Heather Lynn Johnson
email: heather.johnson@ucdenver.edu

Evan Mcclintock
email: evan.mcclintock@ucdenver.edu

Amber Gardner
email: amber.gardner@ucdenver.edu

Leveraging difference to promote students' conceptions of graphs as representing relationships between quantities

Keywords: Graphs, Computer Simulation, Instructional Design, Learning Theories, Secondary school mathematics

By creating different Cartesian graphs to represent the same relationship between quantities, students can expand their conceptions of what graphs represent. Interweaving Marton's variation theory and Thompson's theory of quantitative reasoning, we designed digital task sequences to promote students' conceptions of graphs as representing relationships between quantities. In the tasks, which link animations and dynamic graphs, students created different graphs to represent the same relationship between quantities. We report results of a qualitative study (n=13) investigating secondary students' interactions with the digital tasks in an individual interview setting. We found that the digital tasks were viable for promoting students' creation of graphs to represent relationships between quantities. Our findings have implications for task design. Namely, students should have opportunities to create different graphs to represent the same relationship between quantities.

The term representation can have many meanings (e.g., [START_REF] Kaput | Representations, inscriptions, descriptions and learning: A kaleidoscope of windows[END_REF]. We use representation as both a noun and a verb. Employing the term representation as a noun, a student can conceive of a graph as a representation of a relationship between quantities. Employing the term representation as a verb, a student can engage in representation by creating a Cartesian graph to represent a relationship between quantities. Interweaving Thompson's theory of quantitative reasoning [START_REF] Thompson | Quantitative reasoning, complexity, and additive structures[END_REF][START_REF] Thompson | Didactic objects and didactic models in radical constructivism[END_REF]) and Marton's variation theory [START_REF] Kullberg | What is made possible to learn when using the variation theory of learning in teaching mathematics?[END_REF][START_REF] Marton | Necessary conditions of learning[END_REF], we designed digital task sequences linking dynamic animations and graphs to engender secondary students' creation of Cartesian graphs to represent relationships between quantities. In this study, using individual clinical interviews, we investigated what secondary students (n=13) intended to represent when interacting with digital tasks linking Cartesian graphs and dynamic animations.

Theoretical and conceptual framing

Representation and intention

We distinguish a representation from an inscription, the latter of which refers to some observable artefact (e.g., [START_REF] Kaput | Representations, inscriptions, descriptions and learning: A kaleidoscope of windows[END_REF]. From our perspective, an inscription can only be a representation if that inscription represents something for an individual or group. When we claim that a student is "representing," we interpret that the student did something more than just creating some observable artefact (e.g., a graph). We mean that the student intended to represent some "thing" with that graph, and that we have evidence to support our claim.

We aim to study what students intend to represent when working on digital tasks linking Cartesian graphs and dynamic animations. In any task setting, there are tensions between the intentions of the task designers/researchers and the intentions of the students engaging with the tasks [START_REF] Johnson | Mathematical tasks and the student: navigating "tensions of intentions" between designers, teachers, and students[END_REF]. Theoretically, we acknowledge that we cannot know the intentions of others. We can only infer those intentions based on observable evidence. Furthermore, we do not assume that students will share a stated task aim with that of the designer/researcher. For example, we intended to provide students multiple opportunities to create different Cartesian graphs to represent the same relationship between quantities, and we did not assume that students interacting with the tasks would share our intentions.

