Katerina Kalfopoulou
MEd, Secondary School Maths' teacher, interested in the combination of Maths and Literature and in environmental issues investigated through Maths.
Location Thessaloniki, Greece
Activity
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Katerina Kalfopoulou made a comment
1fact/3 fictitious elements.
Half an hour ago I started a new course in FutureLearn.
Till the end of it I will be a professional on writing fiction, at leas I should be, because I have already been asked by a famous publisher to write tree books. I have finished the first one.3 fictitious elements/1fact
Last year I registered to a course concerning... -
Katerina Kalfopoulou replied to Maureen H
I totally agree with you David! "Its all in the mind you know". Everything depends on the definition!
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Katerina Kalfopoulou made a comment
I like it! It made me think "arithmetically"!
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Katerina Kalfopoulou made a comment
Nice!
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Katerina Kalfopoulou replied to Maureen H
It depends on the set. Prime numbers are natural numbers, not integers. [There are not negative prime numbers]. Euclide proved that prime numbers are infinite and the era he did it (about 300 B.C.) the integers were still unknown.
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In the bottom of the page there is "DOWNLOADS" and bellow that there is a PDF. By clicking on it the page will be downloaded.
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Solving puzzles is like unfolding a mystery!
Unfolding a mystery enhances the self esteem!
Is there anyone who doesn't care of their self esteem? :) -
Katerina Kalfopoulou made a comment
I am interested in this course for more than one reasons.
I surely enjoy maths puzzles!
On the other hand I teach maths in a high school so I often challenge my own students by a math puzzle similar to the content of the topic we study.
Finally, I admire many contremporary mathematicians from your country. :)
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Katerina Kalfopoulou made a comment
"The story will be driven by the consequences of character's choices" and, yet, character will no be finished until the film will be made!
I like it.
I'm wondering what will happen if my own choices differ of character's choices. :) -
Katerina Kalfopoulou made a comment
Developing characters is what I'm looking forward... :)
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Katerina Kalfopoulou made a comment
During the first week of this course the way I see a film has been dramatically changed.
A lot of technical issues come into my attention for the first time.
Thank you. -
Katerina Kalfopoulou made a comment
I haven't thought before that the first part of a film show me how to "read" the film!
Actually, it is what unconsciously happens! Well, from now on this will be done consciously. :) -
Katerina Kalfopoulou made a comment
I'm going to try it asap!
It seems really great technique. I hope that it will work for me! :) -
Katerina Kalfopoulou made a comment
Great team!
Thank you! -
Katerina Kalfopoulou made a comment
I have heard about amygdala's function in a previous course, "Mindfulness for wellbeing and peak performance" and I almost knew how to control my reaction against a "threat", but I have never think before about my pupils reaction caused of their amygdala. I think that from now on I'm going to be much more tolerant to a short of inappropriate behaviour of my...
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Katerina Kalfopoulou made a comment
In different countries and throwought different topics of teaching the problems are almost the same.
It may depends a lot on the cultural (or the multicultural) state of the class.The last 30 years I earn my living by teaching maths...
Many things have been changed during this time, but mainly it is me who had been a totally different teacher than I... -
Katerina Kalfopoulou made a comment
Hi!
I teach mathematics in a greek high school and I'm interested in STEM to improve my teaching and to help my pupils.
Thank you for this opportunity. -
I've started this course by chance, but it changed the way I think and I breath.
Thank you! -
Katerina Kalfopoulou made a comment
All the forth objectives of this lesson are extremely interesting.
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Katerina Kalfopoulou made a comment
Hi, I am from Greece. Given that I'be been born and raised in Thessaloniki, the second biggest city of the country, I remember myself to live in an electricity operated world.
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Katerina Kalfopoulou made a comment
It is a very interesting topic. As a math teacher in high school I like to combine math concepts to environmental issues during my teaching.
This course is an opportunity for me! -
Katerina Kalfopoulou made a comment
Thank you for this great course! Everything I've learnt is really useful in my every day life!
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Katerina Kalfopoulou made a comment
This is the first time I haven't missed not even a week of a MOOC!
I like this course a lot because everything I've learned these five weeks can be applied in my day life and makes me feel more peaceful and at the same time more effective. -
High Maria Tereza!
I am 54 now and I only recently feel self compassion.
I think that self compassion takes time to be grown.That's one of the good things that occurs in life as we get older!
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Hi Claudia!
Ten words you use are enough to describe precisely what I feel so far throughout this course! -
Even though it is totally off-topic, I would like to make a comment.
I am from Greece and both "how are you going?" and "how are you doing?" are meaningful for me, because in Greek we use them both informal. The formal type is "how are you?". -
Katerina Kalfopoulou made a comment
So far I find my self to be changed by becoming more aware and conscious.
