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Файл:Integration of Natural Science and Maths in Scientific Thought and Education. The materials of Russian - German Seminar in Moscow - Cologne, 2014
.pdf
Key-words
Integrated studies, biology classes, mathematical methods, mathematical terms,
laboratory works
Introduction
Integrated study is an extremely effective approach, helping students to develop
multifaceted expertise and grasp the important role interrelationships can play in the
modern world. Integrated studies bring together diverse disciplines in a
comprehensive manner, enabling students to advance meaningful understanding of
complex associations and influences within a topic. (Edutopia Team, 2008) Though
integrated studies are not a new idea (it's been around in one form or another almost
for a century), the approach does seem to have attracted newfound acceptance in
recent years. (Cruickshank D., 2008).
Frequently, mathematics and biology courses are taught in near independence of each
other. (Gross, 2000) This approach often leaves students with parallel tracks of
knowledge but unable to understand how each discipline informs and influences the
other. It's difficult for students to apply their knowledge from one course to another
and are often unable to synthesize their knowledge into a cohesive framework. (Feser
J. et al., 2013)
Leonardo da Vinci once said, "No human enquiry can be called science unless it
pursues its path through mathematical exposition and demonstration." (Kline M,
1972) This is also an appropriate premise for teaching biology at school. Even though
some students will not be mathematicians, mathematics is usually an indispensable
element in careers of different people.
During our school practice we noticed that some themes in the biology course require
using of several mathematical methods. Taking it into account we decided to analyze
practical and laboratory works at school and find those where the mathematical
methods are demanded.
Hypothesis : Using and training mathematical methods are realized by students
during their studying biology at school.
Laboratory works are an essential part of studying biology, because they help to form
notions about the variety of creatures on our planet, their mechanisms of
development. Also it cultivates careful attitude to the nature. There are certain
methods that are often used in such works: observation, experiment, work with
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literature resources and technical devices. After getting some data, one should
form
Name of the
laboratory work
The aim/short description
used mathematical
methods or terms
6
“External structure
of the stems of
plants”
The aim: to examine transects of stems and
identify its form. It may be: round,
triangular, tetragonal.
cross section, types of
polygons
6
“Determination of
the age of the tree by
annual rings”
The aim: to count annual rings and
determine the age.
cross section, circle,
ellipse, proportionality
7
“Symmetry of
animals”
The aim: to determine the type of
symmetry of the animals.
axis, types of symmetry
(radial, bilateral and
asymmetric)
8
“Identification of
flatfoot”
Take a sheet of paper and make a footprint
using your wet foot. Than draw necessary
lines and make some calculations. And you
will find out whether you have flatfoot or
not.
length of the segment,
midpoint, perpendicular
8
“Depiction of a
human head with
compasses and
ruler”
Many people have the same length of a
face and a palm. Knowing that, we can
make an image of the human face with the
help of a compasses and a ruler. *
Proportion, circle,
diameter, radius,
tangent, chord.
10
“Modification
variability”
The aim: construction of a variational
series and curve.
construction of a
diagram, reading
diagram
process it. In many cases it is the task of Maths.
Results.
The list of lab works in biology courses at school in Russia.
1. Botany. 6 form. “External structure of the stems of plants”
2. Botany. 6 form. “Determination of the age of the tree by annual rings”
3. Zoology. 7 form. “Symmetry of animals ”
4. Anatomy 8 form. “Identification of flatfoot”
5. Anatomy 8 form. “Depiction of a human head with compasses and ruler”
6. General Biology 10 form “Modification variability”
We explained the aim of each laboratory work and named mathematical methods or
terms used to complete the laboratory work. The results are presented in Table 1.
Table 1. Results of the investigation of the biology laboratory works.
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*Construction. Draw a circle of a random radius, make a vertical diameter that goes
beyond the circle, and divide it into 3 equal parts. Draw chords AN & KL, tangent ST
perpendicular to diameter. Draw another circle from the point P of a radius which
takes one third of the big circle. Draw a chord CM in the middle or the radius PB.
The upper segment of a big circle is the hair-line, chord KL is for eyes. Point P is for
nostrils. Connect on the left and on the right 2 circles with tangents – here will be
ears.
Discussion
We have confirmed our hypothesis. Educational material of maths and biology
courses at school in Russia provides a comprehensive approach to the study of
creatures and phenomena of Nature. The integration leads to the efficient use of
learning time.
