Overall this quarter I have worked more in depth with mathematics than ever before. In hindsight, I cannot believe it has only been a couple months. This experience would have been valuable starting in September. It is if we have only scratched the surface of teaching children math.
In conjunction with the third grade class I student teach in, the quick images activity was very useful. I taught it alongside my first math lesson, which was also their first day of multiplication. The flexibility of this activity is truly amazing. Additionally the talk moves we learned this quarter has completely revolutionized my teaching. I use them in every lesson I teach to deepen the responses I receive from my students. My mentors have even noticed!
I'm excited in the next two months, and my future profession, to continue to apply what I've learned. I plan on using math in the TPA and I hope i'm able to adapt the curriculum handed to me to meet the needs of my students.
Showing posts with label Math Winter 2012. Show all posts
Showing posts with label Math Winter 2012. Show all posts
Friday, March 2, 2012
Mathematical Interviews
At the end of our quarter, we spent time interviewing students about how they saw themselves as mathematicians. Initially the two children I asked told me that in order to be good at math, you must be quick and get the right answer. Honestly, their answers didn't surprise me. I probably would have answered the same way in elementary or even high school. We discussed earlier this quarter that students do not view themselves as being "good" at math unless they are fast, but I had never asked a student directly.
During the interview I explained to them that I had a list of different ways of being smart at math. Each person has their own strengths, and something they are working on. Being smart doesn't always mean you get the right answer, but how you use your smarts to try to solve a problem or work with others. Both of my students were shy. I got them to talk more and help me find examples for each point on the list. At the end the girl wrote four or five things at the bottom she wanted to improve. The boy didn't want to change anything. I asked if he could think of a smart that wasn't on the list. When he said no, we discussed strategies he used to solving a division problem his teacher left on the board. I asked him if using multiple strategies to solve a problem would be a math smart? Both students agreed.
Ultimately, my students were quiet but I think we had a great conversation about math. Even if this discussion doesn't change their mind, it opens them up to the possibilities of other ways to be smart. Math was difficult for me, so I can understand how it may be difficult to view "math smarts" in other ways.
It was a great end to our time at Woodmoor! I cannot believe there is only one more week.
During the interview I explained to them that I had a list of different ways of being smart at math. Each person has their own strengths, and something they are working on. Being smart doesn't always mean you get the right answer, but how you use your smarts to try to solve a problem or work with others. Both of my students were shy. I got them to talk more and help me find examples for each point on the list. At the end the girl wrote four or five things at the bottom she wanted to improve. The boy didn't want to change anything. I asked if he could think of a smart that wasn't on the list. When he said no, we discussed strategies he used to solving a division problem his teacher left on the board. I asked him if using multiple strategies to solve a problem would be a math smart? Both students agreed.
Ultimately, my students were quiet but I think we had a great conversation about math. Even if this discussion doesn't change their mind, it opens them up to the possibilities of other ways to be smart. Math was difficult for me, so I can understand how it may be difficult to view "math smarts" in other ways.
It was a great end to our time at Woodmoor! I cannot believe there is only one more week.
Sunday, February 19, 2012
Choral Count on Valentine's Day
This week I facilitated another choral count, this time counting by 6's. For the first time I felt prepared to use all of my talk moves (revoicing, reasoning, restating, adding-on, and wait time). I have been practicing them in each lesson I teach in my main placement to great success. When students know you expect more from them than the "right answer", they rise to the challenge and explain their thinking.
During this choral count, there were five students. Three boys nearest to the white board participated with a lot of energy and input. The two girls in the back seemed distracted near the end. This could have been because it was hard for them to hear or because the boys occasionally spoke over them. The choral count also went on too long. Our group discussed later that it would have been more productive to switch numbers and find new patterns.
During the choral count we listed numbers by 6's horizontally to 30 before starting a new row. Once we counted to 54, I asked the students to find patterns. They caught on to the ones place staying the same, while the tens place adding three (when looking vertically). This allowed for a long discussion on predictions for future numbers. We then continued to count to see if our patterns continued. Throughout the process we asked students to revoice each other's explanations, explain how they found their patterns, and apply each other's patterns to other parts of the problem. Once my group member noticed the girls we not participating, I made a greater effort to involve them.