Interweaving Marton's variation theory and Thompson's theory of quantitative reasoning

To frame our study, we interweave two theories: Thompson's theory of quantitative reasoning [START_REF] Thompson | Quantitative reasoning, complexity, and additive structures[END_REF][START_REF] Thompson | Didactic objects and didactic models in radical constructivism[END_REF]) and Marton's variation theory [START_REF] Kullberg | What is made possible to learn when using the variation theory of learning in teaching mathematics?[END_REF][START_REF] Marton | Necessary conditions of learning[END_REF]. In his theory of quantitative reasoning, Thompson explains students' mathematical thinking in terms of students' conceptions of attributes. [START_REF] Thompson | Quantitative reasoning, complexity, and additive structures[END_REF] posited that quantities were something different from units of measure. Rather, quantities depend on students' conceptions. If a student can conceive of the possibility of measuring some attribute, then that attribute is a quantity for the student. For example, a student may view an animation of a "Cannon Man," who is shot vertically into the air, then comes back down to the ground. In this situation, there are many different attributes. Cannon Man's total distance traveled-both up and down-would be a quantity for that student only if she can conceive of the possibility of measuring Cannon Man's total distance. Difference, rather than sameness, forms the essence of variation theory (e.g., [START_REF] Kullberg | What is made possible to learn when using the variation theory of learning in teaching mathematics?[END_REF][START_REF] Marton | Necessary conditions of learning[END_REF]. With variation theory, Marton and colleagues explain how designers can develop instructional sequences to promote students' discernment of critical aspects of objects of learning. Kullberg et al. (2017, p. 560) link discernment and variation, core components of variation theory, positing "Discernment cannot happen without the learner having experienced variation." Furthermore, the type of variation matters. If a designer intends for students to discern critical aspects of an object of learning, students should have opportunities to experience variation (difference) in those critical aspects [START_REF] Marton | Necessary conditions of learning[END_REF].

In designing our study, we intended to provide opportunities for students to conceive of a graph as representing a relationship between quantities. Drawing on Marton's variation theory, we argue that students' conceptions of what is possible for Cartesian graphs to represent is inseparable from their experiences with different Cartesian graphs. Drawing on Thompson's theory of quantitative reasoning, we argue that designers' choices of attributes can impact students' opportunities to conceive of Cartesian graphs as representing relationships between quantities.

Students' conceptions of what Cartesian graphs can represent

It is useful for students to have opportunities to conceive of graphs as representing relationships between quantities (e.g., [START_REF] Bell | The interpretation of graphs representing situations[END_REF]Johnson & McClintock, 2018;[START_REF] Kerslake | The Understanding of Graphs[END_REF][START_REF] Leinhardt | Functions, Graphs, and Graphing: Tasks, Learning, and Teaching[END_REF][START_REF] Moore | Breaking conventions to support quantitative reasoning[END_REF][START_REF] Thompson | Didactic objects and didactic models in radical constructivism[END_REF]. Yet, researchers have documented secondary students' challenges with creating and interpreting Cartesian graphs [START_REF] Bell | The interpretation of graphs representing situations[END_REF]Johnson & McClintock, 2018;[START_REF] Kerslake | The Understanding of Graphs[END_REF][START_REF] Leinhardt | Functions, Graphs, and Graphing: Tasks, Learning, and Teaching[END_REF]. We identify three key challenges. First, students may interpret graphs as needing to share characteristics with a physical object, such as a hill [START_REF] Bell | The interpretation of graphs representing situations[END_REF][START_REF] Leinhardt | Functions, Graphs, and Graphing: Tasks, Learning, and Teaching[END_REF]. Second, students may interpret graphs as sharing physical characteristics with the physical path of an object, such as a person's walk from one location to another [START_REF] Bell | The interpretation of graphs representing situations[END_REF][START_REF] Kerslake | The Understanding of Graphs[END_REF]. Third, students may interpret graphs as representing a single varying quantity, rather than as a relationship between quantities (Johnson & McClintock, 2018).

To engender opportunities for students to interpret graphs as relationships between quantities, designers can incorporate variation in individual attributes within a single graph and variation across different graphs incorporating the same attributes. [START_REF] Thompson | Didactic objects and didactic models in radical constructivism[END_REF] argued that students could use their fingers as tools, sliding them along each axis of a graph, to represent change in individual attributes. In a study investigating prospective secondary teachers' reasoning, [START_REF] Moore | Breaking conventions to support quantitative reasoning[END_REF] incorporated different graphs representing the same attributes on different axes. When making choices about the kinds of variation to incorporate within and across our digital task sequences, we drew inspiration from the work of Thompson and Moore.

