Friday, December 11, 2009
Tuesday, November 24, 2009
Assignment 3 - Origami Polyhedra
The dodecahedron our group made:
Benefit of the project:
• Hands-on activity
• Help students to visualize the 3 dimensional worlds. For instance, finding information about edges, vertices, faces and etc
• Avoid boredom in the classroom
• Incorporate other subjects such as Arts
• Make students familiar with the background and history of polyhedra
Weaknesses of the project:
• Time-consuming due to making origami: it might be annoying for students, and as a result it might lead to frustrations and confusion.
• Time wise: it might be hard to fit this project into the curriculum.
Uses of the project :
• Make the students to feel for 3-D world
• Make them familiar with what geometry is, in particular polyhedra
• A fun classroom activity to follow
How to modify the project:
• Avoid making the students to do the origami: give them other options for origami. For instance, cut the segments and tape them together. This way, it is less time-consuming, and it gives the students the same result.
Extension of the project:
• We can ask our students to think about volume, surface area, and some other physical properties
Our project (Surface Area):
• Grade level : Grade 9
• Purposes:
- To make a fun activity in the class
- Avoid boredom about the teaching subject
- Make the students to get a notion for a 3-D object/world,
- Practice the concept of “Area” in mathematics.
• Description:
There are two choices for this project:
1. Students must build a “Reasonable” shape object such as a house, car, flower, and etc using at least two 3-D objects.
2. Build a complex structure using only one type of 3-D object of their choice.
Students must choose only one of the above options.
For either one they must follow the below criterions.(2-3 people per group)
- Students must hand in an informal proposal for this project.
- They need to build the structure.
- They need to write a report including the followings:
i) How they got the surface area of the object they made in details. This includes a verbal explanation and diagrams.
ii) Measuring and calculating the surface area of the object in two different units. ( ex. cm and inch)
• Time:
- First session: 20 min for proposal in the class.
- Second session: A full class time for material and making objects.
- Giving them a weekend for the final work.
• Production: Reports and structures.
• Marking Criteria:
- Communication ( how well they explain the work) - 35%
- Calculations(how they got the surface area and units) - 50%
- Structure ( what they made) - 10%
- Creativity - 5%
Benefit of the project:
• Hands-on activity
• Help students to visualize the 3 dimensional worlds. For instance, finding information about edges, vertices, faces and etc
• Avoid boredom in the classroom
• Incorporate other subjects such as Arts
• Make students familiar with the background and history of polyhedra
Weaknesses of the project:
• Time-consuming due to making origami: it might be annoying for students, and as a result it might lead to frustrations and confusion.
• Time wise: it might be hard to fit this project into the curriculum.
Uses of the project :
• Make the students to feel for 3-D world
• Make them familiar with what geometry is, in particular polyhedra
• A fun classroom activity to follow
How to modify the project:
• Avoid making the students to do the origami: give them other options for origami. For instance, cut the segments and tape them together. This way, it is less time-consuming, and it gives the students the same result.
Extension of the project:
• We can ask our students to think about volume, surface area, and some other physical properties
Our project (Surface Area):
• Grade level : Grade 9
• Purposes:
- To make a fun activity in the class
- Avoid boredom about the teaching subject
- Make the students to get a notion for a 3-D object/world,
- Practice the concept of “Area” in mathematics.
• Description:
There are two choices for this project:
1. Students must build a “Reasonable” shape object such as a house, car, flower, and etc using at least two 3-D objects.
2. Build a complex structure using only one type of 3-D object of their choice.
Students must choose only one of the above options.
For either one they must follow the below criterions.(2-3 people per group)
- Students must hand in an informal proposal for this project.
- They need to build the structure.
- They need to write a report including the followings:
i) How they got the surface area of the object they made in details. This includes a verbal explanation and diagrams.
ii) Measuring and calculating the surface area of the object in two different units. ( ex. cm and inch)
• Time:
- First session: 20 min for proposal in the class.
