Reflection on our microteaching “arithmetic sequences”
The evaluation sheet that everyone filled out after me, Jenny, and Candice finished our micro-teaching taught me a lot of valuable lessons. Our micro-teaching had both many strengths and weaknesses that I would like to share.
Most people were happy about our lesson plan. They said that it was really clear and well prepared. We also got great comments about the worksheet that we provided our students with. Our worksheet basically got most of our students engaged with the key ideas that we were putting on the board and helped them to develop a better understanding of “arithmetic sequences”. Also, if someone had a difficulty seeing the board, they could at least rely on the worksheet.
In contrast, our microteaching had some weaknesses that I, as a student teacher must focus on more. One of the problems that I even noticed myself when I finished, was that I only looked at half of my students and left the other side of the class with no eye contact. It was really interesting that I found the same problem with other teacher candidates while they were teaching and as one of their students, I felt not really happy about it. Thus, I must make sure to have my eye contact with everybody in my class so that no one feels left out. Another concern was about our writings. I totally admit that what we put on the board was a little messy. Some people asked for some visual explications which was a little difficult for us to push with the subject that we were teaching. However, as teacher candidates we must make sure to provide our students with different methods and ways that help our students learn better.
In summery, I learned many precious lessons from this microteaching and I must make sure that next time to make a better eye contact with my students. Also, I must keep in mind that writing messy on the board is not going to help my students learn math better. In addition to that, I should be aware of the fact that providing my students with different methods of learning is a crucial part of the teaching.
Thursday, October 15, 2009
Sunday, October 11, 2009
Reflection on "Citizenship Education in the Context of School Mathmatics"
Reflection on “Citizenship Education in the Context of School Mathematics”
In compliance with Elaine Simmt, the author of the article Citizenship Education in the Context of School Mathematics, “Mathematics has a role in citizenship education because it has the potential to help us understand our society and our role in shaping it.” As teacher candidates, it is crucial for us to understand that mathematics is more than teaching students about numeracy and looking for “right” answers. It is important to know that mathematics is all about “truth” and we must teach our citizens, our students, to “understand and critique the formatting power of mathematics in society.” There are techniques and methods that we can offer in our classes in order to educate our youth for active involvement in society. One of the techniques that I would use in my classroom is that I would attempt to provide my students with problems and questions that force them to utilize their “powers of patterning, generalizing, specializing and reasoning”. By doing so, I encourage the youth to focus on their interactions with mathematics and to look for the truth rather than looking for the “right” answer. In addition to that, our demand for more details and explanations in problems and question that we are giving our students is really essential. Teaching our young students to pose problems, explain themselves in such way that others can understand is a way to help them develop their interactions and involvements with society and community that they live in.
In compliance with Elaine Simmt, the author of the article Citizenship Education in the Context of School Mathematics, “Mathematics has a role in citizenship education because it has the potential to help us understand our society and our role in shaping it.” As teacher candidates, it is crucial for us to understand that mathematics is more than teaching students about numeracy and looking for “right” answers. It is important to know that mathematics is all about “truth” and we must teach our citizens, our students, to “understand and critique the formatting power of mathematics in society.” There are techniques and methods that we can offer in our classes in order to educate our youth for active involvement in society. One of the techniques that I would use in my classroom is that I would attempt to provide my students with problems and questions that force them to utilize their “powers of patterning, generalizing, specializing and reasoning”. By doing so, I encourage the youth to focus on their interactions with mathematics and to look for the truth rather than looking for the “right” answer. In addition to that, our demand for more details and explanations in problems and question that we are giving our students is really essential. Teaching our young students to pose problems, explain themselves in such way that others can understand is a way to help them develop their interactions and involvements with society and community that they live in.
Saturday, October 10, 2009
"Sequence" worksheet for Micro-teaching!
Sequence worksheet
We have a sequence such as: 3, 7, 11, 15,19,23,27...
Part (l): Sequence Terms:
1. What is the first term? _____
2. What is the second term? _____
3. What is the difference between first and second term? _____
4. Now what is the third term? _____
A.Finding difference “d”:
1. What is the difference between second and third term? _____
2. What is difference between any consecutive numbers in the sequence? _____
Call this “d”.
