Compiled Messages: ------------------------------------------------------------ Message no. 343 Posted by Julia Newsom (10231769) on Thursday, October 7, 2004 4:11pm Subject: Questions 1. What are the strategies, big ideas and models you see these children using? 2. How are these children developing mathematical ideas? 3. How is the context (for the first grade and kindergarten videos) influencing the learning? ------------------------------------------------------------ Message no. 344[Branch from no. 343] Posted by Julia Newsom (10231769) on Thursday, October 7, 2004 4:45pm Subject: Julia Newsom Hey guys. I went ahead and posted what I think are the questions from the assignment page. I'm answering from the video, rather than the reading--I think that's what I'm supposed to do, but I'm not sure! My examples all come from the folder titled "Games." 1. I saw students using a variety of strategies. The boy playing Capture 10 was using a derived facts strategy. He knew that 7+9 was 16, so he figured out that 8+7 must be 15, because 8 is one less than 9. The students playing Racing Dice were using a modeling strategy. In order to find the answer they count all the dots on the dice. Some big ideas the students are learning include skip counting by twos in the board game example. Rather than count 10 steps, when the student rolled double fives he counted only five pairs of steps. Another big idea for the students playing Compare is the concept of number size: which numbers are bigger, and which are smaller. Models being learned in these classrooms include the numbers the girls playing Racing Dice are tracing. After tallying the total number of dots on the dice, they then associate that number with a symbol, i.e. a printed number. The boys playing Capture Ten have learned to accept that the symbol "+" can be called called "and" as in "this one is 9 and 7." They have associated the addition symbol with the concept of putting two numbers together. 2. These students are developing mathematical ideas by grappling with the problems and the materials that have been given to them. They are not simply trying to figure out how to use an algorithm to solve a problem, but how to actually solve the problem logically while paying attention to the strategy that you used. Developing ideas this way requires higher-order thinking, because the question is not simply, "what do you do?" but, rather, "why did you do that?" Although hard to answer, this question can lead students to a deeper understanding of matematic ideas. 3. The students in these 1st grade and kindergarten classrooms are learning in a hands- on enviroment. They have the opportunity to form ideas, test them, and modify them if necessary. Because they are in a social context, they are not required to sit quietly and listen or work, but can move around, and talk about what they are learning. The students playing the Shoe Game question each other's solution, then return to the problem to see who is right. The social, interactional, and game-based context allows for learning to take place that is both meaningful and fun for the students. ------------------------------------------------------------ Message no. 356[Branch from no. 344] Posted by Margaret Saylor (10279519) on Sunday, October 10, 2004 1:23pm Subject: Re: Julia Newsom Reply to #3. These students did have the freedom to move around and share their thoughts with their peers. This type of collaborative learning promotes a sense of ownership in the lives of the students. By using their prior knowledge to connect to big ideas, the students acquire a better understanding of the material . ------------------------------------------------------------ Message no. 391[Branch from no. 344] Posted by Kristen Massey (10288759) on Monday, October 11, 2004 7:19pm Subject: Re: Julia Newsom Julia, I totally agree with you. Being a 4th grade teacher I forget the strategies and basics that primary teachers have to start out with. After watching the videos it made me realize that upper elementary teachers should have a greater appreciation for lower elementary teachers. All the videos revolved around addition and subtraction. In 4th grade I tend to teach the process of carrying, borrowing, regrouping. Seeing the capabilities of these students makes me feel guilty. I need to be giving my students more of an opportunity to explore and use manipulatives. In my class we use number lines and group tens and hundreds, etc... but not to the extent that I need to. I get into the rut of the traditional method. One of my favorite big ideas was also when the student was skip counting with the feet. I loved the way when the student rolled 10 or double 5's he counted 5 sets of feet. He knew that feet come in pairs so he counted 5 set of feet. So he practiced skip counting. The teacher explained back to the students what had just happened. In the energetic way that she did this I know the student must have felt a great sense of accomplishment. The teacher and students do a great job of modeling. I think all students enjoy learning in a hands-on environment. Younger children need to flexibility to be able to do this. Their attention span seem to last longer with the freedom to move aorund and talk with their peers. The teachers do a great job of utilizing guided learning in the class and never make the student feel like they are wrong. I liked it when