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.
Friday, October 30, 2009
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.
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