Thursday, December 10, 2009
Monday, November 23, 2009
Assignment 3
MAED 314 – Assignment 3
•Vincent Collins
•Gregory Thiessen
•Rosemary Qi
November 23, 2009
Part 1 – (8) Develop a project of own choice based on the in-class library. Topics include Goldbach’s Conjecture (from novel), infinities, fractals, paradoxes, etc.
Grade: 11
Purpose:
This activity is both a history project as well as an activity to have the students think mathematically. These mathematical concepts can be very difficult to grasp and by doing this project, students will have to go beyond instrumental comprehension to fully understand the given topics and produce the desired results. Students will get the opportunity to work in small groups and present their findings to the rest of the class in a short presentation.
Description of Activity:
Project
In groups of 2 or 3 you will choose a topic from the provided list. Feel free to research and choose your own, however, please confirm your decision with me before proceeding.
• Goldbach’s Conjecture
• Infinities
• Fractals
• Paradoxes (Choose only one to work with)
A paradox is a statement that goes against our intuition but may be true, or a statement that is self-contradictory. Examples of some mathematical paradoxes are:
• Zeno’s paradoxes of motion (the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox or the stadium paradox
• Russell paradox (Barbershop paradox)
• Greeling paradox
• Petersburg paradox
• Galileo’s paradox
• Etc.
Once you have made your decision, the following tasks must be completed:
1. Research your topic through the internet or by using books from the school library. I will provide a list of books that are available in the library.
2. Produce a visual representation of your topic. This can be in the form of a poster, tables, comic, performance, etc. Include a brief history of the topic including the person who developed the concept.
3. Present your work to the class in a short presentation of no more than 5 minutes.
Marking Criteria:
Your grade will be dependent on your understanding of the mathematical paradox which will be conveyed through your final product and presentation. Effort and contribution to the team will affect your final mark. There will be a peer evaluation at the end.
Due Date: 2 weeks from day assigned.
This project is expected to be completed primarily outside of class.
Sources:
http://www.stormloader.com/ajy/paradoxes.html
http://www.suitcaseofdreams.net/Content_Paradox.htm
Mazur, Joseph. Zeno’s Paradox: Unravelling the Ancient Mystery Behind the Science of Space and Time.
Part 2 – Evaluation of the project
This project is an enrichment project designed to make students think mathematically about concepts not ordinarily encountered throughout life. Benefits and weaknesses of this project are listed below.
Benefits:
Students will learn of various mathematicians who have contributed to mathematical knowledge over the centuries.
Students will have to critically think about concepts of math outside of what they usually experience.
Students will have to work in groups to accomplish tasks.
Students will have to present their findings in a clear manner such that peers will understand.
Weaknesses:
Not all of the topics are connected to the grade 11 IRP’s. Some of the mathematical concepts may be more suited for grade 12.
Students may have a difficult time comprehending some of the paradoxes.
Students may not comprehend the purpose or necessity of this project and may view is as another mundane task they must work through.
Trying out the project as a sketch
Our group has decided to tackle this project by focusing on Zeno’s paradoxes of motion.
History of Zeno of Elea
The Greek philosopher Zeno of Elea, born around 490 B.C., proposed four paradoxes that are still discussed 2500 years later. He wanted to challenge the accepted notions of space and time that he encountered in various philosophical circles. His paradoxes confounded mathematicians for centuries, and it wasn't until Cantor's development (in the 1860's and 1870's) of the theory of infinite sets that the paradoxes could be fully resolved.
Zeno's paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics. His four famous paradoxes include the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox and the stadium paradox.
http://mathforum.org/isaac/problems/zeno1.html
Part 3 – New Math Project Design
Grade: 11
Purpose:
The goal of this math project is for students to examine cyclical patterns in an artistic, fun and unique way. The students are presented with a classic problem that has been posed in an abstract way, to see if they can discover the numerical relationship. The students will be challenged to recreate and experiment with the ‘celtic knot’ pattern and hopefully they will begin to see that math exists is science and in art too. This is an enrichment project that promote deeper thinking in the students.
Description of activities:
1. Follow the guide (see below) for producing a ‘celtic knot’ and produce a 4 by 3 knot. Decorate it as necessary to show how the pattern loops.
2. If the knot has m vertices along the left side and n vertices along the top side, determine the formula/algorithm for determining the number of loops present in an m by n knot.
3. What other patterns of loops can be made by combining loops of various sizes. What are the limitations of this pattern, if any?
Guide:
The (1) blocks are placed at the four corners of the pattern (see below), each rotated 90 degrees from each other. The (2) blocks are placed next to them, cascading along the edge of the knot pattern to form a perimeter. The (3) blocks are placed in the middle to fill the space and complete the knot design. The picture below illustrates how this works. Under ‘Graphic’, there is a drawing of a completed knot for reference.
Sources:
There is no source for the creation of this knot pattern. This is original artwork that shall now be examined for mathematical inquisition.
Length of time that project will take:
Students are given 1 week from the date assigned to complete this project. If time permits, a small section of class time may be devoted to beginning the project. Otherwise, it is to be work upon outside of class in groups of 2-3.
What students are required to produce:
1. The students must draw a 4 by 3 ‘celtic knot’ and decorate it to make it easy to see.
2. The students must derive a formula for determining the number of loops in an m by n knot.
3. The students must create a new knot pattern by opening & closing loops to create their own knot pattern.
Graphic:
m=4, n=4, # of loops: 4 (highlighted as purple, red, green & blue)
Marking Criteria:
1. /4 - Completed drawing of 4 by 3 ‘celtic knot’.
2. /4 - Formula for the # of loops.
3. /2 - Originality of design.
•Vincent Collins
•Gregory Thiessen
•Rosemary Qi
November 23, 2009
Part 1 – (8) Develop a project of own choice based on the in-class library. Topics include Goldbach’s Conjecture (from novel), infinities, fractals, paradoxes, etc.