Focused on my breath I can control my mind and keep it away from wandering off.
I feel more calm and I avoid to be anxious or nervous by having an eye at my amygdala! -
Katerina Kalfopoulou made a comment
The best thing I’ve discovered about the importance of acceptance and letting go is that I don't lose time and my good mood doesn't change because of the bad on inappropriate behaviour of another person. I keep on being calm and focus on what I have to do and I do it mindfully. And that is great!
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Katerina Kalfopoulou made a comment
Even though I am not the kind of person who is often distracted, all these I learned so far help me a lot to be mindful on being ... mindful!
This is the first open massive course during which I am totaly on track. :) -
Katerina Kalfopoulou made a comment
Cultivating gentleness and friendliness towards myself will make me to behave more gently and friendly to all the others, even to them for some reason I don't like at all! So, being calm and gently to the others I'll be able to succeed the peak performance avoiding frustration and anxiety! :)
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It was a great allegory! From now on anytime I catch my mind to wander off I'm going to treat it as a cute puppy!
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Katerina Kalfopoulou made a comment
Cultivating curiosity will make me somehow a bit wiser, I think.
I mean if I feel curious about what happens in my mind or how I feel my breath any time my amygdala fires my fight/flight response then I'll be focus on my body at least for a few seconds. These few seconds suppose to be enough for me to rethink, even analyse, what causes the fight/flight... -
Some of the suggested activities are really easy to be done mindfulness!
Next time I'll find my self to wait in a line or at a red light I'll try to be focus to my breath! But what I have to do first of all is to be mindful when I eat. I have to reflect on where the food has come from... I am quite sure that I will consume less food if I eat being mindful! -
Hi Lynn!
I felt the same way. -
Katerina Kalfopoulou made a comment
When my fight/flight response is triggered my hart beats faster and faster...
I usually calm me down very easy by breathing deeply and counting. -
Katerina Kalfopoulou made a comment
I'll try to track my progress by using the template. I am sure it will be helpful.
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Katerina Kalfopoulou made a comment
The body scan was an awesome experience for me!
I have already repeated it four times in order to have the better result!
I am sure this will help me to be calm and mindful. -
Katerina Kalfopoulou made a comment
In the end I couldn't open my eyes...
So very relaxing, and the voice so calm!
My mind wandered once, (because of an unknown english word) but it was easy for me to brink it back. I think that this is what I have to listen to every night before going to bed! :) -
Hi Becky!
Thank you for sharing such an amazing experience with me!
What you describe I often experience when I am in the classroom...
Every time I manage to control my feelings and to be polite and calm I feel a bit proud for myself... :-)
To tell you the truth I have to do it all the time in order to cope with my teen students.
I haven't taken part... -
Katerina Kalfopoulou made a comment
What I did really find interesting was the awareness of the function of the amygdala!
(Amygdala is the greek word for almonds, by the way).
From now on, I believe that anytime I feel to turn on or to get angry for some reason the first thing I have to think about is that small almond shape thing in my brain which is responsible for my feeling.
And I'll try... -
Katerina Kalfopoulou made a comment
As a teacher of Maths in a high school I often spent time to explain to my pupils that they must not be distracted during the course...
Now, I can see some techniques I could apply to them and to me as well in order to be mindful. :) -
Katerina Kalfopoulou made a comment
Well, having on all the alerts on my computer is something I have to stop at once!
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Katerina Kalfopoulou made a comment
This was an amazing experience!
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Katerina Kalfopoulou made a comment
Hi!
I can’t wait to see what you have designed for this course! -
Katerina Kalfopoulou made a comment
Hi!
It sounds very interesting! -
Katerina Kalfopoulou made a comment
The last two years I teach Mathematics to a high school to 12-15 years old pupils. I love it.
[Before, for about 20 years, I had been teaching 16-18 years old and I mainly prepared them to take part to the national exams for State University.]
I have found out that teaching Mathematics in younger pupils could be an amazing adventure, but the centralised... -
It will be the same in Greece Christina Y. Year by year as the crisis increases (all over the Europe) budget cuts will make the situation in Education even worst, unfortunately. At the moment I teach in very small classes of around 20 pupils, and it is great.
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Thank for your answer, Jing Gao!
In my country 30 is the maximum number of pupils in one class!
A class of 30 is concerned as a packed class and it is a really difficult task for a teacher. :) -
Hi Jing Gao!
I am Katerina from Greece and I teach maths to 12 to 15 years old pupils.
I would like to ask you who many pupils are there in your class (or classes)?
