I see many comparisons between literacy and numeracy already.
I realized the importance of teaching children estimation and how to make "guesstimates." To make estimates, discuss them, and defend them can be very powerful in the classroom. It helps children make sense of the math and the processes.
Positive self-talk is something that I will encourage much more. Especially with students who are scared of challenges, positive self-talk is something they can really benefit from in any given situation, math or not. I loved the end of this section when it compared maintaining mental stamina with professional baseball.
I really like the idea of Working Answer Keys when learning a new skill and/or concept. It's a great way for the students to take ownership of their own learning, collaborate with others, and repair their understanding. This is something I'd love to attempt this year.
Defending their guesstimates will help them put language to their numeracy. Math journals are a great way to do this. Having a common stem, "Explain your thinking...and tell why?" works for nearly every grade level.
I think "slow down" will be a priority in my teaching/classroom this school year. Students need to read, reread, and look again to clarify meaning, but often they hurry to just "get it done".
Although mental math is stressed in every math program, I believe increasing the mental math ability in our students is critical to constructing numerate understanding (that inner conversation). I like the idea of using friendly numbers to make meaning.
Finally, I feel that "think aloud" is an important part of teaching, but I don't really have students teach each other that way. I will definitely try that especially because it's recommended for mixed ability groups!
In looking at our data, we noticed that number sense and numerical operations will give us the biggest bang. "Think aloud" can be done by the teacher, too. Modeling metacognition helps students recognize their own.
I really found all the repairing and monitoring strategies to be very helpful. Nothing new, but a great reminder for next year.
The three repairing strategies that stood out the most to me were: "Does what I'm doing make sense so far?", try solving the problem a different way, and slow down.
1) Does what I'm doing make sense so far - this strategy was a great because the concept of "Reasonable" can be used in so many different subjects. This concept will help those students that tend to guess and feel that they gave their best effort. Teaching this strategy with examples and non-examples is how I will incorporate this into my classroom.
2)Try solving the problem in a different way - If students are able to take their thinking from a problem and show their understanding by using another strategy for the same problem, then they have truly evaluated and thought about what they are trying to show.
3)Slow Down - Students are in such a rush to be the first one finished. This is something that I am really going to work on this year. Having the students slow down and appreciate what they are learning will help them to understand.
The measurement ideas and the answer key strategy were great ideas that I would like to try this next school year!!
Isn't "Reasonable" such a powerful word. How can we use this word with kids all the time? I don't remember if it was at Maggie Math Moments, but they talked about giving the answer to kids and having them work out some problems. Maybe have them "guesstimate" the answer, give them the real one and tell how far off they were and why.
"When we repair our understanding we figure out what to do when we are confused." Three strategies: 1-Build stamina; (Daily Five talks about stamina for reading and writing also.) 2-Providing the answer key; I am processing how this could look in kinder.... 3-I like how our everyday math (home connections book especially) has a focus to the everyday math moments needed.
I have always seen a value of having students estimate their answers, but I had not seen it through the lens of mathematical thinking. By asking students to arrive at reasonable estimates, they are lead to better understand the process needed to find the answer. As Walton says, “Guestimation is numerate thinking in action.”
2. “Seek help from an outside source”
We know collaboration with peers is crucial to learning, but it takes place more often during content areas other than math. After thinking about this first chapter, it seems to me that conversation during math is extremely important. Especially with the younger grade levels, when writing and (accurate) drawing may not be the easiest/quickest/most direct way of expressing mathematical thinking, conversations need to happen. Students need to ask one another for help and engage in conversations about the process. This will help to strengthen their internal conversations, mathematical vocabulary, and overall understanding of content.
3. “Solve a problem two different ways”
By solving the same problem using two different methods, students first and foremost can compare their answers and look for discrepancies (leading to the “why” and “how” questions about the process). Students can also think about the process of arriving at the answer and why each of the two cross-checking methods work. This reminds me of the “Math Moments with Maggie Schaeffer” when she had us solve an addition/subtraction problem and then showed us an alternative method used by a parent of hers in Mexico. When she asked us “why” the second algorithm worked, I feel like I gained a whole new understanding of the general process of something I do without even thinking about anymore.
I can see how having students solve in two different ways will really help them stretch their thinking. A simple way I see students collaborating is solving the problem alone and then comparing their answers with a partner or table groups. When there are different answers, that forces them to do some rethinking. Megan, you are right about vocabulary! When they have time to use the math vocabulary in context it becomes part of their own vocabulary.