In addition, integration deals with the extent to which teachers use examples, data,
and information from a variety of disciplines and cultures to illustrate the key
concepts, principles, generalizations, and theories in their subject area or discipline
(Banks, 1993).
References
1.Banks J. Multicultural education: Development, dimensions, and challenges. Phi Delta Kappan,
1993, 22-28
2.Cruickshank D. Kaleidoscopic Learning: An Overview of Integrated Studies. 2008
(http://www.edutopia.org)
3.Edutopia Team. Why Should Schools Embrace Integrated Studies?: It Fosters a Way of Learning
that Mimics Real Life. 2008 (http://www.edutopia.org)
4.Feser J., Vasaly H., Herrera J. On the Edge of Mathematics and Biology Integration: Improving
Quantitative Skills in Undergraduate Biology Education. CBE Life Sci Educ. 2013, 12(2): 124–128.
5.Gross L.J. Education for a biocomplex future. Science. 2000; 288: 807.
6.Kline M. Mathematical Thought From Ancient to Modern Times: Vol. 1. 1972, p. 224
53
PHYSICAL TASKS IN MATHEMATICS AND NATURAL SCIENCE
SUBJECTS
BY THE EXAMPLE OF STATE GRADUATION EXAM (SGE-11 AND SGE-9)
Anastasia Pautova
Moscow State Pedagogical University
In Russia pupils have the state graduation exam at the end of ninth grade and
then at the end of eleventh. These exams are testing, which are carried out centrally
across the country. At the end of 9th grade pupils have The Obligatory State Exam.
And at the end of 11th grade they have the Unified State Exam. Russian language and
mathematics are mandatory for graduates.
Science subjects and mathematics are connected closely with each other.
Mathematics and physics are connected especially closely, because mathematics is
used at all physics lessons. For example, we use different graphs, when we study laws
of movement. We can use differentiation and integration with some tasks at profound
study of physics. In other natural-science subjects mathematics is used for the
analysis of different graphs and diagrams. And, of course, we often use different
equations.
Subjects of a natural-science cycle are also connected among themselves. For
example, when we study the theme “Pressure” at physics lessons, we can speak about
the blood pressure and about the reasons of influence of atmospheric pressure
changes upon humans’ health. When we study the phenomenon of capillarity we can
speak about getting liquid by tops of plants. About a substance structure, its states
and an atom structure at physics lessons start speak earlier, than at chemistry lessons.
Respectively at biology and chemistry lessons when pupils study corresponding
theme teacher shall speak about communication with physics. Also the uniform
principles of scientific knowledge are used in all sciences. We will give examples of
the tasks which show such communication from final tests of natural-science subjects
and mathematics.
Biology
The Obligatory State Exam
I. The uniform principles of scientific
knowledge are used in this task:
1. What scientific method does this picture
illustrate?
54
1) modeling;
Atmospheric pressure, mm Hg
Height, km
2) measuring;
3) experiment;
4) supervision
II. The Knowledge of optics are used in this task:
2. Hyperopia is corrected with
1) reception of medicines;
2) a surgery on a retina;
3) special exercises for eyes;
4) biconvex lenses.
Chemistry
The Unified State Exam
Speed of reaction of nitrogen with hydrogen will decrease at
1) fall of temperature;
2) increase in concentration of nitrogen;
3) use the catalyst;
4) increase of pressure in system.
Mathematics
Physical tasks are most often used in mathematics. It can be tasks in which
graphs of dependence of values or formula are used.
OSE (part “real mathematics”)
1. On graphics you can see
the dependence of atmospheric
pressure (in millimeters of
mercury column) from height
above sea level (in kilometers).
At what height (to km) does the
balloon fly, if the barometer in a
sphere basket shows pressure of
540 of mercury column?
55
2. The period of fluctuation of a mathematical pendulum T (in seconds)
approximately can be calculated on a formula , where l – thread length (in
meters). Using this formula, find length of a thread of a pendulum (in meters) which
period of fluctuations is 3 seconds.
USE
1. The locator of the bathyscaphe which is evenly plunging vertically down lets
out an ultrasonic signal with a frequency of 749 MHz. The receiver registers the
frequency of the signal reflected from an ocean floor. Speed of immersion of a
bathyscaphe (in m/s) and frequencies are connected by a ratio
Where c=1500m/s – sound speed in water, f0 – the frequency of a let-out signal
(in MHz). Find the frequency of the reflected signal (in MHz) if the bathyscaphe
plunges with a speed of 2 m/s.
