Wednesday, September 30, 2009
Reflection to Dave Hewitt’s film
There were several things that intrigued me in Dave Hewitt’s film. Firstly, I was impressed by Hewitt’s way of introducing simple algebra. To be frankly honest, I haven’t seen a math topic introduced in such a creative, interactive, fun and exciting way. Secondly, I also liked how he manages his class. In particular, I liked how he was able to engage his students throughout the lesson in an innovative way such that he was able to encourage his students to think about the same problem in different ways. Thirdly, I liked how he was able to get the whole class to participate in the lesson by getting them all to speak out the answer because it promotes the students to self-check their answer when they hear an answer very different to their own. It was also great that no student was put on the spot to feel embarrassed since the whole class was engaged in shouting out the answer. Lastly, I really liked how he taught the lesson by starting simple and gradually building up the concept and introducing x as a simple introduction to algebra. Thus, I will definitely consider incorporating some of his innovative teaching techniques into my teaching.
Monday, September 28, 2009
Reflection to Battleground Schools – Mathematics Education
Summary:
There are two main stances in mathematics education and they are the progressive and the conservative views. The progressivists’ goal is to understand mathematics relationally whereas the conservatists’ goal is to understand mathematics instrumentally through fluency.
The Progressivist movement occurred from 1910-1940 and was “led primarily by John Dewey.” This movement aimed at stirring away from the traditional instrumental learning of “meaningless memorized procedures” to focusing more at understanding “mathematics through activity and inquiry.”
The New Math movement in the 1960s was an initiative led by the School Mathematics Study Group (SMSG) and was “strongly influenced by the Bourbaki group of mathematicians in France.” The movement introduced a new curriculum “to be taught throughout the K-12 system” in an attempt to educate future scientists and intellectuals. New Math supporters “combined mainly conservative with some progressive features,” however, the movement quickly came to an end when it was “denounced in the press and popular media”.
The National Council of Teachers of Mathematics (NCTM) developed its own standards program after anticipating “imposition of national curricular standards in the US.” The NCTM was influenced by progressive and constructivists approaches. From the mid 1990s to present day, there have been continuous “battles over mathematics curricula and teaching methods.”
Response:
It was nice to be able to get some background knowledge of how mathematics education came to be today. Although, I am not in favor of any particular movement, I think there is nevertheless something for me to benefit from. In particular, I think it is beneficial for the students if they can learn math instrumentally and/or relationally; as I believe it will help to consolidate the students’ understanding when math is taught from different perspectives. Also as a future teacher, I think it is crucial that I am flexible, open-minded and well-prepared for my classes so that when a ‘new math program’ is introduced my students aren’t left confused in the dark.
There are two main stances in mathematics education and they are the progressive and the conservative views. The progressivists’ goal is to understand mathematics relationally whereas the conservatists’ goal is to understand mathematics instrumentally through fluency.
The Progressivist movement occurred from 1910-1940 and was “led primarily by John Dewey.” This movement aimed at stirring away from the traditional instrumental learning of “meaningless memorized procedures” to focusing more at understanding “mathematics through activity and inquiry.”
The New Math movement in the 1960s was an initiative led by the School Mathematics Study Group (SMSG) and was “strongly influenced by the Bourbaki group of mathematicians in France.” The movement introduced a new curriculum “to be taught throughout the K-12 system” in an attempt to educate future scientists and intellectuals. New Math supporters “combined mainly conservative with some progressive features,” however, the movement quickly came to an end when it was “denounced in the press and popular media”.
The National Council of Teachers of Mathematics (NCTM) developed its own standards program after anticipating “imposition of national curricular standards in the US.” The NCTM was influenced by progressive and constructivists approaches. From the mid 1990s to present day, there have been continuous “battles over mathematics curricula and teaching methods.”
