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Taller: From content-based teaching to CLIL: making it work and making it fun

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Subido el 11 de enero de 2011 por EducaMadrid

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Taller "From content-based teaching to CLIL: making it work and making it fun" por Dª.Francesca Ida Carducci, celebrado en el I Congreso Internacional sobre Bilingüismo en Centros Educativos el 14 de junio de 2010 dirigido a profesores de primaria, secundaria y universidades, a investigadores y responsables políticos interesados en la educación bilingüe y en metodología AICOLE (Aprendizaje Integrado de Contenidos y Lengua)

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I'd like to show you a short video of some classroom activities with some student interviews. 00:00:00
And then I'm going to integrate a few fun activities that some of you might be interested 00:00:12
in if you happen to have the opportunity to teach math or science at, let's say, a middle 00:00:18
school level. 00:00:24
Some things that anyone can do if you've gone through the normal curriculum that you would 00:00:26
have in science in any high school. 00:00:32
So I wanted to give you some things that you could actually perhaps use if you do have 00:00:34
this opportunity, even if you don't have any specific scientific background. 00:00:39
Due to a series of events that I won't get into because it's kind of a long story, I 00:00:49
was asked to work with middle school students, third year middle school students, that is 00:00:54
students of approximately 13 to 14 years of age, in the middle school that happens to 00:00:59
be in front of my house. 00:01:03
So that's how it all started. 00:01:05
After a year or two, I decided, after two years actually, I decided that it would be 00:01:09
interesting to introduce a science lesson into the program, to the normal language program. 00:01:13
I had no idea of what CLIL was. 00:01:19
I had no idea of what content-based language was. 00:01:21
I just simply thought it would be a good idea to teach one subject or one lesson in science 00:01:25
just to see how the students would accept it because it seemed like a logical thing 00:01:32
to do, to show them how what they've learned in school can actually be applied. 00:01:36
Because students are used to learning English to do their exercises. 00:01:41
They're used to learning English to write letters. 00:01:44
They're not used to using English for practical purposes. 00:01:47
Can you hear me now? 00:01:52
Is it too loud? 00:01:53
Too loud? 00:01:54
No? 00:01:55
All right, so our first lesson was on the cell. 00:01:56
It was a normal science lesson with multiple choice answers afterwards. 00:02:02
Students were encouraged to ask some questions. 00:02:07
And since the students were very enthusiastic about having applied what they know, I asked 00:02:09
the principal, the headmaster of the school, if it would be possible perhaps to continue 00:02:16
this experience. 00:02:23
And she seemed to be very happy about it. 00:02:25
In fact, she told me immediately, ah, this is CLIL. 00:02:27
And that was the first time I'd ever heard CLIL, the abbreviation. 00:02:30
So at that point, I started to look into it and I started to become familiar with the 00:02:35
program. 00:02:44
And over the years, what was initially simply content-based teaching, science, basically 00:02:45
science lessons in English, slowly came to be science and math lessons that were taught 00:02:50
in English but were integrated also with grammar, vocabulary, and language skills in general. 00:02:55
Our first lesson was on the cell, as I've told you. 00:03:03
One of the things that I had to do was to develop the materials. 00:03:07
So the first thing I did was go into the archives of the school, where they have all the textbooks 00:03:11
that sales representatives leave to the school. 00:03:17
They leave several copies of things. 00:03:21
So I took a look at them to see exactly what students would be learning in their third 00:03:24
year of middle school. 00:03:28
From that point on, I decided that it would not be a good idea to overlap too much with 00:03:30
what was normally being done by the core subject teachers. 00:03:37
Why? 00:03:41
Because as maybe some of you have noticed, sometimes the presence of a CLIL teacher can 00:03:43
be a little bit intrusive. 00:03:52
The core subject teacher might feel a little bit uncomfortable with a third person coming 00:03:56
in and not only teaching their subject, but teaching their subject in another language. 00:04:00
So I thought it would be a good idea to avoid overlapping my course too much, to avoid 00:04:07
any tension between the core subject teacher, not that I had had any particular evidence 00:04:12
of this, but I thought it would probably be a good idea not to overlap too much. 00:04:19
So at that point, when I was sure of what they were doing, I chose subjects that I thought 00:04:23
would be complementary to those that they were doing at school and useful also in the 00:04:28
following year. 00:04:35
In Italy, they go into high school after the third year of middle school. 00:04:36
I chose the subjects and then during a trip to the United States, I picked up all kinds 00:04:42
of materials that I thought would be useful for preparing lessons. 00:04:47
These materials were materials for mother tongue students of English. 00:04:51
They weren't materials for CLIL specifically or for teaching English as a second language. 00:04:55
They were normal science and math materials. 00:05:02
Over the years, the program increased. 00:05:09
