With the last three videos, we saw how children were taught how to work together to: observe, analyze, conclude, and present. We saw how they learned to listen and value the work of each other. Their engagement and openess toward each other's work, was the same picture presented in this video with the scenery where the four researchers were discussing long term problem.
"The Tower of Hanoe" activity was challenging. The students kept on analyzing their results to the point that they broke them down into pattern within a pattern, then they found the solution.
In part 2, Ms. Janett, the high school math teacher, set the students up with the practice of explaining the lessons to themselves. This was new to me as well as strange. I believe that students deserve explanations, then assign them to solve problems on their own. However, I was intrigued by her strategy.
I observed myself and my students, and note that when I assign them to explain the lesson to themselves, they are better able to focus on the topic, and get more enganged in it then when I explain it to them. I concluded a wild difference between the two situations. The main factor that affects the two situations is the "focus" factor. The main factor for teachers to succesfully relay the lesson, is focus. of any lesson is how to keep their students focused with them so they will understand what they are learning. And I concluded that Ms. Janett's strategy deserves a thumbs-up.
I teach students from fifth to eighth grade. I analyzed that whenever I assigned my students to work on their own in the computer lab, their involvement into that day lesson is always strong. All of them, without exception, were able to present and justify their work.
Saturday, April 10, 2010
Video III, Inventing Notation
Mathematical Notation is the use of symbols which stand for specific quantities, according to the problem, to avoid the writing of long words. It is an abbreviation that helps ease the reading of any solution. However, the most impressive thing that attracted my attention is the use of "0 and 1" as a notation to present a solution by one of the fifth graders. It was excellent. The child used a chart where he wrote the first letter of each topping and 0 for the unused topping and 1 for the used. His presentation was successful. It wasn't only that. He, also, was able to use the "four stories towers" to present the "pizza" activity. The combination he made between the two activities was mathematically correct!
When it comes to the second part, where the children were presenting and discussing their work, they were convincing. They were sure about their solutions, defending and insisting. I would say that the children gain these skills from the activities they were involved in. Thus, hands-on-learning strategy does not only inhance students' learning precess, but also their self-confidence, which I myself consider the highest goal.
When it comes to the second part, where the children were presenting and discussing their work, they were convincing. They were sure about their solutions, defending and insisting. I would say that the children gain these skills from the activities they were involved in. Thus, hands-on-learning strategy does not only inhance students' learning precess, but also their self-confidence, which I myself consider the highest goal.
Are You Convinced?
To start with, teachers must be able to prove certain formulas or rules because some of these formulas are "undigestable" without proofs. In addition, some other rules need to be worked on with the students step by step, so they will completely get them and gain the ability to use them correctly.
Myself, when our professor gave us the "Building Four Stories Towers with Two Colors without Repeating," I thought of this: 0 1 2 3 4 3 2 1 0
0= no mixture of color, the original color
1= one color interapting the original color
2= two of the same color interapting the original
3= three of the same color interapting the original
4= the interapting color gets over the original color
Then, repeat the same thing from the beginning.
And here appears the idea of "Patterns." Some problems in math need the application of "Backward" thinking to be solved, and this is another strategy shown in mathematic textbooks for Problems Solving.
After watching the video, I became convinced that the best way to deliver a proof to young students is with the use of Hands-On-Learning strategy. It is a method that must be included in teachers' daily lesson plan as much as possible. When a child gets in touch with an activity, he/she will learn and understand at the same time much easier than only reading from the text book. Logically, the brain will process freely when it is not framed with rigid instructions. The children in the video were exchanging ideas in a very relaxed environment. More over, there is a big difference between the outcomes of individual work and team or group work, as part II of video II showed.
In the second part, I saw how the students were able to organize and discuss their solutions between each other in a clear platform. They were comparing their conclusions and justifying them. Each one of them was convinced that his way was the correct path to be followed and applyed as a solution to that activity.
To start with, teachers must be able to prove certain formulas or rules because some of these formulas are "undigestable" without proofs. In addition, some other rules need to be worked on with the students step by step, so they will completely get them and gain the ability to use them correctly.
