Personally, I don’t like writing poem at all… because I am bad at it, and it brings me pressure and frustration. Yet it’s impossible to please everyone. However, I really like the ideas of incorporate other subjects into math.
Strengths:
- Free write is a good exercise to introduce students a new topic and concept
- Students have to be active thinking
- It helps brainstorming the ideas associate with the word/topic
- It brings other subjects into math, so people who dislike math might find it interesting and start to like it
Weakness:
- For people who don’t like math and poem for instance, it will bring more pressure to them
- The time limit for free write might brings pressure as well since the students cannot think of anything at that moment
Sunday, October 18, 2009
Poem: Division by Zero
Poem: Division by Zero
Zero is in the middle of the number line
It is the danger zone
If dividing by zero
Every rules break
No consistency, approach different limits
It brings confusion
We don’t like this and we don’t want this
Hence
It is forbidden
Zero is in the middle of the number line
It is the danger zone
If dividing by zero
Every rules break
No consistency, approach different limits
It brings confusion
We don’t like this and we don’t want this
Hence
It is forbidden
Free Write about Divide and Zero
DIVIDE
A mathematic concept
The opposite of multiply
Sharing among people
ie, have a pie or cake at birthday party, and you have ten guests, how much can each person get
ie, when we go out having dinner with friends, and we want to split the cost equally, use division as well
ZERO
It’s nothing, like empty
If the price of something is zero dollar, it means it’s free!
0 --> it’s a circle
Zero is in the middle of the number line
It’s the division between positive and negative numbers
It’s neither positive nor negative
It’s by itself
Anything add or subtract zero doesn’t change anything, stay the same
Zero times any number is zero
Zero divides any number is zero
0! = 1
0 degree Celsius is really cold
Get 0 on the test is really sad : (
A mathematic concept
The opposite of multiply
Sharing among people
ie, have a pie or cake at birthday party, and you have ten guests, how much can each person get
ie, when we go out having dinner with friends, and we want to split the cost equally, use division as well
ZERO
It’s nothing, like empty
If the price of something is zero dollar, it means it’s free!
0 --> it’s a circle
Zero is in the middle of the number line
It’s the division between positive and negative numbers
It’s neither positive nor negative
It’s by itself
Anything add or subtract zero doesn’t change anything, stay the same
Zero times any number is zero
Zero divides any number is zero
0! = 1
0 degree Celsius is really cold
Get 0 on the test is really sad : (
Wednesday, October 14, 2009
Peer Evaluation and Reflection on Mircroteaching in Arithmetic Sequence
Peer Evaluation:
Pros:
- Clear explanations
- Good worksheets for students to follow
– step by step helps to develop good understanding for arithmetic sequence
- Good description of concept
- Good logic
- Definitions were good
- Good preparation work and well thought out
- Class was engaged
Cons:
- Not receptive to questions
- Should speak louder
- Lost control at times
- Should have more organized writing
Suggestions:
- Less lecturing, more activities
- Helping aids such as visuals
- Make eye-contact with everyone
My reflection:
Most of our classmates like the worksheet we provided, and the worksheet really helps them to follow what we were doing. This part went well as we thought. However, there are something didn’t go really well and need improvements. I didn’t know that my writing was not really organized until I read my peers’ evaluation. Then I think back to what I did, I agree that I should write in order, not jumping around, and I use the whole board to avoid confusion. I will definitely keep this in mind next time. Also, I found out it’s hard to teach when someone else in the other side of the room was teaching at the same time. It made my classmate hard to hear what I said, and I didn’t realize some of them have hard time listen to me. I should talk louder. Overall, I think the microteaching went well and the classmates are really supportive.
Pros:
- Clear explanations
- Good worksheets for students to follow
– step by step helps to develop good understanding for arithmetic sequence
- Good description of concept
- Good logic
- Definitions were good
- Good preparation work and well thought out
- Class was engaged
Cons:
- Not receptive to questions
- Should speak louder
- Lost control at times
- Should have more organized writing
Suggestions:
- Less lecturing, more activities
- Helping aids such as visuals
- Make eye-contact with everyone
My reflection:
Most of our classmates like the worksheet we provided, and the worksheet really helps them to follow what we were doing. This part went well as we thought. However, there are something didn’t go really well and need improvements. I didn’t know that my writing was not really organized until I read my peers’ evaluation. Then I think back to what I did, I agree that I should write in order, not jumping around, and I use the whole board to avoid confusion. I will definitely keep this in mind next time. Also, I found out it’s hard to teach when someone else in the other side of the room was teaching at the same time. It made my classmate hard to hear what I said, and I didn’t realize some of them have hard time listen to me. I should talk louder. Overall, I think the microteaching went well and the classmates are really supportive.
