that the candy was a good idea because it really broke the class up well, in not keeping g certain groups together. Once they were in the groups, we asked the class to recall their prior knowledge about slope. They had to really think about it and try to remember but most said the steepness of a linear function, and rise over run. By listening to what the students were saying about slope I thought to myself that they really did not remember much about slope and they did not seem to really understand what it symbolized or what it is used for. Then we passed out our worksheets and explained the CBL; computer based laboratory, to them and how it works. Then we started the problems. Each group would talk amongst themselves about the problem and then we would discuss it as a large group. Then one person, chosen by the group, would come up to the CBL and see if what they thought would, work did indeed work. Sometimes groups would have different ideas to get a certain graph and we would then let each group come up and try their method. As our activity continued the students seemed to get really into it, they came up with some very creative ways to make some of the graphs that we did not even think of. After each question on the had out we asked follow up questions about slope and how it was used in that particular problem, and how it was determined. After a few questions, you could tell that they students really started to understand slope even more than they had before. They began to realize how slope is used, how it is determined, and why we care about slope. At the end of our lesson, we decided to do a challenge question with the class. Rebecca presented the class with a graph that was not a function, this one was a hyperbola, and she asked them if they could create the graph using the CBL, or why would they not be able to create the graph. After a short class discussion and some students saying it could be formed and some saying it could not be formed, the class finally agreed that this particular graph could not be formed. They looked at it by thinking that a person could not be in the same place at two different times. Lastly, we talked about where they would find and use slope outside of the classroom. This is when we really started to see lightbulbs go on. The students realized that slope actually does exist outside the classroom. Our project turned out better then I thought it would. The students got out of the lesson exactly what we wanted them to get out of it and maybe even more. I believe that after this the students will always remember what slope is and what it means because now they can make a connection to it through what we did with them. During our project, the head of the math department, Mrs. Foss, came in to see what we were doing. She thought it was a great activity and she could not believe how well the students were doing with it. Both her and Dan said that even thought there was a lot of talking going on in the classroom it was ALL mathematical discussion, the students were constantly talking about the problems, this is a main part of CTL. Mrs. Foss asked us to please explain the technology to her and put the program onto her TI83 calculator so all the math teachers at the school could use our activity for future classes. That made us feel so good about what we had done. Not only was our project a success but it will continue to be one when the teachers use it again to teach slope. Looking back on our project, I do not think I would change anything. Everything ran very smoothly. The students loved it and our timing turned out to be perfect! We ended about 4 minutes before the end of the class because Dan wanted a few minutes to hand out grades. This project reconfirmed what I already think about CTL, IT WORKS!! These students now understand slope, and realize that it is used other places besides in a math class. I strongly believe that the next time someone asks them what they now about slope they will be able to give them a whole list of things, all of what we helped them realize. From this project, I have realized how important CTL is to the classroom and students. I realized that when you introduce a subject to a class and you make it interesting and exciting the students also get excited and pay attention more. In addition, when you are able to relate the material to the "real world" and students can understand why they need to know the information they tend to not mind learning it as much. Once they realize why they should know and understand slope, how it is used in the world, they suddenly became more interested in what we were doing. We also made it a fun lesson, which helped too. I really have no questions about CTL; I feel that I understand CTL very well and have believed in it for the past 3 years, since I started the program. This was a fun and great experience working hands on with CTL. I loved every minute working with DanŐs class. My group and I, went to Clarke Central High to teach Mr. HunterŐs ninth grade algebra class. Some of the success that we had in our project was that we gave students an understanding of real world algebra applications. They were able to see were algebra was used in everyday life and relate it back to their homework. Mr. Hunter was able to use our activities in his teaching to help the students understand why algebra is important. One of the things that I would probably improve about the activity would be the teaching the GSP program. We really did not have a good idea of how the students would response to the activity with the computers and it showed with our planning. The students were not able to grasp the program and follow the directions as well as we had planned they would. I would probably work on improving a better way to teach student how to use GSP in a less time consuming manner. The thing that I was probably most concerned about was the students making the right connections with the activity. The only way to see if they were or not, would be to give them an assessment. I just wanted to make sure they were making the right connections and not misinterpreting the activity. I wanted the students to get the most out of the activities. The most important thing about CTL right now would be to make sure that the students are still learning and that we are not taking away from that. With this, hopefully the students are having fun and maybe wanting to learn more. Are the students making he right connections with CTL teaching and learning? On Wednesday, February 1 4th, Faith, Julie, Kristen, and I went to Apalachee High School to teach an applied algebra class. We talked to the teacher before hand and found out that they were learning about fractions. We also found out that many of the students in that particular class was basketball players. Our group wanted to make sure that the students could relate fractions to something fun. We decided to tie in fractions with basketball. We talked to the class about how the percentage of free throws made were actually fractions. The fraction was actual how many free throws made to how many shots the basketball player had. We then commented on how this is the same for batting averages in baseball and softball. The students were in awe of this. To teach the fractions we decided that we would get the students to throw 5 balls each into a basket. We would calculate