We say that a quantity is decaying exponentially when it decreases at a rate proportional to its current value. Another way to think of the exponential decay is that the time required for the decaying quantity to fall to one half of its initial value is fixed and independent of the initial amount. This time is called "Half-Life". Most common examples of exponentially decaying quantities are the radio active isotopes. For instance, let's take the radio active phosphorus-32: its half-life is about 14 days which means that if we have an initial amount of Phosphorus-32, say Q0, then, after 14 days the amount left will be ½Q0. In the school book there is a small list of radioactive isotopes and their half-life, which we include below.
Isotope
Half life
Carbon-14
5730 years
Radium-226
1600 years
Polonium-210
138 days
Phosphorus-32
14 days
The sweet experiment
It is really thrilling when the school-algebra meets some applications in the real world, as in the case of the exponential decay. But is it only a piece of information? How could we activate our students to experiment with quantities decaying exponentially and to make them derive the correct rate of decaying? I got my answer from a fellow teacher, Pota Kotarinou, who wrote a wonderful teaching senario titled "The chocolates and the exponential rate law". This was the senario we applied in class with two groups: B2 and B3 on the 4th of April 2016.
The experiment was organised in 7 stages:
1st stage: Each group of students was devided in 3 subgroups of about 6 students each. The small teams got one paper cup with a lid on it -containing exactly 100 chocolates m&ms- and a plastic plate.
2nd stage: Each team would shake well the container of the cup and then spread it on the plate. Without reversing the chocolates, they should pick those with no letters on top (as the letters would be on the bottom) and vanish them. You can imagine how tasty was the vanishing procedure!
3rd stage: They would count the chocolates left after the vanishing stage and would put them back to the cup.
4th stage: Stages 2 and 3 would be repeated as many times as it should take to vanish all the chocolates completely.
5th stage: Each team would complete a table with two columns: the first would number the throws of the chocolates, starting from 0, and the second would be the exact amount of chocolates left after the vanishing proccedure.
6th stage: The pairs of numbers (#throw, amount of chocolates) would be plotted on a graph (GeoGebra spreadsheet was used) and then students would try to fit an exponential decay on them. It was really fantastic that in almost all experiments the best fit was achieved by the function Q(t)=100e-0.7t!
7th stage: Finally, all teams presented their work to the others.
Last 8th March, in the high school Francisco Salzillo, third dissemination event of the project "El español: pasaporte entre culturas" was celebrated with our students.
The verses and melodies composed by Federico García Lorca, poet worked by our Finnish, Greek and Spanish students, joined again.
Ms. Purificación Martínez, principal of IES Francisco Salzillo, opened oficially this act.
Let´s read her works about our project and about the trascendence of this Spanish poet in the three cultures.
Hilkka, Irini, Adela, María, Haris, ….
More than one year ago, I was standing right here giving the opening
speech of this project and I felt afraid of saying your names as I didn’t know
you very well and I didn’t want to call you for the wrong name. Today, although
we haven’t met very often during this time, I consider myself your friend and I
hope you feel the same about me. The time Mercedes and I spent in Helsinki
together with María and Haris was amazing. I won’t forget it. The same happens
with my colleagueS that have shared some time with you in Crete and Helsinki. I
have evidence that they and the students who travelled with them had a great
time. Thank you very much. Our school welcomes you again.
Students
from Finland, students from Greece, welcome and thank you for being here this
week. I also want to thank you and your families very especially for having
made the stay of our students in your countries really pleasant and happy. I
hope they are up to scratch and you are feeling at least as happy here as they
were with you at home.
I
also want to thank our students’ families for their participation and
collaboration making this project possible. Without their support this wouldn’t
have been possible. And what can I say about our students? Seeing you with your
friends from Greece and Finland make me feel that it was worth all the work and
the effort made to carry out this project during these two years.
I
want to thank and congratulate the teachers from our school: Isabel, Elena,
Pepe, Javier, Bárbara, Fina, Inma, Belén, Guiomar, Ángel, Luis, Mercedes and Petra, for the
extraordinary effort and work you have developed over the course of these two
years. You have spared no effort or hesitated to devote part of your free time
to meetings and other necessities so that this can be a successful European
project.