- Second session: A full class time for material and making objects.
- Giving them a weekend for the final work.
• Production: Reports and structures.
• Marking Criteria:
- Communication ( how well they explain the work) - 35%
- Calculations(how they got the surface area and units) - 50%
- Structure ( what they made) - 10%
- Creativity - 5%
Wednesday, November 11, 2009
Wednesday, November 4, 2009
Memorable moments from my short practicum
On the last day of school, every student was on the hallway and read to go home after the last class. I was walking on the hallway to the office. On my way, someone called me, saying”Miss Wu”. I was surprised that someone called me on the hallway. I looked at her. She is one of the students I taught in the grade 9 class, Karen. She said good bye to me, and we had a little chat since it’s my last day of the short practicum. Honestly, I felt so warm when she called me and said good bye to me because some students actually remembered me and called me outside the class even I only taught them for a couple days. I could see that I have built some relationship with students and this made me feel happy and warm.
For the first day I was teaching , it's a math 9 class. I wrote down important notes on the board, and I assumed the students would copy down the notes. So, I didn’t say “Copy this down”. However, when I was walking around the classroom to help them working on the worksheet. I was surprised that not many of the students actually copied down the notes. I asked a couple of them, "Why don’t you copy down the notes?" The reply I got was "I don't know we need to copy it down." After the class, I told my sponsor teacher about this, and she said students need rules and instructions. We need to tell them what do to, otherwise they won't do it.So, the next day, I told them,”This is notes, and it’s important. You need to copy them down. So later on, when you got stuck, you have something to look at.” This time, it worked out better than last time. Most of the students copied down the notes. I was surprised that we need to tell the students precisely what to do.
For the first day I was teaching , it's a math 9 class. I wrote down important notes on the board, and I assumed the students would copy down the notes. So, I didn’t say “Copy this down”. However, when I was walking around the classroom to help them working on the worksheet. I was surprised that not many of the students actually copied down the notes. I asked a couple of them, "Why don’t you copy down the notes?" The reply I got was "I don't know we need to copy it down." After the class, I told my sponsor teacher about this, and she said students need rules and instructions. We need to tell them what do to, otherwise they won't do it.So, the next day, I told them,”This is notes, and it’s important. You need to copy them down. So later on, when you got stuck, you have something to look at.” This time, it worked out better than last time. Most of the students copied down the notes. I was surprised that we need to tell the students precisely what to do.
Sunday, October 18, 2009
Reflection on Exercise of Free Write and Poem
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
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
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.
Tuesday, September 29, 2009
Summary and Response to Battleground Schools
This article is about the three main movements in mathematics education in North America for the twentieth-century. The first movement was Progressivist reform (circa 1910-1940). It changed from “inculcation of meaningless memorized procedures” to “split between knowing and doing, or abstract and applied knowledge, proposing that students must engage in doing math as part of a reflective inquiry if they were to increase their intelligence and gain knowledge develop scientific and democratic thinkers.” Students were given the “challenge of doing and experimentation in math, accompanied by the sense-making activities of reflective practice” rather then “rigidly obedient rule-followers.” The second movement was the New Math reform of the 1960s. After USSR was beating the US in the space race, they changed the math curriculum for K-12, mainly focus on highly abstract math concepts. They wanted to familiarize students with the math basis for future careers as scientists, but many teachers had little knowledge with the new math topics, and they didn’t understand why new ways were being introduced. Therefore, many teachers, parents against the New Math since it trained students to be future scientist but not realize not all of them what to pursue that career. The third movement was the NCTM Standards-based Math Wars, from the 1990s to the present. This is a back-to-basics curriculum. They emphasized the development of flexible problem-solving skills and valued deep understanding and an ability to make math connections above calculation skills, although fluency in calculation was still considered an important goal.