how many baskets they made to how many throws they had. We divided the class into 4 groups. Each group consisted of different number of people so that one group had 3, another group had 4, and two groups had 5. This would allow each group to have a different denominator for their fraction. This difference would later help us teach how to get a common denominator so that you can add fractions. After we calculated the total of number of baskets made in each group over the total number of balls thrown, we got each group to reduce the fractions if it was possible and then put it in decimal form. Once each group did this, we got each group's fraction and added up all the fractions. At this point, all the fractions had different denominators so we got to work with the class on how to get a common denominator. After adding all the fractions, our lesson was over. We ended the lesson asking the class where all they see fractions daily. We talked about fractions in the grocery store, ie meat, in recipes, and with cents. They seem to finally see that fractions are important in our community. I think that our biggest success is that the students really were interested in how we were relating fractions to sports. Many of the f~ en we talked about how often we see fractions and don't even realize that they are fractions, ie batting averages, cents, and recipes. The students were talking to us about how all they had seen was the teacher lecturing on the board. I think that many of them were excited about the way we were trying to teach them in a more contextual way. The students understood what the numerator meant and what the denominator meant. They could see that these numbers actually represent something. These fractions were important to the sport players. Not only did they understand what the fraction was about, but they could see that if you reduce the fraction it is still the same fraction you started off with. I think that the students were also more willing to learn the material because we weren't lecturing them or following straight from a book. They were excited about learning something new in a different way. I think this helped encourage them and catch their attention. Over all I think that it was very successful. We also took the full amount given to us. We weren't trying to make up stuff to fill the time, nor did we need more time given to us. We really planned out this project to fit our time frame to a T. I had a lot of fun doing it. They were little things to improve on. Many of the things that we could have improved on would be easy to fix if we were the teachers. If we had the gym it would have been nice. We could have actually taken free throws and it would have made the students put the lesson in even a more visual learning atmosphere. However, this was not possible. I still think that this lesson is ok to do with the way we did it. We didn't think about the balls bouncing out of the baskets. This happened frequently. Before doing this assignment again, I think I would talk to my group members and decide whether or not to count that. Another thing to improve on is having an exact distance each person has to throw from. This would just make our data more accurate for the class. We also randomly assigned the groups. Some groups had all smart people in them while other groups were struggling big time. If I was the teacher and knew each student's level, I would have mixed up the groups more so that those students who understood the concept of fractions were put with those students who did not. This way we could have this assignment to be a peer tutoring time too. I know that sometimes it takes a student hearing another student explaining something before they can grasp it. The teacher is not always the one who can explain new concepts the easiest. I think students can learn a lot from other students. Again, there were no major problems with out lesson. I was frustrated with the fact that I felt like half the class new exactly what to do with fractions while the other half of the class was lost. I was not sure how much time I should stay on one specific aspect of fractions. Some of the students already knew how to reduce fractions and flew through our worksheet while others had to be told step by step what to do. I hated to waste other students' time ree~cplaining things. I guess that is something as a teacher I have to learn how much to do and when enough is enough. Because I wasn't the teacher of the classroom, I wasn't sure what all had been already covered in class. I just did the best I could. I would have liked to give the kids a worksheet for homework tying in other ways fractions are seen in the community but I couldn't because I wasn't the teacher. I really think that my main things that I would improve but that I couldn't was just being the teacher and knowing these kids more than I did. I personally think that contextual learning is a great thing. I think that it really helps the students grasp new ideas and see why it is important to learn. I do think however that contextual learning causes the teacher to have to do more planing. This is not a bad thing, but teachers need to realize that it is more time consuming. I do feel that contextual learning will help students not only learn the material better but it will also make them remember it longer. Too many students? including myself learn things short time. We learn things just for the test and forget about it. It is called memorization. If we use contextual learning, we relate the information to our community and therefore are able to remember it longer. I think that contextual learning is something that needs to be taught more in schools. This would give the students a joy in learning and a desire to learn. The more students see that what they are learning in schools is important for them to learn, the more they are going to be willing to learn it. I am not saying that everyday should be a contextual learning day, lectures are good sometimes. I just t'eel like that both lectures, and contextual learning needs to be used in the classrooms today. First of all I would like to talk to students more about contextual learning. I would like to know what they think about it. Do they think that it will help them learn the material better and get a better grasp on it? I then would like to compare test scores of those schools that do use a lot of contextual learning to those that don't use any. I think that it would be interesting to see which is higher. In a way I would think that the ones that used contextual learning would be higher because I feel like it is those students who really understand the material, however, contextual learning takes up a lot of time and will those teachers be able to get though all the material needed by test taking time. I know that schools really enforce the curriculum and to get through it all, is it possible to do with contextual learning. I honestly think to some degree it is. I guess I would just like to do more research on how the students think about it and does it really help out test scores. I definitely think that this assignment got me thinking in a whole new way. I really had to think about how I was going to relate community with math. By the end of this task, I really felt like I learned a lot about both contextual learning, and how to use it in an actual classroom.