Now,
it’s time to get to the point. Last year, Mercedes told me that I should do the
opening speech for the first transnational meeting. The topic was Federico
García Lorca. Last month, Mercedes “suggested” that I should do this speech
again and the topic was about the same person, and in English. A very difficult
task, but I’ll try to do my best.
Lorca’s
personality offers a double face: on the one hand, its overwhelming vitality,
overflowing with charm; on the other hand,- deeper - an intimate discomfort, a
pain of living, a feeling of frustration that will appear throughout his work.
Perhaps
the best way to enter his world is to read carefully the poem Romance de la pena negra,Romance of the black grief, which Lorca
considered the most representative of his gypsy Romancero: Frenetic axes of cocks / digging in search of the dawn/ when down from
the dark foothills/ comes Soledad Montoya. / Yellow copper of her flesh
/smelling of horses and murk. /Smoky anvils of her breasts,/ wailing out rounded songs." From now on,
Soledad looks for - says Lorca- "my joy and my person" but she finds a character that
represents the voice of moderation, limits imposed either by reality or by
conventions. That uneasiness, that frustration is present in his poetry, along
with manifestations of bustling creation, full of grace, even playful.
Faced
with this process of poetic creation, he was very strict: "If it is true that I am a poet by the grace
of God, or the devil, I am also a poet because of the grace of technique and
effort, and of realizing what a poem is. " That is, inspiration and conscious
work. "Inspiration," he
said, "gives the image, but not the
dress. And to dress it, it is necessary to observe the quality and the sonority
of the word". It is not a coincidence, then, that in Lorca’s poetry,
passion and perfection, the most human and aesthetically purity coexist This is
to a large extent due to his deep roots in the tradition. Tradition and cultureare also twinned in his work: people's lives and
songs encourage his wise and demanding creation.
After
his stay in New York, an experience that will profoundly mark him, he returned
to Spain and founded La Barraca, a university theatre group with which he
toured some Spanish towns performing classical plays. In 1933 he made a
triumphant tour in Buenos Aires, where his dramas obtained a great success.
And, again in Spain, he continues his tireless work as a poet, playwright,
stage director, lecturer ... This work earned him much admiration and tribute,
but also malicious envy. It is this approach to the people that attracts
hatred, which led to his assassination at the beginning of the Civil War, in
August 1936.
At
that time, what could two Greek poets, Yorgos Seferis and Odiseas Elitis, know
about the work of their Spanish artistic brother? Almost nothing, eight poems
at the most, translated into modern Greek by Nikos Casandsakis. Elitis, in
1938, makes a brief reference to Lorca, among other foreign poets who "...
either they belong to surrealism or not,
they have shown their strength in the eternal topics of nature, love and death."
In the following years, he reads Romancero gitano with the intention to
transfer the deep charm of the Andalusian poet to Greek. Within the atmosphere
of the Athens of occupation (1941-1944), an unpleasant atmosphere but also
ecstatic, full of spontaneous heroism, hunger, death and hopes, the
relationship od Elitis with Lorca deepens.
He
begins to see Lorca as an essential milestone in his poetic progress and sides
him with himself as an ally in the struggle of the poetic avant-garde movement
against those who long for the past. It is then when he translates seven poems
of Romancero gitano. As time went by, he will transform the poems into lines to
be sung, will simplify complex expressions, will add rhymes, will change
titles. He gave these songs to Mikis Theodorakis and the album was released in
1971. It was necessary that the poetry passed through the loudspeaker or the
recording to conquer wide audience. Love, dreams, the Moon, the Mediterranean
sea, the popular culture and Greek tragedy are part of a magical world, shared
by these two great poets. The Andalusian poet will eternally accompany the poet
of the Aegean, where Greece and Spain meet.His memory remains very present from
his entry into the Greek world till nowadays.