Myself, when our professor gave us the "Building Four Stories Towers with Two Colors without Repeating," I thought of this: 0 1 2 3 4 3 2 1 0
0= no mixture of color, the original color
1= one color interapting the original color
2= two of the same color interapting the original
3= three of the same color interapting the original
4= the interapting color gets over the original color
Then, repeat the same thing from the beginning.
And here appears the idea of "Patterns." Some problems in math need the application of "Backward" thinking to be solved, and this is another strategy shown in mathematic textbooks for Problems Solving.
After watching the video, I became convinced that the best way to deliver a proof to young students is with the use of Hands-On-Learning strategy. It is a method that must be included in teachers' daily lesson plan as much as possible. When a child gets in touch with an activity, he/she will learn and understand at the same time much easier than only reading from the text book. Logically, the brain will process freely when it is not framed with rigid instructions. The children in the video were exchanging ideas in a very relaxed environment. More over, there is a big difference between the outcomes of individual work and team or group work, as part II of video II showed.
In the second part, I saw how the students were able to organize and discuss their solutions between each other in a clear platform. They were comparing their conclusions and justifying them. Each one of them was convinced that his way was the correct path to be followed and applyed as a solution to that activity.
Following Children's Ideas in Mathematic
How children develop mathematically? This question was the main purpose observed in video I.
The activity which the children paticipated in was absolutely different from direct addition, subtraction, multiplication, or division operations. It pulled them toward unusual experience where their thinking as well as their hands were both involved in finding the solution. This combination let them use two different strategies to solve the given activity: "Drawing a
Picture" or "Making an Organized List." The two startegies are found in mathematic text books in different levels and grades.
During the activity, the students were engaged in an open discussion, revision, comparison, and presentation of their work. Also, they were able to control and extend their solution. Thus, the algebraic thinking was present. It does exist.
How the algebraic thinking exists in students' mind who were never exposed to it in a direct way? The answer is simple. Let's go back in time and try to look at this students at the age of one and half to four years old. During this stage, children devolop their algebraic thinking -observ, analyze, and conclude when they are: playing -either with toy(s) or in the playground, eating, taking baths... on their own or with partner(s), guided or unguided. They are always looking for answers to their why and how questions. How is it my plate, full with food, is now empty? How is it the bucket was filled many times with sand, and then emptied, and yet the castle is getting larger? Brain development not only allows advancement of supporting yourself, but also how to solve problems in different fields, logically.
Back to our video. The question discussed within was, how children develop mathematically? I would ask: How can teachers guide students to applying algebraic thinking (which is already developed in a child, but simply unused) on their own?
How children develop mathematically? This question was the main purpose observed in video I.
The activity which the children paticipated in was absolutely different from direct addition, subtraction, multiplication, or division operations. It pulled them toward unusual experience where their thinking as well as their hands were both involved in finding the solution. This combination let them use two different strategies to solve the given activity: "Drawing a
Picture" or "Making an Organized List." The two startegies are found in mathematic text books in different levels and grades.
During the activity, the students were engaged in an open discussion, revision, comparison, and presentation of their work. Also, they were able to control and extend their solution. Thus, the algebraic thinking was present. It does exist.
How the algebraic thinking exists in students' mind who were never exposed to it in a direct way? The answer is simple. Let's go back in time and try to look at this students at the age of one and half to four years old. During this stage, children devolop their algebraic thinking -observ, analyze, and conclude when they are: playing -either with toy(s) or in the playground, eating, taking baths... on their own or with partner(s), guided or unguided. They are always looking for answers to their why and how questions. How is it my plate, full with food, is now empty? How is it the bucket was filled many times with sand, and then emptied, and yet the castle is getting larger? Brain development not only allows advancement of supporting yourself, but also how to solve problems in different fields, logically.
Back to our video. The question discussed within was, how children develop mathematically? I would ask: How can teachers guide students to applying algebraic thinking (which is already developed in a child, but simply unused) on their own?
Subscribe to:
Posts (Atom)