=Paper=
{{Paper
|id=None
|storemode=property
|title=The Teaching of Geography Using Dynamic Geometry Software
|pdfUrl=https://ceur-ws.org/Vol-920/p11-herceg.pdf
|volume=Vol-920
|dblpUrl=https://dblp.org/rec/conf/bci/HercegHR12
}}
==The Teaching of Geography Using Dynamic Geometry Software==
https://ceur-ws.org/Vol-920/p11-herceg.pdf
The Teaching of Geography Using Dynamic Geometry
Software
Đorđe Herceg Vera Herceg-Mandić Davorka Radaković
Dep. of Mathematics and Informatics "Jovan Jovanović Zmaj" Mid. Sch. Dep. of Mathematics and Informatics
Faculty of Sciences Novi Sad Faculty of Sciences
University of Novi Sad, Serbia Serbia University of Novi Sad, Serbia
+381 21 485-2861 +381 21 529-185 +381 21 485-2872
herceg@dmi.uns.ac.rs vera.herceg.mandic@gmail.com davorkar@dmi.uns.ac.rs
ABSTRACT we encountered is the need to convert between the geometric
The use of dynamic geometry software (DGS) in all kinds of coordinate system in GeoGebra and the geographical coordinate
mathematical games has become a widespread phenomenon. Rich system used in maps. Although conversion formulas can be
features and availability of free DGS, such as GeoGebra, have implemented in GeoGebra, this may not always be practical.
caused a growing interest for developing teaching materials for Another problem is importing geographic maps into GeoGebra in
subjects other than matematics. We present the teaching materials either vector or bitmap format. Those tasks can be performed, but
that we developed in GeoGebra for the subject of geography at usually at the cost of creating many auxiliary objects which
elementary and middle school level. An interactive component burden the drawing. Furthermore, they can be tedious or simply
that we developed, aimed specifically at applications in computer too complicated for the users.
geography, is also discussed. We developed a specialized interactive compoment, called
GeoMap, for the SLGeometry DGS ([1], [2], [3], [4]) to address
this problem. The GeoMap component is able to display a
Categories and Subject Descriptors selected portion of the world map, place custom markers on the
D.2.2 [Software Engineering]: Design Tools and Techniques – map and handle input from users. It comes pre-loaded with map
Object-oriented design methods, User interfaces; I.3.2 [Comp- data, and it is easy to use.
uter graphics]: Graphics Systems – Stand-alone systems We conducted an experiment in the "Jovan Jovanović Zmaj"
middle school in Novi Sad. The purpose of the experiment was to
General Terms measure the efficiency of the teaching of geography supported by
Design, Experimentation, Human Factors interactive materials that we developed.
Keywords In Section 2 coordinate system transformations are explained.
Dynamic geometry software, GeoGebra, geography games Two interactive drawings, created in GeoGebra, which implement
an exercise in measuring the length of a river and the "Point at
1. INTRODUCTION cities" game, are presented in Section 3. Section 4 covers the
Mathematics can be found in almost any subject taught in school. implementation. Section 5 describes the GeoMap component,
In geography, there are many examples in which mathematics is which we developed. In Section 6 we give an overview of related
used, either explicitly or in a less prominent way. For instance, we work. A short description of the experiment that is being
may need to measure the distance between two points by conducted in the "Jovan Jovanović Zmaj" middle school is given
following a polygonal line, such as a river or a road. Another good in Section 7. Conclusions are given in Section 8.
example is using a compass to find the correct bearing in order to
get from one place to another. Reading maps and determining
2. COORDINATE TRANSFORMATIONS
Every DGS has to maintain at least two coordinate systems: the
locations of various points (e.g. cities) is yet another example.
screen coordinate system (measured in pixels) and the geometric
Geographic maps can be represented as collections of polygons,
coordinate system, which is usually the common Cartesian
polygonal lines and points, therefore dynamic geometry software
coordinate system of the drawing. When a user is working with a
(DGS) can be used to create interactive maps.