Response:
It was nice to be able to get some background knowledge of how mathematics education came to be today. Although, I am not in favor of any particular movement, I think there is nevertheless something for me to benefit from. In particular, I think it is beneficial for the students if they can learn math instrumentally and/or relationally; as I believe it will help to consolidate the students’ understanding when math is taught from different perspectives. Also as a future teacher, I think it is crucial that I am flexible, open-minded and well-prepared for my classes so that when a ‘new math program’ is introduced my students aren’t left confused in the dark.
Saturday, September 26, 2009
Self-Reflection to Teacher and Student Interviews
In my group’s interview with two high school students, it didn’t surprise me that one student said “no one really likes math in high school.” Further, from my encounter with many university students, most people either didn’t like math or had negative experiences with math. The interviews however, did shed some light on ways students would like teachers to teach math. Both students emphasized the importance of interesting the students and making “the class a little more fun and keeps everyone from NOT falling asleep” by allowing group activities. Therefore, as a teacher candidate it’s important that I am open to students’ suggestions and try my best to create a comforting classroom environment that involves plenty of excitement and fun group activities for students to engage in.
In the interview with the math teacher, however, she said she unfortunately “wasn’t accommodating other learners especially those who have learning differences.” Therefore, as a future teacher, I shall work towards being flexible and adaptive in my teaching so that I am able to accommodate or able to reach out to the various types of learners whether it is through simplifying a complex problem into simpler parts or using real life examples to help students relate to math. Lastly, I think it is also important that I am an approachable teacher so that my students will not hesitate to come and ask me for help.
In the interview with the math teacher, however, she said she unfortunately “wasn’t accommodating other learners especially those who have learning differences.” Therefore, as a future teacher, I shall work towards being flexible and adaptive in my teaching so that I am able to accommodate or able to reach out to the various types of learners whether it is through simplifying a complex problem into simpler parts or using real life examples to help students relate to math. Lastly, I think it is also important that I am an approachable teacher so that my students will not hesitate to come and ask me for help.
Summary to Teacher and Student Interviews
In compliance with BCCT standards, “educators will engage in career-long learning”. Similarly, as teacher candidates and future educators we will continue to learn from our professors as well as from teacher and student interviews. In this interview, we have in our group of three collaboratively created a list of nine questions we most wanted to ask high school math teachers and students. From our interview with a math teacher and two high school students, we learned of the various resources and styles of teaching that we can make available to students to facilitate their learning in math.
Our first two interviewees were high school female students in grades nine and twelve respectively. We asked these students if they have troubles doing math, what would they do and why? The grade nine student said “if I have problem[s] doing math, I will go and ask my teacher” since she felt her teacher was approachable. The second student said that she will ask her friends because “discussions with her friends are good enough”. As teacher candidates then, we must recognize that our availability and approachability for students plays an important role in helping them learn math.
We also asked our two interviewees which area of math they find difficult and how their teachers can help them learn the topic better. One student has difficulties with volumes and angles and she prefers to learn “by sitting and taking notes” whereas the other student has difficulties with trigonometry and prefers to learn math “visually.” Thus, as teacher candidates we must keep in mind that each individual’s ways of learning is as different as the colors of the rainbow.
Our forth question was what can teachers do to motivate the students to learn math. In general, both students said it was hard to motivate them in a subject they disliked. However, they suggested that their teachers can try to interest them by making “the lesson a funner [group] activity.” Ironically, this ties into our last question, in which we asked the students how they would define a good math teacher. The grade nine student described “a good math teacher [as] someone [who] makes the class a little more fun and keeps everyone from NOT falling asleep.” On the other hand, the grade twelve student said a good math teacher “shoudn’t be monotone” and should make her “feel interested in what he/she teaches.”
In our interview with the high school math teacher however, we asked her what is the hardest thing to be a good math teacher? She replied “the most difficult part of being a math teacher is getting the students to get excited about Math.” What is interesting, however, is that she told us “some students say that they were once interested in Math” Therefore, as teachers it’s important that we try our best to teach math in fun and interesting ways.