The
historical circumstances could condition the fact that the Greek poet saw in Lorca’s
work and vital career plenty of social, aesthetic and personal coincidences as
to turn him into source of his inspiration. However, one of the most surprising
cultural phenomena of the modern world is the rise of Hispanist studies. The
reasons that explain it are complex, but the intellectuals of the exile have
played an essential role. Finding these lively and restless circles at the
Sorbonne, or in Mexico, or in the shadow of the Sorolla of the Hispanic Society
of New York is in some way natural. But meeting the same concerns bordering on
the architectural creations of Alvar Aalto in Finland is a reason for meditation
out loud. Already in the 70s, the name of Garcia Lorca appears on the
billboards of its national theatre.
His
significancereaches the music with singers like
Anneli Saaristo, and composers of the stature of Einojuhani Rautavara
(1928-2016) who creates Suite Lorca,
based on five poems of the poet from Granada. This interest in the Spanish
language and its culture began in the thirties of the last century when Spanish
lessons are offered in the Helsinki School of Economics and, around the
professor Arturo Lángross, the first group of students interested in Hispanic studies
emerges. During the 1970’s, the Spanish teachers taught differences between “ser”
y “estar”, and in order to explain a Spanish idiom, they opened a page of an
edition of the Lazarillo de Tormes.
As
an example of the universal fame of this Spanish poet, we have the reference
that the Canadian musician Leonard Cohen made in 2011, when he was awarded the
Prince of Asturias Prize:
“You know of my deep association and
confraternity with the poet Federico García Lorca. I could say that when I was
a young man, an adolescent, and I hungered for a voice, I studied the English
poets and I knew their work well and I copied their style, but I couldn’t find
the voice. It was only when I read, even in translation, the words of Lorca when
I understood that there was a voice. I wouldn’t copy his voice, I wouldn’t
dare, but he gave me permission to find a voice, to locate a voice, that is, to
locate a self, a self that is not fixed, a voice that struggles for its own
existence”.
Then
he added that he had a voice but no instrument. “I did not have a song then”. But one day in the sixties he heard a
Spanish guy play the guitar. He asked him to teach him to play like that. In
three days he learned the six chords on which many Andalusian songs are based.
The fourth, the boy did not return. He would find out that the boy took his
life. He felt a great sadness. That's how the great musician found the voice
and the instrument.
As
I re-read these words of Cohen, I remembered the relationship that Lorca
established between the goblin, the angel, and the muse. He said that Germany
has, with exceptions, muse, and Italy has a permanent angel, but Spain has a
goblin, as a country of ancient music and dance and as a country open to death.
The muse stands still. The angel shakes his hair. The goblin ... Where's the
goblin? Garcia Lorca put it in these lines: Leave
the hard ivory of my head, / pity me, break my duel! / That I am love, that I
am nature! (From Oh secret voice of
dark love ...)
One
of the aims of English language teaching is to engage students to the learning
process by exposing them to how they can use the language they are learning to
real life experiences, thus fostering the idea to try harder and acquire those
life-long skills. This year I had decided to give my students more freedom to
choose the topics of their team presentations in the English course.
Additionally, I advised them to opt for topics that pertain to different
disciplines, in our case different school courses. The result was incredibly
creative and authentic, as the students were engaged in topics of biology and
history. They presented their collaborative work to their classmates and to
both me (the English teacher) and their history and biology teachers and in this
way gained positive evaluation in their overall assessment at the end of the school
term (of four months duration). The most representative examples of this
educational practice are the following: 1) “Down
Syndrome” by students of second grade of Lyceum, combining biology and
English and evaluated by their biology teacher Mr George Marakis and me. This
particular group had also made a chromosomes replica to exemplify in a more
tangible way Down Syndrome. 2) “The Gallipolli Campaign” by students of
second grade of Lyceum, combining history and English and supported in their
research by their history teacher, Mr Manolis Kouroumalis and evaluated by both
teachers 3) “Medicine in the Byzantine
Years” combining history and English and evaluated by their history
teacher, Mr Manolis Kouroumalis and me. The last group of students enriched
their presentation with a small role-play at the end which was both creative and
unusual, giving a theatrical touch.
