So hello everyone and welcome to the Scientix webinar Mathematical Modeling and
Real-Life Examples in STEM Education and IBDP. My name is Marina and I will be
moderating this session. With us today we have the speaker of the session Mehmet
Başaran, he is the Scientix ambassador for Turkey. He has been working at the IB
Mathematics teacher in the SANKO Private Science and Technology High
School and he's currently developing his PhD in the field of education in
Gaziantep University. He has also been working on Mathematical modeling of
real-life example for teaching mathematics and has also been involved
in many national and international projects such as Erasmus+ or inGenious
among others. Mehmed will be presenting this evening
topics over the following 45 minutes and for the 15 remaining minutes after he
finishes his presentation you will be welcoming your questions about the topic.
So please don't hesitate to use the chat to ask any of your questions and offer
to share your experiences regarding the topic. Also with us is my colleague Enrique.
He is using the Scientix account and he will be helping you with any
technical problems you might have, so please write to him privately in the
chat if you are experiencing any difficulties attending the session. I would
also like to remind you to please turn off your cameras and microphones during
the talk and address your questions
into the dedicated chat. So that´s everything from my side. I will now give
the floor to Mehmed to be in the session. Thank you very much. Thank
you Marina. Hello everyone I am Mehmed Basaran and today we´ll be together and I will
present you Scientix and STEM education and real-world examples how we can
implement some other mathematical topics in or mathematics lessons and I will also give
some details about IBDP programme and you will learn about how we implement in
IBDP the programme in our lessons. I will first start with the
definition of mathematics and I will give you the information about
their delight in mathematics also then I will give some information of IBDP
The last thing is, I will give some real world examples from lessons.Let´s start with
the definition of mathematics. Mathematics is from Britannica the science
of structure, order and relation that has evolved from elemental practices of counting, measuring,
and describing the shapes of objects. It deals with the logical reasoning and
qualitative
calculation. And probably serious, mathematics is about the logical reasoning and
quantitative calculations and together with
also literal meaning what mathematics is "things which can be counted" now you can
think that counting has vital rolein our daily life, just imagine that there were no mathematics at
all
how would it be possible for us to count days, months and years. As probabably serious, maybe all of you know about
what´s mathematics. Let's talk how we use mathematics in
the daily life.
On a basic level you need to be able to count, multiply, substract or divide. Mathematics is around us.
It is present in different forms whenever we pick up the phone, manage the money, travel to some place
finally meet new friends, unintentionally in all these things mothematics is involved. As you´ve
seen I'll also give some
other examples from mathematics in daily life. For the first set we
concerned that the adventages of mathematics in real world connections. The first thing
is if we develop some investigations in mathematics to teach our lessons in my
classes, increases the motivation and interest in mathematics. For example, you
can check the interest more than you do without real world problems.
The second thing is, real world connections in mathematics helps students to improve conceptual,
meaningful and permanent learning. As you probably fear, the permanent learning is the most
important part of all mathematics stuff. It´s
probably all of the mathematics teachers deal with such problems and also making
connections with the real life in mathematics helps the development of students´ mathematical process skills
for example reasoning, communication, problem-solving and analytical thinking. Later, we will see
IBDP program has a parallel line with real world connections in mathematics lessons. And if we
continue with the advantages of real world connections, the fourth thing is - helps students develop consciousness about their
future career choices by showing occupational fields in which mathematics
is used. And the other thing is real world connections help students develop
a postive attitude towards mathematics.
Probably, as you know the students are excited to learn mathematics because if we don't have any
connections between real life and mathematics, how can they understand mathematics.
As you know, there are many research areas about it, and I will also
give some other important topics to connection between life and mathematics.