Now what we have is a non-mandatory program that students choose to do. 00:05:11
They choose to come after school and stay an hour and 15 minutes or an hour and a half 00:05:17
once a week from November to early April in order to attend CLIL lessons. 00:05:23
This has been very positive. 00:05:32
At the beginning, we had a few problems because naturally, parents tend to interfere. 00:05:34
Their children had to be the children to attend this course and that is not always the case. 00:05:42
Not necessarily because these students were not particularly good students, but either 00:05:47
they had problems with behavior, they didn't have a long enough attention span, and we 00:05:53
all knew this because I had them also during my normal lessons during the day where I teach 00:05:57
as a mother tongue teacher in the school, or they didn't have the language skills, or 00:06:03
they just didn't want to. 00:06:08
Some of those students were our better students. 00:06:10
Maybe they play football and they knew that that was going to interfere with their sports 00:06:12
schedule. 00:06:16
They just didn't want to. 00:06:17
Then what did we have? 00:06:18
We also had a problem with students not wanting to be there. 00:06:19
What we do now is make students responsible for their commitment to come. 00:06:23
These are not always your best students. 00:06:29
Those students who have at least passing marks in English, but not necessarily the best students. 00:06:32
Some of these students who are not our best students are excelling in CLIL, in science 00:06:37
and math taught through CLIL. 00:06:43
Some of the students are even getting better in their core subject English course because 00:06:45
they want to participate in the CLIL course in the afternoon, and they can't unless their 00:06:49
English is reasonably decent, let's say, a passing mark in English, or a full passing 00:06:55
mark in English. 00:07:01
Anything I've forgotten? 00:07:04
Now we have what our CLIL program includes is an introduction to mathematics in English, 00:07:09
science, mostly chemistry, a little bit of biology, the cell, the human heart, et cetera. 00:07:15
Since I'm not a mathematician, I'm a pharmacist, and the amount of mathematics that a pharmacist 00:07:23
uses does not include things like geometry, et cetera. 00:07:27
Most of the math course is actually based on simple mathematics or history of mathematics. 00:07:33
The first thing I wanted to show you is where this course is taught. 00:07:41
It's taught in a little bit of advertisement for the city of Urbino in central Italy. 00:07:48
It's a beautiful Renaissance city with probably one of the most beautiful examples of Renaissance 00:07:53
architecture in the world. 00:07:58
So I'm going to lower this just a moment if I can, I'm not quite sure how, but I will 00:08:02
figure it out. 00:08:07
It's not the end of the presentation, but I'll just lower it like this. 00:08:19
Okay, I want to show you this brief film. 00:08:22
I hope you know it's a classroom setting, so the audio is not fantastic. 00:08:24
What you're going to be seeing is pieces of lessons and student interviews. 00:08:28
It's very hard to make any kind of a film, and I imagine it is here at that age because 00:08:36
you need permission from the parents to film their children. 00:08:40
Students naturally forgot to bring their permission several times, it snowed. 00:08:46
So the lessons that I had prepared, the ones that maybe I'd wanted you to see may not be 00:08:50
in this film. 00:08:55
In fact, these are rather traditional lessons, and what we're going to be doing today is 00:08:56
talking about those elements that you can add to a CLIL course to make it a little more 00:09:00
fun. 00:09:04
Something that makes them want to come back. 00:09:05
Not just a traditional science lesson, but something that makes it a little bit more 00:09:08
attractive to younger students. 00:09:11
Okay, so I'm going to let you see this video, I hope it will be clear enough. 00:09:12
There's one girl who's a multi-tongue speaker of English, another girl who speaks Dutch, 00:09:26
and naturally her English is quite good. 00:09:49
And then there's a mixture of other students. 00:09:52
There we go. 00:09:55
Just a minute. 00:09:58
Technical problems. 00:10:01
There we go. 00:10:04
Just a minute. 00:10:07
Technical problems. 00:10:10
There we go. 00:10:13
There we go. 00:10:17
Just a minute. 00:10:20
Technical problems. 00:10:23
Technical problems. 00:10:26
There we go. 00:10:29
Technical problems with English. 00:10:32
Language. 00:10:35
Time integrated learning. 00:10:37
It's a course that you learn English and like for science, chemistry, biology, or photography. 00:10:40
She's sick in English. 00:10:52
Michael is not here. 00:10:57
Anyone who's not eating? 00:11:00
Okay. 00:11:03
Someone who didn't really want to come? 00:11:06
Someone who didn't want to come? 00:11:09
There it is. 00:11:12
Can she eat? 00:11:15
Who's that? 00:11:18
What is the question? 00:11:21
Who's that? 00:11:24
Who's that? 00:11:27
Let me get that. 00:11:30
Who's that? 00:11:33
Who's that? 00:11:36
Who's that? 00:11:39
Who's that? 00:11:42
Eat. 00:11:45
I said, who are you? 00:11:48
What? 00:11:51
You're 70. 00:11:54
You're a bit too young. 00:11:57
You're a scientist. 00:12:00
Scientist. 00:12:03
Scientist. 00:12:04
Century. 00:12:05
Century. 00:12:06
You produce. 00:12:07
You produce. 00:12:08
You produce. 00:12:09
You produce. 00:12:10
You produce. 00:12:11
You produce. 00:12:12
You produce. 00:12:13
Who's that? 00:12:15
Who's that? 00:12:17
Next. 00:12:18
Next. 00:12:19
Here you go. 00:12:20
Function. 00:12:21
No, here. 00:12:22
Set. 00:12:23
Function. 00:12:24
Function. 00:12:25
