CC BY
8The Journal of Academic Social Science Studies Year: 16 - Number: 94, p. 85-90, Spring 2023
The Role of ICT in Solving Stereometric Type Geometry Questions in
11th Grades*
Ress. Asst. Shahin Aghazade ORCID ID: https://orcid.org/0000-0003-1594-9545 Elazig - TÙRKÎYE
Ress. Asst. Atilla Bingol ORCID ID: https://orcid.org/0000-0003-1594-9545 Firat University, Directorate of it Department, Elazig - TÜRKIYE
Artcile Histor
Submitted: 17.06.2022 Accepted: 27.03.2023 Published Online: 30.03.2023
Keywords
Education Living Geometric Geometric Figure Angle
Equilateral Triangle
Research Article
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DOI:
http://dx.doi.org/10.29228/lASSS.63044
Abstract
In recent years, with the Justice and Development Party coming to power, Turkey has become an active player in the global arena, so that in several international perspectives while paying regard to its Western allies, it has high degree of independence in taking and carrying out its decisions. This has resulted in an intensification of Turkey's foreign and economic policy partnerships with its neighboring countries as well as with previously overlooked regions. In this sense, Latin America and the Caribbean states have been considered as one of the key and very promising lines of Turkey's foreign policy. This study aims to scrutinize Turkey's opening policy in Latin America using the exapmle of Turkish Venezuelan partnership, which has been intensified and diversified as of 2016 after periods of recession and boom. Venezuela is one of the countries with which Turkey has established first diplomatic relations in the Latin America and the Caribbean region, Relations betwen Turkey and Venezuela which have stayed limited for many years mainly because of geographical distance, have gathered a new momentum on account of Turkey's opening policy towards the Latin America and Caribbean as well as mutual high-level visits in recent years. This intercontinental cooperation was reflected in the increasing of trade and economic relations, along with the deepening of diplomatic ties. In the study, the main emphasis is placed on the underlying key elements of this partnership between Turkey and Venezuela. The study reveals that the sudden partnership between Turkey and Venezuela is formed on the basis of struggling against common external challenges. The two states are both under sanctions and pressure by the United States even with a differentiating levels of severity; both economies are facing crisis moments. In this respect, these factors make contribution to the enhancement of economic relations between them on the basis of mutual advantage. The study concludes that the two states has made both material gains and received ideological support as a result of the flourishing relations in recent years.
Reference Information / Atif Bilgisi
Aghazade, S. & Bingol, A. H. (2023). The Role of ICT in Solving Stereometric Type Geometry Questions in 11th Grades. Jass Studies-The Journal of Academic Social Science Studies, 16(94), 85-90.
The Journal of Academic Social Science Studies Yil: 16 - Sayi: 94 , s. 85-90, Bahar 2023
11. Siniflarda Stereometrik Tip Geometri Sorulanmn Qozulmesinde BiT'in Rolu*
Shahin Aghazade Elazig - TURKiYE
Ar§. Gor. Atilla Bingol Firat Universitesi, Bilgi i§lem Daire Bagkanligi, Elazig - TURKiYE
Makale Geomigi | | Oz
Geli§: 17.06.2022 Kabul: 27.03.2023 On-line Yayin: 30.03.2023
Anahtar Kelimeler
Egitim Canli Geometri Geometrik Figur Agi
E§kenar Uggen
Ara§tirma Makalesi
* Bu makale, intihal.net tarafindan taranmi§tir. Bu makale, Creative Commons lisansi altindadir. Bu makale igin etik kurul onayi gerekmemektedir.