Grade: 11
Purpose:
This activity is both a history project as well as an activity to have the students think mathematically. These mathematical concepts can be very difficult to grasp and by doing this project, students will have to go beyond instrumental comprehension to fully understand the given topics and produce the desired results. Students will get the opportunity to work in small groups and present their findings to the rest of the class in a short presentation.
Description of Activity:
Project
In groups of 2 or 3 you will choose a topic from the provided list. Feel free to research and choose your own, however, please confirm your decision with me before proceeding.
• Goldbach’s Conjecture
• Infinities
• Fractals
• Paradoxes (Choose only one to work with)
A paradox is a statement that goes against our intuition but may be true, or a statement that is self-contradictory. Examples of some mathematical paradoxes are:
• Zeno’s paradoxes of motion (the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox or the stadium paradox
• Russell paradox (Barbershop paradox)
• Greeling paradox
• Petersburg paradox
• Galileo’s paradox
• Etc.
Once you have made your decision, the following tasks must be completed:
1. Research your topic through the internet or by using books from the school library. I will provide a list of books that are available in the library.
2. Produce a visual representation of your topic. This can be in the form of a poster, tables, comic, performance, etc. Include a brief history of the topic including the person who developed the concept.
3. Present your work to the class in a short presentation of no more than 5 minutes.
Marking Criteria:
Your grade will be dependent on your understanding of the mathematical paradox which will be conveyed through your final product and presentation. Effort and contribution to the team will affect your final mark. There will be a peer evaluation at the end.
Due Date: 2 weeks from day assigned.
This project is expected to be completed primarily outside of class.
Sources:
http://www.stormloader.com/ajy/paradoxes.html
http://www.suitcaseofdreams.net/Content_Paradox.htm
Mazur, Joseph. Zeno’s Paradox: Unravelling the Ancient Mystery Behind the Science of Space and Time.
Part 2 – Evaluation of the project
This project is an enrichment project designed to make students think mathematically about concepts not ordinarily encountered throughout life. Benefits and weaknesses of this project are listed below.
Benefits:
Students will learn of various mathematicians who have contributed to mathematical knowledge over the centuries.
Students will have to critically think about concepts of math outside of what they usually experience.
Students will have to work in groups to accomplish tasks.
Students will have to present their findings in a clear manner such that peers will understand.
Weaknesses:
Not all of the topics are connected to the grade 11 IRP’s. Some of the mathematical concepts may be more suited for grade 12.
Students may have a difficult time comprehending some of the paradoxes.
Students may not comprehend the purpose or necessity of this project and may view is as another mundane task they must work through.
Trying out the project as a sketch
Our group has decided to tackle this project by focusing on Zeno’s paradoxes of motion.
History of Zeno of Elea
The Greek philosopher Zeno of Elea, born around 490 B.C., proposed four paradoxes that are still discussed 2500 years later. He wanted to challenge the accepted notions of space and time that he encountered in various philosophical circles. His paradoxes confounded mathematicians for centuries, and it wasn't until Cantor's development (in the 1860's and 1870's) of the theory of infinite sets that the paradoxes could be fully resolved.
Zeno's paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics. His four famous paradoxes include the dichotomy paradox, Achilles and the tortoise paradox, arrow paradox and the stadium paradox.
http://mathforum.org/isaac/problems/zeno1.html
Part 3 – New Math Project Design
Grade: 11
Purpose:
The goal of this math project is for students to examine cyclical patterns in an artistic, fun and unique way. The students are presented with a classic problem that has been posed in an abstract way, to see if they can discover the numerical relationship. The students will be challenged to recreate and experiment with the ‘celtic knot’ pattern and hopefully they will begin to see that math exists is science and in art too. This is an enrichment project that promote deeper thinking in the students.
Description of activities:
1. Follow the guide (see below) for producing a ‘celtic knot’ and produce a 4 by 3 knot. Decorate it as necessary to show how the pattern loops.
2. If the knot has m vertices along the left side and n vertices along the top side, determine the formula/algorithm for determining the number of loops present in an m by n knot.
3. What other patterns of loops can be made by combining loops of various sizes. What are the limitations of this pattern, if any?
Guide:
The (1) blocks are placed at the four corners of the pattern (see below), each rotated 90 degrees from each other. The (2) blocks are placed next to them, cascading along the edge of the knot pattern to form a perimeter. The (3) blocks are placed in the middle to fill the space and complete the knot design. The picture below illustrates how this works. Under ‘Graphic’, there is a drawing of a completed knot for reference.
Sources:
There is no source for the creation of this knot pattern. This is original artwork that shall now be examined for mathematical inquisition.
Length of time that project will take:
Students are given 1 week from the date assigned to complete this project. If time permits, a small section of class time may be devoted to beginning the project. Otherwise, it is to be work upon outside of class in groups of 2-3.
What students are required to produce:
1. The students must draw a 4 by 3 ‘celtic knot’ and decorate it to make it easy to see.
2. The students must derive a formula for determining the number of loops in an m by n knot.
3. The students must create a new knot pattern by opening & closing loops to create their own knot pattern.
Graphic:
m=4, n=4, # of loops: 4 (highlighted as purple, red, green & blue)
Marking Criteria:
1. /4 - Completed drawing of 4 by 3 ‘celtic knot’.
2. /4 - Formula for the # of loops.
3. /2 - Originality of design.
Wednesday, November 18, 2009
Tuesday, November 17, 2009
Problem Solving
I scanned my problem-solving worksheet, but I could not put the image in my poster.
My conclusion for the problem sequence on page 192 is that no matter how many digits there are in a sequence of 0s and 1s, if there is no “1” or there are even numbers of 1s, the final digit will be “0”. Otherwise, the final digit will be “1”.
This conclusion is similar to my team workers'.
My conclusion for the problem sequence on page 192 is that no matter how many digits there are in a sequence of 0s and 1s, if there is no “1” or there are even numbers of 1s, the final digit will be “0”. Otherwise, the final digit will be “1”.