Very good. 00:12:26
Fundamental. 00:12:27
Fundamental. 00:12:28
You do. 00:12:29
Structural. 00:12:30
Structural. 00:12:31
Structural. 00:12:32
Structure. 00:12:33
Okay. 00:12:34
Structural. 00:12:35
Special. 00:12:36
Special. 00:12:37
Special. 00:12:38
Special. 00:12:39
Special. 00:12:40
Special. 00:12:41
Special. 00:12:42
Special. 00:12:43
Thank you. 00:12:44
Thanks. 00:12:45
Where did you go? 00:12:46
Matteo? 00:12:50
Science. 00:12:51
Can you tell me what you study? 00:12:52
Yes. 00:12:55
We study biology, chemistry, philosophy, and... 00:12:56
What did you study? 00:13:04
What did you study? 00:13:05
The chemistry. 00:13:06
I studied algebra, mathematics, geography, philosophy. 00:13:08
You know the advertising methodology for Xinjiang, right? 00:13:49
No martini. 00:13:54
That's right. 00:13:55
George Clooney has a bottle of champagne with a bottle. 00:13:58
He says, no martini, no product. 00:14:02
Why? 00:14:05
That's what you think. 00:14:06
But he has... 00:14:07
It's made of cardboard. 00:14:08
Do you have... 00:14:09
Yes. 00:14:10
I learned that... 00:14:11
Wood is better than other materials and different polymer. 00:14:13
The wood is better than other different materials and different polymer. 00:14:17
The gas is better than other different materials and different polymer. 00:14:21
A plasma is better than other different chemicals and other different polymer. 00:14:25
And... 00:14:29
The next one is we're going to learn English. 00:14:40
Do you think wood is a good way to learn English? 00:14:43
Yes, I think wood is a very good way to learn English because the teacher speaks all the time in English. 00:14:45
And she gives us a lot of explanation that we need. 00:14:51
Anybody else? 00:14:56
I think wood is a very good way to learn English because it helps us to understand another way of English. 00:14:57
Anyone else? 00:15:07
Yes, because learning a subject in a foreign language helps to learn the subject but also the language. 00:15:09
Do you think that wood is a good way to learn English? 00:15:18
Yes, I think that... 00:15:21
I think wood is a good way of learning English because it's probably more interesting than the traditional way of learning. 00:15:23
Thank you. 00:15:34
Just to get you to... 00:15:42
Could you hear it enough? 00:15:44
Could you hear it at all? 00:15:45
Was it clear enough? 00:15:46
I know a classroom setting is not the best thing. 00:15:47
Some of those students... 00:15:49
For example, the boy with the scarf, the checkered traditional keffiyeh, I think it's called. 00:15:50
He's not considered... 00:15:55
He's a very bright boy but he's not your traditionally good student. 00:15:56
And he decided that he wanted to take this course. 00:16:00
Actually, he's quite good. 00:16:04
I have to admit that I had not coached them but I had given them questions that I would ask. 00:16:05
Because naturally, the stage fright I thought might kick in. 00:16:11
So I thought I'd give them the questions beforehand. 00:16:15
I'm sorry. 00:16:18
I thought I'd give them the questions beforehand so that they could take a look at them and maybe prepare just a little bit so that they wouldn't get scared in being filmed. 00:16:19
So let's go on with the presentation. 00:16:29
Here are the first pages of part of our science module. 00:16:34
The first is naturally, what is matter? 00:16:38
The second is the smallest part of matter, the atom. 00:16:40
As you can see, some of the words are highlighted in red or written in red. 00:16:43
And I've also included maybe a cognate or some language that they would understand to help them to be able to understand the words that I thought they might not know or probably would not know. 00:16:48
Tiny, for example. 00:17:02
If you say minute, an Italian speaker would automatically know what that is. 00:17:03
So these were our first two lessons. 00:17:10
The third lesson was a short history of atomic theory with the different models of the atom over time. 00:17:14
And then we have a lesson on elements and the periodic table of the elements. 00:17:20
Here I usually introduce a little bit of an activity. 00:17:25
Two activities, actually. 00:17:31
Two things that help students to become familiar because in the third year of middle school, most Italian or our Italian students in this particular school don't get a lot of background in chemistry. 00:17:33
They just get a little bit, perhaps. 00:17:45
So what I did was I wanted them just to simply get to know the periodic table of the elements and be able to deal with it, to become familiar with it so that they wouldn't be, I don't know, a little bit intimidated by it when they got to it in high school. 00:17:48
So now I'm going to give you an activity. 00:18:02
I'm going to give you a periodic table of the elements, which you may not have seen for a long time. 00:18:04
Okay? 00:18:10
I'll pass them around. 00:18:11
Okay? 00:18:13
So even if you haven't found a lot, there are lots of them in there, but this is just to give you an idea. 00:18:14
Can anyone tell me any of the names that they found? 00:18:19
Name something, an element named after a famous person, a famous scientist. 00:18:22
Einsteinium and? 00:18:28
Fermium. 00:18:31
Enrico Fermi. 00:18:32
Okay. 00:18:33
Excuse me. 00:18:34
Yes. 00:18:37
Mendeleev. 00:18:38
No. 00:18:39
Any other ones? 00:18:40
Excuse me. 00:18:41
Yes. 00:18:42
Famous nuclear physicist, if I'm not mistaken. 00:18:43
Okay. 00:18:44
Okay. 00:18:45
Okay. 00:18:46
Okay. 00:18:47
Okay. 00:18:48
Okay. 00:18:49
Okay. 00:18:50
Okay. 00:18:51
Okay. 00:18:52
Okay. 00:18:53
Okay. 00:18:54
Okay. 00:18:55
Okay. 00:18:56
Okay. 00:18:57
Okay. 00:18:58
Okay. 00:18:59
Okay. 00:19:00
Okay. 00:19:01