DGS, transformations between the two coordinate systems are
Such maps can be used for testing or as teaching and self-study constantly performed.
materials. Our aim was to develop a set of teaching and testing
The most commonly used transformation is a combination of
materials which would help the pupils learn more efficiently.
linear planar transformations such as scaling and translation. That
Thanks to its ability to import bitmap images, measure angles and way a rectangular part of the Cartesian plane can be shown in a
draw polygonal lines, GeoGebra is a well-suited tool for rectangular window on the screen. In order to convert mouse
development of interactive teaching materials for geography. position in pixels back to coordinates in the Cartesian plane,
However, in more complex scenarios, GeoGebra has some inverse transformations must be employed.
limitations which can not be easily overcome. The main problem
If a geographic map is to be displayed as a geometric drawing, an
additional set of transformations may be used in order to convert
BCI’12, September 16–20, 2012, Novi Sad, Serbia. geographic coordinates to coordinates in the Cartesian plane (see
Copyright © 2012 by the paper’s authors. Copying permitted only for private and Figure 1).
academic purposes. This volume is published and copyrighted by its editors.
Local Proceedings also appeared in ISBN 978-86-7031-200-5, Faculty of Sciences,
University of Novi Sad.
11
Figure 1: Mapping the geographic coordinate system to the computer screen.
Although the linear transformations which are used here are a
relatively simple concept, they can nevertheless be difficult to
program in a DGS environment. Every point, line and polygon
coordinate needs to be wrapped in a conversion function, that
leads to cluttered definitions which are difficult to read and
manipulate.
3. EXERCISES IN GEOGEBRA
We present two exercises, created with GeoGebra, which are
based on geographic maps. The first example teaches how to
determine the scale of a map and to measure non-linear distances,
e.g. along roads and rivers. A bitmap image of a map was used in
this example.
The second example is a game in which students are required to
guess locations of cities on a map. It is designed to be played by
two players and it has a simple scoring system. The map used in
this example is a polygon in which the coordinates of the vertices
are expressed as longitude/latitude pairs. Figure 2: Measuring the length of the Tisa river on a map.
From the implementation point of view, the second example is
more complex, as it requires the author to first obtain a suitable Maps must be carefully chosen, especially at higher latitudes, as
definition of a map in vector format, extract the needed data from to avoid distortions due to the cylindrical projection, which could
it, create a list of points in a DGS and apply transformations to affect the accuracy of this method.
each point in order to have the map displayed as a polygon on the 3.2 The "Point at Cities" Game
screen. The "Point at cities" game helps pupils learn where the cities in
3.1 Measuring Lengths of Roads and Rivers their home country, and other countries, are. Our GeoGebra
construction implements one variation of the "Point at cities"
Measuring distances along roads and rivers on geographical maps game, designed for two players (see Figure 3).
is one of the exercises which can be too complicated for pupils to
perform by conventional means. In GeoGebra, however, this is The first player needs to place blue dots, representing cities and
easily accomplished by tracing a road or a river with a polygonal towns, on appropriate places on the map. The second player needs
line on a bitmap picture. Figure 2 shows such a polygonal line to do the same with red dots. Players earn points by placing dots
along the Tisa river on a map of Serbia. closer to the correct locations than their opponent. When all the
dots are placed, GeoGebra calculates the score and displays the
The length of the polygonal line is 4.78 units in the drawing. In correct locations.
order to determine the length of the river in kilometers, the scale
of the map needs to be determined. By measuring in Google Scoring was implemented by comparing the distances between the
Earth, we determine that the linear distance between towns of correct locations and the dots placed by players.
Subotica and Sombor is approximately 55km. From there we 4. IMPLEMENTATION DETAILS
calculate the scale of the map by dividing the distance in At each step of the implementation, we encountered several
kilometers with the length of the line segment between Sombor problems, which, in our view, would pose significant difficulty to
and Subotica in the drawing. The scale is determined to be geography teachers who wish to develop their own teaching
55 / 1.67 = 32.86 kilometers per unit. Using these values we can materials in GeoGebra. Each step of the implementation requires
calculate the length of Tisa in Serbia as 4.78 * 32.86 ≈ 157 programming skills, mathematical skills and time, that geography
kilometers. teachers may not have.
12
Figure 3: The "Point at cities" game for two players.
4.1 Obtaining Map Data be a large empty space between them if the original coordinates
In order to draw a country map, geographic coordinates of the were used. In such cases, at least one country's coordinates must
country's borders must be obtained. These data can be be translated, and possibly also scaled by using linear transforms.
downloaded from the Internet, for example, in the ESRI Shapefile In practice, this means that a suitable linear transform must be
format ([14], [15], [16]), or as a list of polygon definitions, using found, and the definitions of each point, line and polygon must be
the CountryData function in Mathematica [17]. In the case of wrapped in the conversion function. This leads to cumbersome
shapefiles, an external program ([18]) must be used to extract expressions in GeoGebra, increases the complexity of drawings
polygon definitions. Extracting data from Mathematica is simpler, and makes subsequent changes difficult (see Figure 4).