This led into our second question inquiring any teaching advice(s) that our interviewee can give to teacher candidates. In her response, she told us we should avoid getting “disillusioned with teaching especially if the students are unmotivated.”In other words, it is important for teachers to overcome any teaching difficulties or harsh criticisms that she/he may encounter in the profession by approaching these problems optimistically and continuing to learn and develop professionally. For example, if a student is distracted, we shouldn’t take it personally and lose our initiative in teaching. Rather, we can refocus students back to the math lesson by “asking the distracted student to answer the question.” Distracted students also serve as a valuable sign in how well teachers are engaging their students in the class.
Thus, we asked the interviewee which is/are the most effective techniques she has used in teaching and why? She replied “I try to use real life examples…so that the seemingly abstract concepts can be more concrete.” This method however, “works only most of the time.” The reason for this as reflected by the interviewee is that she “wasn’t accommodating other learners especially those who have learning differences.” She also noted that “it was challenging to NOT teach the way she learned the concept.” Therefore, as teacher candidates, we should be flexible and adaptive in our teaching so that we are able to accommodate most if not all our students. Another effective teaching technique the interviewee had used all the time was “simplifying a complex concept using simpler examples.”
In conclusion, the interviews with the students helped us gain insight into their expectations from their math teachers and the methods that can be used to facilitate their learning in math. Generally, a great math teacher should be flexible and open-minded in his/her teaching to create a comforting classroom environment that involves plenty of excitement and fun group activities for students to engage in.
by Jenny, Maryam, Candice
Our first two interviewees were high school female students in grades nine and twelve respectively. We asked these students if they have troubles doing math, what would they do and why? The grade nine student said “if I have problem[s] doing math, I will go and ask my teacher” since she felt her teacher was approachable. The second student said that she will ask her friends because “discussions with her friends are good enough”. As teacher candidates then, we must recognize that our availability and approachability for students plays an important role in helping them learn math.
We also asked our two interviewees which area of math they find difficult and how their teachers can help them learn the topic better. One student has difficulties with volumes and angles and she prefers to learn “by sitting and taking notes” whereas the other student has difficulties with trigonometry and prefers to learn math “visually.” Thus, as teacher candidates we must keep in mind that each individual’s ways of learning is as different as the colors of the rainbow.
Our forth question was what can teachers do to motivate the students to learn math. In general, both students said it was hard to motivate them in a subject they disliked. However, they suggested that their teachers can try to interest them by making “the lesson a funner [group] activity.” Ironically, this ties into our last question, in which we asked the students how they would define a good math teacher. The grade nine student described “a good math teacher [as] someone [who] makes the class a little more fun and keeps everyone from NOT falling asleep.” On the other hand, the grade twelve student said a good math teacher “shoudn’t be monotone” and should make her “feel interested in what he/she teaches.”
In our interview with the high school math teacher however, we asked her what is the hardest thing to be a good math teacher? She replied “the most difficult part of being a math teacher is getting the students to get excited about Math.” What is interesting, however, is that she told us “some students say that they were once interested in Math” Therefore, as teachers it’s important that we try our best to teach math in fun and interesting ways.
This led into our second question inquiring any teaching advice(s) that our interviewee can give to teacher candidates. In her response, she told us we should avoid getting “disillusioned with teaching especially if the students are unmotivated.”In other words, it is important for teachers to overcome any teaching difficulties or harsh criticisms that she/he may encounter in the profession by approaching these problems optimistically and continuing to learn and develop professionally. For example, if a student is distracted, we shouldn’t take it personally and lose our initiative in teaching. Rather, we can refocus students back to the math lesson by “asking the distracted student to answer the question.” Distracted students also serve as a valuable sign in how well teachers are engaging their students in the class.