The digital task sequences

We report on two digital task sequences: The Cannon Man and the Toy Car. In each digital task sequence, students engaged in five main tasks, shown in Table 1. We drew on Thompson's theory of quantitative reasoning and Marton's variation theory to design and sequence the tasks in each situation. First, students had opportunities to discern and conceive of measuring attributes (Tasks V, A1). Second, students had opportunities to represent change in individual attributes (Task A2). Third, students had opportunities to represent attributes changing together (Task G1). In Task G2, we introduced a difference, against a background of invariance-a different Cartesian graph, with the same attributes represented on different axes. Across the digital task sequences, the Cannon Man and Toy Car situations served as different backgrounds.

Task Description

Methods

Setting/participants

We implemented the digital task sequences with 13 high school students in a high performing suburban high school in the metropolitan area of a large US city. Five students were in ninth grade (~15 years), and currently enrolled in an Algebra I course. Eight students were in eleventh grade (~17 years), and currently enrolled in an Algebra II course. At the school, 52% of students identified as students of color, and 36% of students qualified for free or reduced lunch (an indicator of low socioeconomic status).

We conducted the study over a 4 week time period near the end of the school year. Students volunteered to participate in the study. Johnson conducted a series of three clinical interviews with individual students (39 interviews). Interviews occurred once or twice per week, with at least one day between interviews. Students who participated in all three interviews received a graphing calculator, which they could use for exams and classwork at their school. We conjecture that students who participated in the study were motivated, in part, by the opportunity to receive a graphing calculator.

Research methods: Clinical interviews, exploratory teaching

During the clinical interviews, Johnson engaged in exploratory teaching [START_REF] Steffe | Teaching experiment methodology: Underlying principles and essential elements[END_REF] to investigate the viability of the digital tasks for promoting students' conceptions of graphs as representing relationships between quantities. In the interview design, Johnson included questions to gather evidence of what students were intending to represent when sketching a graph. These questions included: "What you are trying to graph?"; "Can (How does) your graph show both __ and __ (the task attributes)?"; "Look at a point on your graph, can (how does) this point give you information about __ and __ (the task attributes)?"

The first interview, which served as a preassessment, involved a Ferris wheel situation. In the Ferris wheel situation, students engaged in tasks V, A1, and G1 in the digital task sequence (See Table 1).

The second and third interviews, which incorporated the digital task sequences described in this paper, involved a Cannon Man and a Toy Car situation, respectively. In all interviews, students worked on a digital tablet (an iPad).

Ongoing and retrospective data analysis

All interviews were video recorded. During each interview, either McClintock or Gardner wrote field notes. To promote consistency, we used a field note template, which broke down each interview into sub tasks, to write field notes for each student in each interview. Field notes included evidence of students' conceptions of task attributes as possible to measure and capable of varying, as well as evidence of students' intentions to use a graph to represent a relationship between quantities.

We focused retrospective analysis on students' responses to the Cartesian graphing tasks (Tasks G1 and G2, see Table 1). Across the set of three interviews, students had opportunities to sketch five Cartesian graphs. Johnson and McClintock viewed video of each student's work on each of the Cartesian graphing tasks. In the first pass, we described three aspects of students' work: Sketches of (or attempts to sketch) a viable graph; Explanations of their graph (or attempt) in terms of both attributes; Gestures related to their graphs. In the second pass, we made inferences about students' representing. We used different codes to characterize students' representing. Table 2 provides descriptions of each code. In the third pass, we examined students' shifts in representing across the Cartesian graphing tasks in each interview, building from observable evidence to develop explanations to account for students' shifts.

Code Description of code

Relationships between quantities Students sketched (or attempted to sketch) a single graph. Students described or showed how a single graph could represent a relationship between two quantities.

Individual quantities

Students sketched two separate graphs. Students described each graph in terms of only one quantity (e.g., the "height" graph).