3. Thus d = _____
Part (II): Relationship between each term!
Each number in the sequence is called a “term” and they are indicated as “tn”; for instance, t1 is first term, t2 is the second term, t3 is third term and so on. Now please note that 3+4=7
1. What is 3 in terms of “term”? t? _____
2. What is 7 in terms of “term”? t? _____
3. What is the relationship between t1 and t2?
4. Yes that's right t1 +d= t2
5. Now what is the relationship between t2 and t3? _____
6. What is the relationship between t4 and t3? _____
Part (III): Finding the nth term in the sequence/final formula:
A.Writing each term in terms of t1 and d:
Back to part (II) questions 4 and 5, we found out that
a) t1 +d= t2
b) t2 +d= t3
Now, using a) and b) above, we can write t3 in terms of t1 and d
(Hint: substitute t1 +d= t2 into t2 +d= t3)
t2 +d= t3 and since t1 +d= t2 ------ t1 +d+d= t3 -----
t1 +2d= t3
1.Now using the result above try to write t4 in terms of t1 and d (hint: write t4 in terms of t3 and substitute the above result for t3 and simply the work) what do you get?
2.Again using the result above do the same thing for t5, what do you get?
B.Finding n th term using general formula:
1.Writing each terms in terms of t1 and d using the same method that was shown above we see a trend! By looking at the above examples that we did you notice any trend for writing tn in terms of t1 and d?
The above question leads us to the general formula for finding nth term in the sequence. For instance in our sequence that we had in part (I) by using the general formula we can easily find 5th, 6th term, ……, 100th term and so on.
2.Now using the general formula found above, can you find the 20th and 10th term of the sequence?
We have a sequence such as: 3, 7, 11, 15,19,23,27...
Part (l): Sequence Terms:
1. What is the first term? _____
2. What is the second term? _____
3. What is the difference between first and second term? _____
4. Now what is the third term? _____
A.Finding difference “d”:
1. What is the difference between second and third term? _____
2. What is difference between any consecutive numbers in the sequence? _____
Call this “d”.
3. Thus d = _____
Part (II): Relationship between each term!
Each number in the sequence is called a “term” and they are indicated as “tn”; for instance, t1 is first term, t2 is the second term, t3 is third term and so on. Now please note that 3+4=7
1. What is 3 in terms of “term”? t? _____
2. What is 7 in terms of “term”? t? _____
3. What is the relationship between t1 and t2?
4. Yes that's right t1 +d= t2
5. Now what is the relationship between t2 and t3? _____
6. What is the relationship between t4 and t3? _____
Part (III): Finding the nth term in the sequence/final formula:
A.Writing each term in terms of t1 and d:
Back to part (II) questions 4 and 5, we found out that
a) t1 +d= t2
b) t2 +d= t3
Now, using a) and b) above, we can write t3 in terms of t1 and d
(Hint: substitute t1 +d= t2 into t2 +d= t3)
t2 +d= t3 and since t1 +d= t2 ------ t1 +d+d= t3 -----
t1 +2d= t3
1.Now using the result above try to write t4 in terms of t1 and d (hint: write t4 in terms of t3 and substitute the above result for t3 and simply the work) what do you get?
2.Again using the result above do the same thing for t5, what do you get?
B.Finding n th term using general formula:
1.Writing each terms in terms of t1 and d using the same method that was shown above we see a trend! By looking at the above examples that we did you notice any trend for writing tn in terms of t1 and d?
The above question leads us to the general formula for finding nth term in the sequence. For instance in our sequence that we had in part (I) by using the general formula we can easily find 5th, 6th term, ……, 100th term and so on.
2.Now using the general formula found above, can you find the 20th and 10th term of the sequence?
Micro-teaching lesson plan "Sequences"
MAED 314A – Arithmetic Sequence Microteaching
Bridge:
3, 7, 11, 15, 19, 23, 27…..
Does anyone know what is the 100th or 1000th term of this sequence?
If you don’t know, don’t worry about it. After this lesson, you all will be able to find the 100th and 1000th terms of this sequence. Actually…you can find any term you want to!