For my teaching experience with the CTL assignment in a classroom, I noticed many things that I could change, some stuff I think really well and then maybe one or two things I was uncertain about. I definitely feel that the experience was a positive one and I learned a lot. In looking at the assignment and the successes we had, I feel that the biggest success was the question and answer part that we did at the end. Many of the students had questions about college and we were able to answer some of them. At this point, it was really good that we had five people in our group because the students were able to get many opinions about college. Overall, I feel that most of the students had a realistic view of the cost of college, which surprised me. I feel that since the students had a clue as to what college costs, we should have done a different context. I think that we should have had more communication with the teacher so that we could have had a better idea of what type of context the students had never had before. The teacher we worked with had already been using contextual teaching so it was difficult to find something new. I feel like the students learned a little but they could have learned so much more. We were unaware that we could use the whole time block, so our presentation went quick. This however did provide lots of time for questions, which was good. In thinking about what we could change, I think the biggest area would have been to include the TI's more. I am not very clear how we could have, but I think that it would have been neat to show them some of the things we have learned to do involving stats on 'J the calculator. I feel that contextual teaching and learning is important because it involves the students more and it lets them see how they can really apply their learning to the real world. The thing I am unclear of is how we can do a better job of applying math to the real world and not just having hands on activities. I would love to find more CTL activities that would be good for a high school student. My group chose to teach a class from Apalachee High School about fractions. This class was one of the lower level classes at the school. We wanted to tie in the students' community into fractions. The teacher told us that many of the students in the class were basketball players. Therefore, we did a lesson on fractions by computing the free throws each student made to the number of chances they got. We made the students get into groups where each group member got five turns to ring a ball into a basket. After everyone went, they got back into their groups and added the total of baskets they made to the total they got to throw. Then, we made the students reduce their fraction. We then got back together as a class and added up the total amount of baskets made by the class to the amount they tried for. We did this by adding the fractions of each of the groups. This assignment taught the students about how fractions are used in every day life. This assignment was very successful in the classroom. It got the students to do a hand on project with fractions. It made the students realize that fractions are used in everything. They didn't just hear it from the teacher but they are visually getting to see how fractions are developed and how to solve them and why fractions can reduce. They also get to see how decimals are representations of fractions. The students had a great time doing this assignment. They told us that they got a lot more out of visually seeing things and using their hands to understand the topic being taught. The group work also went well because the group members worked together and taught the ones who were not understanding how to add the fractions. We did really well with time. We had 45 minutes to do the assignment and we used every minute to teach the fractions. We did not run out of time nor did we finish earlier. Everything went smoothly. Overall, I think the teacher and the students were impressed with this activity. There are some parts of this assignment that could be improved. For example, this assignment would be more effective if we could have used the gym. The clothesbasket and balls were not exactly a basketball and a hoop. We had problems with if we needed to count balls that went into the basket and then came out or not. However, this was a minor thing. Also, it would have been easier if I was the teacher because I would have paired students who could add fractions to those who struggled so that the student who knew what he/she was doing could teach the other student. Students say that sometime they learn more from the peers than they do from their teacher and this would have been a great opportunity for the students to teach one another. Overall, there were not any major problems with this assignment. I really had problems deciding on how many fractions to make the students do. I would have liked to give them a worksheet to do at home but since I was not the teacher I could not really do that. I also had a hard time deciding on the difficulty of the worksheets. Some of the students were excellent in adding fractions and reducing them while other students didn't even know where to begin. I had a hard time deciding if the worksheet should have been more difficult or easier. I wanted to make it even for everyone, but I didn't know how to. I don't want to leave a student behind in what the class is doing, but I can't just keep the class back for one student. It is hard deciding what is reasonable to ask the students to do. Overall, there are not many things that I couldn't think of some way to improve.
I think that there are many things that are important with contextual teaching and learning. Contextual teaching and learning helps students visually see what is going on, and it lets students learn from hands on experiences. Most students learn better when they are actually doing something and seeing how it relates to the community and why certain things are important to know. Contextual teaching may be more work for the teacher but in the long run the students will get more out of it then with lectures. Contextual teaching and learning gets the students involved in the topic being taught. I feel that contextual teaching and learning is important because I think that students will learn more through this kmd of learning than from lectures. However, it is important to keep some lectures in the classroom because the students need to be prepared for college and the lectures of every class. Overall, I do agree that contextual teaching and learning is the best way to teach younger students who have little attention spans. From teachers I have talked to, they tell me that they have a certain guideline they have to follow. Some said that they would not be able to do contextual teaching because it would not follow the guideline they have to go by. I would like to talk to the principals at different schools to see what they would allow a teacher to do and not do. I would also like to see what students would like. I think that the students' opinions and the principals' opinions are what really matter. I know that we will be able to do some easy stuff in the classroom, like we did with the free throws, but I don't know about going on field trips and extreme things like that. I am curious to see what schools will allow teachers to do and how far the teacher can go to get the students to understand what is being taught. I am wondering what the guidelines are and how elaborate a teacher can go in making her teaching as interesting as possible. I know that if my school did contextual teaching and learning, I would be able to remember more in what I did in high school and I would probably understand more things better. Overall, I thought this assignment was a lot of fun. It was neat looking at how the students did with our assignment and how they learned from it. I do believe that the students had fun with this assignment and that they really did learn something from it.