Tuesday, October 13, 2009
Microteaching: Lesson Plan for Sequence
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 of 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 arithetmic 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.
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 of 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 arithetmic 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.
Microteaching: Sequence worksheet
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?
Yes that's right t1 +d= t2
4. Now what is the relationship between t2 and t3? _____
5. What is the relationship between t4 and t3? _____
Part (III): Finding the nth term in the sequence/final formula:
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 ------à t1 +d+d= t3 -----à 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?
Finding n th term using general formula:
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.
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?
Yes that's right t1 +d= t2
4. Now what is the relationship between t2 and t3? _____
5. What is the relationship between t4 and t3? _____
Part (III): Finding the nth term in the sequence/final formula:
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 ------à t1 +d+d= t3 -----à 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?
Finding n th term using general formula:
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.
Now using the general formula found above, can you find the 20th and 10th term of the sequence?
Reflection on Citizenship Education in the Context of School Mathematics
In this article, Simmt talks about how mathematics education can link to citizenship education. Most people don’t think math can relate to our society mostly because the math education they received in school is plainly about calculations, steps, procedures, and rules without knowing why. Even me, I have this kind of experience as well. So, it is crucial for teachers to give the students the ideas that mathematics is part of our everyday life and society, and get rid of the assumption that math is nothing to do with our life. Also, one of the good methods to teach students about critical thinking is through mathematics. Critical thinking and problem solving skills are so critical since we encounter problems in different situations everyday. Simmt offer some really usual strategies we can use during the lecture, such as posing problems using variable-entry prompts, the demand for explanation, and mathematical conversations. I will provide students with challenge questions which need more thoughts, analysis, and explanations. Following by group discussion and sharing ideas that focus on “how” they get to the answer instead of “what” is the answer. As a teacher candidate, it’s useful to see how mathematics education can support citizenship education.
Friday, October 9, 2009
Commentary on "What-If-Not"
#1. How can you use "What-If-Not" method in your microteaching?
My group’s microteaching is about series and sequence.
First, we could give students a sequence to look at (WIN: Level 0). Then we ask students for any observation about the sequence, tell us anything about the sequence (WIN: Level 1). For example, the sequence is infinity, the sequence increases by the same number every time, the sum of the first nth number is…, the nth of sequence is … etc. After several observations, we ask what-if-not questions (WIN: level 2a), and come up with the questions (WIN: level 2b). For instance, what if the sequence is finite, the sequence is negative instead of positive, the sequence increases by 3 instead of 2, etc.
Then guide students to come up questions about the statements we have for WIN level 2 (WIN: Level 3). For example, if the sequence is negative, what will be new sequence be? And what will the sum change? What will be the nth term? Finally, try to solve the questions we have for WIN: Level 3 (WIN: Level 4). Finally, we link it to our purpose of the lecture, students would be able to find the nth term of the sequence and find the sum of the sequence.
#2. What are the strengths and limitations of "What-If-Not" approach?
STRENGTHS:
New way of thinking
New way of looking at things that we taking for granted
Make students think deeper
Develop critical thinking and creativity
LIMITATIONS:
Time-consuming
Students might be overwhelmed by the number of questions we have
Students might be confused and don’t know what to focus on
Easy to go of the topic, so hard to focus on the main ideas of the lecture
My group’s microteaching is about series and sequence.
First, we could give students a sequence to look at (WIN: Level 0). Then we ask students for any observation about the sequence, tell us anything about the sequence (WIN: Level 1). For example, the sequence is infinity, the sequence increases by the same number every time, the sum of the first nth number is…, the nth of sequence is … etc. After several observations, we ask what-if-not questions (WIN: level 2a), and come up with the questions (WIN: level 2b). For instance, what if the sequence is finite, the sequence is negative instead of positive, the sequence increases by 3 instead of 2, etc.
Then guide students to come up questions about the statements we have for WIN level 2 (WIN: Level 3). For example, if the sequence is negative, what will be new sequence be? And what will the sum change? What will be the nth term? Finally, try to solve the questions we have for WIN: Level 3 (WIN: Level 4). Finally, we link it to our purpose of the lecture, students would be able to find the nth term of the sequence and find the sum of the sequence.
#2. What are the strengths and limitations of "What-If-Not" approach?
STRENGTHS:
New way of thinking
New way of looking at things that we taking for granted
Make students think deeper
Develop critical thinking and creativity
LIMITATIONS:
Time-consuming
Students might be overwhelmed by the number of questions we have
Students might be confused and don’t know what to focus on
Easy to go of the topic, so hard to focus on the main ideas of the lecture
Sunday, October 4, 2009
10 Qs to ask the author of “The Art of Problem Posing”
10 Qs to ask the author of “The Art of Problem Posing”
1. If one has more knowledge about math compared with one who has less knowledge about math, does it really limit the selection for problem posing?