Geometride uzay geometri egitimi uzun yillardir en onemli problemlerden biri olmu§tur. Uzay-zamani bukulebilen bir kuma§la kar§ila§tiran Einstein, fikrini kanitlamak igin kavisli yuzeylerin geometrisini incelemesi gerektigini fark etti. Bu geli§me, uzay geometrisinden gegmenin mutlakligini koruyan ve geli§en teknoloji temelli egitimi ogrencilere daha iyi ogretmek igin geometri ve teknolojiyi birle§tirmeyi amaglayan tek tarafli bir geli§me olmu§tur. Gunumuzde teknoloji tabanli egitimin yaygmla§masi ile birlikte uzay geometri kavrami degi§ime ugrami§ ve dinamik geometrinin temel bir bolumu olarak "canli geometri" §eklinde kullanilmaya ba§lami§tir. Bu yonuyle degerlendirildiginde canli geometri kavraminin Orta Asya ulkelerinde yaygin olarak kullanilmasina kar§in Azerbaycan egitim programlarinda kullanilmamasi bu alandaki eksikligi ortaya gikarmaktadir. Egitim ile ilgili bilimsel gali§malarm gogunda deneysel metotlar kullanilsa da, bu gali§ma bir soru-cevap gali§masi olmayip diger programlardan farkli olarak geometri ve teknolojiyi birle§tirmeyi amaglamaktadir. Bu amag dogrultusunda; ^alijmada bilginin oz kontrolu, daha etkile§imli geometri gali§malarmda arti§, dinamik geometri kullanimi, stereometrik problemlerin gozumu, uzaklik, agilarin degerlendirilmesi ve matematigin teorik ve egitsel suregleri ele alinmaktadir. Ayrica ogrencilerin problem gozme yontemlerinin analizi, bir arag olarak otokontrol yonetimi ve Canli Geometri hesaplama problemlerinin canli geometriden stereometrik uygulanarak yonetimi verilmektedir. Bu galijmada verilen bu bilgilerin pedagojik onemi vardir ve onumuzdeki yillarda Azerbaycan okullarinda uygulanmasi beklenmektedir. Zira bugune kadar Azerbaycan okullarinda canli geometri terimi okutulmami§ ve bu konuda herhangi bir terim gali§ilmami§tir.
DOI:
http://dx.doi.org/10.29228/JASSS.63044
Shahin Aghazade & Atilla Bingol
INTRODUCTION
What opportunities does a student have to check the answer he found while the self-solving of a math problem? The student is well aware that if it is required to find the roots of an algebraic equation, results must be substituted into this equation and check whether the left side of the equation coincides with the right side or not. A mismatch means errors in either calculations or in the used formula. Since most of the problems of elementary geometry are taken from practice and are of an empirical nature, the reliability of the result of certain calculations with a high degree of probability can be checked empirically, using a specially constructed geometric configuration that simulates the solution of the problem. First of all, this applies to planimetric problems of a metric nature, since the drawing accompanying the solution of such a problem, if necessary, can be performed so that the graphic images of these segments and angles will be close to those values that are specified by the condition of the problem. In this respect, the value of the object (part, angle, etc.) desired to be installed on such a drawing will be closer to the truth, especially if the drawing is made using information technologies rather than by hand (Leung, 2008).
Method
Unfortunately, while solving metric problems in Euclidean space, the self-control technique practically does not work. Due to the fact that when stereometric figures are depicted on the plane, the distances between points and the angles, generally speaking, are not preserved. The solutions of such problems are sometimes accompanied by the construction of a solid model of the investigated geometric configuration that satisfies all requirements listed in the problem statement. To check the solution, the real value of the desired quantity is found on this model, then it is compared with the one obtained as a result of theoretical reasoning. This type checking technique of the solution is occasionally used by teachers for solving one or two simple problems, and this is done rather to demonstrate the importance of geometric modeling as such. When solving a large number of stereometric problems, its usage as a means of self-control is irrational.
You can get around the difficulties that arise if you take advantage of the constructive, dynamic and computational capabilities of one of the interactive geometric environments, for example, "Live Geometry". Let us substantiate this thesis.
Results and Discussion
As you know, to solve a stereometric problem for calculating the desired value and assessing the result, it is recommended to perform the following steps:
- to build a correct and sufficiently visual image of the geometric configuration, which is specified by the condition of the problem; isolate from the constructed configuration those objects that are involved in calculating the desired value; if these objects are obscured by other elements of the drawing - change the angle of the image;
- to construct auxiliary figures, which, together with the previously found objects, allow expressing the value of the required quantity through these quantities, calculating the value of the required quantity;
- to exercise self-control, evaluating the result obtained from the point of view of its reliability.
The use of the computer environment "Living Geometry" in teaching of the solution of these
tasks, which are quite important in the geometric preparation of schoolchildren, makes it possible to effectively perform each of the above actions.
Indeed, the image of the geometric configuration under study on the working field of the "Live Geometry" allows you to avoid many manual construction errors. For example, exclude the drawing of perpendicular lines that are not such and others. All electronic constructions are performed quickly and accurately.
The Role of ICT in Solving Stereometric Type Geometry Questions in 11th Grades
When you isolate the desired objects on the constructed image, it often becomes clear that the configuration under study should be depicted somewhat differently for greater clarity. The "live" drawing allows you to position the shape in a few seconds with the mouse so that the elements necessary for solving the problem are presented with the maximum degree of clarity.