There are different types of sequences: geometric, arithmetic and other sequences. In our lesson, we will focus on arithmetic sequence.
Definition: An arithmetic sequence is a sequence where each term is formed from the preceding term by adding a constant (positive or negative)
Learning Objectives:
-Students will be able to calculate and predict terms in an arithmetic sequence where the first term and common difference are known
-Students will be able to calculate and predict terms in an arithmetic sequence where only one of the first term or common difference is known
-Students will be able to write an expression to represent general terms for an arithmetic sequence and be able to apply these expressions to solve problems
Teaching Objectives:
-To teach the students to predict and calculate the terms and common difference in an arithmetic sequence
-To engage students in classroom discussions of arithmetic sequence
-To guide students to formulate an expression for calculating the terms and common difference in an arithmetic sequence
Pre-test:
These questions will be asked during the bridge phase:
-Does anyone know much about arithmetic sequence?
Can anyone predict the 100th or 1000th term in the sequence?
Participation:
-Students will be encouraged to participate in class discussions and/or answer questions posed by the teacher
Post—test:
-Students will be asked to solve a challenge problem which will test them on the material just covered
Summary:
In this lesson, we taught students to write an expression for arithmetic sequence. After this lesson, students will be able to find the common difference and any term in an arithmetic sequence. However, there is more to that. Next class, we will focus on the case of calculating and predicting terms in an arithmetic sequence where both the first term and common difference are unknown. In the class after, we will introduce arithmetic series, which is the sum of a sequence. And in the near future, we will also introduce other types of sequence, such as geometric sequences.
Bridge:
3, 7, 11, 15, 19, 23, 27…..
Does anyone know what is the 100th or 1000th term of this sequence?
If you don’t know, don’t worry about it. After this lesson, you all will be able to find the 100th and 1000th terms of this sequence. Actually…you can find any term you want to!
There are different types of sequences: geometric, arithmetic and other sequences. In our lesson, we will focus on arithmetic sequence.
Definition: An arithmetic sequence is a sequence where each term is formed from the preceding term by adding a constant (positive or negative)
Learning Objectives:
-Students will be able to calculate and predict terms in an arithmetic sequence where the first term and common difference are known
-Students will be able to calculate and predict terms in an arithmetic sequence where only one of the first term or common difference is known
-Students will be able to write an expression to represent general terms for an arithmetic sequence and be able to apply these expressions to solve problems
Teaching Objectives:
-To teach the students to predict and calculate the terms and common difference in an arithmetic sequence
-To engage students in classroom discussions of arithmetic sequence
-To guide students to formulate an expression for calculating the terms and common difference in an arithmetic sequence
Pre-test:
These questions will be asked during the bridge phase:
-Does anyone know much about arithmetic sequence?
Can anyone predict the 100th or 1000th term in the sequence?
Participation:
-Students will be encouraged to participate in class discussions and/or answer questions posed by the teacher
Post—test:
-Students will be asked to solve a challenge problem which will test them on the material just covered
Summary:
In this lesson, we taught students to write an expression for arithmetic sequence. After this lesson, students will be able to find the common difference and any term in an arithmetic sequence. However, there is more to that. Next class, we will focus on the case of calculating and predicting terms in an arithmetic sequence where both the first term and common difference are unknown. In the class after, we will introduce arithmetic series, which is the sum of a sequence. And in the near future, we will also introduce other types of sequence, such as geometric sequences.
Thursday, October 8, 2009
Problem Posing Strategy , "What_If_Not"
Problem Posing using “What-If-Not” strategy
Problem posing is one of the essential elements in teaching mathematics. As teacher candidates, we must be able to pose valuable problems that lead our students’ attitude toward exploring and discovering math. One of the great problem posing strategies that I just learned is “What-If-Not.” The strength of this problem posing strategy is that it makes many questions available for the teacher to use. In addition, posing problems using “What-If-Not” strategy leads to having more valuable questions that are ambiguous rather than very “clear” and “easily understandable” ones. However, sometimes dealing with such problem posing strategy is difficult since it is time consuming and it may get confusing in some cases.