During this choral count, there were five students. Three boys nearest to the white board participated with a lot of energy and input. The two girls in the back seemed distracted near the end. This could have been because it was hard for them to hear or because the boys occasionally spoke over them. The choral count also went on too long. Our group discussed later that it would have been more productive to switch numbers and find new patterns.
During the choral count we listed numbers by 6's horizontally to 30 before starting a new row. Once we counted to 54, I asked the students to find patterns. They caught on to the ones place staying the same, while the tens place adding three (when looking vertically). This allowed for a long discussion on predictions for future numbers. We then continued to count to see if our patterns continued. Throughout the process we asked students to revoice each other's explanations, explain how they found their patterns, and apply each other's patterns to other parts of the problem. Once my group member noticed the girls we not participating, I made a greater effort to involve them.
Friday, February 10, 2012
Choral Count
During our 3rd grade choral count, another student teacher and myself choose to vertically write multiples of 4, as students counted aloud. We first stopped at 28, because "ethan" noticed that we were adding by 2 each time in the tens place. As we continued to count on, he also made a connection that the ones place repeated the digits: 4,8,2,6,0. "Sara" say that after every three "count-bys" you added 12 overall. This concept was difficult for her table group to understand. When moving left to right on the table, "Sara" also noticed you add 2 to the tens column.
In a larger group, I think there may be more opportunity for a variety of patterns, explanations, and conversation to emerge. The entire process is student generated. In our small group we had a lot of great ideas, but it was difficult for students who didn't understand to revoice. The value of a large group is that multiple people can revoice or explain an "abstract" idea in a way that a teacher or one peer cannot. Students also take ownership of their learning when they explain their answer and justify their reasoning.
-------------------------------->
Add two to the tens column
In a larger group, I think there may be more opportunity for a variety of patterns, explanations, and conversation to emerge. The entire process is student generated. In our small group we had a lot of great ideas, but it was difficult for students who didn't understand to revoice. The value of a large group is that multiple people can revoice or explain an "abstract" idea in a way that a teacher or one peer cannot. Students also take ownership of their learning when they explain their answer and justify their reasoning.
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Add two to the tens column
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4
|
24
|
44
|
64
|
84
|
|
8
|
28
|
48
|
68
|
88
|
|
12
|
32
|
52
|
72
|
92
|
|
16
|
36
|
56
|
76
|
96
|
|
20
|
40
|
60
|
80
|
100
|
Friday, February 3, 2012
Quick Images and Interviews
This quarter we've had the opportunity to work closely with students and practice elicit their thinking in new ways. I have found that in my main placement that structure my lessons around repeating, adding-on, and re-voicing, ect... in the lessons I teach. During our first quick image teaching experience, the questions didn't come naturally to me. I still find that I forget wait time, and to ask students to connect two ideas (reasoning).
During the math interview with one student, I think I was too eager to use my questioning techniques. There is definitely a time and a place. For example, my student was making some great connections without me interjecting to ask how she could expand on her ideas. Additionally during the math cohort meeting, several teachers made the same remark. You won't necessarily use each of the five questioning techniques each lesson, or your kids will get bored. With that said, i'm coming to realize which times are appropriate to ask which questions when I teach. It's very useful!
Last week I introduced weight and mass. A student told me that you'd weight 50lbs more if you were on Jupiter. I asked him why, and once he introduced gravitational force for me, I asked him if I could add on to his idea by comparing the moon and the earth. Our class had an unanticipated and exciting discussion about weight versus mass in the universe. At the end, I asked someone to revoice (retell) what he had said about Jupiter versus the moon. It was SO cool!
During the math interview with one student, I think I was too eager to use my questioning techniques. There is definitely a time and a place. For example, my student was making some great connections without me interjecting to ask how she could expand on her ideas. Additionally during the math cohort meeting, several teachers made the same remark. You won't necessarily use each of the five questioning techniques each lesson, or your kids will get bored. With that said, i'm coming to realize which times are appropriate to ask which questions when I teach. It's very useful!
Last week I introduced weight and mass. A student told me that you'd weight 50lbs more if you were on Jupiter. I asked him why, and once he introduced gravitational force for me, I asked him if I could add on to his idea by comparing the moon and the earth. Our class had an unanticipated and exciting discussion about weight versus mass in the universe. At the end, I asked someone to revoice (retell) what he had said about Jupiter versus the moon. It was SO cool!
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