Okay. 00:19:02
Yeah. 00:19:04
Yeah. 00:19:05
You find them, if I'm not mistaken. 00:19:06
Any other ones? 00:19:07
Curium. 00:19:10
Madame Curie and her brother. 00:19:11
Excuse me. 00:19:12
Nobelium. 00:19:13
Yeah, Nobelium, absolutely. 00:19:14
Then from Greek mythology, we have one named Tantalum, named after Tantalus from Greg mythology. 00:19:15
Iridium, Iris from Greek mythology. 00:19:26
Any others planets? 00:19:29
No. 00:19:32
Plutonium. 00:19:34
Neptunium, I believe. 00:19:38
No. 00:19:40
Helium, the sun, actually. 00:19:42
And if you want a list of these, if you do decide to... Mercury, naturally. 00:19:47
No, we may not have thought of him. 00:19:52
You can easily find on Wikipedia a list of all the names of the elements that have been named after famous people, places, or things. 00:19:54
And there are some interesting stories, too. 00:20:03
Another thing that you can do to have students become familiar with the periodic table of the elements is this exercise. 00:20:05
In their booklets, they have the more serious clue lesson that divides elements, gives a, what would you call it, a concept map of the table of the elements, of matter and the elements. 00:20:14
So matter made of one kind of element, the elements, 118 known or predicted, 90 formed by nature, 25 created in the laboratory, three are missing because when I did this, three had been predicted but not found. 00:20:32
One has been found in the meantime, so I'm going to have to change my numbers a little bit. 00:20:45
These are classified in the periodic table of the elements. 00:20:50
They're written as symbols, arranged by atomic number, and divided by properties. 00:20:53
What I'd like to look at now is how they're written as symbols. 00:20:57
They're written in symbols, usually with one or two letters. 00:21:01
Some of them have three, some of the newer ones. 00:21:03
The first letter is capitalized, and the second letter is in lowercase. 00:21:07
And it's usually the second letter, the third letter, depending on what's already been used. 00:21:12
The question is, imagine that you are a great scientist and the scientific world wants to dedicate a newly discovered element to you. 00:21:21
What would your atomic symbol be? 00:21:28
So, I have a great name for this. 00:21:30
It's absolutely perfect. 00:21:32
My name is Carducci. 00:21:35
So, I want to be Carduccium. 00:21:38
C, the first letter of my name. 00:21:43
That's no good because it's carbon. 00:21:47
I can't be CA, the first and the second letter, because that's calcium. 00:21:49
CR? 00:21:56
I can't be CR because it's already been taken. 00:21:58
It's chromium. 00:22:02
CD, maybe? 00:22:04
No. 00:22:06
Cadmium. 00:22:07
No good. 00:22:08
CU? 00:22:10
Oh, copper. 00:22:12
It's already been taken. 00:22:14
There are only two possibilities left. 00:22:20
CC, but... 00:22:23
None of the other elements have two letters that are the same. 00:22:26
No? So... 00:22:30
What about CI? 00:22:33
Would be the famous Carduccium. 00:22:36
So, what would your symbol be? 00:22:41
What you can do in the classroom is ask students to write their surnames and go through the periodic table trying to find what their symbol would be. 00:22:43
In this way, they're forced to go methodically, element by element, and see which one could be appropriate for them. 00:22:54
So, what would your symbol be? 00:23:04
I was going to ask you maybe to do this, but I think maybe we should go on and do something a little bit different, okay? 00:23:07
Science, the cell. 00:23:14
This is our formal, traditional lesson on the cell. 00:23:17
What is a cell in biology? 00:23:19
A cell is the basic, living, functional, and structural unit of all organisms, and the usual science lesson. 00:23:21
A little bit of history about the microscope. 00:23:27
Then, we have an activity. 00:23:31
How many of you have looked under a microscope, and your professor has told you that there are differences between one slide and another, and in looking at it, they all look totally the same? 00:23:33
Usually, you look at them and you say, I don't know, you say it's a leukocyte, but I really can't tell the difference from any of the other cells you're showing me. 00:23:44
So, we have an exercise in increasing your observation skills. 00:23:53
So, this is what I do. 00:24:01
I give the students a specimen. 00:24:05
I give them a peanut. 00:24:08
I give them a piece of paper, which is this. 00:24:11
I don't know, we're probably not, do I have some volunteers? 00:24:18
Can I have a little group of a few people that would be willing to do this? 00:24:21
Would you come up, please? 00:24:25
I need about five or six people. 00:24:26
Oh, come on. 00:24:29
It's not anything I'm not going to, no magic tricks, no. 00:24:30
Good. 00:24:37
Thank you. 00:24:38
One, two, a few more. 00:24:39
Okay, one, two, three, four, five seats. 00:24:41
Just pull up a chair and sit over here. 00:24:44
Yes, over here. 00:24:48
I'm going to give them what you see there. 00:24:49
It's a photocopy with a circle on it. 00:24:54
Thank you for participating. 00:25:01
Now, what I'm going to do is give you your specimen. 00:25:04
You're not allowed to touch it. 00:25:06
Thank you. 00:25:09
I'm having some technical trouble here. 00:25:17
I'm afraid it might explode. 00:25:20
Yes, please. 00:25:23
You need a man for this. 00:25:24
Okay, we need a man. 00:25:27
There we go. 00:25:32
There we go. 00:25:33
Thank you. 00:25:36
It's the famous, what they call, the Lord of Colombo. 00:25:38
Columbus' egg. 00:25:41
It was probably Brunelleschi's egg. 00:25:42
I'm going to give you a specimen. 00:25:45
And I want you to describe it very, very carefully. 00:25:47