Thus, we asked the interviewee which is/are the most effective techniques she has used in teaching and why? She replied “I try to use real life examples…so that the seemingly abstract concepts can be more concrete.” This method however, “works only most of the time.” The reason for this as reflected by the interviewee is that she “wasn’t accommodating other learners especially those who have learning differences.” She also noted that “it was challenging to NOT teach the way she learned the concept.” Therefore, as teacher candidates, we should be flexible and adaptive in our teaching so that we are able to accommodate most if not all our students. Another effective teaching technique the interviewee had used all the time was “simplifying a complex concept using simpler examples.”
In conclusion, the interviews with the students helped us gain insight into their expectations from their math teachers and the methods that can be used to facilitate their learning in math. Generally, a great math teacher should be flexible and open-minded in his/her teaching to create a comforting classroom environment that involves plenty of excitement and fun group activities for students to engage in.
by Jenny, Maryam, Candice
Interview with High School Math Students
1. If you have troubles doing math, what would you do and why? Would you ask help from your teacher and/or classmate or go to problem sessions? Why or why not?
Student 1 :
I usually ask friends if I have troubles with math, and vice versa. My friends and I would check math assignments together. So when somebody has a question, we’ll discuss about it together. Therefore, it’s not necessary for me to go to problem sessions afterwards because discussions with my friends are good enough.
Student 2:
If i had trouble doing math i would probably go and ask my teacher for help at the end of class. Most kids if they dont understand it they will give up so you have to encourage them to come see you or the teacher after school or at anytime for help. Another thing that i might do is get a tutor that always helps.
2. What area of math do you find the most difficult? Is there anything your teachers can do to facilitate your learning better in this area?
Student 1:
I am not good with graph/sin/cos/tan.
I find myself understanding better if I can logically understand or know why and how things (in this case, math) work. Because trigonometric function is my weakness; it would be better if I can find someone who can explain to me again and again about how sin/cos/tan work.
Student 2:
Volumes and angles seemed a little hard to me and i dont really think there is anything more the teacher can do than to teach us it. i cant remeber i finnished all my math courses so its been a year since i have been in a math class but from what i can remeber; there wasnt much the teacher could do maybe t was because i wasnt listening during the class of explaining angles and volumes i dont remeber but i think the teacher did there share.
3. How would you like to learn math. For example, using diagrams, analogies, computer games etc.
Student 1:
maybe with visuals
I’ve never learnt math with computer games so I’m not sure about that one.
Student 2:
i think the good old way of sitting in a class and listeni8ng and taking notes is the best way its just that the etacher has to make it a fun activitie with every lesson for everyone to pay attention. otherwise everyone gets bored and start fdropping out of that class or they just dont get it.. every lesson has to be a little dummed down. pretend like you are teaching 5 year olds.
4. How can your teacher motivate you to learn a subject that you are really having trouble with or just hate it altogether.
Student 1:
This is a hard question. If I don’t like something, then it is very difficult for me to deal with it all the time. I can only say to make me/myself start feeling interested about it; hopefully to find some fun in it so that I don’t dislike it so much.
Student 2:
makeing the lesson a funner activity, maybe putting us into groups
5. What are your exceptions from a good math teacher or how do you describe a good math teacher?
Student 1:
A teacher who makes me feel interested in what she/he teaches.
Or else I wouldn’t be paying too much attention about what she/he’s talking about, and that eventually results in skipping classes and/or failing tests.
Also, a good teacher to me shouldn’t be monotone while teaching class.
Even if I do like the course, it will still make me fall asleep.
Student 2:
once i had a math teacher that was a really funny guy and everyone seemed to like him alot, he tried really hard to keep us tooned in. the problem with a math class is that no one really likes math in high school well not everyone but most people. i think a good math teacher is someone that makes the class a little more fun and keeps everyone from NOT falling asleep. But that will come after years of being a teacher and being very comfortable with everyone. in the beggining you will feel a little intimidated and the kids will understand that you are new to this and you might be a little awkward. so its all good :). giveing too much homework is never a good idea try to make them learn most of everything IN CLASS. becuase knowing teenagers they barely want to touch homework.