The last thing is, connection facilities generalization and abstraction of
mathematical
ideas and concepts. I give some important topics here because all these six things come from
the research areas, you know, there is a lot of research about real life connections and
mathematics and you know, I put together them here and I just wanted to give some
important possible steps. But I really want to say here, if we just say
the advantages of mathematics and also I must say that what are the disadvantages of real world connections
and mathematics. The first thing, I would like to say, there is not significant disadvantage. But there are
some disadvantages, for example, if given examples are complex to learn mathematical problems
can be difficult. You know, if we give difficult real world examples, then the
mathematics becomes two times complex for students. Then also the other
disadvantage is the heavy content of curriculum and local time may make it difficult to use connections.
There are some disadvantages, as you see here and also you can get them from your
mathematics lessons, there are many disadvantages
to use real connections and mathematics, but the research says, please use real
connection and mathematics. I would like to continue with real world problems are likely
to have multiple solutions and while finding
strategies to solve these problems, so students can have a chance to improve their problem-solving
and analytical thinking skills. As probably see here, if we connect here mathematics topics
with real world then students will try to think analytically. Probably all of
mathematics teachers want students to think analytically and have some skills, for
example critical, analytical and problem solvers skills. That's why the reason if we use
some real connection in our lessons then students will have a chance to think analytically. If we
continue with the use of connections throughout an environment our students develop
multiple mathematical approach to the problems. In this work I would like to emphatize
if we use real connections then we think about the differentiated learning. As you probably see,
students have some different areas and they learn different types of
problems. If we use zero connections then we have minimum
chance to solve the problems in a different way. That was the reason, the mathematics/ real connections gives
us this chance and also students will have bigger chance to solve problems
in a different way. Let me continue, what is IBDP programme, probably many of you have heard about it.
But here I will give some information about it. I made PhD about in IBDP programme
and also will give one example from England, School how they use
mathematics connections in mathematics lessons. First, I´ll start with IBDP meaning.
IBDP has four programmes, what are they?
Primary Years Programme, Middle Years Programme, Diploma Programme and Carrier-related
Programme. Career-related Programme is the newest one but I would like here to mention
about Diploma Programme, because it gives
studets chance to go to university without
an examination. Because IBDP programme has its own examination and
students have more chance to study
on IBDP programme. Also IB programmes have more chance to students to tell the other
programmes, for example
IGCSE, it means International Graduation Certificate Education or GCSE.
If the students want to study for them, then students have more options in IBDB.
My main interest is in IBDP programme because I would like to study a Diploma Programme to give chance
to students to enter the university and continue IBDP. It was established in
1968 the International Baccalaureate Diploma Programme was the first programme offered
by IB and that it is taught to students aged from 16 to 19, as of 22 May 2015 there are
2,795 schools offering the BP in 143 different countries worldwide.
As you probably see here, or if you search on the Internet or many prestigious universities
except IBDP programme. Why I mentioned you IBDP because in IB classes we use
real-world mathematics connections. IB uses these real-world connections in investigations in
mathematics. You will see here the IB learner profile. The IB learner profile is mainly
about
how we use the real-world connections because IB wants students to be inquires, knowledgeable, thinkers,
communicators, principled, exactly as you see here all these things are mainly about students must be open-minded.
As you probably know, the holistic approach is mainly about the students must think how
they can be connected the real world and the topics they learn from their the theoretical
knowledge. And if you continue the assessment in IB there are two types of assessments in IB
What are they? External and internal assessments. Externals assesments solve esseys, their structured problems
short-response questions, data-response questions, case study questions.
Internal assessment - oral work, languages, investigation in mathematics. As you see
here,
students must study investigations in mathematics, they use real-world
connections here, they often have more chance to use mathematics in
investigations in mathematics. Also they must have artistic performance. Four courses in
mathematics courses in IBDP are available, what are they? They are mathematics studies
at standard level - SL, mathematical higher level and the further
mathematics higher level. All these courses in IBDP are mathematics courses.
The aims of these courses are to enable students to develop
mathematics knowledge, concept and principles and also deelop logical, critical and creative thinking
and also employ and refine their powers of abstraction and
generalization. It´s probably serious, students must think logically, critically
and creatively because they have an exam, IBDP exam and also all of exams in their
classes, there's the reason for students should know, how they can
connect the real world and mathematics. You know, they're being a big problem. Now I will give you
some examples for understanding that most people that I attempt here
as a students´ teacher. I will give one example how they implement their lessons -
mathematics and the real-world connections.