I want you to make a picture of it. 00:25:49
All right? 00:25:51
You have to memorize your specimen. 00:25:52
Okay? 00:25:57
Draw a picture of it carefully and quickly, hopefully. 00:25:58
And then I want you to be able to describe it 00:26:01
using some of the vocabulary that you'll find. 00:26:03
I want you to use some of the vocabulary that you'll find here. 00:26:07
For example, some useful vocabulary. 00:26:10
A hole, a filament, a spot, a discoloration, a crack, 00:26:13
an indentation, a protuberance. 00:26:18
Positional words, center, extremity, opposite extremity, 00:26:20
for color, light, and dark. 00:26:25
Okay? 00:26:27
And we're going to let them work on that now for a little bit. 00:26:28
I'll give you a few minutes to work on your peanuts. 00:26:30
And we'll go on with the course. 00:26:33
Peanuts. 00:26:34
Okay. 00:26:43
Part of the course also deals with mathematics, 00:26:46
although I'm not a mathematician. 00:26:49
No? 00:26:52
But one of the things that Italian students, 00:26:53
and probably it's common also to other foreign students, 00:26:57
is saying numbers, saying very large numbers, 00:27:01
saying fractions, saying percentages, 00:27:04
how they're to be said. 00:27:06
They obviously know how to write them, 00:27:08
but they don't know how to say them. 00:27:09
For example, when talking about fractions, 00:27:12
you can explain to them that when the numerator is singular, 00:27:17
the denominator is also singular. 00:27:21
When the numerator is plural, the denominator must be plural. 00:27:23
Just like in English, one third, two thirds. 00:27:26
No? 00:27:30
So these are things that are very helpful. 00:27:31
Then we talk about a classification of numbers. 00:27:34
How different numbers... 00:27:36
I'm sorry, I'm not over here a lot. 00:27:37
How to classify numbers. 00:27:39
Natural numbers. 00:27:41
What are whole numbers? 00:27:42
What are integers? 00:27:43
What are rational numbers? 00:27:44
What are real numbers? 00:27:46
This is also very good for vocabulary building 00:27:48
because we do an exercise on using these words 00:27:50
in normal English, not just for mathematics. 00:27:53
Someone can be irrational. 00:27:57
Someone can be odd. 00:27:59
Someone can be... 00:28:01
Something can be absolutely fantastic. 00:28:03
Many of these words that are used 00:28:07
can also be applied to normal English, 00:28:11
and that's exactly what we use them for. 00:28:14
Some of them they may know, 00:28:17
others they probably wouldn't normally. 00:28:18
For example, to be even. 00:28:21
I pay for the pizza, you pay for the drinks. 00:28:25
Then we'll be even. 00:28:27
So odd, meaning strange. 00:28:28
And we have exercises also in English exercises 00:28:30
using these words. 00:28:33
In mathematics, we also do a short history of mathematics. 00:28:38
We take an early look at mathematics 00:28:41
from the Egyptians, the Greeks, the Chinese, 00:28:43
the Hindus, the Babylonians, and the Mayas' point of view. 00:28:46
We also do exercises on solving word problems 00:28:50
with ratios, proportions, and rates. 00:28:53
In doing this, I try to choose, perhaps, 00:28:56
the vocabulary, things that they might not know. 00:28:58
For example, different types of dogs, 00:29:01
different types of flowers. 00:29:03
The example here is the ratio of bulldogs to all the dogs. 00:29:05
No? 00:29:09
The ratio of basset hounds to all the dogs. 00:29:11
No? 00:29:13
This is also helpful in building vocabulary, 00:29:15
because you can choose words that you think 00:29:17
that they don't know 00:29:19
and that they could learn rather easily like this. 00:29:21
Let's go on to an early look at mathematics. 00:29:24
One of the things that they enjoy doing 00:29:28
is talking about Leonardo Fibonacci, 00:29:30
because many of you have heard of him 00:29:34
through the Da Vinci code. 00:29:36
He's become rather popular. 00:29:38
The Fibonacci sequence 00:29:40
has become rather well-known in recent times. 00:29:42
In the early 1200s, 00:29:47
an influential Italian mathematician 00:29:49
named Fibonacci was one of the strongest advocates 00:29:52
– and these are the words that would be in green – 00:29:54
for adopting the Hindu-Arabic 10-digit numbering system 00:29:56
with place value. 00:29:58
In 12002, he wrote a famous algebra text 00:30:00
called Liber Abaci. 00:30:03
This text was not only argued in favor 00:30:05
of the Hindu-Arabic numbering system, 00:30:07
but also included a popular word problem 00:30:09
involving the Fibonacci sequence, 00:30:12
a series of numbers with various interesting properties 00:30:14
observed repeatedly in science and nature, 00:30:17
including areas like plant growth and heredity. 00:30:21
Shall we see how our peanut project is going? 00:30:25
Okay. 00:30:28
I need something. Just a moment. 00:30:33
All right. 00:30:39
You memorized your peanuts. 00:30:45
You know them personally? 00:30:47
Okay. 00:30:49
Please put your peanut on this dish. 00:30:51
Okay. 00:30:53
All right. 00:30:55
Now what we're going to do is take a small group. 00:30:57
You can even take a larger group than this. 00:30:59
And then you take their peanuts, 00:31:01
and you take them and you mix them 00:31:03
with approximately, I don't know, 00:31:05
a bunch more? No? 00:31:07
Then we mix them up. 00:31:09
And I hope this is going to work. 00:31:11
It is a bit like a magic act. 00:31:13
I want you to find your peanut 00:31:15
and tell me why it's yours. 00:31:17
All right? 00:31:19
Now you can touch them. 00:31:21
Why is that peanut yours? 00:31:24
I'm going to tell you why this peanut is mine. 00:31:26
Okay. Good. Exactly. That's exactly what I want. 00:31:28
This peanut is mine because right here 00:31:30