--Make a logical guesstimate - one that many kinders need a lot of practice with - modeling with a think aloud would be key. --Seek help from an outside source - collaboration. --Connect to background knowledge - scaffolding. --Try to get a picture in your mind-important to model with a think aloud for kinder and for increasing mental math ability. --Building stamina
"The main good of math should be to deeply understand concepts, not just memorize facts and procedures."
This really struck a chord with me. While some memorization of basic facts is needed, if students don't understand the concepts behind the procedures then they will never know when their answers are way off base.
I also liked the "Working Answer Key" idea. When I first learned to use Everyday Math the trainer suggested this technique for going over homework. I have never tried it, but it seems like it would not only be a paperwork time saver but also a great teaching time for them to monitor and repair there learning. It could work with Math Boxes, too.
I'm going to be more cognizant of Think Aloud in my teaching and help the kids to do the same so they can teach others.
Here are some of the things from Ch.1 in my book that fit into your discussion: 1) the importance of discussing strategies for finding solutions, rather than focusing only on outcomes 2) modeling mistakes and recovery for students, sometimes by discussing conflicting ideas about answers 3) the importance on using the word "already" in describing what a student currently knows, and "yet" when discussing something they don't know (getting them to say," I don't understand how to do that "yet."
These are my top three strategies that I would use. 1. Make a logical guesstimate - This one is important to start at a young age. The younger they are when they learn how to make a logical guesstimate, the better they will understand it in later grades. I see this becoming a regular part of math time. Students in Kinder could start off guesstimating the amount of objects on the table and defending how they know their answer is correct. This could be done as group work at the beginning of the year to learn the vocabulary needed. Later they could guesstimate the number of object in two groups (adding). 2. Connecting the problem with background knowledge - This strategy is so important, especially for ELL students. It helps students connect to their learning. Relating the problem to their everyday lives will also make it more meaningful. 3. Solve a problem in two different ways - I know that in Investigations they solve every problem using pictures, numbers, and words. I have noticed that my personal children, when they are paying attention, notice when their picture problem and their number problem don't match. They then have to relook at their work and find their mistake.
Mystery measures to develop a sense of size and space. Mystery staff member measurement can be used for introducing different units of measurement, plus it would be fun. Send answer sheet home with homework. Most would find their own mistakes and parents would come to understand it.
I see many comparisons between literacy and numeracy already.
ReplyDeleteI realized the importance of teaching children estimation and how to make "guesstimates." To make estimates, discuss them, and defend them can be very powerful in the classroom. It helps children make sense of the math and the processes.
Positive self-talk is something that I will encourage much more. Especially with students who are scared of challenges, positive self-talk is something they can really benefit from in any given situation, math or not. I loved the end of this section when it compared maintaining mental stamina with professional baseball.
I really like the idea of Working Answer Keys when learning a new skill and/or concept. It's a great way for the students to take ownership of their own learning, collaborate with others, and repair their understanding. This is something I'd love to attempt this year.
Defending their guesstimates will help them put language to their numeracy. Math journals are a great way to do this. Having a common stem, "Explain your thinking...and tell why?" works for nearly every grade level.
DeleteI think "slow down" will be a priority in my teaching/classroom this school year. Students need to read, reread, and look again to clarify meaning, but often they hurry to just "get it done".
ReplyDeleteAlthough mental math is stressed in every math program, I believe increasing the mental math ability in our students is critical to constructing numerate understanding (that inner conversation). I like the idea of using friendly numbers to make meaning.
Finally, I feel that "think aloud" is an important part of teaching, but I don't really have students teach each other that way. I will definitely try that especially because it's recommended for mixed ability groups!
In looking at our data, we noticed that number sense and numerical operations will give us the biggest bang. "Think aloud" can be done by the teacher, too. Modeling metacognition helps students recognize their own.
DeleteI really found all the repairing and monitoring strategies to be very helpful. Nothing new, but a great reminder for next year.
ReplyDeleteThe three repairing strategies that stood out the most to me were: "Does what I'm doing make sense so far?", try solving the problem a different way, and slow down.
1) Does what I'm doing make sense so far - this strategy was a great because the concept of "Reasonable" can be used in so many different subjects. This concept will help those students that tend to guess and feel that they gave their best effort. Teaching this strategy with examples and non-examples is how I will incorporate this into my classroom.
2)Try solving the problem in a different way - If students are able to take their thinking from a problem and show their understanding by using another strategy for the same problem, then they have truly evaluated and thought about what they are trying to show.
3)Slow Down - Students are in such a rush to be the first one finished. This is something that I am really going to work on this year. Having the students slow down and appreciate what they are learning will help them to understand.
The measurement ideas and the answer key strategy were great ideas that I would like to try this next school year!!
