I think this is a great shift and dovetails nicely with the 4th shift about creating language rich classrooms. I am a bit concerned with some of Leinwands' examples though. When I think about the math that my 5th grader is doing, she is no where near ready to tackle this level of difficulty yet, so I wonder what age group Leinwand is writing for and wish that some of his examples were questions that elementary aged teachers could use. Younger students can learn to interpret basic graphs or create graphs from a set of numbers. Students can also learn to make conjectures about data, like we did in class a few weeks ago. Unfortunately, I think most students will need to be taught how to do this since it has not incorporated into the math curriculum before.
Lyanne-you make a great point about teaching this to all students. The more exposure that they get, the more comfortable they will become reporting and interpreting data. I think students need to be reminded to read what information is included on the graph or table before they begin to answer any questions
I agree with Jeanne. When you questioned the age group that Leinwand was targeting, I think you were on to something. By starting to introduce graphs and charts to the younger grades, this will only make students more comfortable working with them in the future.
I liked how Leinwand talked about having the students formulate the questions or have the students predict what the data on a chart, table, or graph represents. This was similar to the activity we did in class in regards to lengths of babies at birth, height of NBA players, and length of snakes etc. These types of activities encourage the students to think about the information more that simply solving the task at hand and promotes a stronger sense of numbers. I also liked how he had the students perform a number of tasks using the information found on the visual representations.
Jeanne- I am glad that you mentioned our learning in your post. When I read from this book I always relate the information to my students, or the students of an elementary age, which I shouldn't. Thank you for sharing that perspective because now I am thinking of this chapter as teaching high school and college aged students and my how it is very different from the lessons I was thinking of for kindergarten!
I was definitely interested when reading this chapter because Leinwand provided numerous opportunities to incorporate real world data into the application of mathematics. We don't realize how much math is a part of our daily lives. By giving students the opportunity to collect data and show it in a visual representation is a really great strategy to help them build a better understanding of where all this is coming from. I think that one of the best instructional shifts would be this one because a lot of learners, especially students with special needs, need to have a visual in front of them to help understand concepts we're teaching in math. It may seem like such an obvious technique, but it is something teachers need to do more often in their classrooms.
I agree Holly. I think it especially important to all students, not just the younger ones even, to have concrete examples to refer back to. I've seen this in my classroom this semester with eighth graders. Their concepts of place value and how many a six in the thousands place represents seemed amazingly abstract and a challenging question for them. I think that we do miss how much math is part of our daily lives and that all students need to have concrete real life examples to better understand math concepts.
Holly - I complete agree with you. It is so important for visual learners to have the ability to "see" the math they are working on by charting it in a graph or table. Students, and in fact most people, do not realize how much math they do each day without even realizing it. We have all heard about how important it is to incorporate real world situations into our teaching and having students make graphs, charts and tables of things they are doing each day is a great way to teach number sense - which we just read about in Shift 5 - to younger learners.
The exercises and ideas Leinwand presents in this chapter are really exciting. The collaboration between the students, and the teachers adopting a "So" strategy is a way to capture students attention. Add in some relevant data and you've got a winning lesson plan. The questions that can be asked will generate more than one right answer and help to strengthen reasoning skills as well. The use of data encourages a range of mathematical skills. The use of technology can be included or not.
I agree with Liza here, and think that a lesson plan similar to this, with students of any age, would be exciting and captivating and the students would leave the lesson with a deeper understanding of numbers. I would be more interested in learning to incorporate some technology! Any ideas?
Again, I have to say that I'm impressed by the conversation piece that Leinwand emphasizes here. It is so important to get students to be able to hold a conversation and share their views, especially when it comes to data, charts, and graphs. Everyone sees things in a different light, and it is important that we let students express these views in order to open everyone's mind in the classroom.
I found in very interesting that what Leinwand did in the first example of a chart with four numbers is something that we do with students (at the pre-K, K, and elementary levels) every single day. I was really proud to know that I am already implementing this "milking" strategy in the classroom. How many of you, or your children, do a weather chart in the morning for a morning meeting job? Instead of asking which type of weather is it today, we graph the information, and then we ask the children a series of questions about it; Which weather have we had the most of? Which weather have we had the least of? Why do you think there are no boxes colored above the snow picture on our graph? How many days have we been in school so far? Have we had the same amount of days with two different types of weather?
All of these questions are asking the students to analyze and think about more than just the one piece of information a textbook is looking for. It allows the students to use their number sense from the previous shift.
I really liked this chapter because I feel that often, teachers get stuck in their math books. I find myself getting sucked in to the text book and following the guided math book and not diverging from how the book wants to teach the subject. I appreciated the four different examples on how one could take a lesson on graphing, charts and table and apply it to different subjects, such as English with inferential reasoning, to current events, as the author did by finding the different numbers in the newspaper. I think that teachers get stuck in a box almost when concerning math and don't think of how to connect math, especially the simpler subjects to connect like tables and graphing, to different topics and real world occurrences.