I remember there were cracks. 00:31:32
Uh-huh. Exactly. 00:31:34
And right in the center 00:31:36
there were several spots 00:31:38
and then it had this little dippity thing. 00:31:40
A dippity thing. All right. 00:31:42
Perfect. Did you find your peanut? 00:31:48
Let me see. Which one is it? 00:31:50
Why is it yours? 00:31:53
It has a long crack here 00:31:55
and the center is discolored. 00:31:57
Okay. Good. 00:31:59
So that was what you determined. 00:32:01
Did you find your peanut? 00:32:03
Okay. I think this one here is mine 00:32:05
because there's no peanut. 00:32:07
It has no holes, no cracks, 00:32:09
no discoloration. 00:32:11
It's the perfect peanut. 00:32:13
It's the perfect peanut. 00:32:15
And yours? 00:32:17
I know this is my peanut. 00:32:19
Uh-huh. 00:32:22
Perfect. See? 00:32:28
So this is a fun activity that you can add 00:32:30
once you've done some 00:32:32
more serious activities. 00:32:34
You can add this just to lighten things up a little bit. 00:32:36
Thank you very much. 00:32:38
Thank you. 00:32:40
All right. Let's go back to our Fibonacci sequence. 00:32:48
Are any of you familiar with the Fibonacci sequence? 00:32:50
No? 00:32:52
The Fibonacci sequence is a series of numbers. 00:32:54
It's a sequence of numbers 00:32:56
in which each number 00:32:58
is the sum 00:33:00
of the two numbers that precedes it. 00:33:02
For example, 1, 2, 00:33:04
1 plus 2, 3. 00:33:06
Oop. Didn't want to do that. Sorry. 00:33:08
You just touch it and it moves. 00:33:10
1 and 2 00:33:12
equal 3. 2 and 3, 00:33:14
5. 3 and 5, 8. 00:33:16
5 and 8, 13. 00:33:19
8 and 13, 21, and so on. 00:33:21
This is the Fibonacci sequence. 00:33:23
Why is it 00:33:25
particularly important? 00:33:27
Because these are the 00:33:29
proportions that we can 00:33:31
find also in nature, 00:33:33
in architecture, 00:33:35
and in art. 00:33:37
They're considered 00:33:39
numbers of, let's say, 00:33:41
beauty in proportions. 00:33:43
No? 00:33:45
The phalanges. 00:33:48
There's a ruler up above. 00:33:50
2, 3, 5, 8. 00:33:52
Other examples? 00:33:54
In normal plant growth, 00:33:56
one stem that branches out 00:33:58
into 2, 00:34:00
3, 5, 00:34:02
and 8. 00:34:04
There are also some in the Last Supper, 00:34:06
but I don't remember and you can't see 00:34:08
the picture very well. 00:34:10
But if you do look it up online, 00:34:12
you'll find the different proportions. 00:34:14
The proportion 00:34:16
in the rectangle. 00:34:18
The Vitruvian Man. 00:34:20
This is also very good 00:34:22
as an exercise. 00:34:24
As you can see, if you get a perfectly proportioned 00:34:26
photograph of the original, 00:34:28
you can see Da Vinci's 00:34:30
scale 00:34:32
at the bottom. 00:34:34
What I've done with students is give them a piece of cardboard, 00:34:36
it has to be cut very precisely, 00:34:38
and had them use this 00:34:40
part of the scale that's nice and clear 00:34:42
to make a sort of 00:34:45
a ruler. 00:34:47
When you use this ruler, you can actually see 00:34:49
that the nose is exactly 1, 00:34:51
the distance between the eyes is exactly 2, 00:34:53
the mouth is exactly 1, 00:34:55
the wrist, this is good for learning parts of the body 00:34:57
that they might not know, 00:34:59
the wrist, the ankle, waist, 00:35:01
shoulders, 00:35:03
etc. 00:35:07
Expect middle school 00:35:11
students, the first thing that they're going to measure 00:35:14
will obviously be 1, 00:35:16
and it is a perfect 1. 00:35:18
This is 00:35:20
the word problem, 00:35:22
I don't know how much time we have, 00:35:24
10 minutes? Ok, I'll try to hurry up. 00:35:26
The Fibonacci sequence actually 00:35:28
was expressed in Liber Abici under the form 00:35:30
of a riddle. He didn't just write 00:35:32
a mathematical problem, he wrote a riddle. 00:35:34
It talked about 00:35:36
rabbits, and it said exactly, 00:35:38
I hope I have it here easily, 00:35:40
It said, 00:35:44
a certain man 00:35:46
put a pair of rabbits 00:35:48
in a place surrounded on all sides 00:35:50
by a wall. 00:35:52
How many pairs of rabbits can be produced 00:35:54
from that pair in a year 00:35:56
if it is supposed that every month 00:35:58
each pair begets 00:36:00
a new pair from which the second month on 00:36:02
becomes productive? 00:36:04
So what have we got? 00:36:06
This is a pair 00:36:08
of rabbits, 00:36:10
this is our first month 00:36:12
we have one pair, not one rabbit, 00:36:14
a pair of adult rabbits. 00:36:16
In the second month we have that same rabbit 00:36:18
and it's one pair of offspring. 00:36:20
In the third month 00:36:22
I have the original rabbit plus the baby rabbit 00:36:24
it has produced, plus this rabbit 00:36:26
which has reached maturity. 00:36:28
In the fourth month I will have my original rabbit 00:36:30
plus the baby rabbit, plus this 00:36:32
rabbit which has grown up, 00:36:34
this rabbit who is here and has produced 00:36:36
now a new pair of rabbits. 00:36:38
Fifth month the same thing, the original rabbit 00:36:41
baby rabbit, this one has grown up 00:36:43
and if you go on you'll find 00:36:45
all these numbers are Fibonacci 00:36:47
numbers, one, two, three, 00:36:49
five, eight, 00:36:51
etc. 00:36:53
A number in the Fibonacci sequence 00:36:59
divided by the number that comes 00:37:01
immediately before it results in 00:37:03
a number very close to the golden ratio 00:37:05
or phi. The higher number 00:37:07
in the sequence, the closer the quotient is to the value 00:37:10
of phi, an irrational number believed 00:37:12
to have divine properties representing 00:37:14
the word or signature in God in nature. 00:37:16
Okay, I don't think we have too much 00:37:18
time for this, but if you want to, something 00:37:20