There is a very big area and very sofisticated. One of the
lessons from difficult mathematical lessons, they use real world problems
and also real-world connections. First, they read about the problem and the
teacher gives them a chance think about how can they solve the problems with using real world. For
example, they should make macaroni and they use kilograms and other things and
how they can put together them in one place and how they must solve the problems in
a suitable way. I will give you some examples here from the pictures, from lessons,
mathematics lessons, that was interesting for me because in our
country don´t use such area
to teach mathematics from the real life. They have more options here. This
was the difficult one from private school, and students had chance to cook
the meals in labs, as you see here. For example the picture from their cooking, they
first measure that and they must use the kilograms and they must
count, they must calculate, you know, probably you see here the real connection and
mathematics.
At the end of the lesson they put on board their writings and what they
learned from this lesson. And here I want to give you one example from IBDP
class how I use in my IB class mathematics. First I start with real
work mathematics, I ask my students where do we use parabolas in real life.
I come up with this question on our way to students to think about,
where can we use the parabolas. After the discussion 5 or 15 minutes, I give them the
real-world examples from parabolas. For example, we use the parabolas in
McDonalds, for example in the nature, probably they saw these things, but
they had never thought this is the parabola or how can they write the question of
dish parabolas.
I come up with these first things to think critically and analytically. And also I give
some real-world examples because giving more examples I visualize them the abstracting
thing and go beyond it, you know, follow it, you have to deal it with right
questions of a parabola, because if discuss for a student thinking first abstractly,
if we give a chance them first real world examples, then they will
think, yes, we use the parabolas in the real life and how can we write the
equation and then I give more examples. I every time try to prepare before my
lessons. I know this will take time but actually I must do this because I want
to teach my lessons in investigations in mathematics. I also give real
bridges and they use parabolas in the occasions, for example here and
here.
Hearing more examples, you know, after giving these examples and I ask my students:
"How can you write these equations?"
Yes, you'll solve this problem and you'll see the real-world examples and how can
be used to write the equation of this parabola? Students of IBPD have more chance
to write it, because they have many options, for example, TI calculators
TI calculators give students more chance to write an equation what
they have, for example they can write and an equation of the parabola or other
things and they know how to write an equation in TI calculator also
they can use GeoGebra programme. Many times I use GeoGebra programme because
it gives me more chance to make real world connections and try
the equations in a different way because in GeoGebra programme there are sliders
that give me chance to move the equations in left, right or up and
That´s the reason, why sometimes I use GeoGebra programme. Students also know
how to use the GeoGebra programme, too. You know, giving some examples in our
mathematics lessons, students will come up with you, then how can we use the limits or
differentiation or integral,
how can we use in the real world, and how can we write the equation,
such things with using the technology?
This was the reason in our IB classes
we sometimes use such things but all in all in IB classes we don´t
such things because, you know, our students must study to succeed in for
their university exams. They must solve many different questions,
they must use different solving styles, in my country using
mathematics is a really big problem because they must solve many many
different question types and they must solve them in one minute,
therefore just one mathematics question. But in IB classes I have
more chance in our country, this is the new change that, you know, using
mathematics and real-world connections. Probably you use your real world connections in
your lessons but in my country this is so difficult, but actually I had a chance to see
different countries, for example: Belgium, England and France and such
countries use real-world problems in mathematics because they really want to
think the students critically and analytically, you know, this is the twenty-
first century skills.
If the students want to move higher and if we want students to go beyond, you
must use in our mathematics lessons such mathematical topics. I know findings
from mathematics topics from the real-life are really difficult but I advise you -
please write, find different mathematics topics for your teaching lessons.
This is my presentation if you like to ask some questions,
please, ask me
thank you everyone.