thanks to the built-in Export function, but still requires technical 4.4 Placing Additional Shapes on Maps
knowledge. Cities, rivers and text labels are drawn on maps as circles,
4.2 Drawing Maps in GeoGebra polylines and text objects respectively. Their coordinates must be
GeoGebra has the Polygon keyword, which draws a closed transformed by the same transforms which were applied to the
polygon defined by a list of vertices. For countries which consist map itself. These additional shapes also appear as independent
of one continuous territory, maps are easily drawn by executing objects in drawings.
the Polygon((x1, y1), (x2, y2), ..., (xn, yn)) command. A single
named polygon is then generated in GeoGebra's list of objects. If a
country consists of several disjointed territories, a separate
polygon must be drawn for each territory, producing several
unrelated named objects. Geographic coordinates belong to the
interval [-180, 180] × [-90, 90]. As GeoGebra can easily draw
polygons defined by vertices from this interval, coordinate
conversion may not be necessary in this step. However, the
resulting maps will be shown in cylindrical projection only. If a
different projection is needed, coordinate conversion must be
performed for each polygon. This conversion may be simple, but
also very complex, depending on the projection type.
4.3 Scaling and Translating Maps
If only a single map needs to be shown in a drawing, then the
view can be adjusted so that the map, defined by geographic
coordinates, is shown accross the entire screen. However, if two
or more country maps need to be placed next to each other, then
their geographic coordinates are not suitable. For example, if
France and Japan need to be shown side-by-side, then there would Figure 4: Partial list of the many objects contained in
the "Point at cities" drawing.
13
Figure 5: Two instances of the GeoMap component in SLGeometry.
5. THE GEOMAP INTERACTIVE example, measure distances between the marker and some
predefined locations, such as cities.
COMPONENT
We decided to take the concept of geographic maps in DGS one 6. THE EXPERIMENT
step further. Our goal was to have several interactive maps We conducted an experiment with the pupils of the "Jovan
displayed on screen at the same time, with each map able to Jovanović Zmaj" middle school in Novi Sad, Serbia. The purpose
display a different part of the world and handle user input. Also of the experiment was to measure the efficiency of the teaching of
we wanted to hide the complexities of implementing geographic geography supported by interactive materials that we developed.
maps, covered in Section 4, from the final user. We developed an
During the first phase of the experiment, the pupils were taught
interactive component, called GeoMap, for the SLGeometry DGS.
about map scales. The first lecture was presented in the "classical"
The component is displayed as a rectangular area, inside of which
way. In the second lecture, an example in GeoGebra was
a part of the world map is shown.
presented. The pupils were taught how to import a bitmap image
The GeoMap component has the following features: of a map into GeoGebra and how to determine the scale of the
• Displays a rectangular region of the map, specified by map relative to the coordinate system of GeoGebra. Afterwards,
geographic coordinates, inside an rectangular area on they were shown how to trace a river with a polygonal line, and,
the screen; finally, how to calculate the real length of the river by using the
previously obtained scale of the map. The whole process was
• Has a library of predefined geographic maps in vector demonstrated in class, and lecture notes were published on a web
format; site [6]. Similar exercises were assigned as optional homework
• User can select which countries are to be shown; and a deadline of one week was given.
• Can import and display custom maps; The pupils' response to the lecture was overly positive. Also,
almost all pupils handed in their homework. However,
• Can render points, lines, polygonal lines, polygons, preliminary results show that only about 16% of the pupils were
arrays of points, strings; able to complete the assignment successfully, while another 40%
• Supports a movable marker that can be placed on the completed it partially.
map, either by mouse or programatically; In the second phase of the experiment, we organized a
• Has a number of properties which affect visual competition between the pupils in class, based on the "point at
appearance and behavior, that can be accessed cities" game. As a result, the pupils were highly motivated to learn
programatically. the locations of the cities.