that's very, an interesting 00:37:22
activity is to have students 00:37:24
write 00:37:26
on a piece of paper, do they have this? 00:37:28
No? 00:37:30
This other one? 00:37:32
I don't know if we'll have time, but we'll try it 00:37:36
anyway. You can do it at home if you don't have time here. 00:37:39
What I want you to do is 00:37:41
write on these lines 00:37:43
These are 00:37:49
examples of the divine proportion 00:37:51
in art, 00:37:53
the flagellation of Christ, 00:37:55
Piero della Francesca, the Mona Lisa, 00:37:57
we have a perfect 00:37:59
golden triangle. 00:38:01
I don't know if I can maybe explain that to you 00:38:03
quickly. 00:38:05
The golden triangle is based on the 00:38:07
proportion 00:38:09
based on a proportion of a line segment. 00:38:13
A line segment 00:38:15
divided so that A 00:38:17
plus B is to A 00:38:19
as A is to B. 00:38:21
Simple as that. The number that 00:38:23
we come up with when we express this proportion 00:38:25
is a number, 00:38:27
an irrational number like pi 00:38:29
called phi. 00:38:31
If we take a perfect 00:38:34
square and divide 00:38:36
it in half, 00:38:38
exactly in half, 00:38:40
and then draw a 00:38:42
diagonal to the corner, 00:38:44
and from this diagonal draw a 00:38:46
circle, and then we 00:38:48
bring this up 00:38:50
to meet the 00:38:52
circumference, we will 00:38:54
have a perfect golden 00:38:56
triangle. And this golden triangle 00:38:58
can be found in art 00:39:00
in architecture 00:39:03
in nature, and just 00:39:05
about everywhere. 00:39:07
The Vitruvian Man, Piero della Francesca, 00:39:09
divided exactly here, 00:39:11
the face of the Mona Lisa, which is 00:39:13
a golden rectangle 00:39:15
dividing the face 00:39:17
in perfect proportion. 00:39:19
Seashells, 00:39:21
golden rectangle, 00:39:23
what happens here is 00:39:25
if we take this golden rectangle 00:39:27
and we 00:39:29
find a 00:39:31
perfect square, we will be 00:39:33
left with another golden 00:39:35
rectangle. 00:39:37
If we take this golden rectangle 00:39:39
and we take a square out of it, 00:39:41
we will be left with another golden 00:39:43
rectangle. If we take that 00:39:45
golden rectangle and 00:39:47
we take a square out of it, we will be left 00:39:49
with another 00:39:51
golden rectangle and this will go on 00:39:53
and on and on to infinity. 00:39:55
No? So 00:39:57
I think I'm going to have to speed 00:39:59
things up a bit. How much time have we got? 00:40:01
Okay. Try this. 00:40:03
Choose any two successive numbers 00:40:05
in the Fibonacci sequence, the lower 00:40:07
before the higher. For example, two 00:40:09
and three 00:40:11
or five and eight. 00:40:13
They have to be low numbers because 00:40:15
your calculators won't be able to do 00:40:17
them otherwise. 00:40:19
So choose two low numbers 00:40:23
in the Fibonacci sequence 00:40:25
and do this 00:40:28
problem. Now, add these two numbers 00:40:30
and put their sum on the third nine. 00:40:32
So let's say I have five and eight. 00:40:34
I add them and I put their sum on this line. 00:40:36
Then I add this number to this number 00:40:38
and I put that number here. 00:40:40
The number before and then 00:40:42
the number before added to the number 00:40:44
that comes after it. 00:40:46
Then, 00:40:48
I have to do this twenty times. 00:40:50
Do I have anyone who would be willing 00:40:52
to do that quickly with a calculator? 00:40:54
Anyone who would like 00:40:56
to do a quick math problem? 00:40:58
A vision? 00:41:00
Anyone who would like 00:41:03
to do a quick math problem? 00:41:05
A vision? 00:41:07
These are word analogies. 00:41:33
We won't have time to do them today, 00:41:35
but they're very, very useful. 00:41:37
If you do want to look into them, 00:41:39
it's very easy to find out 00:41:41
what word analogies are 00:41:43
and how are they related to, 00:41:45
for example, a simple proportion. 00:41:47
For example, five is to ten, 00:41:49
is twenty-five is to fifty, 00:41:51
is twenty-five to fifty, 00:41:53
is twenty-five to fifty, 00:41:55
is twenty-five to fifty, 00:41:57
is twenty-five to fifty, 00:41:59
is twenty-five is to fifty. 00:42:01
We can also do word analogies, 00:42:03
such as, bee is to buzz, 00:42:05
as cow is to moo. 00:42:07
Or, 00:42:09
cabbage is to vegetable, 00:42:11
as rose is to flower. 00:42:13
You can make up some simple multiple choice 00:42:15
problems. 00:42:17
All kinds of facts. 00:42:19
George Washington is to first, 00:42:21
as Abraham Lincoln is to sixteenth. 00:42:23
And these work just very similar 00:42:25
to do a proportion. 00:42:27
The other as something else 00:42:29
is to something else. 00:42:31
Okay? 00:42:33
I think I have to conclude. 00:42:35
A little bit? Okay. 00:42:37
Alright, the results of an anonymous questionnaire 00:42:39
that I gave to my pupils. 00:42:41
I had about 42 pupils, 00:42:43
which is, I'd say, 00:42:45
a good one-third of all the students 00:42:47
that are in the third year. 00:42:49
So it's a nice sample in two different classes. 00:42:51
So 36 of them 00:42:53
answered this questionnaire because they were at the lesson. 00:42:55
And it was an anonymous 00:42:58
questionnaire. 00:43:00
I wanted them to give me honest 00:43:02
answers to these questions. 00:43:04
Students were asked 00:43:06
to evaluate the difficulty of the course 00:43:08
on a scale of 00:43:10
extremely difficult, 00:43:12
difficult, quite difficult, 00:43:14
not so difficult, 00:43:16
quite easy, very easy. 00:43:18
No? 00:43:20
I asked them how much easier it was to 00:43:22
understand the lessons toward the end of the course 00:43:24
as compared to the beginning. 00:43:26
I asked them how positive or negative the experience 00:43:28
