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.
Sunday, November 29, 2009
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.
Sunday, November 1, 2009
Reflection on the poem
Reflection on the poem
There are times that we think of math as an abstract, rigid subject that we are dealing with. However, there are methods and tricks that we can use to hide that abstractness and by doing so we can deliver our points more sufficiently to our students. One of these methods was writing my thoughts and a poem on the two subjects, zero and division; I found that we can give a little bit of softness in the abstractness. This is a great method to use in order to understand the concept better. For instance, it is difficult for some people, especially high school students to understand or remember that if we are dividing any number by zero, our answer is infinity, or goes to infinity. By using methods like writing poems and thinking about each concept differently and then combining them together we might feel division and zero as two real things. This method takes away the stress about the abstractness and it makes it more fun and attractive to listen to. Also, we are able to lead our students’ attention to the main concept in a better way. It is also useful to give such activity to our students to understand what and how they think about math and how they can learn it better. So I believe it is both ways, one way is that the teacher who makes the poem and provide the information in the it, and the other way it to get the students do that , so that we as teachers can understand their thoughts about the concept.
There are times that we think of math as an abstract, rigid subject that we are dealing with. However, there are methods and tricks that we can use to hide that abstractness and by doing so we can deliver our points more sufficiently to our students. One of these methods was writing my thoughts and a poem on the two subjects, zero and division; I found that we can give a little bit of softness in the abstractness. This is a great method to use in order to understand the concept better. For instance, it is difficult for some people, especially high school students to understand or remember that if we are dividing any number by zero, our answer is infinity, or goes to infinity. By using methods like writing poems and thinking about each concept differently and then combining them together we might feel division and zero as two real things. This method takes away the stress about the abstractness and it makes it more fun and attractive to listen to. Also, we are able to lead our students’ attention to the main concept in a better way. It is also useful to give such activity to our students to understand what and how they think about math and how they can learn it better. So I believe it is both ways, one way is that the teacher who makes the poem and provide the information in the it, and the other way it to get the students do that , so that we as teachers can understand their thoughts about the concept.
2 poems / combined / zero + division
Poem)
Division combined with zero:
Dividing and dividing and diving,
Oh, what is dividing?
It is tilted or straight,
Oh does it have a zero in it?
Bigger or smaller I don’t know
But what goes on the top I call numi
And what goes on the bottom I call deni
My numi travels to infinity ,
If and only if my deni is a zero
Oh division division,
What did you do to my numi
My deni was a zero
Cannot find my numi!
Where is my numi
Is it traveling into infinity?
It is going faster that the light
It is going into the space
It is meeting all the dark matters
It is meeting all the big zero shape planets
Oh division division,
Look what you did to my numi
My numi is still going to infinity
Traveling into the space
Finding all its zero friends
Oh gosh cannot stop my numi
Because my deni was a zero
And look what you did division
Poor numi is going and going into the space
Going into infinity but why it is so
You poor thing numi, you were anything except zero
Your friend deni took you away
Since the deni was a zero
Good luck my numi in the space
Meeting all your zero friends
Cannot find you any more numi
You are traveling faster than I thought
Bye Bye my numi
Hope you can stop one day :S
Division combined with zero:
Dividing and dividing and diving,
Oh, what is dividing?
It is tilted or straight,
Oh does it have a zero in it?
Bigger or smaller I don’t know
But what goes on the top I call numi
And what goes on the bottom I call deni
My numi travels to infinity ,
If and only if my deni is a zero
Oh division division,
What did you do to my numi
My deni was a zero
Cannot find my numi!
Where is my numi
Is it traveling into infinity?
It is going faster that the light
It is going into the space
It is meeting all the dark matters
It is meeting all the big zero shape planets
Oh division division,
Look what you did to my numi
My numi is still going to infinity
Traveling into the space
Finding all its zero friends
Oh gosh cannot stop my numi
Because my deni was a zero
And look what you did division
Poor numi is going and going into the space
Going into infinity but why it is so
You poor thing numi, you were anything except zero
Your friend deni took you away
Since the deni was a zero
Good luck my numi in the space
Meeting all your zero friends
Cannot find you any more numi
You are traveling faster than I thought
Bye Bye my numi
Hope you can stop one day :S
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