In my opinion, I doubt that the reason for students in Asian countries have higher ranked in the world is because they have deeper conceptual understanding of mathematics. This is because I heard most of my Asian friends said they learned mathematic almost one hundred percent instrumentally before they came. Also, author said most people have negative attitude toward math. The reason might be that we didn’t have good math teacher at elementary school so seldom students understand the concepts, and students started to dislike math. Therefore, I think we definitely should have math specialized teacher at the elementary school.
In my opinion, I doubt that the reason for students in Asian countries have higher ranked in the world is because they have deeper conceptual understanding of mathematics. This is because I heard most of my Asian friends said they learned mathematic almost one hundred percent instrumentally before they came. Also, author said most people have negative attitude toward math. The reason might be that we didn’t have good math teacher at elementary school so seldom students understand the concepts, and students started to dislike math. Therefore, I think we definitely should have math specialized teacher at the elementary school.
Sunday, September 27, 2009
Summary to Interviews with Teacher and Students
In compliance with BCCT standards, “educators will engage in career-long learning”. Similarly, as teacher candidates and future educators we will continue to learn from our professors as well as from teacher and student interviews. In this interview, we have in our group of three collaboratively created a list of nine questions we most wanted to ask high school math teachers and students. From our interview with a math teacher and two high school students, we learned of the various resources and styles of teaching that we can make available to students to facilitate their learning in math.
Our first two interviewees were high school female students in grades nine and twelve respectively. We asked these students if they have troubles doing math, what would they do and why? The grade nine student said “if I have problem[s] doing math, I will go and ask my teacher” since she felt her teacher was approachable. The second student said that she will ask her friends because “discussions with her friends are good enough”. As teacher candidates then, we must recognize that our availability and approachability for students plays an important role in helping them learn math.
We also asked our two interviewees which area of math they find difficult and how their teachers can help them learn the topic better. One student has difficulties with volumes and angles and she prefers to learn “by sitting and taking notes” whereas the other student has difficulties with trigonometry and prefers to learn math “visually.” Thus, as teacher candidates we must keep in mind that each individual’s ways of learning is as different as the colors of the rainbow.
Our forth question was what can teachers do to motivate the students to learn math. In general, both students said it was hard to motivate them in a subject they disliked. However, they suggested that their teachers can try to interest them by making “the lesson a funner [group] activity.” Ironically, this ties into our last question, in which we asked the students how they would define a good math teacher. The grade nine student described “a good math teacher [as] someone [who] makes the class a little more fun and keeps everyone from NOT falling asleep.” On the other hand, the grade twelve student said a good math teacher “shoudn’t be monotone” and should make her “feel interested in what he/she teaches.”
In our interview with the high school math teacher however, we asked her what is the hardest thing to be a good math teacher? She replied “the most difficult part of being a math teacher is getting the students to get excited about Math.” What is interesting, however, is that she told us “some students say that they were once interested in Math” Therefore, as teachers it’s important that we try our best to teach math in fun and interesting ways.
This led into our second question inquiring any teaching advice(s) that our interviewee can give to teacher candidates. In her response, she told us we should avoid getting “disillusioned with teaching especially if the students are unmotivated.” In other words, it is important for teachers to overcome any teaching difficulties or harsh criticisms that she/he may encounter in the profession by approaching these problems optimistically and continuing to learn and develop professionally. For example, if a student is distracted, we shouldn’t take it personally and lose our initiative in teaching. Rather, we can refocus students back to the math lesson by “asking the distracted student to answer the question.” Distracted students also serve as a valuable sign in how well teachers are engaging their students in the class.
Thus, we asked the interviewee which is/are the most effective techniques she has used in teaching and why? She replied “I try to use real life examples…so that the seemingly abstract concepts can be more concrete.” This method however, “works only most of the time.” The reason for this as reflected by the interviewee is that she “wasn’t accommodating other learners especially those who have learning differences.” She also noted that “it was challenging to NOT teach the way she learned the concept.” Therefore, as teacher candidates, we should be flexible and adaptive in our teaching so that we are able to accommodate most if not all our students. Another effective teaching technique the interviewee had used all the time was “simplifying a complex concept using simpler examples.”
