Tuesday, December 8, 2009
Sunday, November 29, 2009
“Relational and Instrumental Understanding"
Comments on “Relational and Instrumental Understanding"
Going through Dr.R. Skemp article, I liked the fact that he contrasted relational and instrumental understanding by emphasizing on “faux amis” (a word which sounds the same or alike in two languages, but whose meanings are different). According to Skemp, "understanding" is also a faux amis.
In his article, Skemp, mentions that “instrumental mathematics is usually easier to understand; sometimes much easier.” Instrumental mathematics might be easy to understand, but not for “all” the students. Students have different abilities in learning. Sometimes they learn visually, they have to see things, or touch things in order to understand the concepts better. In this case, in a class with thirty or more students, instrumental method is not making things easier. On the other hand, I also agree with the fact that “‘some’ topics… are difficult to understand relationally” and therefore, they must be taught instrumentally. Thus, instrumental methods could be used but within a limit.
According to Skemp, “it is nice to get a page of right answers” by using instrumental method, but the work, or the mark has no value since everything was memorized and students would not be able to remember anything after a week or so.
A page of right answers might “restore [a student’s] self-confidence”, but it also can do the opposite in long-term since the material learnt by instrumental method are easy to forget. Skemp also chains this idea by saying: “It is easier to remember [using relational method]” which is true indeed.
Going through Dr.R. Skemp article, I liked the fact that he contrasted relational and instrumental understanding by emphasizing on “faux amis” (a word which sounds the same or alike in two languages, but whose meanings are different). According to Skemp, "understanding" is also a faux amis.
In his article, Skemp, mentions that “instrumental mathematics is usually easier to understand; sometimes much easier.” Instrumental mathematics might be easy to understand, but not for “all” the students. Students have different abilities in learning. Sometimes they learn visually, they have to see things, or touch things in order to understand the concepts better. In this case, in a class with thirty or more students, instrumental method is not making things easier. On the other hand, I also agree with the fact that “‘some’ topics… are difficult to understand relationally” and therefore, they must be taught instrumentally. Thus, instrumental methods could be used but within a limit.
According to Skemp, “it is nice to get a page of right answers” by using instrumental method, but the work, or the mark has no value since everything was memorized and students would not be able to remember anything after a week or so.
A page of right answers might “restore [a student’s] self-confidence”, but it also can do the opposite in long-term since the material learnt by instrumental method are easy to forget. Skemp also chains this idea by saying: “It is easier to remember [using relational method]” which is true indeed.
Saturday, November 21, 2009
project on oragami and polyhedral
2) Benefit of the project:
• It is a hands on activity
• Helps students to visualize the 3 dimensional worlds. For instance, how many vertices there are, finding information about edges, sides, and etc?
• Avoids boredom in the classroom and incorporates other subjects such as Arts.
• It makes students familiar with the background and history of polyhedral.
Weaknesses of the project:
• The project is indeed very time-consuming due to making origami. That might be annoying for students and as a result it might leads to frustrations and confusion. Furthermore, students might loose their interest toward the subject.
• Time wise, might be hard to fit this project in the curriculum.
Uses of the project :
• Making the students to feel for 3-D world.
• Make them familiar with what geometry is, in particular polyhedral.
• It might be a fun classroom activity to follow.
How to modify the project:
• We can avoid making the students to do the origami in the classroom.
• Give them other options for origami. For instance, cut the segments and tape them together. This way, it is less time consuming and it gives the students the same result.
Extension of the project:
• We can ask our students to think about volume, surface area, and some other physical properties such as the number of edges, angels, and etc afterward, or for future
3) Our project (Surface Area):
• Grade level : Grade 9
• Purposes: To make a fun activity in the class, avoid boredom about the teaching subject, make the students to get a notion for a 3-D object/world, practicing the concept of “Area” in mathematics.
• Description: There are two choices for this project:
1. Students must build a “Reasonable” shape object such as a house, car, flower, and etc using at least two 3-D objects.
2. Or build a complex structure using only one 3-D object of their choice.
Students must choose only one of the above options. For either one they must follow the below criterions.(2-3 people per group)
o Students must hand in an informal proposal for this project.
o They must build the structure.
o They must write a report including the followings:
i) How they got the surface area of the object they made in details. This includes a verbal explanation and diagrams.
ii) Measuring and calculating the surface area of the object in two different units. ( cm, and mm)
• Time:
o First session: 20 min for proposal in the class.
o Second session: A full class time for material and making objects.
o Giving them a week for the final work.