Student 1 :
I usually ask friends if I have troubles with math, and vice versa. My friends and I would check math assignments together. So when somebody has a question, we’ll discuss about it together. Therefore, it’s not necessary for me to go to problem sessions afterwards because discussions with my friends are good enough.
Student 2:
If i had trouble doing math i would probably go and ask my teacher for help at the end of class. Most kids if they dont understand it they will give up so you have to encourage them to come see you or the teacher after school or at anytime for help. Another thing that i might do is get a tutor that always helps.
2. What area of math do you find the most difficult? Is there anything your teachers can do to facilitate your learning better in this area?
Student 1:
I am not good with graph/sin/cos/tan.
I find myself understanding better if I can logically understand or know why and how things (in this case, math) work. Because trigonometric function is my weakness; it would be better if I can find someone who can explain to me again and again about how sin/cos/tan work.
Student 2:
Volumes and angles seemed a little hard to me and i dont really think there is anything more the teacher can do than to teach us it. i cant remeber i finnished all my math courses so its been a year since i have been in a math class but from what i can remeber; there wasnt much the teacher could do maybe t was because i wasnt listening during the class of explaining angles and volumes i dont remeber but i think the teacher did there share.
3. How would you like to learn math. For example, using diagrams, analogies, computer games etc.
Student 1:
maybe with visuals
I’ve never learnt math with computer games so I’m not sure about that one.
Student 2:
i think the good old way of sitting in a class and listeni8ng and taking notes is the best way its just that the etacher has to make it a fun activitie with every lesson for everyone to pay attention. otherwise everyone gets bored and start fdropping out of that class or they just dont get it.. every lesson has to be a little dummed down. pretend like you are teaching 5 year olds.
4. How can your teacher motivate you to learn a subject that you are really having trouble with or just hate it altogether.
Student 1:
This is a hard question. If I don’t like something, then it is very difficult for me to deal with it all the time. I can only say to make me/myself start feeling interested about it; hopefully to find some fun in it so that I don’t dislike it so much.
Student 2:
makeing the lesson a funner activity, maybe putting us into groups
5. What are your exceptions from a good math teacher or how do you describe a good math teacher?
Student 1:
A teacher who makes me feel interested in what she/he teaches.
Or else I wouldn’t be paying too much attention about what she/he’s talking about, and that eventually results in skipping classes and/or failing tests.
Also, a good teacher to me shouldn’t be monotone while teaching class.
Even if I do like the course, it will still make me fall asleep.
Student 2:
once i had a math teacher that was a really funny guy and everyone seemed to like him alot, he tried really hard to keep us tooned in. the problem with a math class is that no one really likes math in high school well not everyone but most people. i think a good math teacher is someone that makes the class a little more fun and keeps everyone from NOT falling asleep. But that will come after years of being a teacher and being very comfortable with everyone. in the beggining you will feel a little intimidated and the kids will understand that you are new to this and you might be a little awkward. so its all good :). giveing too much homework is never a good idea try to make them learn most of everything IN CLASS. becuase knowing teenagers they barely want to touch homework.
Interview with a High School Math Teacher
1. What is the hardest thing to be a good math teacher (or teacher in general) speaking from your own experience?
Answer: I believe the most difficult part of being a math teacher is getting the students to get excited about Math. Most students I've taught are either bored with Math or just plain uninterested. What is interesting is that some students say that they were once interested in Math, but obviously, somewhere in their school life, something, or someone made them lose interest.
2. The thoughts you have about teaching, is it the same after you started teaching? What stays the same and what changed?
Answer: I used to think before I started teaching that if I try to teach any grade level in some creative way in Math, that I can get them interested again. I thought that if I use real life experiences, that I can help them relate to Math in a more realistic way. Unfortunately, I found out when I started teaching that this method, works only most of the time - still more often than not. I later found out that I wasn't accommodating other learners especially those who have learning differences. Not only was it very challenging to get these students to understand Math, but it challenging to NOT teach the way I learned the concept.