Motion of objects

Students sketched a graph that showed the motion of an object in the situation (e.g., a toy car moving along a path). Students described the graph in terms of motion.

Iconic/Familiar objects Student sketched a graph that looked like an iconic object or familiar graph. Students described the graph in terms of its physical characteristics.

Table 2: Descriptions of codes characterizing students' representing

Viewing video alphabetically by students' pseudonyms, we completed the first and second passes for each Cartesian graph task in the Ferris wheel and Cannon Man situations. Next, we analyzed the Toy Car situation, which resulted in refinements to our codes. In particular, we expanded the code for relationships between quantities to include attempts to represent quantities not explicitly represented (e.g., time). In each pass, we first coded individually, then vetted codes as a team.

Although some students demonstrated evidence of more than one form of representing within a task, we elected to use a single code for students' representing within that task. When we coded a form of representing for a task, a student may have shifted to engaging in that form of representing after an "aha" moment or engaged in that form of representing throughout their work on the task. If a student demonstrated partial evidence of one form of representing, but engaged more consistently in another form of representing, we weighed the evidence, then coded the form of representing that we interpreted to best characterize the students' reasoning in that task.

Results

We found that the digital task sequences were viable for promoting students' creation of Cartesian graphs to represent relationships between quantities. Table 3 shows the numbers of students engaging in each type of representing across the Ferris Wheel, Cannon Man, and Toy Car graphing tasks. In the Ferris Wheel preassessment graphing task (Ferris Wheel G1, see Table 3), four students (two ninth grade; two eleventh grade) created graphs to represent relationships between quantities. All four of these students continued to represent relationships between quantities in the Cannon Man and Toy Car graphing tasks (Cannon Man G1 and G2, Toy Car G1 and G2, see Table 3). We share results from the nine students who, in the Ferris wheel preassessment graphing task (Ferris Wheel G1), demonstrated forms of representing other than relationships between quantities. By the end of the Cannon Man and Toy Car task sequences, four of these nine students shifted to representing relationships between quantities (Harun, Aisha, David, and Amanda). Five of these nine students (Kara, Gemma, Carmen, Keshia, and Eliza) continued to represent (or shifted to representing) the motion of objects.

Code

Shifts to representing relationships between quantities

The two students (Harun, eleventh grade; Aisha, ninth grade) who represented individual quantities on the Ferris Wheel preassessment graphing task (Ferris Wheel G1) represented relationships between quantities by the end of the interview sequence. Harun shifted to representing relationships between quantities on the first Cannon Man graphing task (Cannon Man G1). Across the Cannon Man and Toy Car task sequences, Aisha continued to represent individual quantities for the first graphing tasks (Cannon Man G1, Toy Car G1). It was only on the second graphing task in each sequence (Cannon Man G2, Toy Car G2), that Aisha shifted to representing relationships between quantities.

The three students who represented iconic objects/ familiar graphs on the Ferris Wheel preassessment graphing task (Ferris Wheel G1) were in eleventh grade. Two of those students, David and Amanda, shifted to representing relationships between quantities in the Cannon Man task sequence. Amanda shifted in the first graphing task (Cannon Man G1), relating directions of change in Cannon Man's height and distance. In contrast, in the first graphing task (Cannon Man G1), David represented the path of Cannon Man. It was not until the second graphing task (Cannon Man G2) that David worked to represent relationships between Cannon Man's height and distance. Notably, David was the only student who shifted from representing motion of objects to representing relationships between quantities.

Two of the four students (Kara, eleventh grade; Gemma, ninth grade) who represented motion of objects on the Ferris Wheel preassessment graphing task (Ferris Wheel G1) demonstrated partial evidence of representing relationships between quantities on the Cannon Man graphing tasks (Cannon Man G1, G2). In the second Cannon Man graphing task (Cannon Man G2), both Kara and Gemma explained how their graphs represented Cannon Man's height and distance. Yet, in both Toy Car graphing tasks (Toy Car G1, G2), they attempted to represent the physical path of the toy car.