The GeoMap component hides the complexities of its inner After the classes, the pupils were polled for opinions (Table 1).
workings (coordinate conversion etc.) from the user, and enables Table 1: Poll Results
easy creation of teaching materials based on interactive
geographic maps. Maps are placed on the screen (see Figure 5) by Question Yes No
executing the following commands in SLGeometry: Did you like these classes? 53 4
a = GeoMap("Australia") Were the classes like you imagined? 35 22
b = GeoMap("Canada") Was your task difficult? 9 46
The position of the marker is exposed through the Was your task too complicated? 12 43
GeoMap.Marker property. The property is of the Point data type
and it is updated dynamically as the user moves the marker on the Was the teacher helpful? 54 2
map. It can be used in various expressions in order to, for Should the teacher help less? 3 51
14
7. RELATED WORK [4] D. Radaković, Đ. Herceg: The Use of WPF for Development
There exist a multitude of frameworks for rendering geographic of Interactive Geometry Software, Acta Univ. M. Belii ser
maps and spatial data, such as SharpMap [7]. They support Mathematics 16 (2010), pp. 65-79
coordinate system transformations and loading of geographic data [5] Geometrijica – a Silverlight geometry framework:
in various formats, such as ESRI Shapefiles [8]. The list of http://sites.dmi.rs/personal/hercegdj/geometrijica/
features provided by SharpMap includes:
[6] Merenje dužine reke na geografskoj karti pomoću GeoGebre
• Easy-to-use mapping library for use in web and desktop http://djordjeherceg.wordpress.com/2012/02/27/merenje-
applications; duzine-reke-na-geografskoj-karti-pomocu-geogebre/
• Access to many types of GIS data; [7] SharpMap – Geospatial Application Framework for the CLR
http://sharpmap.codeplex.com/, Accessed March 2012
• Spatial querying;
[8] ESRI Shapefile Technical Description, An ESRI White
• Map rendering; Paper—July 1998
• Built-in coordinate transformation functions; http://www.esri.com/library/whitepapers/pdfs/shapefile.pdf,
Accessed March 2012
• Creating clickable maps;
[9] Canadian Council for Geographic Education: The importance
• Support for layers: WMS layer, ShapeFile layer,
of geography in the school curriculum
PostGIS layer, Label layer;
http://www.ccge.org/programs/geoliteracy/docs/importance_
• Rendering X and Y columns from a database as points. in_curriculum.pdf, Accessed March 2012
Also, there are many web sites which incorporate Flash or Java [10] Sheppard Software's geography games
applets with interactive geographic maps. Most of these web sites http://www.sheppardsoftware.com/Geography.htm, Accessed
are designed as learning games ([10], [11], [12], [13]). March 2012
8. CONCLUSIONS [11] Geography Games For Kids
Contemporary methods of the teaching geography rely on http://www.kidsgeo.com/geography-games/, Accessed March
interactive electronic teaching materials, that can be developed in 2012
dynamic geometry software (DGS). Although the majority of [12] Digital Dialects - Geography Games
DGS present today were not developed primarily for geography, http://www.digitaldialects.com/geography_games.htm,
they can be and are used by teachers in schools. Accessed March 2012
This paper demonstrates one use of GeoGebra for developing [13] GEOGRAPHY-MAP-GAMES.COM
exercises based on interactive maps. There are some problems http://www.geography-map-games.com/, Accessed March
which stem from the fact that GeoGebra was not designed for 2012
such applications. An interactive visual component, developed for
[14] GADM database of Global Administrative Areas,
the SLGeometry DGS, which enables easy handling of multiple
http://www.gadm.org/, Accessed March 2012
geographic maps and simplifies the task of coordinate conversion
is also presented. An experiment to assess the efficiency of [15] World map for APRS,
computer aided teaching using our exercises and software was http://aprsworld.net/gisdata/world/, Accessed March 2012
conducted. Poll results show that the pupils show more interest in [16] Centro Internacional De La Papa Data Server,
learning geography when interactive learning materials are used. https://research.cip.cgiar.org/gis/index.php, Accessed April
Further information on SLGeometry can be found at [5]. 2012
[17] Wolfram Mathematica 8,
9. REFERENCES http://www.wolfram.com/mathematica/, Accessed March
[1] Silverlight, 2012
http://www.silverlight.net/, Accessed March 2012
[18] WPF Application for Importing ESRI Shapefiles,
[2] Đ. Herceg, D. Radaković: The Extensibility of an Interpreted http://www.c-
Language Using Plugin Libraries, Numerical Analysis and sharpcorner.com/uploadfile/nschan/shapefile0225200713483
Applied Mathematics ICNAAM 2011, AIP Conf. Proc. 1389, 4pm/shapefile.aspx, Accessed October 2011
(2011) pp. 837-840
[3] D. Radaković, Đ. Herceg, M. Löberbauer: Extensible
expression evaluator for the dynamic geometry software
Geometrijica, PRIM 2009, Novi Sad (2010), pp. 95-100
15