Week 7
Think about the questions students ask you about the mathematical concepts and procedures that they are studying in the classes that you teach. Also, think about how you respond to these questions.
Give some examples of questions that students ask you about mathematical concepts and procedures. How do you respond to their questions? What do you learn from their questions? What have you learned from responding to their questions?
I try to welcome student questions as many times as possible during my lessons. I don’t want to have students fall behind because they are confused and didn’t have the opportunity to ask. When I am teaching I do not feel students take advantage of the time I give them to ask questions. There are a few students I can count on to ask questions that others may have. When they ask these questions, it is typically for me to clear up something I said or for me to explain a procedure I carried out, or for me to check their work (this seems to be the most popular question) “Did I do this correct? Is this answer right?”. There are a few students in all the classes that have asked a question about linking concepts together. More questions are asked individually rather than as a class. The comfort level of one on one interaction probably plays into this.
When students ask me to check their work, I try to have them explain to me what they did to get that answer instead of me just simply seeing if they have the right answer. I want them to be able to explain how they arrived at the answer and the process they took to get it. This gives me an opportunity to assess their understanding, and answer their questions as well.
With more advanced questions, I try to help them answer their own question rather than just simply give them what they are looking for. I want them to learn from their questions instead of me telling them the correct answer. This will help them learn and work at a deeper level. I lead them to the correct answers.
Responding to their questions has taught me what students struggle with during lessons. I can focus on things that I know they will struggle with while I teach them. I have also learned after I answer their question, to ask if they understand what I just said. I have had several times where I will answer their question and then move on to someone else, and I notice they still have a confused look on their face. By asking if they understand gives them a chance to ask a follow up question or for clarification.
Once I answer a question, especially on a homework problem, I like to observe them work through their problem they are working on to see if they are understanding what I helped them with. This gives me an opportunity to check their understanding and level of ability on the new material.
Monday, February 28, 2011
Monday, February 21, 2011
Teacher Thoughts
As a teacher I am finding more value for the little things in life such as:
-Paper Clips
-Post-It Notes (Sticky Notes)
-Working Dry Erase Markers/Overhead Markers
-An abnormally strong Immune system
-Hand Sanitizer
-Kleenex
-Patience
-Extra pencils and paper for those students who somehow forgot theirs
-The "ah ha" moment from a student who was struggling with a concept but now understands it
-A "thank you" from that student
-Presidents Day, Snow/Ice Days, Two-Hour Delays, etc
Its the little things in a teacher's life....
-Paper Clips
-Post-It Notes (Sticky Notes)
-Working Dry Erase Markers/Overhead Markers
-An abnormally strong Immune system
-Hand Sanitizer
-Kleenex
-Patience
-Extra pencils and paper for those students who somehow forgot theirs
-The "ah ha" moment from a student who was struggling with a concept but now understands it
-A "thank you" from that student
-Presidents Day, Snow/Ice Days, Two-Hour Delays, etc
Its the little things in a teacher's life....
Sunday, February 20, 2011
Week Six Goals (2/14 - 2/18)
Week Six Goals:
1. I want to get more of my students involved with my lessons.
There are students in each of my classes that will sit there during my lessons and not participate, even when I try to get them involved. I need to find a way to have them involved in their learning process. With the chapter that I am teaching now, I think there are several engaging activities that I can use to help the students become involved in the lesson. The activities will allow students to actually see and experience the math concepts being taught.
2. I need to have the students work until the end of the class.
Recently one of my classes has gotten the idea that they can stop working 5 minutes before the end of the class and socialize with each other. This has led to several discipline issues that I am having to face. This week I want to become a little more strict with students during the end of the class. This has only become a problem in one of my Geometry classes. I think if I am able to keep them busy until the bell rings, the problems that arose should not be an issue anymore.
1. I want to get more of my students involved with my lessons.
There are students in each of my classes that will sit there during my lessons and not participate, even when I try to get them involved. I need to find a way to have them involved in their learning process. With the chapter that I am teaching now, I think there are several engaging activities that I can use to help the students become involved in the lesson. The activities will allow students to actually see and experience the math concepts being taught.
2. I need to have the students work until the end of the class.
Recently one of my classes has gotten the idea that they can stop working 5 minutes before the end of the class and socialize with each other. This has led to several discipline issues that I am having to face. This week I want to become a little more strict with students during the end of the class. This has only become a problem in one of my Geometry classes. I think if I am able to keep them busy until the bell rings, the problems that arose should not be an issue anymore.
Week Six Prompt (2/14 - 2/18)
Week 6 Prompt
Think about the discourse occurring in the classes that you are teaching. (One way to think about discourse is the dialogue that occurs in the classroom.) In particular, think about the questions that you are asking students and about their responses.