Thank you. -
Katerina Kalfopoulou made a comment
I knew Vygotsky's ZPD, as his theory is what we learn -among others- in Greece and I always have on mind ZPD, when I plan my lessons. (I teach maths in a public high school)
I have never heard Csíkszentmihályi's Flow before and I found very interesting the way he has classified the eight situations in his graph. However, I see that Vygothsky's theory concern... -
Katerina Kalfopoulou made a comment
I'll try to keep my study journal throughout the whole course.
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Katerina Kalfopoulou made a comment
Hello everyone!
I teach maths in high school, but I have never got involved in science before, even though I always love to. :)
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Katerina Kalfopoulou made a comment
Like so many others in this comments area, I haven't heard about "hinge point" question before. I only could suppose what this kind of questions is.
I am really glad to learn new things. -
I think that grid could help a math teacher as well, conceding that what someone notes in it is the observations of his or her course.
I teach math as well, and I am going to try it. :) -
Katerina Kalfopoulou made a comment
I am going to try it. Thank you!
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Katerina Kalfopoulou made a comment
I teach Mathematics in a state school in Thessaloniki, Greece, ages 12 to 15, and even though I teach Mathematics for more than 20 years to older students (16 to 18) I am not experienced in so young pupils I teach this year.
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Katerina Kalfopoulou made a comment
To elicit students' knowledge is an ancient greek method aplyed by Socrates. :)
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Katerina Kalfopoulou made a comment
By tte end of the week you'll be able to interpret a statistical graph
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Katerina Kalfopoulou made a comment
I usually start describing what we are going to learn and why we need to learn this new concept or procedure by linking it to a future topic.
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Katerina Kalfopoulou made a comment
I teach mathematics to K6 - K12 and the learning objectives I mostly share with my students are how the new mathematical concepts will support their future mathematical knowledge and cultivate their thinking skills in general and on the other hand how this new knowledge will be useful in their every day life.
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Katerina Kalfopoulou made a comment
This is a very useful list. Thank you!
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Katerina Kalfopoulou made a comment
Even though I teach maths in Greek (at least up till now) I always do what Kay and Paul describe in this video. After all maths is a ... foreign language itself.
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Katerina Kalfopoulou made a comment
Ι most looking forward to learning how math teachers from all over the world overcome the difficulties they usually faced when they teach Maths!
O.k. I am joking!I mostly like to learn how to do my instruction in English and to interact with as many colleagues as possible. :)
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Katerina Kalfopoulou made a comment
Hello!
I am from Greece. I teach maths in a secondary public school for more than ten years!
At the moment I am teaching only in Greek, but I would like to think about my teaching subject in English because I think this will ... open my mind!
On the other hand I believe that this course provides me the opportunity to find out what is the core of secondary... -
Katerina Kalfopoulou made a comment
Good morning teachers and tutors from all over the world!
I am a Greek secondary school Maths teacher, (K12 - K18), and I am really very happy to join this specific course.
It will be great to interact with all of you! -
Katerina Kalfopoulou made a comment
I teach Mathematics, but in Greece Mathematics Curricula in Secondary School is dramatically separated by the other fields and no applications of it are generally taught.
So, what I am trying to do is to lean towards STEM and adopt some good exams in my own instruction. To this point of view this course was really supporting.
Thank you. -
Katerina Kalfopoulou made a comment
Very useful! Thank you.
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Katerina Kalfopoulou made a comment
The course was great!
Thank you! -
Katerina Kalfopoulou made a comment
This was a great course. Thank you!
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Katerina Kalfopoulou replied to Fiona Lund
This is the argument I wished to write if I could speak English much better than I do! :)
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Katerina Kalfopoulou made a comment
Even more interesting than "Pohutukawa tree case study" was Pohutucawa tree itself. I haven't seen such a tree before.
Lisa Prager' s article is no doubt a really good argument.
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Katerina Kalfopoulou made a comment
"If you cannot convince them, confuse them"! :)
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Katerina Kalfopoulou made a comment
Hi! I am a greek teacher of Mathematics in secondary school and the development of students' critical thinking is one of the main goals of my teaching. (Or at least it should be...)
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Katerina Kalfopoulou made a comment
In Thessaloniki, a city of 789,191 inhabiters, there are only 4 Starbucks, but not because people don't use to drink coffee here. On the contrary, there are more than 2023 coffee-places (according to Yellow Pages), it means that there are 2.5633845292204295 per capita! (So very close to the number A I've calculated in the previous step. :) )
I suppose that...
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Katerina Kalfopoulou made a comment
I live in Thessaloniki, the second biggest city of Greece. The population according to the 2011 census was 789,191 and there are about 410 gas stations in the area.
Applying the formula: G=AxP^0.77, turns out that A=2.4096480866375664116!OMG! It looks to be a huge number comparing to the others' A!
Shall we survive?P.S. After the first shock I...