was for them, which subject they 00:43:30
enjoyed the most, math, science, or geography. 00:43:32
I added a couple of geography lessons 00:43:34
on the United States 00:43:36
and Canada just to round the course 00:43:38
out a bit. No? 00:43:40
So there just wouldn't all 00:43:42
be math and science. 00:43:44
I asked how comfortable they would be with 00:43:46
following courses involving CLIL methodology 00:43:48
in the future because in Italy 00:43:50
they're planning on introducing 00:43:52
CLIL methodology 00:43:54
in the high schools 00:43:56
in a mandatory way. 00:43:58
I asked if they would recommend the course 00:44:02
to other kids their age 00:44:04
and that if learning English with CLIL methodology 00:44:06
seemed easier than with 00:44:08
traditional methods, and if so, 00:44:10
how much easier? 00:44:12
I also asked them if any 00:44:14
new things they learned, both in content 00:44:16
and in language. I asked them simply, 00:44:18
how much did you learn? 00:44:20
Did you learn nothing? Something? 00:44:23
A lot? 00:44:25
Moltissimo? Which you can't translate 00:44:27
very well into English. No? 00:44:29
And these were our results. 00:44:33
50% 00:44:35
of the students approximately thought 00:44:37
the course was difficult or quite difficult. 00:44:39
50% approximately said it was 00:44:41
easy. 00:44:43
73% said that 00:44:45
it was easier or much easier to understand 00:44:47
the lessons by the end of the course. 00:44:49
89% 00:44:53
said the course was a positive or 00:44:55
a very positive experience. 00:44:57
43 liked science 00:45:01
best. 43% liked science best. 00:45:03
Math and geography approximately 00:45:05
were even. 00:45:07
100% said that they felt at least 00:45:13
a little more comfortable about future CLIL 00:45:15
experiences, and 64% 00:45:17
said they were much 00:45:19
more comfortable 00:45:21
with future CLIL experiences. 00:45:23
94% would recommend this course 00:45:27
to other kids their age, and that was 00:45:29
the one I was probably most proud of. 00:45:31
75% said 00:45:37
that learning English with CLIL was much easier 00:45:39
or much easier 00:45:41
than with traditional methods. 00:45:43
64% said 00:45:47
that they learned a lot of new things, 00:45:50
and 100% said that they learned 00:45:52
something new. 00:45:54
The next question will now be 00:45:58
I didn't put this on the questionnaire, 00:46:00
but next year I will. 00:46:02
Was it fun? 00:46:04
I don't know if you didn't hand out any of those 00:46:08
cards, but if anybody has any... 00:46:10
The results. 00:46:12
Did you come up with the results? 00:46:14
What's the number? 00:46:20
Okay, that's the final number 00:46:24
on the 20th line. All right, now take that number, 00:46:26
the final number, and divide it 00:46:28
by the number that comes before it. 00:46:30
And what did you get? 00:46:32
It should be, 00:46:36
if you did the calculation correctly... 00:46:38
I'm sorry. 00:46:46
I might have to do it. 00:46:50
Come on. 00:47:08
It's taking me a while. 00:47:14
Oh well. 00:47:16
Okay. 00:47:20
It should be 00:47:30
1.683. 00:47:32
No? 00:47:34
And be an infinite number. 00:47:36
Is that the result you got? 00:47:38
It should correspond 00:47:40
exactly to the number 00:47:42
5, which is... 00:47:44
What number did you get? 00:47:46
1.... 00:47:48
16444. 00:47:52
It should get very, very close 00:47:54
to that number. 00:47:56
I think that's about all. 00:47:58
Is it about time 00:48:00
that I'm supposed to finish? 00:48:02
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Idioma/s:
en
Etiquetas:
Miscelánea
Autor/es:
Dª.Francesca Ida Carducci
Subido por:
EducaMadrid
Licencia:
Reconocimiento - No comercial - Sin obra derivada
Visualizaciones:
432
Fecha:
11 de enero de 2011 - 12:49
Visibilidad:
Público
Enlace Relacionado:
Universidad Rey Juan Carlos de Madrid en colaboración con la Consejería de Educación de la Comunidad de Madrid
Descripción ampliada:

La Universidad Rey Juan Carlos de Madrid en colaboración con la Consejería de Educación de la Comunidad de Madrid acogió el I Congreso Internacional sobre Bilingüismo en Centros Educativos que se celebró en Madrid en la Universidad Rey Juan Carlos los días 14, 15 y 16 de junio de 2010.


En los últimos años, se ha observado una implicación cada vez mayor en los países europeos respecto a la educación bilingüe con el fin de preparar a sus alumnos para sus futuros estudios, trabajo y vida en una Europa cada vez más multilingüe. Si el objetivo es conseguir una Europa multilingüe, el Aprendizaje Integrado de Contenidos y Lengua (AICOLE) sería el instrumento necesario para conseguir esta meta. Como consecuencia, el AICOLE ha provocado un gran interés en los últimos años en Europa, y  especialmente en España.


Por otro lado la Comunidad de Madrid se ha convertido en una región de referencia gracias a su decidida apuesta por el bilingüismo en los centros educativos. Un ambicioso proyecto iniciado en el año 2004 que cuenta en la actualidad con 242 colegios públicos en los que se desarrolla una enseñanza bilingüe de gran calidad. Este curso 20010-2011 el modelo alcanza a la enseñanza secundaria donde se extenderá con la puesta en marcha de 32 institutos bilingües. Estas políticas educativas están produciendo resultados muy apreciables y han generado un gran interés entre los profesores que se sienten cada vez más atraídos por este tipo de enseñanza.


Por estas razones, este I Congreso Internacional sobre Bilingüismo en Centros Educativos ha estado dirigido a profesores de primaria, secundaria y universidades, a investigadores y responsables políticos interesados en la educación bilingüe y en metodología AICOLE.
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