2. In the spring the boat goes against the stream of the river in
time more
slowly, than on a current. In the summer the current becomes 1 km/h more slowly.
Therefore in the summer the boat goes against the stream in 1,5 times more slowly,
than on a current. Find current speed in the spring (in km/h)
3. Find m from equality of F=ma, if F=84, a=12.
4. The snail climbs up a tree on 3 m in a day, and goes down on 2 m in night.
Height of a tree is 10 m. For how many days the snail will rise by tree top?
Physics
You can see graphics of dependence of the
passable way from time for two bodies in picture.
At what value speed of the second body v2 is
more than a speed of the first body v1?
1) 10 m/s
2) 20 m/s
3) 25 m/s
4) 40 m/s
So, we can conclude. Nature science closely related to each other. That’s why
it is necessary to study each subject in close connection with other. So, teacher should
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built studying with interdisciplinary communication. Such studying will form a
student of natural science picture of the world.
LABORATORY WORKSHOP WITH USING OF IT-TECHNOLOGIES AS A
METHOD TO FORM SCIENCE THINKING OF STUDENTS OF
PEDAGOGICAL SPECIALTIES
Alexandra Pavlova
Moscow State Pedagogical University
Changing of modern man’s life causes permanent changes in the system of
education, including natural sciences. To see the current state of education, we looked
at the results of PISA 2012. PISA has the purpose to assess the ability of 15-year-olds
use the acquired school knowledge and experience to a wide range of vital tasks in
various spheres of human activity, communication and social relationships (estimated
readership literacy, mathematical literacy and scientific literacy).
In Russia there are some problems with scientific literacy. Pupils do not have
sufficient knowledge of science to give possible explanations in familiar situations or
make conclusions based on simple investigations. The greatest difficulties for
Russian students are analysis of experimental setups, unfamiliar actions, explaination
the phenomena presented in an unfamiliar context, comparing information from
different sources or integrating information of two or more facts. The results showed
that students have difficulties in analyzing the results of experiments with the release
of additional factors that influence the outcome of experiments. Also we can see
some difficulties with using of various technical devices and technologies[3].
These results suggest the demand of the significant changes in science
education [5].
The term "scientific literacy" is used as a final characteristics of the student. In
order to achieve this result, scientific thinking should be formed.
Scientific thinking is the integrative thinking of students, formed and
developed in the learning process of natural science picture of the world, through
which there is a reflection of the objective world in concepts, judgments and
inferences, which manifests itself in solving the problem tasks specific to the mental
activity of the scientist [1].
Scientists in pedagogic think that it is necessary to solve the problem of the
formation of scientific thinking in the future teachers of physics, biology, chemistry
and natural sciences [4].
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The formation of different types of thinking is built on the basis of mental
techniques that depend on particular types of thinking. Style of thinking is impossible
to create with algorithmic methods strictly.
If we are talking about existing studies and methodologies related to the
formation scientific thinking, such methods can be mentioned: lectures, seminars,
round tables, discussions, etc.
In our view, the development of scientific knowledge has always been the
result of attempts to explain the observed phenomena, and modeling them in the
laboratory, conducting experiments to investigate these models [2].
Thus, the idea of the experiment is an essential element and the hallmark of
scientific knowledge and scientific thinking. Observation - hypothesis - modeling experiment - a confirmation / refutation of the hypothesis - theoretical conclusions practice and further movement of the spiral - this chain of logically interrelated
cognitive components is characteristic only of scientific thinking. In our opinion good
opportunities for the formation of this type of thinking are the courses of physics,
which are based on the use of experiments.
We think it is possible to create a gradual transition from observing the
phenomenon in nature or its model to complex tasks, to finding the phenomena of the
world, similar to a laboratory situation.
An important element of the course is using IT-technologies for fixing and
calculating and presentations of results. The use of IT-technologies should be only a
support for students, not the only action.
Experience of doing such physics courses will not only contribute to the
formation of separate elements of scientific thinking of students, but also a holistic
world view of natural science. Maturity of scientific thought, philosophy, natural
science picture of the world in the future teachers will give us the opportunity to form
a complex scientific thinking in students.