Shifts to other forms of representing

Two of the four students (Carmen, eleventh grade; Keshia, ninth grade) who represented motion of objects on the Ferris Wheel preassessment graphing task (Ferris Wheel G1) shifted to representing change in individual attributes on at least one of the Cannon Man graphing tasks. In the second Cannon Man graphing task (Cannon Man G2), both Carmen and Keshia attempted to represent change in Cannon Man's height and distance. Yet, in both Toy Car graphing tasks (Toy Car G1, G2), they attempted to represent the physical path of the toy car. Furthermore, one of the students who represented iconic objects/ familiar graphs (Eliza, eleventh grade) shifted to representing the motion of objects in the first Cannon Man graphing task (Cannon Man G1). Once shifting to representing the physical path of Cannon Man, Eliza continued to represent motion of objects in the rest of the tasks.

Discussion

We aimed to leverage difference to promote students' conceptions of graphs as representing relationships between quantities. By interweaving Marton's variation theory and Thompson's theory of quantitative reasoning, we worked to achieve our aim. Drawing on Marton's variation theory, we incorporated difference within and across task sequences. Within each task sequence, students had opportunities to create different graphs to represent the same relationship between quantities. Across task sequences, we incorporated different backgrounds (Cannon Man/Toy Car), as well as different kinds of graphs (linear/nonlinear). Thompson's theory of quantitative reasoning informed our choices about the kinds of differences that might engender students' quantitative reasoning. Because Cartesian graphs represent relationships between quantities, students had opportunities to vary each quantity represented in a graph. Furthermore, we argue that variation within a graph is insufficient to foster students' conceptions of a graph as some "thing" capable of representing a relationship between quantities. Drawing inspiration in part from the tasks reported in [START_REF] Moore | Breaking conventions to support quantitative reasoning[END_REF], we incorporated different graphs representing the same relationship between quantities.

We posit that our descriptions of codes indicate increasing levels of sophistication in students' representing with Cartesian graphs; however, we do not claim that each of these levels is a necessary step in a progression of reasoning. When representing iconic objects/familiar graphs or the literal path of an object in motion, students are representing physical phenomena in a situation. When representing quantities, or relationships between quantities, students are mathematizing a situation in terms of attributes they can conceive of as possible to measure. We argue that engendering students' shifts from representing iconic objects/familiar graphs or motion of objects to representing individual quantities and relationships between quantities is important for expanding students' conceptions of what graphs can represent.

Students' conceptions of the direction and nature of the motion of objects in a situation can impact their opportunities for representing relationships between quantities. The Toy Car situation proved useful for investigating the stability of students' representing relationships between quantities, in part because the graphs did not share physical characteristics with the literal path of the toy car (e.g., a graph moving up and down as did the Cannon Man). To promote students' creation of Cartesian graphs to represent relationships between quantities, task designers should incorporate graphs that do not share physical characteristics with motion of the objects in task situations.

V

  View video animation. Students viewed a video animation of a situation depicting an object in motion, identified attributes in the situation, and discussed how they might measure those attributes. A1 Identify task attributes. Johnson stated attributes on which that task would focus. If students had not already identified those attributes, they then discussed how they might measure the task attributes. A2 Represent individual attributes. Students dragged dynamic segments along the axes of a Cartesian plane to represent change in individual attributes. Then, students viewed a computer-generated video of the dynamic segments changing together. G1 Represent attributes changing together. Students sketched a single Cartesian graph relating both attributes. Students discussed how their graphs showed (or did not show) both attributes at the same time. Then, students viewed a computer-generated graph. G2 Re-represent attributes in a new Cartesian plane. In a new Cartesian plane, with the same attributes represented on different axes, students re-represented individual attributes, then attributes changing together (Repeat tasks A2, G1).