the male teacher told the student to tell his classmates. That was neat to me because then the students feel like they have a say-so in their classroom. ------------------------------------------------------------ Message no. 396[Branch from no. 391] Posted by Julia Newsom (10231769) on Tuesday, October 12, 2004 10:29am Subject: Re: Julia Newsom I wouldn't feel guilty, if I were you, Kristen! I think most teachers resort to the the "traditional method" for a lot of good reasons. One of those reasons is probably that it works really well for a lot of kids. It has its downsides, however. One is that it is repetitive and can be incredibly boring. However, good teachers can make even boring lesson formats good, so it's not doomed to be boring. Another bigger problem is that the kids who "don't get it" get stuck that way. It's hard for the traditional methods to keep helping kids who are behind to keep learning. They tend to fall further back, rather than stay near or get closer to the class. An advantage to the non-traditional is that it is very adaptive to varying levels. However, non-traditional methods are not by any means perfect. I recently was in a class where we supposedly already knew how to do a specific task when we started the class, but we did it as small group projects just to review. The result: some students did great, but there was also major bombing on the test. I have to think that if we had done a more traditional teacher-taught-lesson-followed-by-individual-worksheet-with-graded- feedback we'd have all figured out what we didn't know before we failed a midterm. My point is, group work is great if everyone is working and understanding, but it is WAY too easy for some to learn and some sit there completely lost and either not say anything, or not even realize they don't know what's going on. ------------------------------------------------------------ Message no. 426[Branch from no. 396] Posted by Glenda Ogletree (10219209) on Friday, October 15, 2004 2:33pm Subject: Re: Julia Newsom I think traditional teaching (if it can really be defined)is just another strategy to reach students. Anything that works in a classroom is a good strategy. ------------------------------------------------------------ Message no. 463[Branch from no. 396] Posted by Angela Boatwright (10169491) on Saturday, October 16, 2004 11:26am Subject: Re: Julia Newsom I understand what you are saying about group work is an easy way for kids to get lost in the cracks. I have been in groups before when I thought I got the concept and I really did not. I have also been in groups where I did not understand but was to embarrassed to let my peers know that I did not get the concept. Lambert was very concious of this in her classroom and was constantly trying to create situations that were beneficial to her students. The journals also helped her to know who was on track and who was not. Group work has to be handled in a way that there is accountability and feedback through out the process otherwise the ones that are behind may only fall further behind. ------------------------------------------------------------ Message no. 460[Branch from no. 391] Posted by Angela Boatwright (10169491) on Saturday, October 16, 2004 11:20am Subject: Re: Julia Newsom I also noticed that this type of instruction seemed to work well for keeping the students attention focused. This is so important for the primary grades when the attention span seems so short to begin with. By linking the math concepts to things they are already familiar with (bunk beds, busses) the students were actively engaged in figuring out how to solve the problem. ------------------------------------------------------------ Message no. 347 Posted by Angela Boatwright (10169491) on Friday, October 8, 2004 11:42pm Subject: Angela Boatwright Julia, it is also my understanding that we answer the questions based on the video. However, the book contains some of the same information as the videos but in a more detailed format. My answers refer to the video clips found in the “Minilessons” folder. 1. What are the strategies, big ideas, and models you see these children using? Strategies – Many strategies were used in the Mini Lessons videos some of them were: rounding before adding, jump counting, number lines, drawing, grouping items before counting or adding, doubles+1, and illustrating the problem. Big Ideas – The big idea that was prevalent in all the videos was addition and subtraction. Grouping and unitizing were also evident. Models – Several models were used by teachers and students some were: circles on the overhead to represent the heads of children playing tag, number lines, Rekenrek (I loved the mini lesson with the bunk beds), and illustrations of jump counting. 2. How are these children developing mathematical ideas? They are developing mathematical ideas by trying to solve a problem posed by the teacher in their own way. The teacher is not showing them how to solve the problem she wants them to figure it out. In so doing the students have to arrive at an answer and be able to explain their thinking to others. They are working through their own thinking and reasoning to prove their answer is correct. Sometimes the answer was not correct and the student would realize it while he was attempting to explain his reasoning. 