References
1. Гайнулина Е.В., Старченко С.А. Становление естественнонаучного мышления
обучающихся педагогического колледжа [Электронный ресурс] // Современные проблемы
науки и образования. – 2013. – № 5. URL: www.science-education.ru/111-10573 (дата
обращения: 15.03.2015).
2. Королев М.Ю. Методическая система обучения методу моделирования студентов
естественнонаучных и математических направлений подготовки в педвузах: дис. … док. пед.
наук – М., 2012 . – 501 с.
3. Основные результаты исследования PISA-2012. [Электронный ресурс] URL:
http://www.centeroko.ru/download/PR_PISA2012.zip (дата обращения: 15.03.2015).
4. Петрова Е.Б. Профессионально направленная методическая система подготовки по
физике студентов естественнонаучных специальностей педагогических вузов : дис. … док.
пед. наук – М., 2010 . – 378 с.
58
5. Разумовский В.Г., Майер В.В., Вараксина Е.И. ФГОС и изучение физики в школе. О
научной грамотности и развитии познавательной и творческой активности школьников:
моногр. - М., СПб.: Нестор-история, 2014. - 208 с.
USING NATURAL SCENTIFIC AND HISTORICAL MATERIAL ON
THE PHYSICS LESSONS
Ekaterina Zakhodyakina
Moscow State Pedagogical University
Nature is so taken care of everything,
that you find everywhere, to learn.
Leonardo da Vinci
Interest in physics at the basic school every year decreases. Fewer and fewer
children are interested in learning physics. Most often this is due to the reduction in
hours of physics at school. For example, in 11th grade in a week just two hours of
physics, specialized classes has three hours a week. Also interest is lost due to the
fact that there is diversity in the program, and all the new skills training on the socalled drill exercises.
In connection with this problem, which is observed in 85% of secondary
schools, I believe that it is necessary to introduce the problem of natural science and
historical problems. Presenting the new material can be through
historical material.
Scientists believe that the first wheels were set in Sumeria
about 5,200 years ago. Before the invention of the wheel, weight on
land was transferred with the help of rollers and levers. With the
development of animal husbandry people have started to use pack
animals, there were wheel-less scrapers, which became the
prototype of the sledge. First extant images wheeled carts found in
Mesopotamia; they date back to the 4th millennium BC.
The ancient Egyptians left behind magnificent monuments of
architecture - the famous pyramids, the tombs of the
pharaohs. Europeans learned about these grand buildings after the
Egyptian campaign (1798-1801 gg.) Bonaparte (the future emperor of France): it was
59
then made the first device description tombs. We prove that the construction
equipment antiquity allowed building such monumental structures. Blocks of
limestone quarries and cut down on the spot, they were treated - hewing and
polished. Performed these operation brass instruments. Stone trimmed carefully so
that further blocks about each other. Masters achieved amazing results - and
millennia later, between the faces of adjacent plates can not even drag the
thread. Then the multi-ton blocks using runners-scraper and simple levers, loaded
onto barges and during flood on a specially dug channels sent to the construction
site. Dragged by a rope blocks copper hooks. The main mystery of the pyramids is
the hard work and talent of the person. In fact, the height of the pyramid of Pharaoh
Khufu (Cheops) reaches 146.59 meters; it is composed of huge stone blocks weighing
2.5 tons each.
The birthplace of glass is considered to be the rich
quartz sand Egypt, where for centuries produced glass
beads. Greeks borrowed from the Egyptians their craft,
perfected it and started making glass vases. Technique of
glass blowing through special pipes and forms appeared in
Syria in the 1st century BC and quickly spread throughout
the Roman Empire. Glass products - cups, glasses - got a lot cheaper and have
become objects of mass consumption.
Presenting new material through historical reports, interest in physics is
increasing as the teacher can show the application of physical laws and knowledge
through the story. The introduction of the material in this way allows you to expand
the horizons of the child.
In order to attract students to the physics of the problem, you can use nature
cycle.
Mushroom Veselka (phallus), common in our area, growing at a rate
of 5 mm per minute, and grows to a height of 30 cm. During which time
the fungus reaches this height?
Although plant banana (Musa) reaches a height of 10 m and has the
thickness of the trunk to 1 m, it is grass. Banana from the beginning
to the development of a ten-height grows in just 8-10
months. Banana leaves are growing at a rate of 0.1 mm per
minute. Each plant produces three harvests per year, which adds up
to 100 kg of fruit. Determine how many centimeters increases
banana leaf per night?
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