2. If it does, how could we do about it? since math teachers certainly have more knowledge in math
3. For the problems we pose, do we need to find out the answer first? since the problems might not have exact answer
4. If there is no precise answer to the problems, wouldn’t students get confused and wondering what is the point of posing the questions?
5. If we ask so many questions in the posing problems, wouldn’t students get frustrating? and lose their interest ?
6. How could we make the posing problems not too broad to keep them focus? since there are many broad questions, and the class would easily go of topic
7. Is there any bad posing problem? How could we avoid it?
8. Is there any data show that using problem posing technique actually makes students have more knowledge and better understanding in math?
9. Is this problem posing technique widely used in current math class?
10. We ask the questions in order to test students’ understanding of the concepts or to let them gain more understanding?
1. If one has more knowledge about math compared with one who has less knowledge about math, does it really limit the selection for problem posing?
2. If it does, how could we do about it? since math teachers certainly have more knowledge in math
3. For the problems we pose, do we need to find out the answer first? since the problems might not have exact answer
4. If there is no precise answer to the problems, wouldn’t students get confused and wondering what is the point of posing the questions?
5. If we ask so many questions in the posing problems, wouldn’t students get frustrating? and lose their interest ?
6. How could we make the posing problems not too broad to keep them focus? since there are many broad questions, and the class would easily go of topic
7. Is there any bad posing problem? How could we avoid it?
8. Is there any data show that using problem posing technique actually makes students have more knowledge and better understanding in math?
9. Is this problem posing technique widely used in current math class?
10. We ask the questions in order to test students’ understanding of the concepts or to let them gain more understanding?
Friday, October 2, 2009
Quick writing: Letters from students
Student One:
Dear Ms. Wu,
The first time I saw you, you gave me a great impression because you are smiling all the time. You are really approachable as you look like. You always give me a lot of help when I needed, and you are really patient with me even if I'm not good at math. Because of you, I don't feel math is that horrible anymore. Thank you very much for the support you gave me, and your encouragement really make me feel better towards math.
Now, I'm not afraid of math anymore :)
Thank you!
your lovely student,
Cindy
Student Two:
Hello Ms. Wu,
I don't enjoy your class at all. Your class is really boring for me, and I still don't know why we need to learn math, it's not helpful or useful in my real life. I really wish we could have more interesting stuffs in the math classes, so at least I have some good memory of it. After all, I just don't like math ... it's really boring and useless...
-Jimmy
My expectation for the future:
I will be a really patient, friendly, and positive teacher for all my students.
I hope all my students will find me approachable.
But I'm afraid my lectures/lessons wont be that interesting for them since I don't think of myself as a really creative person. I'll try to make my lectures as interesting as I can.
Dear Ms. Wu,
The first time I saw you, you gave me a great impression because you are smiling all the time. You are really approachable as you look like. You always give me a lot of help when I needed, and you are really patient with me even if I'm not good at math. Because of you, I don't feel math is that horrible anymore. Thank you very much for the support you gave me, and your encouragement really make me feel better towards math.
Now, I'm not afraid of math anymore :)
Thank you!
your lovely student,
Cindy
Student Two:
Hello Ms. Wu,
I don't enjoy your class at all. Your class is really boring for me, and I still don't know why we need to learn math, it's not helpful or useful in my real life. I really wish we could have more interesting stuffs in the math classes, so at least I have some good memory of it. After all, I just don't like math ... it's really boring and useless...
-Jimmy
My expectation for the future:
I will be a really patient, friendly, and positive teacher for all my students.
I hope all my students will find me approachable.
But I'm afraid my lectures/lessons wont be that interesting for them since I don't think of myself as a really creative person. I'll try to make my lectures as interesting as I can.
Response to Dave Hewitt’s film
I really enjoyed this film, and I wish we could watch the whole film if we have time because it is really good to see this new way of teaching. When we are new to something, we all learn by mimicking. Dave Hewitt has very unique teaching methods. He grabs everyone’s attention right away by using a sticker pointing around the wall. Every student is paying attention and really curious about what he is going to do. It’s amazing that he introduces the new concept unobtrusively. He starts from really simple things students know; he builds up from patterns of numbers, adding and subtracting, then he introduces the concept of unknown. Also, it is surprising that students do not need to take notes, and everyone is really engaging in the class. Usually, when I am busy copying down the notes from the lecture, I cannot think and cannot really focus on what the teacher is saying. His way of teaching is really relational and really helps the students develop the problem solving skills.
Subscribe to:
Posts (Atom)