I think this is a great shift and dovetails nicely with the 4th shift about creating language rich classrooms. I am a bit concerned with some of Leinwands' examples though. When I think about the math that my 5th grader is doing, she is no where near ready to tackle this level of difficulty yet, so I wonder what age group Leinwand is writing for and wish that some of his examples were questions that elementary aged teachers could use. Younger students can learn to interpret basic graphs or create graphs from a set of numbers. Students can also learn to make conjectures about data, like we did in class a few weeks ago. Unfortunately, I think most students will need to be taught how to do this since it has not incorporated into the math curriculum before.
ReplyDeleteLyanne-you make a great point about teaching this to all students. The more exposure that they get, the more comfortable they will become reporting and interpreting data. I think students need to be reminded to read what information is included on the graph or table before they begin to answer any questions
DeleteI agree with Jeanne. When you questioned the age group that Leinwand was targeting, I think you were on to something. By starting to introduce graphs and charts to the younger grades, this will only make students more comfortable working with them in the future.
DeleteI liked how Leinwand talked about having the students formulate the questions or have the students predict what the data on a chart, table, or graph represents. This was similar to the activity we did in class in regards to lengths of babies at birth, height of NBA players, and length of snakes etc. These types of activities encourage the students to think about the information more that simply solving the task at hand and promotes a stronger sense of numbers.
ReplyDeleteI also liked how he had the students perform a number of tasks using the information found on the visual representations.
Jeanne-
DeleteI am glad that you mentioned our learning in your post. When I read from this book I always relate the information to my students, or the students of an elementary age, which I shouldn't. Thank you for sharing that perspective because now I am thinking of this chapter as teaching high school and college aged students and my how it is very different from the lessons I was thinking of for kindergarten!
I was definitely interested when reading this chapter because Leinwand provided numerous opportunities to incorporate real world data into the application of mathematics. We don't realize how much math is a part of our daily lives. By giving students the opportunity to collect data and show it in a visual representation is a really great strategy to help them build a better understanding of where all this is coming from. I think that one of the best instructional shifts would be this one because a lot of learners, especially students with special needs, need to have a visual in front of them to help understand concepts we're teaching in math. It may seem like such an obvious technique, but it is something teachers need to do more often in their classrooms.
ReplyDeleteI agree Holly. I think it especially important to all students, not just the younger ones even, to have concrete examples to refer back to. I've seen this in my classroom this semester with eighth graders. Their concepts of place value and how many a six in the thousands place represents seemed amazingly abstract and a challenging question for them. I think that we do miss how much math is part of our daily lives and that all students need to have concrete real life examples to better understand math concepts.
DeleteHolly - I complete agree with you. It is so important for visual learners to have the ability to "see" the math they are working on by charting it in a graph or table. Students, and in fact most people, do not realize how much math they do each day without even realizing it. We have all heard about how important it is to incorporate real world situations into our teaching and having students make graphs, charts and tables of things they are doing each day is a great way to teach number sense - which we just read about in Shift 5 - to younger learners.
DeleteThe exercises and ideas Leinwand presents in this chapter are really exciting. The collaboration between the students, and the teachers adopting a "So" strategy is a way to capture students attention. Add in some relevant data and you've got a winning lesson plan. The questions that can be asked will generate more than one right answer and help to strengthen reasoning skills as well. The use of data encourages a range of mathematical skills. The use of technology can be included or not.
ReplyDeleteI agree with Liza here, and think that a lesson plan similar to this, with students of any age, would be exciting and captivating and the students would leave the lesson with a deeper understanding of numbers. I would be more interested in learning to incorporate some technology! Any ideas?
DeleteAgain, I have to say that I'm impressed by the conversation piece that Leinwand emphasizes here. It is so important to get students to be able to hold a conversation and share their views, especially when it comes to data, charts, and graphs. Everyone sees things in a different light, and it is important that we let students express these views in order to open everyone's mind in the classroom.
ReplyDeleteI found in very interesting that what Leinwand did in the first example of a chart with four numbers is something that we do with students (at the pre-K, K, and elementary levels) every single day. I was really proud to know that I am already implementing this "milking" strategy in the classroom. How many of you, or your children, do a weather chart in the morning for a morning meeting job? Instead of asking which type of weather is it today, we graph the information, and then we ask the children a series of questions about it; Which weather have we had the most of? Which weather have we had the least of? Why do you think there are no boxes colored above the snow picture on our graph? How many days have we been in school so far? Have we had the same amount of days with two different types of weather?
All of these questions are asking the students to analyze and think about more than just the one piece of information a textbook is looking for. It allows the students to use their number sense from the previous shift.
I really liked this chapter because I feel that often, teachers get stuck in their math books. I find myself getting sucked in to the text book and following the guided math book and not diverging from how the book wants to teach the subject. I appreciated the four different examples on how one could take a lesson on graphing, charts and table and apply it to different subjects, such as English with inferential reasoning, to current events, as the author did by finding the different numbers in the newspaper. I think that teachers get stuck in a box almost when concerning math and don't think of how to connect math, especially the simpler subjects to connect like tables and graphing, to different topics and real world occurrences.
ReplyDelete