This conclusion is similar to my team workers'.
Monday, November 2, 2009
Two stories in my short practicum
One of the exciting things is about the Tablet PC. In the first day, both my sponsor teachers were using Tablet PC in their classes, and I really liked it. They told me that I could use their Tablets in my lesson. However, when I figured out what software they used, I found that I had the software and hardware in my computer. In the other word, my computer is a Tablet PC, and I had never used these functions. Then, I was so excited and started to learn how to use it for my teaching. Finally, I used my Tablet PC in my four lessons, and my sponsor teacher was very pleased to see that.
Another story is about the school. The Prince of Wales Secondary School is a good school, and we, student teachers, were welcomed in the first day in our short practicum. The principal and vice principals showed up, gave the orientation,and offered breakfast and lunch for all student teachers. They also made a list of all classes where we were welcomed to go and observe the teaching, which made us much easier.
Another story is about the school. The Prince of Wales Secondary School is a good school, and we, student teachers, were welcomed in the first day in our short practicum. The principal and vice principals showed up, gave the orientation,and offered breakfast and lunch for all student teachers. They also made a list of all classes where we were welcomed to go and observe the teaching, which made us much easier.
Friday, October 30, 2009
Reflection on Timed Writing
I don't think that I am good at timed writing, and I also don't like it. However, as a teaching skill, it is useful.
Strengths:
Timed writing exercise:
• Makes students concentrate to their work.
• Contributes to classroom management, and it can make students calm down.
• Improves the students’ communication skills.
Weaknesses:
Timed writing exercise:
• Isn’t exactly related to Math teaching.
• Causes unnecessary pressure on students’ study because getting ideas in very short time sometimes makes people frustrated.
• Students might feel boring about this exercise, and it is not an active activity which is really needed in math class.
Strengths:
Timed writing exercise:
• Makes students concentrate to their work.
• Contributes to classroom management, and it can make students calm down.
• Improves the students’ communication skills.
Weaknesses:
Timed writing exercise:
• Isn’t exactly related to Math teaching.
• Causes unnecessary pressure on students’ study because getting ideas in very short time sometimes makes people frustrated.
• Students might feel boring about this exercise, and it is not an active activity which is really needed in math class.
Division by zero
In the world of numbers,
There is a lovely number, zero.
It won’t bother others by adding and subtracting
However,
It makes a number disappear by multiplying.
It is very welcomed if it is added to people’s saving account:
100,
1000,
10,000,
100,000,
1,000,000,
10,000,000,
…
But it is hated while appearing to people’s credit cards.
In an elementary school,
As a divisor,
It is loved by kids if it follows a one,
10,
“It is easy,just move the dividend decimal point one place to the left”, the kids said.
However, if the one is gone, the kids will look at the divisor,
0
“What is the answer a number divided by zero?” the kids are confusing?
“No number can be divided by zero?” they are told.
“Why?”
“Why?”
“Why?”
“ ...”
I don’t know!
There is a lovely number, zero.
It won’t bother others by adding and subtracting
However,
It makes a number disappear by multiplying.
It is very welcomed if it is added to people’s saving account:
100,
1000,
10,000,
100,000,
1,000,000,
10,000,000,
…
But it is hated while appearing to people’s credit cards.
In an elementary school,
As a divisor,
It is loved by kids if it follows a one,
10,
“It is easy,just move the dividend decimal point one place to the left”, the kids said.
However, if the one is gone, the kids will look at the divisor,
0
“What is the answer a number divided by zero?” the kids are confusing?
“No number can be divided by zero?” they are told.
“Why?”
“Why?”
“Why?”
“ ...”
I don’t know!
Thursday, October 15, 2009
Reflection on Microteaching
On Wednesday, since I had E-coach workshop from 12:00 to 1:00, I was late for this class, which made our microteaching short of time. I felt so sorry for my group Laura and Jan.
According to peers’ assessment, most of peers think we had good introduction, integrated technology into the lesson, tried having everyone participate. On the other hand, we rushed for time, should have had everyone individually draw a smiley face, did not have enough time to do group work.
One more thing I realized is that I should not show the graphs through my computer while the students were graphing by using TI-spire. I should go to the students and guiding them how to use the TI-spire to graph. Again, because we didn’t have enough time, this part of activity was not done well.
Finally, I think next time we might need more time to organize the lesson and manage the time well.
According to peers’ assessment, most of peers think we had good introduction, integrated technology into the lesson, tried having everyone participate. On the other hand, we rushed for time, should have had everyone individually draw a smiley face, did not have enough time to do group work.
One more thing I realized is that I should not show the graphs through my computer while the students were graphing by using TI-spire. I should go to the students and guiding them how to use the TI-spire to graph. Again, because we didn’t have enough time, this part of activity was not done well.
Finally, I think next time we might need more time to organize the lesson and manage the time well.
Tuesday, October 13, 2009
Microteaching Lesson Plan
Bridge: Hopefully we can lead in from Sara’s group who discuss translations. Transformations are everywhere: small child -> stretched child, smiley face -> stretched to oval face, motorcycle to transformer
Learning Objectives: SWBAT graph y=af(x); y=1/f(x); y=-af(x); y=f(-ax)
Teaching Objectives: TWBAT have a group work together to ensure that all concepts are understood
Pre-test: Sara’s group activity. Show some pictures of graphs, ask about what kinds of transformations
Participatory Activity:
Materials: peg board, graph paper
1.) graph 1; given transformation instructions, what will the graph look like afterwards?
2.) graph 1b; given the transformation, what was the transformation instructions?
3.) graph 1 and 1b by using TI-Nsprie, let student see how their answers are.
Post-test:
have each group set up a graph using the peg boards, and a set of instructions; pass graph to R and instructions L. following those instructions, transform the given graph.
Summary: review of the transformation rules and translation rules.