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It is extraordinary! I have never seen something like that before!
Even though I cannot see how it will be unfolding, I enjoyed the tasks and I think that it was the first time I didn't face any difficulties since I've started this course.
I am sure that my dreams tonight will be about multiplication of points on conics! :) -
Thank you Chris!
This is really great!
I'm going to see the videos asap, mainly for three reasons with first of all that I do really enjoy Pro Wildberger's lectures!
Thank you again! -
It surely helps, Lawrie. Thank you very much.
In Greek you use also the word "change" for both increase and discrease when we don't refer on a particular changing.
Hense, here "discrease" is using for the relative changing.Thank you, again.
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Or, from the other side y=ax^3+bx^2+cx+d could be y=kx^3, if there is only one root. In this situation is an increasing funcion if a>0 or a discreasing function if a<0.
There are thtee roots roots or just one root.
If there are three roots the curve has ups and downs.
Ths sure is that for any polynomial of odd degree there is at least one real root and... -
I don't think that you can start for y=x^3 and by translation and scaling come to y=ax^3+bx^2+cx+d.
The first one is an always increasing function an goes throw the origin.
The second one has ups and downs. -
Thank you Chris!
What I am looking for in Greek is "The integer root theorem" and applies on polynomials with integer coefficients.
It is a very simple theorem which is taught at 11 G,
just after the theorem (b) you refer above.O.k. I just found it at Google. http://www.mathwords.com/r/rational_root_theorem.htm
[It is obvious that if the...
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Katerina Kalfopoulou made a comment
I have lost the meaning of Q3.
When the n is an odd natural number, such a polynomial always increases as x increases.
Doesn't "always" mean wherever x is?
Then why it is asked which of two functions "decreases" faster than the other? -
Then you are the contemporary Pierre De Fermat! :)
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The blame is on me... :(
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Thank you, Dai, but it seems that it doesn't make any sense what I've written above.
The proof of that theorem is a very easy proof.If P(x)=an*x^n+a(n-1)*x^(n-1)+...+a1*x+a0, where an, an-1,...a1, a0 integers and P(r)=0,
then
an*r^n+a(n-1)*r^(n-1)+...+a1*r+a0=0 <=>
a0=-an*r^n-a(n-1)*r^(n-1)-...-a1*r <=>
a0=r(an*r^(n-1) -a(n-1)*r^(n-2)-...-a1) <=>... -
This is the generalisation of Vieta's formulas.
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How it is know the theorem that state if there is an integer root of a polynomial with integer coefficients then the root is necessary a divisor of the constant?
(I hope that what I've written down makes a sense...)
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Thank you Antonio!
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Katerina Kalfopoulou made a comment
Isn't this the kind of elliptic curves that Andrew Wiles used to prove the last Fermat's theorem?
[Unfortunately I am not able to understand Wiles' proof, but I love to read the historical frame of this great theorem.] -
This week seems to be even more excited than the previous ones!
Good morning everybody!
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Katerina Kalfopoulou made a comment
y=2x-6
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Katerina Kalfopoulou made a comment
For me was a great experience. Thank you!
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Katerina Kalfopoulou made a comment
Great job!
Very helpful for a math teacher, like me, whose native language is not English, and who tries hard to be able to teach maths in English in a Secondary school!
Thank you! -
Katerina Kalfopoulou made a comment
Actually maths is not all about solving equations just for finding the unknown x.
It's much more than that.
Mainly it's about finding out patterns that allow you to predict and correct what you are interested in... :) -
Katerina Kalfopoulou made a comment
Very well organised presentation!
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Katerina Kalfopoulou made a comment
It helps me to get the terminology. Thank you!
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Thank you Suzi.
After reading your comment I calculate again the average taking into account your explanation.
(6*77+7*57)/13, and the result is 66.2%, that make sense now! :) -
Thank you Dai, for encouraging me in such a nice way! :)
I agree that it is not really all about the quiz, however deep inside me there is an eternal young pupil who always cares about its score... :(I am also looking forward to starting teaching next week, [in Greece pupils are still on summer holiday], in order to use all this interesting knowledge...
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I have just finished the quiz of this week and I feel a little bit disappointed... :(
The truth is that mistakes occur not only because of misunderstanding math concepts, but because of language misunderstanding as well.In first week's quiz I got 77%, but this week only 57%!
But my average score seemed to be 66%. Why? It shouldn't be 67%? Did I miss... -
It was a great week for me. I enjoyed a lot studying some simple and well known mathematical concepts expanded in such an interesting way.
I got a lot of brilliant ideas for teaching and at the same time entertaining my pupils.I have to thank Pr. Wildberger for very nice lectures and of course Evanthia Kontogouri and Dai Middleton whose comments are...