Isn't "Reasonable" such a powerful word. How can we use this word with kids all the time? I don't remember if it was at Maggie Math Moments, but they talked about giving the answer to kids and having them work out some problems. Maybe have them "guesstimate" the answer, give them the real one and tell how far off they were and why.
Delete"When we repair our understanding we figure out what to do when we are confused."
ReplyDeleteThree strategies:
1-Build stamina; (Daily Five talks about stamina for reading and writing also.)
2-Providing the answer key; I am processing how this could look in kinder....
3-I like how our everyday math (home connections book especially) has a focus to the everyday math moments needed.
At the Title One submit this week we talked a lot about stamina. A true need.
Delete1. “Make a logical guestimate”
ReplyDeleteI have always seen a value of having students estimate their answers, but I had not seen it through the lens of mathematical thinking. By asking students to arrive at reasonable estimates, they are lead to better understand the process needed to find the answer. As Walton says, “Guestimation is numerate thinking in action.”
2. “Seek help from an outside source”
We know collaboration with peers is crucial to learning, but it takes place more often during content areas other than math. After thinking about this first chapter, it seems to me that conversation during math is extremely important. Especially with the younger grade levels, when writing and (accurate) drawing may not be the easiest/quickest/most direct way of expressing mathematical thinking, conversations need to happen. Students need to ask one another for help and engage in conversations about the process. This will help to strengthen their internal conversations, mathematical vocabulary, and overall understanding of content.
3. “Solve a problem two different ways”
By solving the same problem using two different methods, students first and foremost can compare their answers and look for discrepancies (leading to the “why” and “how” questions about the process). Students can also think about the process of arriving at the answer and why each of the two cross-checking methods work. This reminds me of the “Math Moments with Maggie Schaeffer” when she had us solve an addition/subtraction problem and then showed us an alternative method used by a parent of hers in Mexico. When she asked us “why” the second algorithm worked, I feel like I gained a whole new understanding of the general process of something I do without even thinking about anymore.
I can see how having students solve in two different ways will really help them stretch their thinking. A simple way I see students collaborating is solving the problem alone and then comparing their answers with a partner or table groups. When there are different answers, that forces them to do some rethinking. Megan, you are right about vocabulary! When they have time to use the math vocabulary in context it becomes part of their own vocabulary.
Delete--Make a logical guesstimate - one that many kinders need a lot of practice with - modeling with a think aloud would be key.
ReplyDelete--Seek help from an outside source - collaboration.
--Connect to background knowledge - scaffolding.
--Try to get a picture in your mind-important to model with a think aloud for kinder and for increasing mental math ability.
--Building stamina
"The main good of math should be to deeply understand concepts, not just memorize facts and procedures."
ReplyDeleteThis really struck a chord with me. While some memorization of basic facts is needed, if students don't understand the concepts behind the procedures then they will never know when their answers are way off base.
I also liked the "Working Answer Key" idea. When I first learned to use Everyday Math the trainer suggested this technique for going over homework. I have never tried it, but it seems like it would not only be a paperwork time saver but also a great teaching time for them to monitor and repair there learning. It could work with Math Boxes, too.
I'm going to be more cognizant of Think Aloud in my teaching and help the kids to do the same so they can teach others.
Here are some of the things from Ch.1 in my book that fit into your discussion:
ReplyDelete1) the importance of discussing strategies for finding solutions, rather than focusing only on outcomes
2) modeling mistakes and recovery for students, sometimes by discussing conflicting ideas about answers
3) the importance on using the word "already" in describing what a student currently knows, and "yet" when discussing something they don't know (getting them to say," I don't understand how to do that "yet."
These are my top three strategies that I would use.
ReplyDelete1. Make a logical guesstimate - This one is important to start at a young age. The younger they are when they learn how to make a logical guesstimate, the better they will understand it in later grades. I see this becoming a regular part of math time. Students in Kinder could start off guesstimating the amount of objects on the table and defending how they know their answer is correct. This could be done as group work at the beginning of the year to learn the vocabulary needed. Later they could guesstimate the number of object in two groups (adding).
2. Connecting the problem with background knowledge - This strategy is so important, especially for ELL students. It helps students connect to their learning. Relating the problem to their everyday lives will also make it more meaningful.
3. Solve a problem in two different ways - I know that in Investigations they solve every problem using pictures, numbers, and words. I have noticed that my personal children, when they are paying attention, notice when their picture problem and their number problem don't match. They then have to relook at their work and find their mistake.
Mystery measures to develop a sense of size and space.
ReplyDeleteMystery staff member measurement can be used for introducing different units of measurement, plus it would be fun.
Send answer sheet home with homework. Most would find their own mistakes and parents would come to understand it.