Table 1 : Descriptions of tasks in the Cannon Man and Toy Car digital task sequences

 1

Table 3 : Students engaging in each type of representing across tasks

 3

Acknowledgement

The development of the digital task sequences was supported by a US National Science Foundation Grant (DUE-1709903). This study was supported by a Faculty Development Grant from the University of Colorado Denver. Opinions, findings, and conclusions are those of the authors. We thank Dan Meyer for his support of the development of the digital task sequences in Desmos.


Lemenkova Polina

How Glacier Retreat in Tian Shan Basin A ects the Hydro-Energetic System of Central Asia

The project focuses on the analysis of Central Asian hydro-energetic system and water usage in Tian Shan region. Tian Shan system is important water resource in Central Asia: mountains river waters are intensely taken for hydropower energy, urban systems, irrigation. But geopolitics in Tian Shan is di cult: it crosses ve densely populated countries. Current problem consists in water delivery between territories located in the highlands with excellent water supply and those located in valleys with water shortage. Tajikistan and Kyrgyzstan control river basins, and Kazakhstan and Uzbekistan depend on water supply. The problem of water use causes debates among these countries. Besides, climate warming a ects glaciers and causes water de cit. Altogether, this leads to diculties in hydro-energetics. A multidisciplinary analysis was performed in research: geopolitical problems of water supply in Tian Shan, spatial distribution of hydro-energetic resources and climate impact on hydro-energetics.

Introduction

The paper focuses on environmental analysis of Central Asian energetic system and usage of waters from Tian Shan glaciers. The Tian Shan is a Central Asian mountain system extending to 2,500 km breadthwise. It is one of the major water supply in Central Asia, since it contains 7,590 glaciers with an overall area of 13,271.45 km 2 . Many rivers originate in these glaciers and snow elds and feed major river streams. Intensely taken for hydropower energy production, sustainable functioning of urban systems, agricultural activities, irrigation and other human needs, river waters are highly important hydrological resource for local population. At the same time, geopolitical location of Tian Shan is di cult: it crosses ve densely populated Central Asian countries. Therefore, actual problem of water usage system region consists in water delivery pattern.

Figure 1: Study region: Tian Shan Mts., Central Asia. Source: Britannica Encyclopaedia Tian Shan region can be divided on territories located in the highlands of plateaux with rich hydrological resources and excellent water supply, and region with water shortage, located in the lowlands and valleys. For example, Tajikistan and Kyrgyzstan control basins of Syrdaria and Amudaria rivers, while Kazakhstan and Uzbekistan are dependent on water delivery. Nowadays, the problem of water supply is a subject of discussions and con icts among neighboring countries in Tian Shan region.

Apart from geographic location, there are impacts of environmental and climate change on water resources. Global climate warming seriously a ects Tian Shan hydrological system and causes glacier reduction, decrease of snow coverage in high mountains, and de cit of waters. Multiplied by geopolitical questions, this leads to di culties in water supply and usage. A multidisciplinary analysis was performed in current work: geopolitical problems of water supply in Tian Shan caused by regional distribution of hydropower resources, and impact of climate change on the hydrological settings within study area.

Geographic Settings of Tian Shan Region

Geographic location of the study area

The Tian Shan is a Central Asian complex mountain system extending in westward direction (Fig. 1). Geographically Tian Shan straddles ve countries with population mostly supporting traditional style of life which include livestock husbandry, intense grazing, farming and other agricultural activities. Tian Shan is the northernmost existing montane range with elevations of peaks reaching higher than 7.000 m. Environmental settings of Tian Shan are in uenced by combination of Northern (boreal) and Asian climatic factors. Therefore, Tian Shan has unique and diverse montane environment, with more than 4000 wild species, many of which are endemic, rare and relict. The Tian Shan (sometimes referred as Tien Shan), or Celestial Mountains, is one of the largest high mountain systems in continental climate of Central Asia, covering covers 800 000 km 2 . Geographically, Tian Shan extends 2,500 km westwards across Central Asia between 39°-46°N and 69°-95°E. The Tian Shan ranges compose large, isolated montane system, surrounded by the Tarim desert basin of north-western China, Lake Issyk Kul, and north-western desert regions in Uzbekistan and Kazakhstan. The altitude belt of the mountain range lies between the 2,800 and 7,400 m Above Mean Sea Level (AMSL) with most major peaks located at 4000-6000 m, and the highest altitude reaching 7,349 m.