On Friday I started a new chapter. This new chapter is over Transformations, which is almost completely different from our previous chapter on Trigonometry. The first lesson I taught was over Translations and how to carry them out on a coordinate plane. A question I asked during each of the three classes I taught this lesson was “How can you apply a translation in a real life situation?”
This question allowed me to see if my students understand what a translation is. A student used an example of a teacher moving where two students sit in the room. The teacher wants to keep them together so he must move them the same number of desks. This response really surprised me because I did not think about using the desks as a coordinate plane. I thought this was a great way to apply a translation to a real life situation, so I used it as an example in my last class as well.
A majority of my questions are to assess my students’ understanding of the concepts and topics I just taught. I use the questions to see if I am moving to fast through new material, need to go back and clear up misconceptions, or have students apply the new knowledge in a different and more challenging way.
I have realized how hard it is to get students to give you feedback, so whenever I do get a student to share their opinion or ask a question I try to thank them. I am hoping that this will give other students more confidence when asking or answering a question. Student responses are typically not very in depth and are mostly asking for clarification. When they answer my questions, they can sometimes surprise me at how fast they grasped the new knowledge or the level of understanding they are at.
Think about the discourse occurring in the classes that you are teaching. (One way to think about discourse is the dialogue that occurs in the classroom.) In particular, think about the questions that you are asking students and about their responses.
On Friday I started a new chapter. This new chapter is over Transformations, which is almost completely different from our previous chapter on Trigonometry. The first lesson I taught was over Translations and how to carry them out on a coordinate plane. A question I asked during each of the three classes I taught this lesson was “How can you apply a translation in a real life situation?”
This question allowed me to see if my students understand what a translation is. A student used an example of a teacher moving where two students sit in the room. The teacher wants to keep them together so he must move them the same number of desks. This response really surprised me because I did not think about using the desks as a coordinate plane. I thought this was a great way to apply a translation to a real life situation, so I used it as an example in my last class as well.
A majority of my questions are to assess my students’ understanding of the concepts and topics I just taught. I use the questions to see if I am moving to fast through new material, need to go back and clear up misconceptions, or have students apply the new knowledge in a different and more challenging way.
I have realized how hard it is to get students to give you feedback, so whenever I do get a student to share their opinion or ask a question I try to thank them. I am hoping that this will give other students more confidence when asking or answering a question. Student responses are typically not very in depth and are mostly asking for clarification. When they answer my questions, they can sometimes surprise me at how fast they grasped the new knowledge or the level of understanding they are at.
Sunday, February 13, 2011
Week Five Goals (2/7 - 2/11)
Week Five Goals:
1. I need to become more strict with students and when they turn in homework and other assignments.
I have been very lenient with students turning in their assignments late. I want to give them credit for their effort, but I feel like I have been cutting them too many breaks when it comes to late assignments. I have now completely taken over the three Geometry classes and I make all the decisions with the students. My cooperating teacher is usually more strict when it comes to late work, and I feel she is very fair when it comes to this topic. I want to start to place stricter limits on due dates. This will help me control the classroom more effectively.
2. I want to find a way to help motivate those students who are doing poorly on the tests because they do not care, and not because they do not understand the material.
There are several students who are in my Geometry classes who seem to be strong mathematics students but are doing poorly on the quizzes and tests. I have talked to them multiple times about what they need help on, but they say they are understanding it. I need to find a way to reach them and help them understand the material. If I can find a way to motivate them to learn I feel they will do a lot better in the class and grasp the concepts being taught.
1. I need to become more strict with students and when they turn in homework and other assignments.
I have been very lenient with students turning in their assignments late. I want to give them credit for their effort, but I feel like I have been cutting them too many breaks when it comes to late assignments. I have now completely taken over the three Geometry classes and I make all the decisions with the students. My cooperating teacher is usually more strict when it comes to late work, and I feel she is very fair when it comes to this topic. I want to start to place stricter limits on due dates. This will help me control the classroom more effectively.
2. I want to find a way to help motivate those students who are doing poorly on the tests because they do not care, and not because they do not understand the material.
There are several students who are in my Geometry classes who seem to be strong mathematics students but are doing poorly on the quizzes and tests. I have talked to them multiple times about what they need help on, but they say they are understanding it. I need to find a way to reach them and help them understand the material. If I can find a way to motivate them to learn I feel they will do a lot better in the class and grasp the concepts being taught.
Saturday, February 12, 2011
Week Five Prompt (2/7 - 2/11)
Week 5 Prompt:
Describe and discuss one mathematical error you have seen students make or one mathematical misconception that they hold that surprised you. How did you help students correct this error or misconception?
Describe and discuss one important mathematical connection that you have seen students make. What factors contributed to students’ success in making this connection?