3. From your teaching experience, which is/are the most effective techniques you have used in teaching and why? Also, at which grade level is this most effective for?
Answer: I believe that one of the reasons why the students are finding Math very difficult is because they don't understand how valuable the concepts and how they can be used in real life. So whenever I teach, I try to use real life examples - applications if you will - so that the seemingly abstract concepts can be more concrete. Although, as I mentioned, this method does not work, there are still students whom I've taught who were able to understand the concept. Another method that I use all the time is simplifying a complex concept using simpler examples. For example, if a student doesn't understand how to simplify radicals, I use simpler examples such as simple fractions and use cross cancellation, etc. The steps are basically the same with the simpler examples but the numbers being used are just more complicated.
4. What teaching advice(s) or tip(s) can you give to teacher candidates? What would you do to draw back students’ attention when they become distracted?
Answer: I haven't been a teacher for that long. But I can definitely say that once I started teaching, it was easier to get disillusioned with teaching especially if the students are unmotivated. But that's exactly we should avoid. As teachers, we should aspire to continue learning so our skills don't stagnate. If we let our disillusionment get the better of us, we risk losing our drive and impetus to continue learning and continue developing professionally. When students become distracted, I usually try to refocus them by making them stop and asking the distracted student to answer the question. 5. What type of techniques do you use to teach math? Instrumental or relational?
Answer: I believe the most difficult part of being a math teacher is getting the students to get excited about Math. Most students I've taught are either bored with Math or just plain uninterested. What is interesting is that some students say that they were once interested in Math, but obviously, somewhere in their school life, something, or someone made them lose interest.
2. The thoughts you have about teaching, is it the same after you started teaching? What stays the same and what changed?
Answer: I used to think before I started teaching that if I try to teach any grade level in some creative way in Math, that I can get them interested again. I thought that if I use real life experiences, that I can help them relate to Math in a more realistic way. Unfortunately, I found out when I started teaching that this method, works only most of the time - still more often than not. I later found out that I wasn't accommodating other learners especially those who have learning differences. Not only was it very challenging to get these students to understand Math, but it challenging to NOT teach the way I learned the concept.
3. From your teaching experience, which is/are the most effective techniques you have used in teaching and why? Also, at which grade level is this most effective for?
Answer: I believe that one of the reasons why the students are finding Math very difficult is because they don't understand how valuable the concepts and how they can be used in real life. So whenever I teach, I try to use real life examples - applications if you will - so that the seemingly abstract concepts can be more concrete. Although, as I mentioned, this method does not work, there are still students whom I've taught who were able to understand the concept. Another method that I use all the time is simplifying a complex concept using simpler examples. For example, if a student doesn't understand how to simplify radicals, I use simpler examples such as simple fractions and use cross cancellation, etc. The steps are basically the same with the simpler examples but the numbers being used are just more complicated.
4. What teaching advice(s) or tip(s) can you give to teacher candidates? What would you do to draw back students’ attention when they become distracted?
Answer: I haven't been a teacher for that long. But I can definitely say that once I started teaching, it was easier to get disillusioned with teaching especially if the students are unmotivated. But that's exactly we should avoid. As teachers, we should aspire to continue learning so our skills don't stagnate. If we let our disillusionment get the better of us, we risk losing our drive and impetus to continue learning and continue developing professionally. When students become distracted, I usually try to refocus them by making them stop and asking the distracted student to answer the question. 5. What type of techniques do you use to teach math? Instrumental or relational?
Wednesday, September 23, 2009
Reflection to Robinson’s Article
After reading Robinson’s article, it made me reestablish the importance of being a flexible teacher. In particular, I liked how Robinson had assessed herself on her teaching and made changes to it. Her “changes included lecturing less, providing opportunities for higher-level student thinking, and developing classrooms norms to support student-student dialogue.” I agree with Robinson that using the Think-pair-share was a valuable tool that generated rich discussion among students and provided an opportunity for students to engage in mathematical learning. I also liked how she changed the format of her exam questions by focusing more on critical thinking, reasoning and communication skills. This gives students the opportunity to demonstrate their knowledge in math and not just on how well they can remember the procedures for solving a specific type of math question.