3. How is the context (for the 1st and K videos) influencing the learning? The type of context visible in the videos is teaching children from an early age that they are capable of talking about mathematics with peers and the teacher. It is helping them to get comfortable sharing their ideas and reasoning with others. They are also experiencing how math occurs in daily life. This type of teaching allows for multiple ways to solve problems because there is no set algorithm to follow. What is important is that the students understand the mathematical “big idea” in a real way. It is also allows for interaction with peers when struggling to solve a problem. I especially liked the clip of the man’s (Michael) classroom when one student was disagreeing with the thinking of one of his peers. He was trying to explain to the teacher why he disagreed and the teacher told him to tell that peer why he disagreed. I thought this taught so many things such as: we can learn from others, we can disagree in a calm fashion, and share our ideas in a community of learners. It is nice to see how others are implementing this type of teaching instead of merely reading about it. I am enjoying the videos. ------------------------------------------------------------ Message no. 353[Branch from no. 347] Posted by Glenda Ogletree (10219209) on Sunday, October 10, 2004 11:37am Subject: Re: Angela Boatwright The students were using jump counting. It's evident that they've been taught that term. I have used that strategy with students, but never used that term. I'm going to try to teach it to my class this week. Modeling was evident in that abacuses were used to represent bunk beds and buses. ------------------------------------------------------------ Message no. 397[Branch from no. 347] Posted by Julia Newsom (10231769) on Tuesday, October 12, 2004 10:36am Subject: Re: Angela Boatwright Angela, I too enjoyed the videos. I think it's cool to have some "real kids" even though this is distance ed. I like your description of how students develop mathematical ideas. It is not just spoon- fed formulas, but real thinking to solve real problems. It's like what =engineers must do when they are faced witha jet engine that is faulty. They don't just perform mindless memorized tables (although I'm sure that's an important part of it), but they use what they know about principles, and apply them to a problem in new ways. It's a completely different mindset than filling out worksheets gives a student. I think it's cool. ------------------------------------------------------------ Message no. 351 Posted by Glenda Ogletree (10219209) on Sunday, October 10, 2004 10:09am Subject: discussion The big ideas used in the videos showed students unitizing and using patterns. The strategies that were used basically gave the students freedom to discover the answer. There was no "right" way to solve problems. Individual students used whatever way was comfortable to them to find the answers. The teachers constantly asked questions, and they continually encouraged students to explain how they arrived at an answer. Children were developing mathematical ideas through solving problems and explaining their answers. This also helped show other students that there are many ways to arrive at an answer. The students had a lot of freedom. The context used provided real life situations for the students. The video about playing tag was actually what the teacher had observed her students doing so the students knew this was a real situation. Most students know what bunk beds are and really like bunk beds. The students could visualize children climbing up and down the bunk beds. It was age appropriate. The double-decker bus wouldn't be quite as familiar to young children, but the teacher actually had a toy bus to show them. They may have seen a double- decker bus on TV, but probably all of them had not seen one. Double-decker buses are fascinating to Americans because we don't use them. ------------------------------------------------------------ Message no. 355[Branch from no. 351] Posted by Margaret Saylor (10279519) on Sunday, October 10, 2004 1:20pm Subject: Re: discussion I agree the strategies that the students used were their own. They made connections with what they already new about the patterns. In the playing tag example, the students were developing patterns to add up to the number 10. The teacher allowed the students to perform different strategies to arrive at the same conclusion. The students arrive at their own conclusions and derive meaning from their own strategies. In the bunk bed example, the students were developing the big idea of addtion and subtraction. Some of the students knew that if they took one away, then they had to add that one to the other bunk. They used different strategies to arrive at the same conclusion. The context of these mathematical situations is used for constructing meaning at the beginning of the lesson. The teacher poses a situation and allows the students to develop their own ideas to find the solution. She does not show them an algortithm that they must do to solve the porblem. Instead, she poses a problem and allows the students to solve it based on their understanding of the problem. She guides them in the mathematical direction that they need to go. Lampert was similiar in her model. She used the problems, rather than the method, to promote discussion and learning. ------------------------------------------------------------ Message no. 354 Posted by Mary Steppe (10318942) on Sunday, October 10, 2004 1:09pm Subject: Mary Ann-Discussion I enjoyed watching the videos! I agree with what Angela, Julia, and Glenda have already discussed. The students in the videos were challenged to find the right answer their way. The students were using the statregies of number patterns. They also used this to develop their mathematical ideas. I read some of the text and in one of the examples in the number line a little girl found the correct answer, but had switched numbers in the problem, for example, if the problem was 52+99=, this little girl did 59+92= and got the same answer. The teacher accepted this because the student explained what she did. I enjoyed watching the bunk beds lesson and watching the students use the counter. They were really enjoying that lesson! Glenda was right on about the context being real life situations. The teachers all were teaching these counting patterns in a context that the students could use. The context for learning for the kindergarteners and first graders was fun lessons where they could apply their math concepts that they know and have a good time. Learning is suppose to be fun. The teachers did lessons where the students were sitting on the floor or playing games. I did see students sitting in desk doing worksheets. ------------------------------------------------------------ Message no. 398[Branch from no. 354] Posted by Julia Newsom (10231769) on Tuesday, October 12, 2004 10:39am Subject: Re: Mary Ann-Discussion Hi, Mary Ann! I liked the way the teachers were so attentive to their students. Honestly, I found a lot of what the students said hard to follow (as did their teachers at times!) but they listened, asked questions, and were sincerely interested in what the students were saying. I don't think it would be possible to get students to discuss their ideas and thinking unless they knew that you the teacher cared about what they think. ------------------------------------------------------------ Message no. 412[Branch from no. 398] Posted by Margaret Saylor (10279519) on Wednesday, October 13, 2004 4:44pm Subject: Re: Mary Ann-Discussion I agree. It reminds me a lot of the "Richard" example in Lampert's book. He was only able to adopt a new mathematical mindset when he knew that his thoughts counted. Like a lot of our students, they just want to be accepted and do the right thing. I need to do a better job listening to my students and try to make sense of their thinking. ------------------------------------------------------------ Message no. 438[Branch from no. 398] Posted by Rebecca Gregory (10474735) on Friday, October 15, 2004 10:12pm Subject: Re: Mary Ann-Discussion Margaret, I agree with you whole heartedly. Children are often intimidated easily especially if they are not comfortable in their learning environment. They can never be put down in any manner or they "shut down". I put so much effort into trying to make my children feel comfortable and to always be positive in my responses. There is always something positive to say about their thinking so they don't feel bad about what they have done or are thinking. Creating that comfort for each child, I think, is half your battle as a teacher. when they feel they can express themselves freely and never be made to feel embarassed they will open up and learn. I am not as comfortable with math myself so I know exactly how they feel. And Julie, Yes you do have to determine your goal. Is it the process or the correct answer. In my classes of sp. ed. my children so often reverse their numbers. I can check for correct answers or I can take the time to check their process and they have the right answer for what their mind worked with. 21 + 14 = 35, but they put 26 which is right for 12 + 14. It makes our job a little tougher and time consuming but we are teachers and to me understanding the processes they use is just as important as the correct answer. ------------------------------------------------------------ Message no. 409[Branch from no. 354] Posted by Emily King (10309206) on Wednesday, October 13, 2004 12:20am Subject: Re: Mary Ann-Discussion Mary, I agree that learning should be fun! I too noticed the worksheets/handouts. I began to not feel so bad when I have those days a few times a month where I am to sick/exhausted to stand around small groups and facilitate learning. (sad but true) When you brought up the example about the little girl rearranging her numbers, it reminded me of something that happened in college. I made the same type of error and I got the problem right. My professor told me that in the "real world" there is no room for error and I need to work with the correct information that was given. Do you feel that this is true? Or do you think it was true for a class at the college level? Where do you draw the line? Emily King ------------------------------------------------------------ Message no. 416[Branch from no. 409] Posted by Julia Newsom (10231769) on Thursday, October 14, 2004 2:23pm Subject: Re: Mary Ann-Discussion I think it depends a whole lot on the situation. You have to determine what the goal of your instruction will be and strive to achieve that. If your goal is for students to accurately reproduce a method, I would correct it. If, however, your goal is a specific concept, detailed number accuracy