One error I have seen a number of times in the Algebra class deals with students trying to add and subtract positive and negative numbers. They struggle when they are faced with adding or subtracting a positive and a negative number, adding two negative numbers, and subtracting two negative numbers. They could not understand how or why the answer would be positive or negative. I talked to several of the students individually during their work time and used the concept of money and debt to help them with this. If they were adding a negative number and a positive number (like -10 + 4) I would say, “having negative $10, is like being in debt or owing to me $10 dollars. Then if you pay me $4 your debt is going to be smaller and it would be -$6.” Putting this in terms of money seemed to really help these students grasp the concept.
Another way I tried to help them drawing a number line so they could visually see why the answer would be positive or negative. This really helped for one of the students I work with. She was able to get a better understanding with the concept of adding and subtracting positive and negative numbers.
There was one student in the same class that really surprised me on her connection with the two-step equations they were solving and the relations between dividing a number across the equation. My cooperating teacher and myself have been teaching them a certain way to solve these equations. If you were given an equation 12 = 2x + 4, and asked to solve for x, we taught them to subtract 4 from both sides and then divide by 2. While working with these a student asked me if you could divide by 2 first like she did on her paper. Before looking at her work I began to explain that if you do that you need to divide the 4 on the left side too. She showed me her paper and said she did. I apologized and told her that was correct.
This surprised me because we did not teach this concept. She saw the answer would be affected if she did not divide the 4 as well. That was really interesting to me because she was able to form that by herself. She was able to recognize this because she worked out the problem without dividing the 4 and realized that the answer she arrived at was too big and did not make sense. It was great to see a student look at her answer and see if it made sense for the problem she was working with.
Describe and discuss one mathematical error you have seen students make or one mathematical misconception that they hold that surprised you. How did you help students correct this error or misconception?
Describe and discuss one important mathematical connection that you have seen students make. What factors contributed to students’ success in making this connection?
One error I have seen a number of times in the Algebra class deals with students trying to add and subtract positive and negative numbers. They struggle when they are faced with adding or subtracting a positive and a negative number, adding two negative numbers, and subtracting two negative numbers. They could not understand how or why the answer would be positive or negative. I talked to several of the students individually during their work time and used the concept of money and debt to help them with this. If they were adding a negative number and a positive number (like -10 + 4) I would say, “having negative $10, is like being in debt or owing to me $10 dollars. Then if you pay me $4 your debt is going to be smaller and it would be -$6.” Putting this in terms of money seemed to really help these students grasp the concept.
Another way I tried to help them drawing a number line so they could visually see why the answer would be positive or negative. This really helped for one of the students I work with. She was able to get a better understanding with the concept of adding and subtracting positive and negative numbers.
There was one student in the same class that really surprised me on her connection with the two-step equations they were solving and the relations between dividing a number across the equation. My cooperating teacher and myself have been teaching them a certain way to solve these equations. If you were given an equation 12 = 2x + 4, and asked to solve for x, we taught them to subtract 4 from both sides and then divide by 2. While working with these a student asked me if you could divide by 2 first like she did on her paper. Before looking at her work I began to explain that if you do that you need to divide the 4 on the left side too. She showed me her paper and said she did. I apologized and told her that was correct.
This surprised me because we did not teach this concept. She saw the answer would be affected if she did not divide the 4 as well. That was really interesting to me because she was able to form that by herself. She was able to recognize this because she worked out the problem without dividing the 4 and realized that the answer she arrived at was too big and did not make sense. It was great to see a student look at her answer and see if it made sense for the problem she was working with.
Tuesday, February 8, 2011
Gotta be FLEXIBLE
Tuesday, February 8th
Today was supposed to be the day I taught an introduction to trigonometry to my three geometry classes. However, when I was going over the homework with the classes from the previous two lessons, which were over The Pythagorean Theorem and Special Right Triangles, I noticed a majority of the class was still struggling on the material. I wanted to keep moving on to the new concepts, but without a solid grasp of the older concepts I felt that moving on would end disastrously. After making a decision I decided to go over several of the problems on the worksheet and then give the rest of the shortened class time to the students to work on their homework that was suppose to be due today.
I am now learning that a teacher needs to be flexible with their daily and weekly plans, have confidence in their decisions, and have plenty of erasers to change the lesson plan book.
Today was supposed to be the day I taught an introduction to trigonometry to my three geometry classes. However, when I was going over the homework with the classes from the previous two lessons, which were over The Pythagorean Theorem and Special Right Triangles, I noticed a majority of the class was still struggling on the material. I wanted to keep moving on to the new concepts, but without a solid grasp of the older concepts I felt that moving on would end disastrously. After making a decision I decided to go over several of the problems on the worksheet and then give the rest of the shortened class time to the students to work on their homework that was suppose to be due today.
I am now learning that a teacher needs to be flexible with their daily and weekly plans, have confidence in their decisions, and have plenty of erasers to change the lesson plan book.
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