With all the changes geared toward helping the students to learn better, I question and doubt the value of lecturing less in class. I think restricting lecture time “to a maximum of 60 minutes per week” can be hurtful for the students in that they will not get enough instructional time to develop a good understanding in harder topics. However, I must applaud Robinson’s efforts for trying out new ways to facilitate learning in her students and for her efforts to become a better teacher.
With all the changes geared toward helping the students to learn better, I question and doubt the value of lecturing less in class. I think restricting lecture time “to a maximum of 60 minutes per week” can be hurtful for the students in that they will not get enough instructional time to develop a good understanding in harder topics. However, I must applaud Robinson’s efforts for trying out new ways to facilitate learning in her students and for her efforts to become a better teacher.
Tuesday, September 22, 2009
My Most Memorable Teachers
One of my most memorable math teachers was Mr. Freisen. His writing was neat and legible and notes were clear and easy to understand. I also liked how he would give his students time every class to do homework. It was helpful because it allowed his students to seek help if necessary. I also liked how he would tell us stories that are not necessarily related to math. The stories made math classes more fun and interesting. Overall, he was a great teacher because he cared about his students’ learning. Even if you were no longer in his class, he would stay afterschool to help you learn math.
My second most memorable teacher was my university professor, Dr. Pierce. He was really passionate and enthusiastic about his teaching. He gets really excited when students are engaged and he loves it especially when students ask him challenging questions. He would always answer them with passion and excitement. He is also really helpful during his office hours. Dr. Pierce cared very much about his students’ learning because he would often stay past office hours to make sure everyone has had their chance to clarify misunderstandings and confusions.
Reflecting back to these two teachers, I guess what makes them such great teachers was that they had a broad knowledge in math that they wanted to share. They were both passionate and enthusiastic about math. They were both helpful and dedicated to making sure that their students were learning math. They are good role models to learn from and I wish to carry their good qualities into my own teaching.
My second most memorable teacher was my university professor, Dr. Pierce. He was really passionate and enthusiastic about his teaching. He gets really excited when students are engaged and he loves it especially when students ask him challenging questions. He would always answer them with passion and excitement. He is also really helpful during his office hours. Dr. Pierce cared very much about his students’ learning because he would often stay past office hours to make sure everyone has had their chance to clarify misunderstandings and confusions.
Reflecting back to these two teachers, I guess what makes them such great teachers was that they had a broad knowledge in math that they wanted to share. They were both passionate and enthusiastic about math. They were both helpful and dedicated to making sure that their students were learning math. They are good role models to learn from and I wish to carry their good qualities into my own teaching.
Saturday, September 19, 2009
My First Microteaching Assessment
My peers thought that:
- There was a clear learning objective
- Some thought the bridge was good and some don’t remember it
- There was a pretest of prior knowledge
- There was good participation
- There was a good post-test
- There was a good conclusion
- I had great patience
Some strengths of the lesson include:
- Good time management
- Fun, interesting and engaging
Some improvements for the lesson include:
- Preparing the origami paper
- Start with easier origami
Self-Assessment:
Things that went well in my lesson include:
- Good interaction and good group participation
- good introduction/pretest
If I were to teach this lesson again, I would improve by:
- Slowing down the lesson pace.