The "Live Geometry" environment makes it possible to quickly include the desired object in a particular auxiliary shape, color it, making this fragment of the drawing more vivid and visual. If it turns out that the choice is made poorly, you can easily switch to other auxiliary shapes without reducing the image quality.
And finally, one of the most tangible advantages is that the Live Geometry environment provides additional features related to evaluating the result. Using the graphical and computational options of computer environment, you can either make sure that the solution to the problem is most likely corrector establish that the solution is wrong.
The most common metric problems in stereometry are finding the values of angles and distances. To find the value of the angle between two straight lines, Gahramanova, Karimov and Huseynov (2007) in the textbook recommend "to build a triangle on the image of a given figure, one of the angles of which is equal to the desired angle, find all the sides of this triangle and then use the cosine theorem". The use of information technologies in solving such problems is described in the manual (Tooke and Henderson, 2001).
We illustrate the use of the "Living Geometry" environment as a means of computer self-control in solving the following problem of stereometry (Serin, 2017).
Task. Two vertices of some face of the cube are fixed, not at the same time. belonging to one ref. Find the cosine of the angle between the planes, one of which contains the midpoints of the three edges of the cube coming from one fixed vertex, the second — the midpoints of the three edges of the cube coming from another fixed vertex.
Conclusion
Using the "Live Geometry" environment, we will build a" live " cube ABCDEFGH on its working field (Fig. 1), the length of its edge is denoted by "a". The planes referred in the problem condition are represented by sections of the cube-triangles MKN and PQL. Since the line of intersection of these planes is quite far outside the cube, consider the ACCA and Serb planes parallel to the data and intersecting in a straight line CE. It is clear that the angle between these planes is equal to the desired one.
Let us find the linear angle of the dihedral angle formed by the planes ACE and CFH. We draw in the first plane the perpendicular AT to the straight line CF, in the second plane the perpendicular HT, where T is the middle of CE It is clear that ¿.ATH is the desired linear angle.
Find all the points of the icosceles triangle
88
.-.-" = . : = .-.-=..-.::-;-:= - ^ = - I, where a is the length of the edge of the
cube.
G
N
B
F
H
a
D
Figure 1: 3D view of the cube figure
Using the cosine theorem for the triangle ATN, we obtain the desired value of comp 1/3.
Computer self-control.
In order to estimate the probability that the found solution is correct, let's take advantage of the design and computational capabilities of the "Living Geometry" environment.
To do this:
Build an arbitrary segment a, on this segment, as on the side, we build a square ABCD — one of the faces of the cube (Fig. 2).
"Lay" the triangle AFC in the plane of the drawing, turning it around the straight line AC to 89 align the plane of the triangle with the plane of the face. Since the sides of the triangle are diagonals of equal faces of the cube, it is enough to use virtual compasses and a ruler to build an equilateral triangle on the segment AC as on the side.
base AN = AC and equal sides AT and HT. Using the "Angle" command in the "Measurements" command menu, we find the value of the ATN angle and display it on the working field (in Fig.2 ), then use a graphical calculator to calculate the cosine of the angle (P. Note that this value (0.333... ) coincides with the value found above 1/3.
F
a
A
a
D
A
a
¡72
H
Figure 2: Other Angles of the 2D View of the 3D View of the Cube Figure
The Role of ICT in Solving Stereometric Type Geometry Questions in 11th Grades
By changing the size of the segment AD with the mouse, we notice that the value of the angle ATH remains constant. All this allows us to assume with a high degree of probability that the solution found is the right one.
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Sorumlu Yazar: Atilla Bingol
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REFERENCES
Qahramanova, N., Karimov, M. & Huseynov, M. (2007). Umumtahsil Maktablarinin 10-cu Sinifi Ugun
Riyaziyyat Fanni Uzra Darsliyin Metodik Vasaiti. Baku: Radius Nagriyyati. Tooke, J. & Henderson, N. (2001). Using Information Technology in Mathematics Education -1st Edt., ISBN
9780789013767 Published October 11, 2001. Florida: CRC Press. Serin, H. (2017). The Effects of Interactive Whiteboard on Teaching Geometry. International Journal of
Social Sciences & Educational Studies, 4(3), 216-219. Leung, A. (2008). Dragging in a Dynamic Geometry Environment Through the Lens of Variation. International Journal of Computers for Mathematical Learning, 0(13), 135-157.