Now, thank you Mehmed for this presentation, we do have some time for a
question and I if anyone wants to share something in the chat, feel free to
share it now,
but I can´t see anything in the chat, would you like to expand on any of the topics that
you have mentioned maybe? ok I can, if I have chance, I would like to give some
websites about real-world connection, I like to give
them
Here are some useful websites for using mathematics and real life examples
you can find practical use of Maths and science here, you can use different kinds of
mathematical topics and real-world connections, you can click one of them and you can
find a real-world connections, for example how big is the world
just click and you can find the example and you can download it, you can re-arrange it and you
can use in your lessons. One of I use in my lessons and others. Maths in real
life you can use in your lessons here, there is the great example of a lot of mathematical
websites using real-world examples and other things, Maths motivation I also use
here, in Maths classes you can use different kinds of the mathematical topics from real life
connections and also you can use some Maths videos here.
Mehmed, sorry for interrupting, but we see that video slow so when you talk about the pages
wait, we don't see that page. It's ok.
We can see it now. Ok. Here´s another good example of the website using Mathematics and real life.
You can use these mathematical topics here you can choose one of them and
you can arrange yourself but mostly I use News Maths and also free Maths
and videos. You can here find some videos and further examples, Maths lessons
to motivate the students to hook them before the lessons, starting from your lesson.
Also you can give some teaching channel. Here you can find some good videos and
a real-world connection, there are great videos here to use in your Mathematics lessons.
there's it, probably you use them in your lessons but actually I advise you prepare
your own mathematics and real-world examples because using the prepared ones
gets mostly, you know, using them for example your own mathematics and
real-world connections will give chance you to differentiate the lessons. If you use
them, you can use them for years.
If you have some questions, you can ask me now.
Mehmed, since the website was not really working in the beginning, if you could add the links
that you were using on the chat, maybe this could help people to enter the
websites on their own. Yes, I will add now on the chat. In the meantime there's anyone who has a
specific question or any other web sites mentioned. They all seemed very
interesting, so if anyone has used them or had any comment on them. Yes.
Here are the websites.
I copied them on the chat box. Thank you and maybe we can give a couple of minutes to
everyone so if they want to check any website they can and if they have any
questions they can use this space to talk, to make a question. If you would
like to mention about for example maybe you use your lesson in mathematics and real world
connection - what are the disadvantages in your lessons and I really wonder such things
because I am working on them now, I am searching them, I am searching the
disadvantages of using Mathematics and real-life connections. There are many
research studies but it differs from country to country. I know all the things
for my country but actually I wonder other countries, if you´d like to mention about
them I would like to hear your voice.
Ok, so please if anyone has something to share about the
experiences as teachers in the country, please feel free to read it on the chat,
anything negative as Mehmed said or even any positive experience as well, that would
be good to know
for software
There is one question on the chat Liliana Meety, she's asking as she works with
young learners seven to nine years old and she's asking if there are any examples
or suggestions for for people/ for students of this age
the PUMAS website is most suitable for the ages from seven to nine years, also you
can use this website, it's the more suitable for students net in a real life.
Probably you see here the website here, at lessons worth sharing, you can use
this web site for your lessons.
There is another comment from somebody, he's asking, he is saying that the main
problem using this method is having a lot of topics, more topics and less time.
Would you like to comment it? I must say, the research studies say if you´d like
to use your Maths and real world connections, you should start with small things, you know, for
example giving them to talk before the lesson, for example, where do we use the parabolas, where do we use
the limits, where do we use the differentiation. Just asking such questions may be more
appropriate for the first time after that you can differentiate your
lessons according to your topic, you know. I´d like here to emphasize that
using all, using mathematics and real-world connections is not
appropriate for all mathematics topics. I know using mathematics and real world connection
is more difficult to use such, for example the topics, for example relations
and you know, facts, it´s more difficult to use real- world connections. That's one reason I´ like
to say, please use some small things, starting with giving some questions. Where do we use
such things in our real life? Have you ever seen before that? Just to hook them
before the lesson. After that you can continue, other days you can use
some difficult ones.