Overall,
the attempt to encourage team work, interdisciplinary study, freedom of choice
and practice of presentation skills was a very successful one, helping students
to become more involved in their learning process while being creative and
having fun at the same time.
During this school year, we have been developing different activities related to our Erasmus + project “ El español: pasaporte entre culturas”.
As one of our Etwinning projects we have been using to work these activities with our students, is coming to an end, we would like to report on what have been done during these months:
-Our e- magazine “ Somos Erasmus+”
-Our “ A Christmas Carol” performance
-“Telling in short”, our work about digital narration, using the digital tool Storybird.
Would you like to know how this has been organized from Spain, Greece and Finland?
-Twinspace and groups (We are Erasmus + project)
The cooperation among school students was held through the twinspace platform. In the beginning of the project, the Greek Erasmus students who were selected in the Erasmus+ project “El español, pasaporte entre culturas”, gained passwords and user names for the platform, with the assistance of I. Kassotaki. Afterwards they created their profiles and powerpoint presentations introducing themselves, in English and Spanish, with the assistance of the English (M. Pitsaki) and Spanish (H. Dimitrakopoulos) teachers.
Spanish students were registered in early October 2016 and have been working on different pages in Twinspace where their work has been explained. Every Tuesday, during these two school years, they have been meeting to develop all the steps to write and publish their articles coordinated by the Spanish Language and Literature teacher Mercedes Guzmán.
Firstly, they were organized into different groups with students from all three countries, having to work cooperatively to decide the topic for their articles. All students could be in contact through Twinspace, their e-mails, and once they met, throughmobile (whatsapp, viber…).
M.Pitsaki (English teacher), was the teacher-instructor for the contribution of Greek team –for both school years, 2015/2016, 2016/2017-for the common electronic magazine issued by all three partner schools.
During the first year of eTwinning project SOMOS ERASMUS+, the teacher started by explaining to the 20 students that they had to work in groups of four and then cooperate with students from the Spanish and the Finnish school. Once the interschool groups were formed and they were announced via Twinspace platform, the students brainstormed on the topics of the magazine they wanted to research on and propose through Twinspace to the students of the other European schools. Some of the suggested topics were the following: Refugee crisis, Multilingualism in Europe, Unemployment in Europe , Social Media , Philosophy, Scientific revolution, Cinema & literature, European Personalities, Customs and traditions, Educational System, Climate change, Ecology & environment, Tourist attractions & unique landscapes, Studies and future, Fashion & Traditional costumes, Terrorist attacks in NY and Paris (11th September 2001 versus 13th November 2015.The students also used other internet means, such as their email or Facebook accounts to facilitate communication among the members of the teams.
At first, Spanish, Greek and Finnish students had to write their articles in English and then translate them into their different languages. In fact, you can read the articles in English, Spanish, Greek and Finnish in both editions of our magazine. The work of Maria Pitsaki has been really important because she has edited and supervised the articles written in English. Irini Kassotaki, Mercedes Guzmán and Hilkka Roose Nurmi edited and supervised the articles in their different vernacular languages.
In the second year, some of the articles were written during the week of the 2nd Transnational Training, Teaching and Learning activities (students’ exchange) that took place in Helsinki from 8th to 13th November 2016. There, students from the three different schools had the chance to exchange their sources and ideas and write their common article together. However, the rest of the articles were written by the members of the teams using emails and Twinspace.Here are the topics of this year’s e-magazine: “Adaptation of animals to their environment”, “Spanish, Finnish and Greeks travel…” “Hagia Sophia”, “Typical celebrations in Murcia (Spain) and Greece”,“Greek and Finnish Dances”, “Differences in cuisine”, “The sport of basketball in Greece and Spain”, “Football: the most beautiful sport in the world”, “The ancient Olympic Games”,“Wild animals of Finland and Greece”, “The book thief”, “The 39 steps”, “How music affects psychology”, “Traditions of our places relevant to water”, “Music in our countries”, “Passport between our countries and their music”, “Christmas customs in Finland, Spain and Greece”, “European Space Agency”, “High Schools in Finland, Greece and Spain”, “Popular sports in Finland, Spain and Greece”.