Learning Objectives: SWBAT graph y=af(x); y=1/f(x); y=-af(x); y=f(-ax)
Teaching Objectives: TWBAT have a group work together to ensure that all concepts are understood
Pre-test: Sara’s group activity. Show some pictures of graphs, ask about what kinds of transformations
Participatory Activity:
Materials: peg board, graph paper
1.) graph 1; given transformation instructions, what will the graph look like afterwards?
2.) graph 1b; given the transformation, what was the transformation instructions?
3.) graph 1 and 1b by using TI-Nsprie, let student see how their answers are.
Post-test:
have each group set up a graph using the peg boards, and a set of instructions; pass graph to R and instructions L. following those instructions, transform the given graph.
Summary: review of the transformation rules and translation rules.
Monday, October 12, 2009
Reflection of "Citizenship Education in the Context of Mathematics"
I have never thought about the mathematic’s role in citizenship education until I read Elaine Simmt’s article, “Citizenship Education in the Context of School Mathematics”. The article really opened my mind.
Mathematic education and citizenship education are both very important for secondary-school students. Although students spend a lot of time in school every day, they also belong to our societies. Math teachers do have the responsibility to get the citizenship education involved into their classroom by posing problems, demanding for explanation, and encouraging conversation in classrooms.
In addition, I think that having democratic environment in a classroom is the key to leading mathematic teaching to prepare the students for citizenship. First, after posing problems, teachers should allow the students to feel free to ask questions, give various solutions, as well as negotiate and judge the appropriateness and adequacy of their own and peers’ questions and solutions. Second, when students give their explanations, the teachers should encourage them express their ideas in various ways instead of just judging the explanation are right or wrong. Finally, in order to make students interact with each other through mathematical conversation, such as offering examples and conjectures, as well as posing problems, the teachers should provide democratic environment in the classroom which makes everybody feels free to talk.
Mathematic education and citizenship education are both very important for secondary-school students. Although students spend a lot of time in school every day, they also belong to our societies. Math teachers do have the responsibility to get the citizenship education involved into their classroom by posing problems, demanding for explanation, and encouraging conversation in classrooms.
In addition, I think that having democratic environment in a classroom is the key to leading mathematic teaching to prepare the students for citizenship. First, after posing problems, teachers should allow the students to feel free to ask questions, give various solutions, as well as negotiate and judge the appropriateness and adequacy of their own and peers’ questions and solutions. Second, when students give their explanations, the teachers should encourage them express their ideas in various ways instead of just judging the explanation are right or wrong. Finally, in order to make students interact with each other through mathematical conversation, such as offering examples and conjectures, as well as posing problems, the teachers should provide democratic environment in the classroom which makes everybody feels free to talk.
Thursday, October 8, 2009
Reflection of "What-If-Not"
“What-IF-Not” is a good problem posing strategy that can be used after choosing a starting point and listing the possible attributes. When the problems are posted, analyzing problems will be the last step. Next week, in our microteaching, we are going to talk about trigonometry. I am not sure if it is possible for us to use WIN in our microteaching class because it is just 15 minutes, and we might not have time to use WIN and ask question deeper and deeper. However, we still can assume that if we have enough time, we will ask students to solve a triangle. In the first step, we might let students try to find different ways to solve a triangle based on the givens. For example, in a right triangle, the students might find an angle by subtracting another acute angle. Then, we would like to ask the students what if it is not allowed to use subtraction to solve the problem and ask them to try to use trigonometry.
Strength:
• Helping open people mind and makes people think a mathematic topic deeply.
• Leading people to combine their knowledge together to solve a problem.
• Engaging the students who really like math and would like to try different way to approach a mathematic topic
Weakness:
• Might cause the students who have basic knowledge of math to get bored.
• Not fit a microteaching because it costs a lot of time to post problems and analyze them.
• Really depends on the students’ level and their interest. I think it might be used with grade 11 and grade 12 students in a secondary school because the grade 8 to 10 students maybe not have the ability to analyze these kind of questions
Strength:
• Helping open people mind and makes people think a mathematic topic deeply.
• Leading people to combine their knowledge together to solve a problem.
• Engaging the students who really like math and would like to try different way to approach a mathematic topic
Weakness:
• Might cause the students who have basic knowledge of math to get bored.
• Not fit a microteaching because it costs a lot of time to post problems and analyze them.
• Really depends on the students’ level and their interest. I think it might be used with grade 11 and grade 12 students in a secondary school because the grade 8 to 10 students maybe not have the ability to analyze these kind of questions
Monday, October 5, 2009
10 Qs and Comments
1.Are the author secondary-school Math teachers or mathematicians?
2.What happened if the questions the students asked are too far away from the topic? Or how to make the questions back to the topic such as X2 + Y2 = Z2?
3.Are the secondary –school students interested in problem posing? If yes, how many percent?
4.Does a teacher have enough time to do the problem posing and answering in an 80-minute class? And how?
5.Should the problem posting be used in the math textbooks in the secondary schools? If yes, and how?
6.Should the problem posting be used in just secondary schools, or this teaching style should start in elementary school?
7.I think it would contribute to students’ understanding and thinking independently if the problem posting was involved in the mathematics classroom.
8.I also think that it might be a challenge for the teachers to apply the problem posting into their classes if they did not learn math by this way.
9.I agree with the author’s some points. For example, “Students and teachers do not usually ask questions for such purposes; rather, they are interested in making sure that their students understand and can execute what is expected of them.”( Pp: 14, ) I think that the mathematics field always trains people to give the answers – “right” or “wrong”. For example, asking a kindergarten student 3+2=6. Is it right or wrong? There are just two answers, and it is impossible to have another answer: sometimes it is right, and sometimes it is wrong, like the answers for some controversial issues in our society. Math teachers usually expect the right answer to make sure students’ understanding.
10.I believe that the problem posting will contribute not only students’ studying but also teachers’ teaching. Teachers could get some unexpected ideas or solutions from students.
2.What happened if the questions the students asked are too far away from the topic? Or how to make the questions back to the topic such as X2 + Y2 = Z2?
