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.
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