Both years, M. Pitsaki helped them to learn how to do research using research tools such as questionnaires, interviews and literature review. The next step involved interpreting their data and writing their articles for our common magazine. The teacher helped them by doing the editing of the articles for those who had written in English while Irini Kassotaki (Greek teacher), corrected the Greek articles.
You can see in our links how our Twinspace has been organized:
- Work of the students: in distance and on-site (Helsinki) for writing the articles.
Working in Vaskivuoren Lukio (Helsinki)
During the 2nd student’s exchange in Helsinki (8th -13th November 2016), it was scheduled that the interschool groups (Spanish, Finnish and Greek) would work together about the magazine's articles. So, one whole day, they met all together and started working on the topics they had decided through their previous distance communication (twinspace platform, mail, facebook, Viber, Whatsapp etc). Each group’s member was responsible for one specific sub-topic and using the research tools that their instructors explained to them in previous weeks, the students used laptops and Smartphones for searching and writing at the same time. One member of each group was responsible for having a cohesive text of group's work and afterwards he/she sent it to the responsible teacher in charge, in order for the text be uploaded to Twinspace magazine’s files.
Once all articles were uploaded to different folders in our Twinspace:
-Articles in English
-Articles in Greek
-Articles in Spanish,
The Spanish coordinator wasresponsible for the layout of the magazine. We have used a program called “PUBLISHER”. For this work, we have had the help and collaboration of the Technology teacher D. Luis Gómez.
When we hadit finished, we shared it in a pdf file with the Finnish and Greek teachers in case some changes had to be made. Once teachers and students had reviewed the magazine and agreed, we published it through the platform ISSUU, that provided us with the appearance of a digital magazine.
The last step - one of the most important - has been the diffusion of our work through different ways: facebook, twitter, Etwinning, EDUCARM, and of course, this blog.
- The Christmas theater
The first year’s Christmas fairytale that the students were working on was “The Nutcracker” (El Cascanueces). Using the script in English, the whole team (20 Greek Erasmus students) collaborated to make a video of the Christmas fairytale "El Cascanueces" in Spanish, with the assistance of the Spanish teacher (H. Dimitrakopoulos). As it was difficult for the very beginners in Spanish language students to act their roles, the teacher and the students decided together to present it as a video of handmade images, covered by the students' voices.
As far as the second year’s Christmas fairytale is concerned, the Greek students participated in the production of the video "A Christmas Carol/Un cuento de Navidad". All the students played a role by voice in the famous Dickens' fairytale and some of them helped in a technical way such as the recording and the montage of the selected pictures, in order to be visualized. The recording was in Spanish, as it formed part of our Spanish lessons, and it was accompanied with English subtitles.
Both Christmas theaters were an activity part of the Beginner’s Spanish course offered as a weekly hourly lesson, after the school’s core curriculum timetable (Instructor: H. Dimitrakopoulos).
In Spain, our Erasmus+ Christmas workshop has been developed in English and in Spanish:
-“El Cascanueces y el Príncipe de los Ladrones” ; The Nucktracker and the Prince of Mice” , for Christmas 2016
-“Cuento de Navidad” or “Christmas Carol” for Christmas 2017
This activity has been coordinated by Bárbara Vicente from the English Department and Inmaculada Lacal, María Belén Martínez and Mercedes Guzmán from Spanish and Literature Department.
During the first term of our school year (from October to December) we organized two theatrical performances: one in English and one in Spanish. Obviously, our students had more difficulty in playing it in English but they made a great effort.
Students that have participated in this activity belong to different levels: from first course (twelve years old) to third course, so they had different levels in English competence as well.We consider this activity one of the most enriching because this had helped to improve students’ different competences:
-Linguistic competence in Spanish and English
-Artistic competence
-Social competence
We represented these Christmas plays in December and we invited all the families, taking advantage of the fact that our high school has a large auditorium.