3.Are the secondary –school students interested in problem posing? If yes, how many percent?
4.Does a teacher have enough time to do the problem posing and answering in an 80-minute class? And how?
5.Should the problem posting be used in the math textbooks in the secondary schools? If yes, and how?
6.Should the problem posting be used in just secondary schools, or this teaching style should start in elementary school?
7.I think it would contribute to students’ understanding and thinking independently if the problem posting was involved in the mathematics classroom.
8.I also think that it might be a challenge for the teachers to apply the problem posting into their classes if they did not learn math by this way.
9.I agree with the author’s some points. For example, “Students and teachers do not usually ask questions for such purposes; rather, they are interested in making sure that their students understand and can execute what is expected of them.”( Pp: 14, ) I think that the mathematics field always trains people to give the answers – “right” or “wrong”. For example, asking a kindergarten student 3+2=6. Is it right or wrong? There are just two answers, and it is impossible to have another answer: sometimes it is right, and sometimes it is wrong, like the answers for some controversial issues in our society. Math teachers usually expect the right answer to make sure students’ understanding.
10.I believe that the problem posting will contribute not only students’ studying but also teachers’ teaching. Teachers could get some unexpected ideas or solutions from students.
Friday, October 2, 2009
A boring teacher in my secondary school
Ms.Qi, my math teacher in grade 12 was very boring. She always talked too much and tried to let us know the theory. I did not want to know the theory of each formula, I just wanted to know the rules and use it, Another thing is that she was not a humorous person and always took everything seriously.
(Making math class interesting is the biggest challenge for me)
(Making math class interesting is the biggest challenge for me)
A lovely Teacher
Ms. Qi is one of my favorite teachers in my secondary school. I love her because of her cares. She cares each student in her class no matter how their marks are. She always encourages the students to do their best. She is there to help not only for the As+ students but also for the C- students. She gives clear explanation in each class, and she always tried use relative understanding teaching and lets students know "why" and "how" to solve the problems. he also gives us group work and some activities to make math interesting for each student.
Thursday, October 1, 2009
Reflection on video "Teaching the Marked Case"
The video titled “Teaching the marked case” gives an interesting view about mathematics teaching. The teacher was like a director and made the lesson like a show. The students really got involved into “the show” by following the teacher’s questions step by step, and it also gave the students a good way of understanding algebra. I like the way how the teacher introduced algebra to the students. I also like that the teacher delivered the content from simple questions to complex questions. It really contributes to the students’ understanding and interest. The teacher also tried different ways to engage students, such as asking questions, asking students to solve the problems on the board, and making group discussions. One thing I did not see in the video and I think it is important is that the teacher should give a conclusion about the main points of the lesson by writing a note on the board. By taking the notes, the students could review what they learned before the next class or during doing their homework. Another thing I am concerned is the teacher’s voice. The teacher’s voice was always calm through the whole class, which was easy to make people’s brains get tired. I think the effective tone of voice would make the students more active and enjoy the class.
Tuesday, September 29, 2009
Summary and Reflection on "Battleground Schools"
Summary
In the article titled “Battleground Schools”, there were three reform movements in mathematics education during twentieth-century in US.
The first movement was Progressivist Reform which was from 1910 to 1940. People in this time:
· argued that students learned mathematics by following the rules which showed them how to get an answers, but students did not know why the particular procedures worked and how to approach the same question with alternate ways.
· Made some topics, such as pure and applied mathematics, covered in the prescribed curriculum.
· Proposed students to engage in doing mathematics as part of a reflective inquiry even though inquiry was more difficult to control than just teaching students.
· Got “programming the environment” involved.
(Page: 395-396)
As the second movement, the New Math in 1960s:
· Set the theory, abstract algebra, linear algebra, calculus and other topics be taught throughout the K-12 system.
· Met the lack of who teachers had familiarity with the mathematical topics that they were supposed to teach. In addition, the parents had difficulties to help their children with their math homework.
· Came to the end by the early 1970s.
(Page: 397-398)
Math Wars, the third movement, was based on the NCTM Standards in 1990s, the reforms were:
· Publishing some NCTM Principles and Standards for School Mathematics.
· Making content of the standards to support a balanced, progressive approach.
(Page: 399)
The article also mentioned about some negative public views of Mathematics and teachers. “Mathematics is hard, cold,…”. “ Those who like mathematics are eggheads, nerds,…”. “ There is no shame …for those who claim to be incapable of doing and understanding mathematics.” (Page: 393)
Reflection
It is good for us who are going to be math teachers to know the history of mathematics. The article also lets us know how important math is in the secondary school, and it was keeping changing in order to make students qualified to go to a college or university and become highly trained scientists.
Through the negative public views of mathematics and teachers, I can see that not only secondary-school students need a teacher who has the knowledge of mathematics, but they also need the teacher knows how to teach, and the latter might be more important than the former.
In the article titled “Battleground Schools”, there were three reform movements in mathematics education during twentieth-century in US.
The first movement was Progressivist Reform which was from 1910 to 1940. People in this time:
· argued that students learned mathematics by following the rules which showed them how to get an answers, but students did not know why the particular procedures worked and how to approach the same question with alternate ways.
· Made some topics, such as pure and applied mathematics, covered in the prescribed curriculum.
· Proposed students to engage in doing mathematics as part of a reflective inquiry even though inquiry was more difficult to control than just teaching students.
· Got “programming the environment” involved.
(Page: 395-396)
As the second movement, the New Math in 1960s:
· Set the theory, abstract algebra, linear algebra, calculus and other topics be taught throughout the K-12 system.
· Met the lack of who teachers had familiarity with the mathematical topics that they were supposed to teach. In addition, the parents had difficulties to help their children with their math homework.
· Came to the end by the early 1970s.
(Page: 397-398)
Math Wars, the third movement, was based on the NCTM Standards in 1990s, the reforms were:
· Publishing some NCTM Principles and Standards for School Mathematics.
