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.
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.
-------------------------------->
Add two to the tens column
|
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
|
Classroom Differences
Classroom Set-up
Aside from my third grade placement, I observed two teachers at Medina this week. Each classroom had a different routine for starting their day, and a creative means of using their classroom space to reflect and enhance student learning. In the fifth grade classroom I observed, I noticed student artwork in several places. There was also a literacy wall, science wall, and a math wall with equations they had been learning. A standing white board in the front listed the schedule, and included a space at the bottom for students to sign up in advance for show and tell. In the fourth grade classroom, there were literacy vocabulary cards and concept posters covering all the walls. In the back of the room are large posters with questions paper clipped to the top and boxes drawn in below for students to attach a post it corresponding to their student number. The literacy posters ask students to practice making predictions, address cause and effect, make inferences, connect the text to themselves, and ask questions. This teacher has an especially large attachment to literacy because she piloted the Journeys reading curriculum for the district last year. In the third grade there is a nice balance of science, literacy, and math on the walls. Some posters are left blank, and there is some student work from earlier in the year. There were several table groups in each of the classrooms I visited as well as a space on the floor in the front of the room for lessons. Recently the third grade classroom I work in has changed to table groups of 2, in rows facing the front.
Morning Routine
Morning routines were also completely different in each classroom. For example, I observed a fifth grade teacher who expected her children to enter the classroom at 8:05, look at the smartboard for instructions, and begin morning work without directions. At 8:15 she went over the schedule, and began a morning meeting. Overall students are given a lot more work at this age. For example, the teacher interrupted morning work to remind students about two independent science articles they were responsible to read at home in preparation for a lesson. The fourth grade classroom read their schedule off the board and then attended a specialist. In the third grade classroom where I am an intern, the morning looks different. Children at this age need more direction, even though they have had a similar routine all year. In the 3rd grade, students are not let into the classroom until 8:05. Upon entering they will sometimes find directions on the board, and they are otherwise expected to silent read or work on "to-do" work until 8:15. The teacher does not go over the schedule, although the kids usually take notice and make comments individually. We also do not conduct morning meetings regularly.
Morning Meetings
The fifth grade teacher I observed used The Morning Meeting Book to start her lesson. Students sat on the floor in a large circle, and each said hello to one another according to the piece of paper and name they received. After introductions, they discussed nuts and bolts followed by show and tell. One student gives the class three clues, and the class asks that student questions to guess what they are sharing about. I have not observed my MT do a class meeting in the same way, but I have implemented a couple of steps to respect lessons using greetings from this book. I similarly did not observe the 4th grade teacher run a morning meeting, however they were a regular part of the second grade schedule during my dyad. Second graders shook hands in a chain around the circle, sang songs, talked about news, and played a game. I'm hoping to incorporate classroom meetings in my future classroom to build a sense of community and respect.
Aside from my third grade placement, I observed two teachers at Medina this week. Each classroom had a different routine for starting their day, and a creative means of using their classroom space to reflect and enhance student learning. In the fifth grade classroom I observed, I noticed student artwork in several places. There was also a literacy wall, science wall, and a math wall with equations they had been learning. A standing white board in the front listed the schedule, and included a space at the bottom for students to sign up in advance for show and tell. In the fourth grade classroom, there were literacy vocabulary cards and concept posters covering all the walls. In the back of the room are large posters with questions paper clipped to the top and boxes drawn in below for students to attach a post it corresponding to their student number. The literacy posters ask students to practice making predictions, address cause and effect, make inferences, connect the text to themselves, and ask questions. This teacher has an especially large attachment to literacy because she piloted the Journeys reading curriculum for the district last year. In the third grade there is a nice balance of science, literacy, and math on the walls. Some posters are left blank, and there is some student work from earlier in the year. There were several table groups in each of the classrooms I visited as well as a space on the floor in the front of the room for lessons. Recently the third grade classroom I work in has changed to table groups of 2, in rows facing the front.
Morning Routine
Morning routines were also completely different in each classroom. For example, I observed a fifth grade teacher who expected her children to enter the classroom at 8:05, look at the smartboard for instructions, and begin morning work without directions. At 8:15 she went over the schedule, and began a morning meeting. Overall students are given a lot more work at this age. For example, the teacher interrupted morning work to remind students about two independent science articles they were responsible to read at home in preparation for a lesson. The fourth grade classroom read their schedule off the board and then attended a specialist. In the third grade classroom where I am an intern, the morning looks different. Children at this age need more direction, even though they have had a similar routine all year. In the 3rd grade, students are not let into the classroom until 8:05. Upon entering they will sometimes find directions on the board, and they are otherwise expected to silent read or work on "to-do" work until 8:15. The teacher does not go over the schedule, although the kids usually take notice and make comments individually. We also do not conduct morning meetings regularly.
Morning Meetings
The fifth grade teacher I observed used The Morning Meeting Book to start her lesson. Students sat on the floor in a large circle, and each said hello to one another according to the piece of paper and name they received. After introductions, they discussed nuts and bolts followed by show and tell. One student gives the class three clues, and the class asks that student questions to guess what they are sharing about. I have not observed my MT do a class meeting in the same way, but I have implemented a couple of steps to respect lessons using greetings from this book. I similarly did not observe the 4th grade teacher run a morning meeting, however they were a regular part of the second grade schedule during my dyad. Second graders shook hands in a chain around the circle, sang songs, talked about news, and played a game. I'm hoping to incorporate classroom meetings in my future classroom to build a sense of community and respect.
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!
Constructive Feedback
On the 26th of January I taught a science lesson on making comparisons of measurements with my class of third graders. I spent a lot of time preparing for the lesson with my master teacher, and it ended up being the best lesson i've taught. I planned for the kids to continue our investigation from the previous day on arm span, compare class data, make frequency tables, and draw conclusions about the investigation's original question. I was integrating Math Expressions, and the FOSS kit. In addition to the objectives of the lesson, my goal was to pace my time well and utilize my master teacher during the lesson. My field instructor felt I met both my goals. I appreciated her feedback that I use a "firm but kind voice" with my students when asking for their attention. This is something I strive for, and I have been using the past week as well. Yesterday, I was so impressed with their attention and response, I awarded the class ten "free time" minutes.
I appreciated my field instructor's feedback on assessment, and knowing how each student learned the material. Lessons go by quickly, and walking by each table group doesn't give you the whole picture. I collected group work, asked questions during the whole group lesson and collected conclusions. One suggestion she gave another student teacher was to write notes on index cards as you walk around which note your observations of student thinking. I'd like to try this!
I appreciated my field instructor's feedback on assessment, and knowing how each student learned the material. Lessons go by quickly, and walking by each table group doesn't give you the whole picture. I collected group work, asked questions during the whole group lesson and collected conclusions. One suggestion she gave another student teacher was to write notes on index cards as you walk around which note your observations of student thinking. I'd like to try this!
Subscribe to:
Posts (Atom)