Our microteaching project is about determining the nth term in a sequence, or its sum. The way that I related this problem posing strategy, “What-If-Not”, to our project was really simple. First, I started from a “concrete material”, level (0), and thought about infinite random numbers; then, I moved to level (I) and listed some its attributes such as: they are infinite, they are random, they start from 1, and so on. Next, I thought about negating each attributes, or in the other words “What-If-Not [ing]” them (level II). For instance, what if these numbers are not infinite, then they are finite, and what if they are not random, then they are non-random numbers and the difference between the two consecutive ones is d. After doing so, I used these new alternatives as a basis for my new questions (level III). For example, ‘what is the sum, or nth term of this finite sequence?’ After selecting some of my new questions I tried to analyze them (level IV) and come up with a logic answer which finally I did. Overall, posing problems by using “What-If-Not” strategy helped me a lot in posing my micro-teaching questions and provided me with more questions than I ever thought.
Problem posing is one of the essential elements in teaching mathematics. As teacher candidates, we must be able to pose valuable problems that lead our students’ attitude toward exploring and discovering math. One of the great problem posing strategies that I just learned is “What-If-Not.” The strength of this problem posing strategy is that it makes many questions available for the teacher to use. In addition, posing problems using “What-If-Not” strategy leads to having more valuable questions that are ambiguous rather than very “clear” and “easily understandable” ones. However, sometimes dealing with such problem posing strategy is difficult since it is time consuming and it may get confusing in some cases.
Our microteaching project is about determining the nth term in a sequence, or its sum. The way that I related this problem posing strategy, “What-If-Not”, to our project was really simple. First, I started from a “concrete material”, level (0), and thought about infinite random numbers; then, I moved to level (I) and listed some its attributes such as: they are infinite, they are random, they start from 1, and so on. Next, I thought about negating each attributes, or in the other words “What-If-Not [ing]” them (level II). For instance, what if these numbers are not infinite, then they are finite, and what if they are not random, then they are non-random numbers and the difference between the two consecutive ones is d. After doing so, I used these new alternatives as a basis for my new questions (level III). For example, ‘what is the sum, or nth term of this finite sequence?’ After selecting some of my new questions I tried to analyze them (level IV) and come up with a logic answer which finally I did. Overall, posing problems by using “What-If-Not” strategy helped me a lot in posing my micro-teaching questions and provided me with more questions than I ever thought.
Sunday, October 4, 2009
Letter from a students who hated me :(
Dear Ms.Alam,
I have always tried to put away all my bad memories and not think about them, however I decided to write this letter and get it out of my chest. I wanted to let you know that in the year 1997 when you taught our grade 8 math class, I didn't enjoy your class at all because of our every other day mini quizzes.I also hated your voice so much since it was too loud. Also, you called everybody "guys" and I was a girl.Just wanted to tell you how much I hated you and your class. That's all.
Hope to never see you again in my life and never hear your voice!
Eliana
I have always tried to put away all my bad memories and not think about them, however I decided to write this letter and get it out of my chest. I wanted to let you know that in the year 1997 when you taught our grade 8 math class, I didn't enjoy your class at all because of our every other day mini quizzes.I also hated your voice so much since it was too loud. Also, you called everybody "guys" and I was a girl.Just wanted to tell you how much I hated you and your class. That's all.
Hope to never see you again in my life and never hear your voice!
Eliana
Letter from a student who liked me :)
Dear Ms.Alam,
It is interesting that how some teachers have bad and good influences on their students' life. You were one of those who impacted my life in such way that I am pursing a career in teaching since you made me fall in love with this career. Your passion and love for teaching and educating your students has been always beyond words. You taught me how to be strong and fight for goods. You indeed taught from heart and not from the book. You were always had this positive energy that it really made me want to be a teacher like you. I can never forget how much you patiently listened to our problems and tried your best to be there for each of us. I just wanted to thank you for all these and god bless you.
yours,
Joanna
It is interesting that how some teachers have bad and good influences on their students' life. You were one of those who impacted my life in such way that I am pursing a career in teaching since you made me fall in love with this career. Your passion and love for teaching and educating your students has been always beyond words. You taught me how to be strong and fight for goods. You indeed taught from heart and not from the book. You were always had this positive energy that it really made me want to be a teacher like you. I can never forget how much you patiently listened to our problems and tried your best to be there for each of us. I just wanted to thank you for all these and god bless you.
yours,
Joanna
10 questions from the Author
1)Why do you believe that it is necessary first to get “caught up in” (p.2), or “trapped by in” (p.2) the activities in order to know where we are headed?