• Production:
o Reports and structures.
• Marking Criteria:
o Communication ( how well they explain the work) 35%
o Calculations(how they got the surface area and units) 50%
o Structure ( what they made) 10%
o Creativity 5%
• It is a hands on activity
• Helps students to visualize the 3 dimensional worlds. For instance, how many vertices there are, finding information about edges, sides, and etc?
• Avoids boredom in the classroom and incorporates other subjects such as Arts.
• It makes students familiar with the background and history of polyhedral.
Weaknesses of the project:
• The project is indeed very time-consuming due to making origami. That might be annoying for students and as a result it might leads to frustrations and confusion. Furthermore, students might loose their interest toward the subject.
• Time wise, might be hard to fit this project in the curriculum.
Uses of the project :
• Making the students to feel for 3-D world.
• Make them familiar with what geometry is, in particular polyhedral.
• It might be a fun classroom activity to follow.
How to modify the project:
• We can avoid making the students to do the origami in the classroom.
• Give them other options for origami. For instance, cut the segments and tape them together. This way, it is less time consuming and it gives the students the same result.
Extension of the project:
• We can ask our students to think about volume, surface area, and some other physical properties such as the number of edges, angels, and etc afterward, or for future
3) Our project (Surface Area):
• Grade level : Grade 9
• Purposes: To make a fun activity in the class, avoid boredom about the teaching subject, make the students to get a notion for a 3-D object/world, practicing the concept of “Area” in mathematics.
• Description: There are two choices for this project:
1. Students must build a “Reasonable” shape object such as a house, car, flower, and etc using at least two 3-D objects.
2. Or build a complex structure using only one 3-D object of their choice.
Students must choose only one of the above options. For either one they must follow the below criterions.(2-3 people per group)
o Students must hand in an informal proposal for this project.
o They must build the structure.
o They must write a report including the followings:
i) How they got the surface area of the object they made in details. This includes a verbal explanation and diagrams.
ii) Measuring and calculating the surface area of the object in two different units. ( cm, and mm)
• Time:
o First session: 20 min for proposal in the class.
o Second session: A full class time for material and making objects.
o Giving them a week for the final work.
• Production:
o Reports and structures.
• Marking Criteria:
o Communication ( how well they explain the work) 35%
o Calculations(how they got the surface area and units) 50%
o Structure ( what they made) 10%
o Creativity 5%
Sunday, November 15, 2009
Reflection on problem solving and 2 col
When I started solving the problem, I was not quite sure how to solve it. By doing the col and writing about what I am going through and where I am stuck, I really felt the difference. I was no more staring at the blank sheet of paper and wasting time. By writing out my feelings, or the steps that I was taking I have noticed that I came to the conclusion( which I am not sure if it is 100% right, or not) faster than I thought and I need to admit that this is the most productive way of solving problems. As I was solving and writing, I did indeed enjoy the process more and understood the steps way better. Great experience it was.
Wednesday, November 4, 2009
practicum
I must admit that I enjoyed my practicum very much. My school was great and all the kids were well behaved. The most memorable part for me was to make a quiz for them and it was so much of fairness and judgment that I had to use. I totally found out that in order to be a good teacher you need to be a good judge and apply fairness everywhere. Also, I got to teach the adapted grade 8 and 9 class and I was really surprised that how much I enjoyed this particular class more than any other regular classes that I taught. I also found out that teaching is something that it comes to you gradually and it is not something that you can learn it over a night. You need to make your mistakes and you need to learn from them. Teacher are indeed long time learners. I got to watch other classes such as music and social studies which were a lot different than math and saw how classroom management was different in each class. I found out that in order to be a successful teacher we need to think that we are teaching our own kids instead of thinking that we are teaching others kids. I also had experiences that I found out that we need to be firm and show students that we are not their friends, but we can be friendly to them. Students need to understand that there is boundary between teachers and students and they cannot cross that at all. All in all, my two weeks practicum was great and I enjoyed every bit of it.
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