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.
Tuesday, September 29, 2009
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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