· Making content of the standards to support a balanced, progressive approach.
(Page: 399)
The article also mentioned about some negative public views of Mathematics and teachers. “Mathematics is hard, cold,…”. “ Those who like mathematics are eggheads, nerds,…”. “ There is no shame …for those who claim to be incapable of doing and understanding mathematics.” (Page: 393)
Reflection
It is good for us who are going to be math teachers to know the history of mathematics. The article also lets us know how important math is in the secondary school, and it was keeping changing in order to make students qualified to go to a college or university and become highly trained scientists.
Through the negative public views of mathematics and teachers, I can see that not only secondary-school students need a teacher who has the knowledge of mathematics, but they also need the teacher knows how to teach, and the latter might be more important than the former.
Sunday, September 27, 2009
Individual Reflection of interviews
Through our group’s interviews, I find that most of the students think that Math is an important subject for their lives and for their future. They also have high expectations for their Math teachers. For example, they would like a fun and energetic teacher. They also hope that Math teachers can give simple and clear explanation for each question. Most students agree with having homework as long as it is not too much and repeated questions. The students also prefer learning rules to equations instead of proving equations. In addition, most of the students don’t remember that they have had a creative lesson. Therefore, I think that giving a creative lesson might be a big challenge for a Math teacher.
By other group’s interviews, I realize that boys and girls have different interests for learning math. Girls like to sit down and do their work, and boys like to try different things. I also learned that a Math teacher should give intelligent students some challenging questions and give them chance to tutor other students. Meanwhile, a Math teacher should try to keep the struggling students from giving up like giving them extra time for their tests. From other’s interview, I also realize that most of the students like interacting teachers.
By other group’s interviews, I realize that boys and girls have different interests for learning math. Girls like to sit down and do their work, and boys like to try different things. I also learned that a Math teacher should give intelligent students some challenging questions and give them chance to tutor other students. Meanwhile, a Math teacher should try to keep the struggling students from giving up like giving them extra time for their tests. From other’s interview, I also realize that most of the students like interacting teachers.
Group report about interviews
We have interviewed two teachers, Mr. Freire and Mr. Navdi. Both of them are math teacher at Vancouver College, a private secondary school. We also got three students to answer our questions by emails. They are Juancho in grade 9, Gabriella in grade 10, and Steph in grade 11. Our five questions are as following:
1. How important do you think secondary school Math really is in getting a good job?
2. Are there any tips that you can provide, so that we can engage students into wanting to learn Math? (What do you expect your teacher to do?)
3. Should students have math homework everyday? How much homework do they have in your class? About one hour a day or more?
4. Do you emphasize more on computational mathematics or more analytical mathematics? (Would you rather learn math by learning rules to equations or by proving equations and why it works?)
5. What is your the most creative lesson you have had? (What is your the most creative lesson you've been taught?)
Q1: All of the three students think that secondary school Math is important not only for a good job, but also for their lives. Mr. Navdi also thinks that math is important for getting a good job. However, Mr. Freire think that if getting a good job means earning more money, secondary school Math is not important. Some jobs, such as musician, lawyer, and plumber, do not need academic standard of Math. The students just need have foundation Math to graduate and get into college or university.
Q 2: Mr. Freire thinks that creating real life situations in the class and having good relationships with students are important tips to engage students to learn Math. Mr. Navdi thinks that being positive to any math topic and relating Math to the reality are important. The student, Juancho, thinks, “If it’s a fun and energetic teacher, the students would most often approach the subject the same way. But the same goes for the opposite. If a teacher is boring and just talks and talks and talks the whole class then assigns the homework 5 minutes before class is about to end, is lame!” Gabriella said,” I am only engaged when I understand it. As long as a math teacher simplifies enough that you really understand it, that’s all I expect”. Steph said, “I prefer a teacher that just teaches with examples, gives us work to let us try, and then is there as support if we have further questions”.
Q3: Mr. Freire thinks that students should have homework everyday, but Mr. Navdi just gives students class work instead of homework. Juancho thinks that students should have a fair and reasonable amount homework—not too much, but Gabriella thinks that math homework helps students review what they learned, so students should have at lest a sheet of homework everyday. Steph thinks that homework should be optional. For students who understand what they learned should not repeat the same types of problems.
Q4: Both teachers think that both computational mathematics and analytical mathematics are important for students. Computational mathematics contributes to the students’ principle exams, and analytical mathematics makes students understand what comes out. All of the students would rather learn Math by learning rules to equations.
Q5: Steph remember making 3-D shapes while learning about surface area and volume. Juancho and Gabriella don’t remember having a creative lesson in Math class. Mr. Freire’s most creative lesson is magic moment lesson. Mr. Navdi is proud of his designing a bridge, proving area of a triangle, shaping their pictures, and videotaping something that related to Math.
1. How important do you think secondary school Math really is in getting a good job?
2. Are there any tips that you can provide, so that we can engage students into wanting to learn Math? (What do you expect your teacher to do?)
3. Should students have math homework everyday? How much homework do they have in your class? About one hour a day or more?
4. Do you emphasize more on computational mathematics or more analytical mathematics? (Would you rather learn math by learning rules to equations or by proving equations and why it works?)
5. What is your the most creative lesson you have had? (What is your the most creative lesson you've been taught?)
Q1: All of the three students think that secondary school Math is important not only for a good job, but also for their lives. Mr. Navdi also thinks that math is important for getting a good job. However, Mr. Freire think that if getting a good job means earning more money, secondary school Math is not important. Some jobs, such as musician, lawyer, and plumber, do not need academic standard of Math. The students just need have foundation Math to graduate and get into college or university.