We designed a program for the families with the names of the students and the character they played. Something so simple was really motivating for our students and their families, very satisfied with this activity.
- Storybird (our tales or "telling in short")
In the Greek literature classes (teacher: Irini Kassotaki) students used story-telling as a way of literature presentations in school years 2015-2016 & 2016-2017. In the first year of etwinning & Erasmus+ project, the students were taught about “Gender in the literature” and they had worked for 4 months. They searched the role of the woman through centuries and how this is presented in Greek and foreign literature. The students worked in groups of 4-5 with a specific role and responsibilities for each member of the group. Each of the groups had a different topic with subtopics for all members. The main and common search questions for all groups were about the role and the position for the woman and the role of dowry through the ages. The literature works that groups studied were: Vincenzo Kornaros, "Erotokritos" (poem, 1626-1646), Andreas Lascaratos, "The mysteries of Cephalonia" (article, 1855), Alexandros Papadiamantis, "The murderess" (novel, 1903), Konstantinos Theotokis, "The virtue and the money" (novel, 1914), Andreas Fragias, "People and Houses" (story/narrative, 1955)
During the one hour lesson, the students were informed about Storybird tool and how it works. The teacher created an account for them, for one student of each group and she was watching the progress of each group's work through storybird’s class.
There were two stages of presentations. In the first one, in September's lessons, the topic was about the book/work that was selected by each group and it was presented to the rest of the class. The students used the interactive whiteboard and through Storybird tool, each group presented the literature work they studied, information about the writer, the main heroes of the book/story. In the second presentation, (November-December), students showed to the rest class, using powerpoint or videos, their study about the specific questions/topics referred above.
In the second year of eTwinning project, students were taught about common themes in traditional and modern literature, Greek and foreign. A topic that was really interesting for them and finally they worked on, was Helen’s myth diachronically. Using Storybird tool, the students searched how Helen was presented by creators such as Homer, Stesichorus, Euripides, Goethe, Seferis, Ritsos, Sappho.
The student’s work with storybird tool is corrected and uploaded in the Twinspace “SOMOS ERASMUS+” platform by the teacher of the classes and their English texts were corrected by M.Pitsaki (English teacher).
Storybird is one of the most creative digital tools used by different teachers of Spanish Language and Literature in their classes in order to work the narrative as a kind of text and literary genre.
This tool has a very positive aspect for teachers who can create their own classes in their dashboard with a student code. This way, you can always see, read and correct what your students have written.
In Spanish classes this tool was used to do different activities:
-Horror tales in Halloween, for example.
-Tales with different points of view in an story: internal and external narrator.
-“Writing challenge”: the teacher gives the students “a number of conditions” ( first and last picture, number of characters…)
It is a really motivating tool for students. In Erasmus+ program (and Etwinning project) an activity called “Telling in short” has been used during the two years of the project. Different students from different levels have participated in this activity and teachers have uploaded the results to Twinspace.
Firstly, students have to watch a short film. In our project we have selected three films for the two years that you can find on YouTube:
-Los libros voladores del Sr. Morris or Fantastic Flying books of Mr. Morris Lessmore
Once they have seen the short film ( there is no dialogue in them), students must write the story in their notebook with some conditions:
-you are the main character or secondary character.
-tell the story in the third person…,
and finally, they had to create their storybird as a long form book, one of the possibilities of this tool. Some of the results are really surprising and nice.
You can read and see much more in our Twinspace page.
All the activities that we have described in this entry , in which students from the three countries have participated,have been coordinated through an Etwinning project that was called: We are Erasmus+, as our digital magazine. We have created different pages for these activities in Twinspace, forums for the topics, folders to organize the materials...
This eTwinning Project has been an example of the collaborative work, for both, teachers and students, one of the most positive aspects offered by Erasmus+ and Etwinning.
María Pitsaki, Irini Kassotaki, Haris Dimitrakopoulos