In conclusion, the interviews with the students helped us gain insight into their expectations from their math teachers and the methods that can be used to facilitate their learning in math. Generally, a great math teacher should be flexible and open-minded in his/her teaching to create a comforting classroom environment that involves plenty of excitement and fun group activities for students to engage in.
by Jenny, Maryanne, Candice
Our first two interviewees were high school female students in grades nine and twelve respectively. We asked these students if they have troubles doing math, what would they do and why? The grade nine student said “if I have problem[s] doing math, I will go and ask my teacher” since she felt her teacher was approachable. The second student said that she will ask her friends because “discussions with her friends are good enough”. As teacher candidates then, we must recognize that our availability and approachability for students plays an important role in helping them learn math.
We also asked our two interviewees which area of math they find difficult and how their teachers can help them learn the topic better. One student has difficulties with volumes and angles and she prefers to learn “by sitting and taking notes” whereas the other student has difficulties with trigonometry and prefers to learn math “visually.” Thus, as teacher candidates we must keep in mind that each individual’s ways of learning is as different as the colors of the rainbow.
Our forth question was what can teachers do to motivate the students to learn math. In general, both students said it was hard to motivate them in a subject they disliked. However, they suggested that their teachers can try to interest them by making “the lesson a funner [group] activity.” Ironically, this ties into our last question, in which we asked the students how they would define a good math teacher. The grade nine student described “a good math teacher [as] someone [who] makes the class a little more fun and keeps everyone from NOT falling asleep.” On the other hand, the grade twelve student said a good math teacher “shoudn’t be monotone” and should make her “feel interested in what he/she teaches.”
In our interview with the high school math teacher however, we asked her what is the hardest thing to be a good math teacher? She replied “the most difficult part of being a math teacher is getting the students to get excited about Math.” What is interesting, however, is that she told us “some students say that they were once interested in Math” Therefore, as teachers it’s important that we try our best to teach math in fun and interesting ways.
This led into our second question inquiring any teaching advice(s) that our interviewee can give to teacher candidates. In her response, she told us we should avoid getting “disillusioned with teaching especially if the students are unmotivated.” In other words, it is important for teachers to overcome any teaching difficulties or harsh criticisms that she/he may encounter in the profession by approaching these problems optimistically and continuing to learn and develop professionally. For example, if a student is distracted, we shouldn’t take it personally and lose our initiative in teaching. Rather, we can refocus students back to the math lesson by “asking the distracted student to answer the question.” Distracted students also serve as a valuable sign in how well teachers are engaging their students in the class.
Thus, we asked the interviewee which is/are the most effective techniques she has used in teaching and why? She replied “I try to use real life examples…so that the seemingly abstract concepts can be more concrete.” This method however, “works only most of the time.” The reason for this as reflected by the interviewee is that she “wasn’t accommodating other learners especially those who have learning differences.” She also noted that “it was challenging to NOT teach the way she learned the concept.” Therefore, as teacher candidates, we should be flexible and adaptive in our teaching so that we are able to accommodate most if not all our students. Another effective teaching technique the interviewee had used all the time was “simplifying a complex concept using simpler examples.”
In conclusion, the interviews with the students helped us gain insight into their expectations from their math teachers and the methods that can be used to facilitate their learning in math. Generally, a great math teacher should be flexible and open-minded in his/her teaching to create a comforting classroom environment that involves plenty of excitement and fun group activities for students to engage in.
by Jenny, Maryanne, Candice
Self-Reflection on Interview with Teacher and Students
In our interview with two female high school students, they both said that a good math teacher should make math classes more excited and more fun, which is not surprising since I agree that the most challenge part to teach math is to get the students interested and excited in math, and this corresponds with our teacher interviewee’s response. One way to make math more fun is group activities!