Q 2: Mr. Freire thinks that creating real life situations in the class and having good relationships with students are important tips to engage students to learn Math. Mr. Navdi thinks that being positive to any math topic and relating Math to the reality are important. The student, Juancho, thinks, “If it’s a fun and energetic teacher, the students would most often approach the subject the same way. But the same goes for the opposite. If a teacher is boring and just talks and talks and talks the whole class then assigns the homework 5 minutes before class is about to end, is lame!” Gabriella said,” I am only engaged when I understand it. As long as a math teacher simplifies enough that you really understand it, that’s all I expect”. Steph said, “I prefer a teacher that just teaches with examples, gives us work to let us try, and then is there as support if we have further questions”.
Q3: Mr. Freire thinks that students should have homework everyday, but Mr. Navdi just gives students class work instead of homework. Juancho thinks that students should have a fair and reasonable amount homework—not too much, but Gabriella thinks that math homework helps students review what they learned, so students should have at lest a sheet of homework everyday. Steph thinks that homework should be optional. For students who understand what they learned should not repeat the same types of problems.
Q4: Both teachers think that both computational mathematics and analytical mathematics are important for students. Computational mathematics contributes to the students’ principle exams, and analytical mathematics makes students understand what comes out. All of the students would rather learn Math by learning rules to equations.
Q5: Steph remember making 3-D shapes while learning about surface area and volume. Juancho and Gabriella don’t remember having a creative lesson in Math class. Mr. Freire’s most creative lesson is magic moment lesson. Mr. Navdi is proud of his designing a bridge, proving area of a triangle, shaping their pictures, and videotaping something that related to Math.
Tuesday, September 22, 2009
Response of Robinsan's article
Heather J. Robinson made a great change from a lecture-driven teacher to a facilitator. There are several Robinson's points which I really agree with .
I agree with that a teacher should make his or her lecture short. It is easy for a teacher to talk in the whole class time, but the students will feel boring, and then they will not pay attention to what the teacher said. The best way is to get the student involved and give the questions to let the students to answer by using the lesson activities and cooperative group activities.
Another point in the article is changing the questions on the quiz. The questions in Figure 4.2 give the students more chance to think and communicate than the questions in Figure 4.1. In addition, the question in Figure 4.3 is the best way to encourage students to solve the problem in the exam. After the students figure out the answer, they will remember it and have no problem when they face the same question.
Finally, I love the Robinson's TPS, Think- Pair-Share. It is one of the best tools for students cooperative learning in a small group. As a teacher, Robinson is a facilitator who provides the topic of discussion and raises questions to deepen the discussion. the students really get involved and interact with each other. That is great.
I agree with that a teacher should make his or her lecture short. It is easy for a teacher to talk in the whole class time, but the students will feel boring, and then they will not pay attention to what the teacher said. The best way is to get the student involved and give the questions to let the students to answer by using the lesson activities and cooperative group activities.
Another point in the article is changing the questions on the quiz. The questions in Figure 4.2 give the students more chance to think and communicate than the questions in Figure 4.1. In addition, the question in Figure 4.3 is the best way to encourage students to solve the problem in the exam. After the students figure out the answer, they will remember it and have no problem when they face the same question.
Finally, I love the Robinson's TPS, Think- Pair-Share. It is one of the best tools for students cooperative learning in a small group. As a teacher, Robinson is a facilitator who provides the topic of discussion and raises questions to deepen the discussion. the students really get involved and interact with each other. That is great.
Reflection of the last post
Through these two teachers' work, I can see that being a teacher is very valuable. Miss Zhao's hard work made many students' lives different, and Mrs. Xu 's guide showed me where I should go. I really appreciate them and miss them. I also want to be a person who can make a difference in the young people's lives.
My most memorable math teachers
1. Miss Zhao was my math teacher when I was in grade 5. She was one of my favorite teachers because of her caring and contribution for my improvement in Math. At that time, grade 5 was the last year for students in the elementary school. For students, there was a promotion examination after they graduated from elementary schools, and the scores of the exam decided weather the students went to good schools or bad schools. In order to send more students to go to good schools, Miss Zhao gave us extra classes each week in evenings or on weekends. She worked very hard to correct our homework and give us extra practice, as well as she never got extra payment for that work. Finally, most of the students in my class went to the good schools, which included me.
2. My another favorite Math teacher is Mrs. Xu. I love her because not only she taught me knowledge of Math, but she also guided my career in my future. Mrs. Xu taught me Math when I was in grade 12. She was professional and knowledgeable. She explained questions in different ways until she was sure that all the students understood. She also paid attention to each student's personality and skills and guided them to set up their goals. One day, Mrs. Xu told me," you are very careful when you do your homework in order to avoid making mistakes. You would be a good teacher or a doctor if you chose these two career." Her words might really influenced me. After I graduated from high school, I went to a normal university and wanted to be a teacher.
2. My another favorite Math teacher is Mrs. Xu. I love her because not only she taught me knowledge of Math, but she also guided my career in my future. Mrs. Xu taught me Math when I was in grade 12. She was professional and knowledgeable. She explained questions in different ways until she was sure that all the students understood. She also paid attention to each student's personality and skills and guided them to set up their goals. One day, Mrs. Xu told me," you are very careful when you do your homework in order to avoid making mistakes. You would be a good teacher or a doctor if you chose these two career." Her words might really influenced me. After I graduated from high school, I went to a normal university and wanted to be a teacher.
Monday, September 21, 2009
The website of AMS UBC Whistler Lodge
Hi everyone,
Here is the website http://www.ubcwhistlerlodge.com/. Hope it is helpful for your accommodation in Whistler conference.
Rosemary
Here is the website http://www.ubcwhistlerlodge.com/. Hope it is helpful for your accommodation in Whistler conference.
Rosemary
Saturday, September 19, 2009
Self assessment: Microteaching Sept. 18/09
Self evaluations:
I :
I :
- finished all of content that I wanted to teach in ten minutes.
- prepared the powerpoint presentation which is really contributed to students' understanding.
- got everybody's attention by talking to people on my both sides.
- chose the topic that the students are interested in.
If I were to teach this lesson again, I would:
- have more interaction with students.
- use a projecter, and then students can see my powerpoint easily and clearly.
- speak louder.
- use different ways to engage the audience.