is not necessarily important enough to interupt the lesson for. Of course, you have to take care not to confuse the students with someone's incorrect numbers! ------------------------------------------------------------ Message no. 488[Branch from no. 416] Posted by Shannon Huff (10321480) on Saturday, October 16, 2004 9:21pm Subject: Re: Mary Ann-Discussion In response to Emily and Julie's conversation on transposing (or rearranging) the numbers. Emily, I agree with Julie and say that it depends on the situation. Of course in "real life" sometimes there IS no room for error in mixing up numbers even if the answer is right. For example, doctor's or nurses in amount of medication, construction worker's in measurements, etc. I think you get the picture. Sometimes it is very important to get the numbers right and not just the process in which to do it. Maybe that is what the professor was trying to get across to you and I would have to agree with that. There may even be instances at school that student's would have to be right in like paying for lunch or snack, giving back change, etc. that it would be important that it is right. However, in the classroom when your goal is for students to understand the PROCESS, I don't think it would be such a big deal if numbers were turned around if the answer was right. ------------------------------------------------------------ Message no. 378 Posted by Emily King (10309206) on Sunday, October 10, 2004 11:59pm Subject: discussion After typing more than 2 pages in response to my group members, I realized that I simply agreed with all of them, Angela, Mary, Glenda and Julia. I an sum up my response by saying that their are several differernt strategies, big ideas and models that were evident in the book, and CD. Strategies ranging from facts strategies to rounding and adding up. The big ideas such as skip counting, differentiating nymber size where all investigated by the student. The teacher only posed problems and allowed the students to think things through without labeling as right or wrong. They did however learn how to reason out their answers. In modeling, I too viewed the game of Racing Dice where the students traced numbers. On top of other models, this example took me back to my primary teaching days. I have been a part up intermediate grades for so long, I had forgotten that children needs models such as this to improve mathematical skills. ------------------------------------------------------------ Message no. 390[Branch from no. 378] Posted by Glenda Ogletree (10219209) on Monday, October 11, 2004 5:52pm Subject: Re: discussion Modeling was an important aspect of the math lessons. It seems to me that I sometimes get in a hurry to teach the math content without connecting the lesson to real life. ------------------------------------------------------------ Message no. 399[Branch from no. 390] Posted by Julia Newsom (10231769) on Tuesday, October 12, 2004 10:41am Subject: Re: discussion I think it's easy to overlook modeling because we find the problem to be straightforward and obvious. We see A and immeadiately think of B. For students, A and B may or may not have any connection to one another. How did we get from one to the other is the essence of modeling. ------------------------------------------------------------ Message no. 408[Branch from no. 399] Posted by Emily King (10309206) on Wednesday, October 13, 2004 12:01am Subject: Re: discussion I must first apologize to all of my spelling errors. I try not to ever let anything slip, and that was horrific!!!! In response to Julia and Glenda, I teach a higher, advanced math class, and oftentimes the children are 'in a sense' modeling for me or each other. I often forget how important steps like these are for me to show them, because I take for granted that there might actually be something that my students don't know. ------------------------------------------------------------ Message no. 439[Branch from no. 390] Posted by Rebecca Gregory (10474735) on Friday, October 15, 2004 10:16pm Subject: Re: discussion Glenda, I agree. We have a timeline and get in that spinning wheel and just teach content and don't allow the time to apply to life. I have found in my planning to just stop one day and make it sort of a play day or game day and use the concepts we have been learning and let them play games or like in kindergarten or 1st grade play store when we are learning about money and just sit back and watch and listen. We are surprised quiet often at how they have internalize the learning when we thought they weren't listening. Rebecca ------------------------------------------------------------ Message no. 459[Branch from no. 390] Posted by Angela Boatwright (10169491) on Saturday, October 16, 2004 11:17am Subject: Re: discussion I think the "hurriedness" we sometimes feel is the pressure to get it taught before testing time. ------------------------------------------------------------ Message no. 572[Branch from no. 459] Posted by Emily King (10309206) on Sunday, October 17, 2004 6:47pm Subject: Re: discussion I agree once again and this testing timeline goes back to the question, "Am I reaching the needs of all of my students, or am I just teaching to test?" This class had opened my eyes to a new way of thinking, I hope I just don't drown in my thoughts! Emily ------------------------------------------------------------