From teacher interviewee’s responses, I learn that we have to know various ways of solving same problems since every student learn and understand concepts differently, so we have to use different methods to teach them. From our interview with students, one like taking notes, yet one learn better by group activities, so it is really important for teachers to try different methods of teaching. To sum up, we have to flexible and open-minded.
Furthermore, interviewee said she ask teacher for help and the other one said she ask friends for help. So, I think it is really important to make myself approachable to students, and encourage them to come to me if they have questions; also, have some office hour or extra time outside the class.
From teacher interviewee’s responses, I learn that we have to know various ways of solving same problems since every student learn and understand concepts differently, so we have to use different methods to teach them. From our interview with students, one like taking notes, yet one learn better by group activities, so it is really important for teachers to try different methods of teaching. To sum up, we have to flexible and open-minded.
Furthermore, interviewee said she ask teacher for help and the other one said she ask friends for help. So, I think it is really important to make myself approachable to students, and encourage them to come to me if they have questions; also, have some office hour or extra time outside the class.
Wednesday, September 23, 2009
Response to Heather J. Robinson’s Article
“Using Research to Analyze, Inform, and Asses Changes in Instruction”
by Heather J. Robinson’s
I agree that she said “students learn best when they are actively engaged in the thinking about and doing mathematics.” Hence, I think teacher should give some time for group work and group discussion for every lecture and I think it is easier for students to talk to classmates rather than teachers. In addition, it is important to build an atmosphere “where students appreciate each other’s ideas and not afraid to be wrong in order to accomplish learning.” Hence, we have to encourages freedom of expression and value their own ideas, as well as respect and reward unusual or different ideas.
However, I’m doubtfully about how practical we can help students develop their critical thinking and problem solving skills since most of our curriculum topics are hard to teach them thinking critically, and plus group discussion takes a lot of time. Due to the topics/skills we need to teach students according to curriculum, it might be hard to give students a lot of time for discussion and teach them all the skills they have to know, sometimes it is just simply don’t have enough time, and ultimately and unfortunately people evaluate students by their grades/scores on the exam.
I have one more question about why her students score so high in class grade, but poorly in common final exam. Is it because she teaches total instrumentally, so students don’t understand it that they just simply memorize the formulas/rules, so they don’t know which one to apply when all kinds of questions are mixed together in final exam? Or is it because the questions on the final exam are just too different? Nevertheless, as a teacher, we are all life-long learners; we learn from experience, peers and students.
by Heather J. Robinson’s
I agree that she said “students learn best when they are actively engaged in the thinking about and doing mathematics.” Hence, I think teacher should give some time for group work and group discussion for every lecture and I think it is easier for students to talk to classmates rather than teachers. In addition, it is important to build an atmosphere “where students appreciate each other’s ideas and not afraid to be wrong in order to accomplish learning.” Hence, we have to encourages freedom of expression and value their own ideas, as well as respect and reward unusual or different ideas.
However, I’m doubtfully about how practical we can help students develop their critical thinking and problem solving skills since most of our curriculum topics are hard to teach them thinking critically, and plus group discussion takes a lot of time. Due to the topics/skills we need to teach students according to curriculum, it might be hard to give students a lot of time for discussion and teach them all the skills they have to know, sometimes it is just simply don’t have enough time, and ultimately and unfortunately people evaluate students by their grades/scores on the exam.
I have one more question about why her students score so high in class grade, but poorly in common final exam. Is it because she teaches total instrumentally, so students don’t understand it that they just simply memorize the formulas/rules, so they don’t know which one to apply when all kinds of questions are mixed together in final exam? Or is it because the questions on the final exam are just too different? Nevertheless, as a teacher, we are all life-long learners; we learn from experience, peers and students.