Ok, so thank you very much for responding to the questions. I don't see any other
question in the chat at the moment. But wait, there's one thing that teachers are
afraid of changing traditional methods. Exactly for thereating. Generally,
in my country Turkey teachers are afraid to change traditional methods, yes
you are right, because of, you know, the examination system in our country.
The students must solve different kinds of problems, also the teachers should solve
different kinds of problems. Also the teachers must solve the mathematics
problems quickly, you know, because the students have just one minute for each
question. That was the reason - teachers are afraid to change the traditional methods
and also probably they don´t know how they can use the technology in their lessons
because using mathematics and real-world connections requires some
technological content and knowledge. That´s why the reason in my country some teachers are afraid
of changing the traditional methods. You are right in fact.
If we compare students´achievements using this method versus traditional one, yes, there are many
research studies there, but actually I made one of them in IBDP classes if we use
some mathematics and real world connections, students get more high
course in their in the exams because the students must know how to use their
TI calculators in IBDP classes, that was the reason, we should give them
more examples of investigations in mathematics they also come up with new
ideas to solve mathematics problems and to solve different kinds of, you know,
mathematical ideas. I actually investigated in my MAB classes and
MAB classes for Turkey. If we use zero connections, the students get
lower scores because they must solve mathematics problems quickly. If we
use mathematics in the real life, they don't have a chance to solve the mathematics
quickly and they are advantageous, you guess. IBDP and
in my traditional MAB classes it
was different and this was the reason I gave one example from the IBDP classes.
Ok, thanks again if there is any question please say it in the chat. Ok, it doesn't seem
there aren´t any more questions. I'm going to intervene now, because I'm getting some messages
on the private chat, so present your messages to be seen by everyone. I'm
going to share the questions that were asking so there was another
question from Linda Daroy, she was asking for free games
regarding Maths for thirteen-year old kids and there is another comment on Catarina
Ivanovic, she is saying that lack of teaching materials. Yeah, exactly,
a problem - lack of materials. we can use, you know, if we
don't have to use some materials to show students how can we connect
real life and mathematics,
please try to just show them just one video from YouTube or other platforms and that
also gives chance to the students to think critically, you know, I don't want to
advise you- please prepare your lessons, all lessons according to the
real world and mathematics and it is, difficult but just using some small parts
in your lessons, using real-world and mathematics leads students genius to think
in a different way, you know. If we give them just theoretical knowledge, they will just
try to think abstractly, you know, we must consider how
can we differenciate our lessons, That was the reason
in the last two decades, there is the resource topic and the research studies about it
how can we come up with new ideas to teach mathematics, you know, they want students
to think critically and analytically, you know, many skills because the
mathematics, the nature of the mathematics is too, you know, strict and
too complex. If we try to make it easier for students
it'll get a chance to think more actively and critically.
There is another question from Linda, she's asking what software you use for modelling.
Thank you Linda, I use for software, Marina, GeoGebra and center, for example for
my IBDP students, they use TI calculators because it is handled,
they can use more comfortably, to use in the mathematics lessons. They also use
TI calculators for their exams. One with using TI calculators and one
exam without using TI calculators. This was the reason,
I want to give them chance to use TI calculators, but for my lessons I use
GeoGebra because it gives me more chance to use sliders and other things to
make the equations more suitable for my mathematics topics. Ok, thank you.
Any other questions? Please, share it under the general chat, so we can all see them.
Ok, we're gonna leave it open for one more minute. If anyone has another
question and if not, we´re gonna close it, so if you have
anything you´d like to share on the chat right now.
Yes, I think, there's no more questions, so I guess I´m gonna close it now.
Many thanks to Mehmed for presenting in this webinar and to everybody for
participating and sharing your ideas
The next session and next webinar is gonna be on the 24th of February and
The topic will be Free/Libre Software and Inclusion in Schools, so feel
free to join through the usual channels, for this one you will receive an email
with all the relevant information in the following days and again thank you
everyone for participating.
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