2)How we can we avoid any “foolish” (p.4) problem posing?
3)In posing a problem, how can we make it more “significant [and] meaningful” (p.5) as you mentioned?
4)How we can relate the role of problem posing in education of different gender? In other words, if problem posing has any role in education of women? If so how?
5)What is the hardest part of problem posing? And why?
6)How “general” we should think when posing problems compare to the level of understanding of each student in class?
7)What do you think about posing open ended problems (referring back to x²+y²=z²: while reading that I thought about an open ended problem and their benefits)? Are there any benefits into it?
8)What are the things/ aspects/ criteria that we need to be “cautious” (p.17) about when posing a sensible mathematical problem?
9)Are the “standards” in problem posing part of schools’ curriculum nowadays?
10)Do you think problem posing(from the title of your book) itself is an art? Why?
2)How we can we avoid any “foolish” (p.4) problem posing?
3)In posing a problem, how can we make it more “significant [and] meaningful” (p.5) as you mentioned?
4)How we can relate the role of problem posing in education of different gender? In other words, if problem posing has any role in education of women? If so how?
5)What is the hardest part of problem posing? And why?
6)How “general” we should think when posing problems compare to the level of understanding of each student in class?
7)What do you think about posing open ended problems (referring back to x²+y²=z²: while reading that I thought about an open ended problem and their benefits)? Are there any benefits into it?
8)What are the things/ aspects/ criteria that we need to be “cautious” (p.17) about when posing a sensible mathematical problem?
9)Are the “standards” in problem posing part of schools’ curriculum nowadays?
10)Do you think problem posing(from the title of your book) itself is an art? Why?
Thursday, October 1, 2009
Comment and Reflection on in class video that was watched on Sep 30th regarding “teaching by patterns”:
Comment and Reflection on in class video that was watched on Sep 30th regarding “teaching by patterns”:
There are many diverse techniques that assist teachers to help their students learn math better. One of them is learning by patterns that we watched last class. The method that the class teacher was using to teach his students was amazing. He was using patterns and sounds by hitting a ruler on the board and wall to teach students how to count from smaller to bigger number and vice versa, additions, subtractions, and etc. It was really interesting that he started off teaching his students really simply and then introduced them to more difficult terms and concepts such as “unknowns.” I personally think that introducing students to new concepts, which are not really necessary for them to learn at that grade, is a great idea because when they confront it later in higher grades, they will not panic as much and face it easier than usual. I also really liked the idea that the teacher drew his students’ attention by hitting on the wall and the board. Most students in specially math classes have high tendencies to get bored; thus, as student candidates we must learn how to draw students’ attention in the classroom to avoid any boredom. Overall, watching this tape aided me to learn about various methods of teachings on top of many other valuable tips, which I mentioned above, that I can utilize in my classroom to assist my students learn math better.
There are many diverse techniques that assist teachers to help their students learn math better. One of them is learning by patterns that we watched last class. The method that the class teacher was using to teach his students was amazing. He was using patterns and sounds by hitting a ruler on the board and wall to teach students how to count from smaller to bigger number and vice versa, additions, subtractions, and etc. It was really interesting that he started off teaching his students really simply and then introduced them to more difficult terms and concepts such as “unknowns.” I personally think that introducing students to new concepts, which are not really necessary for them to learn at that grade, is a great idea because when they confront it later in higher grades, they will not panic as much and face it easier than usual. I also really liked the idea that the teacher drew his students’ attention by hitting on the wall and the board. Most students in specially math classes have high tendencies to get bored; thus, as student candidates we must learn how to draw students’ attention in the classroom to avoid any boredom. Overall, watching this tape aided me to learn about various methods of teachings on top of many other valuable tips, which I mentioned above, that I can utilize in my classroom to assist my students learn math better.
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