Two of my most memorable math teachers
One of my most memorable teachers is my junior math teacher, Mr. Hsu. He is really strict; I think he is the strictest teacher I ever had, but he is really reasonable. He has great knowledge in math. His thoughts are clear, and he is really good at explaining math concepts, he makes sure everyone understands them. He gives us a lot of homework since he says math need a lot of practice in order to be good at it. Most students don’t really like him at that time because everyone thinks he gives us too much homework, yet unbelievable he is the one who builds my cornerstone for math! I learn so much from him. I realize I have a strong math basic skill after I go into senior math class. He makes me realize that no pain, no gain. I have to admit that I don’t really like him that much at that time, but now I really thank him for what he taught me!
My second most memorable math teacher is Mrs. C. She is so passionate about math, and she knows the subject really well. Her writing is neat, and notes are really organized and clear. It’s surprised how often I refer back to her notes later on. During the class, she sometimes told us a lot of stories/experience she has, which made the class so much fun! Also, she is really approachable and always concerns about students. She is available after school if someone needs helps. She has such a great rapport with students!! Everyone just loves her!
Even thought the personalities are so different between these two wonderful teachers, but both of them have great knowledge in math and good at explaining the concepts! In order to be a great math teacher, we not only have to know our subject well, but also have to know how to explain clearly so students can understand.
Sunday, September 20, 2009
Reflection on Microteaching
Peer’s evaluation:
Strengths of my lesson:
It’s interesting, engaging, and fun to follow activity
Good time management
Clear explanation
Visual demonstration and hands-on activities
Areas need further work and development:
Could be a little louder voice (hard to hear in a noisy classroom)
Maybe give a little history of origami
Maybe give students chances to learn it on their own by looking at the handout
Self assessment:
Things went well in my lesson:
Time management was good.
I made sure everyone followed me step-by-step so no one was behind.
Everyone made their own origami by the end of lesson
If I were to teach again, I would work to improve it by:
More information about origami, such as the history of origami
If I got more time, I’ll have a fun activity at the end by using the origami they just made
Here are some things I reflected on based on my peers’ feedback:
I should work on voice, speak louder next time.
Most people think the learning object was clear, but some think it’s not too clear, so I could talk a bit more about origami before I start to teach them how to fold a motorboat.
Most people think it’s a good way to show the origami I made in order to catch people’s attention and interests. Also, most people think it's good that I check to see how everyone was progressing and provide a useful link for people who are interested in origami.
Strengths of my lesson:
It’s interesting, engaging, and fun to follow activity
Good time management
Clear explanation
Visual demonstration and hands-on activities
Areas need further work and development:
Could be a little louder voice (hard to hear in a noisy classroom)
Maybe give a little history of origami
Maybe give students chances to learn it on their own by looking at the handout
Self assessment:
Things went well in my lesson:
Time management was good.
I made sure everyone followed me step-by-step so no one was behind.
Everyone made their own origami by the end of lesson
If I were to teach again, I would work to improve it by:
More information about origami, such as the history of origami
If I got more time, I’ll have a fun activity at the end by using the origami they just made
Here are some things I reflected on based on my peers’ feedback:
I should work on voice, speak louder next time.
Most people think the learning object was clear, but some think it’s not too clear, so I could talk a bit more about origami before I start to teach them how to fold a motorboat.
Most people think it’s a good way to show the origami I made in order to catch people’s attention and interests. Also, most people think it's good that I check to see how everyone was progressing and provide a useful link for people who are interested in origami.
Friday, September 18, 2009
Lesson Plan for Microteaching
BOOPPPS lesson plan for making a motorboat origami !!
BRIDGE
We can have any kind of objects by folding a piece of paper.
Show students some origami I made.
Teaching OBJECTIVES
Get students interested in origami
Learning OBJECTIVES
Students will be able to fold a motorboat using a piece of paper.
PRETEST
Asking students “Do anyone know about origami?” and “Do anyone know how to fold anything using a piece of paper?”