- Making sure some of the folding procedures was clearer so that everyone can see and understand
- Helping some people more
Based on my peers’ feedback I would like to make the following changes for this lesson:
- Making a stronger and more memorable bridge and pretest since some people did not recall them
- Perhaps choose an easier origami figure
- There was a clear learning objective
- Some thought the bridge was good and some don’t remember it
- There was a pretest of prior knowledge
- There was good participation
- There was a good post-test
- There was a good conclusion
- I had great patience
Some strengths of the lesson include:
- Good time management
- Fun, interesting and engaging
Some improvements for the lesson include:
- Preparing the origami paper
- Start with easier origami
Self-Assessment:
Things that went well in my lesson include:
- Good interaction and good group participation
- good introduction/pretest
If I were to teach this lesson again, I would improve by:
- Slowing down the lesson pace.
- Making sure some of the folding procedures was clearer so that everyone can see and understand
- Helping some people more
Based on my peers’ feedback I would like to make the following changes for this lesson:
- Making a stronger and more memorable bridge and pretest since some people did not recall them
- Perhaps choose an easier origami figure
Thursday, September 17, 2009
Microteaching 1: Making an Origami Crane
Microteaching 1: Making an Origami Crane
Bridge:
I will begin with a brief introduction to origami. I will start by explaining what “ori” and “gami” means in Japanese. Then I will ask the students if they can guess where origami originated from. After which, I will explain that origami originated from China.
Teaching Objectives:
1) To build a classroom community.
2) To create a fun icebreaker activity.
3) To encourage students to participate in classroom activities.
Learning Objectives:
1) Students will be able to make an origami crane.
2) Students will be able to define the term origami.
Pretest:
These questions will be asked in the bridge phase.
1. Ask the students if they know what “ori” and “gami” refers to in Japanese.
2. Ask the students if they know where origami originated from.
Participatory activity:
I will demonstrate how to make an origami crane and encourage students to talk to each other and help each other if they are having problems when making the crane.
Post-test:
I will ask the students to make a second origami crane on their own without any help.
Summary:
I will go over the procedures needed to make an origami crane. After which, I will end by giving students additional origami links. The students will be able to challenge themselves at making harder origami figures at their own leisure.
Origami Links – Diagrams of Various Origami Figures
1. http://dev.origami.com/diagram.cfm
2. http://www.tinyshiny.com/How-to_Projects.php
3. http://www.oriland.com/studio/main.asp
4. http://www.origami-club.com/en/pageB.htm
Video Links – Vidoes of Various Origami Figures
1. http://www.videojug.com/tag/origami
2. http://www.pem.org/sites/origami/
Wednesday, September 16, 2009
Commentary on “Relational Understanding and Instrumental Understanding” by Richard R. Skemp
Skemp distinguishes between ‘relational understanding’ which is “knowing what to do and why” and ‘instrumental understanding’ which is “described as rules without reasons.”
In his opinion, “pupils whose goal is to understand instrumentally…won’t want to know all the careful groundwork…” True for some students but not for all students since it is possible to convince and engage the student in the groundwork or theory. Like he said “if people get satisfaction…[they may] try to understand relationally new material.” Skemp also claims that instrumental mathematics is usually easier to understand.” Is this the case for everyone? Each student has his/her own unique way of learning; some are visually learners, some are audio learners while others are hands-on learners. What is easier to understand depends on the student’s learning ability.
However, I agree that sometimes “relational understanding of a particular topic is too difficult” and “takes too long.” Thus, forcing teachers to turn to instrumental learning. After all, life is not without challenges. These challenges include “over-burdened syllabi” which Skemp claims, "almost all syllabi would be much better if much reduced in amount so that there would be time to teach them better.” Instead of always reducing course content, isn’t better to find an alternative means of teaching that better facilitates learning? Furthermore, I do not think it’s always fair and better to teach students less materials.
According to Skemp, relational learning will provide students with advantages such as "building up a schema” and/or increasing self-confidence since there are “ways of getting there without outside help.” I, however, think that the combination of relational and instrumental understanding will provide students with the most benefits to learning as relational understanding will cover the weaknesses of instrumental understanding and vice versa. For example, instrumental learning often follows a rigid set of instructions and not as adaptable to other situations. Relational learning however, fosters independent thinking and is more flexible for use in other situations.
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