Peers evalations:
My peers thought that I:
- gave the useful information.
- gave a short guide about how to set up a website.
- looked at both sides of the students.
- gave a pretest by asking if they know anything about wordpress and blogs at the beginning of the presentation.
Peers suggested me:
- to speak louder.
- to give a handout of each steps which would make students easy to follow.
- to use a projector which make everyone easy to see.
- to ask them some questions to check whether each person is following up.
Comment on Skemp’s article
According to Skemp’s article, “Relational Understanding and Instrumental Understanding”, there are many points that I agree with, but I also have different opinions in some aspects.
There are three points that I agree with the author. First, in the article, the author says, “There are two kinds of mathematical mis-matches which can occur: 1. Pupils whose goal is to understand instrumentally, taught by a teacher who wants them to understand relationally. 2. The other way about”. I totally agree with that. Based on my working experiences, I have met the two kinds of students. I worked with an adult student, Linda, as a math tutor in a college last year. While I was explaining the reason of a2 + b2 = c2, she told me that it was too much and difficult for her to remember the reason, and she just wanted to memorize the formula and use it. Actually, in her practice, she did very well for using the formula to solve the questions. On the other hand, when I taught a grade 8 student about the formula, she asked me “why” as soon as I gave her the formula.
Second, in order to avoid the mis-matches mentioned above, I agree with that point in the article—“All of these imply, as does the phrase ‘make a reasoned choice’, that he is able to consider the alternative goals of instrumental and relational understanding on their merits and in relation their merits and in relation to a particular situation.” A math teacher should use different ways—relational way or instrumental way to teach based on the students’ demands.
Third, I totally agree with “If what is wanted is a page of right answers, instrumental mathematics can provide this more quickly and easily” and “Just because less knowledge is involved, one can often get the right answer more quickly and reliably by instrumental thinking than relational”. “That relational understanding of a particular topic is too difficult, but the pupils still need it for examination reasons.” Linda, the student mentioned above, is a good example of this point. At that time, she is working on her GED math test. Her purpose is to pass the test. Since her basic knowledge of math is poor, the relational understanding is more difficult for her than the instrumental understanding. In fact, the instrumental understanding that we used made her pass her test smoothly and successfully.
However, when talking about the “blame” of the negative attitude to mathematics, the author thought it was the widespread failure to teach relational mathematics—“If for ‘blame’ we may substitute ‘cause’, there can be small doubt that the widespread failure to teach relational mathematics…”. I think the failure is one of the causes, but it is not the main causes. I think that if math teachers can apply the relational and instrumental understanding to students based on the students needs, the negative attitude to mathematics would change to positive attitude.
There are three points that I agree with the author. First, in the article, the author says, “There are two kinds of mathematical mis-matches which can occur: 1. Pupils whose goal is to understand instrumentally, taught by a teacher who wants them to understand relationally. 2. The other way about”. I totally agree with that. Based on my working experiences, I have met the two kinds of students. I worked with an adult student, Linda, as a math tutor in a college last year. While I was explaining the reason of a2 + b2 = c2, she told me that it was too much and difficult for her to remember the reason, and she just wanted to memorize the formula and use it. Actually, in her practice, she did very well for using the formula to solve the questions. On the other hand, when I taught a grade 8 student about the formula, she asked me “why” as soon as I gave her the formula.
Second, in order to avoid the mis-matches mentioned above, I agree with that point in the article—“All of these imply, as does the phrase ‘make a reasoned choice’, that he is able to consider the alternative goals of instrumental and relational understanding on their merits and in relation their merits and in relation to a particular situation.” A math teacher should use different ways—relational way or instrumental way to teach based on the students’ demands.
Third, I totally agree with “If what is wanted is a page of right answers, instrumental mathematics can provide this more quickly and easily” and “Just because less knowledge is involved, one can often get the right answer more quickly and reliably by instrumental thinking than relational”. “That relational understanding of a particular topic is too difficult, but the pupils still need it for examination reasons.” Linda, the student mentioned above, is a good example of this point. At that time, she is working on her GED math test. Her purpose is to pass the test. Since her basic knowledge of math is poor, the relational understanding is more difficult for her than the instrumental understanding. In fact, the instrumental understanding that we used made her pass her test smoothly and successfully.
However, when talking about the “blame” of the negative attitude to mathematics, the author thought it was the widespread failure to teach relational mathematics—“If for ‘blame’ we may substitute ‘cause’, there can be small doubt that the widespread failure to teach relational mathematics…”. I think the failure is one of the causes, but it is not the main causes. I think that if math teachers can apply the relational and instrumental understanding to students based on the students needs, the negative attitude to mathematics would change to positive attitude.
Friday, September 18, 2009
Lessonplan1
Microteaching Lesson Plan
Topic: WordPress
Ø Bridge: Ask students two Questions:
1. What is a website used for?
2. Do you want to have your own website ?
Ø Teaching Objectives:
· Getting everybody involved when they are doing their activity.
· Working to overcome people’s hesitancy to build up their own website
· Making sure students understand the relationship between WordPress and Blogs
Ø Learning Objectives:
Students will:
· Know what is WordPress
· Learn how to install the WordPress
· Set up a blog –having their own website
Ø Activity:
Ask students:
· What are they going to post in their blog when they have their own websites?
· To make a list of information that they want to post, and keep the list for next class to use.
Topic: WordPress
Ø Bridge: Ask students two Questions:
1. What is a website used for?
2. Do you want to have your own website ?
Ø Teaching Objectives:
· Getting everybody involved when they are doing their activity.
· Working to overcome people’s hesitancy to build up their own website
· Making sure students understand the relationship between WordPress and Blogs
Ø Learning Objectives:
Students will:
· Know what is WordPress
· Learn how to install the WordPress
· Set up a blog –having their own website
Ø Activity:
Ask students:
· What are they going to post in their blog when they have their own websites?
· To make a list of information that they want to post, and keep the list for next class to use.
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