PARTICIPATORY Activity Ideas
Students have a piece of paper and follow me step-by-step.
POST-TEST
Students have their origami motorboat and know how to folding a motorboat by themselves. I’ll provide a handout which has the steps in case they forget.
SUMMARY
Folding a boat is just an easy one of origami.
Give students a useful website of origami, so they have more resources if they are interested, and they could try harder origami by themselves.
Commentary on Skemp's article
In Skemp’s article, he defines the differences between instrumental understanding and relational understanding, and provides several examples to demonstrate the differences, which makes the readers easier to understand the concepts. He shows he believes relational understanding is better, yet he tries to understand why others use instrumental understanding. This shows he is reflective.
According to Skemp’s article, he says “there are two kinds of mathematical mis-matches which can occur.”(4) This is such a good point I never really thought about before. After I give it some thoughts, I believe it is inevitable, and a way to reduce this is to use both instrumental and relational understanding when teaching. This leads to how often and when to use which. For the concept of relational understanding is not too complex, teach relational first. After a while, teach instrumental for students who could not understand relational, so they would not feel they are beyond and still get a sense of confident. For instance, the concept of area that we can teach how to find the area of triangles, trapezoids, etc. relational first, and then instrumentally tell students those really convenient formulas for area. By doing this, we can satisfy both group of students. And this gets more elaborate when he says “I used to think that maths teachers were all teaching the same subject, some doing it better than others. I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’.”(6) A good teacher is flexible. People often agree that relational is better, but what if a teacher teach relational all the time, but none or seldom of his students can understand it. This would just make things worse. A good teacher will teach either relational or instrumental understanding or both depending on the students he has. Skemps also mentions that relational “is easier to remember.”(9) I agree, but not always. I have some rules I learned in elementary, and I still remember them now; those rules just stick in my mind. I agree that Skemps says “relational understanding of a particular topic is too difficult,”(11) and students just could not understand them at that stage. Relational understanding might just scared them away, and they would feel overwhelming and start to dislike math. He also mentions “a junior teacher in a school where all the other mathematics teaching is instrumental.”(11) This back to beginning where a good teacher should be responsible and know what is suitable for his students, relational or instrumental, since every teacher has different kinds of students every class, every term, and every year.
According to Skemp’s article, he says “there are two kinds of mathematical mis-matches which can occur.”(4) This is such a good point I never really thought about before. After I give it some thoughts, I believe it is inevitable, and a way to reduce this is to use both instrumental and relational understanding when teaching. This leads to how often and when to use which. For the concept of relational understanding is not too complex, teach relational first. After a while, teach instrumental for students who could not understand relational, so they would not feel they are beyond and still get a sense of confident. For instance, the concept of area that we can teach how to find the area of triangles, trapezoids, etc. relational first, and then instrumentally tell students those really convenient formulas for area. By doing this, we can satisfy both group of students. And this gets more elaborate when he says “I used to think that maths teachers were all teaching the same subject, some doing it better than others. I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’.”(6) A good teacher is flexible. People often agree that relational is better, but what if a teacher teach relational all the time, but none or seldom of his students can understand it. This would just make things worse. A good teacher will teach either relational or instrumental understanding or both depending on the students he has. Skemps also mentions that relational “is easier to remember.”(9) I agree, but not always. I have some rules I learned in elementary, and I still remember them now; those rules just stick in my mind. I agree that Skemps says “relational understanding of a particular topic is too difficult,”(11) and students just could not understand them at that stage. Relational understanding might just scared them away, and they would feel overwhelming and start to dislike math. He also mentions “a junior teacher in a school where all the other mathematics teaching is instrumental.”(11) This back to beginning where a good teacher should be responsible and know what is suitable for his students, relational or instrumental, since every teacher has different kinds of students every class, every term, and every year.
Subscribe to:
Posts (Atom)