Environment of Tian Shan: current problems

Since mid-1970s the observation of the remotely located areas of the Earth has been facilitated due to the development of the satellite industry, which provided remote sensing data for glacier monitoring. Systematic monitoring of the mountainous areas enabled to detect rapid changes in the glacier coverage of Tian Shan since past four decades. According to the numerous reports , there are changes in the current glaciation in Tian Shan mountains, which causes changes in hydro-energetic resource supply. There are twofold reasons for environmental and hydrological changes in this area, caused by climate reasons and by the anthropogenic factors. These factors are discussed below.

Impact of climate on hydro resources

The main reason for the deglaciation is overall increase of summer temperatures and decrease of the precipitation, which are the consequences of the climate change. Thus, the average rise in air temperature in Tian Shan mountains is 0.01°C/yr over the range, and the precipitation in the Tian Shan increased to 1.2 mm/yr since 1950s. Due to the geographical diversity of Tian Shan, there are certain variations in the temporal changes of environmental parameter, such as surface air temperature, precipitation, runo , glacier mass, and snow thickness. Hence, the precipitation increase is lesser at high altitudes at above 2000. The low altitudes in northern and western regions are mostly a ected by climate change comparing to inner and southern regions.

Recently increased in air temperatures in Tian Shan reinforced thawing of the glaciers, the period and intensity of melt. However, due to the strong impact of the geographic location and local climate factors, glaciers in di erent regions of Tian Shan melt with di erent rates. The most intensive glacier retreat is detected on the northern ranges of Tian Shan: -361km 2 , which constitutes 14,3%, while the southern areas are the least a ected. Also high rates in melt are detected in the central and inner areas: 287 and 244 km2 with 10% and 5% respectively. Climate change has also a ected hydrological systems of semi-desert area of Aral Sea, which in turn are a ecting seasonal water availability for irrigation in the Aral Sea. Thus, it is reported that recently the summer oods, which is necessary for irrigation in Uzbekistan is reduced in the last decades. Water shortage necessarily a ecting hydro-economic sectors of the countries located in the disaster area, such as Uzbekistan and Kazakhstan.

Impact of anthropogenic factors

Possible anthropogenic threats, that can induce environmental changes, include overgrazing at higher elevations by the local people, and local deforestation, which may lead to the partial decrease in biodiversity of the Tian Shan. Finally, the work of forest management and guarding has been weakened in the last years. As a result of cattle overgrazing, res, deforestation, terracing of slopes, assignment of the grounds under construction of various objects and other factors there is an essential reduction of an area of distribution of wood and tangled vegetation. Due to the environmental threats and increased anthropogenic pressure on such fragile environment, the environment of Tian Shan will degrade: for example, the mountain forest area would decrease by 10-20% with 50 years. Another problem is connected to Aral Sea: due to the salinization and drying of the Aral Sea in Central Asia, which is a part of Tian Shan basin, the large areas of saline soil have now formed. Additionally, monsoon winds carry over towards south direction of Tajikistan and Kyrgyzstan, naturally contribute to the intensive melting of glaciers. It is demonstrated that the Aral Sea basin has su ered an enormous shortage of water resources during the last decades. The consequences of drying lakes and rivers have extremely negative e ects on the society, economic sector and hydro energy supply. The human-controlled hydrological regime of the major tributary rivers, Amu Daria and Syr Daria, owing into Aral Sea, is a major factor a ecting ecosystem sustainability, which are especially sensitive in the conditions of the semi-arid climate of Aral Sea Basin.

Hydro-Energetic Resources of Tian Shan

Glaciation of Tian Shan

The general hydrologic settings and distribution of glaciers in Tian Shan are largely in uenced by the climatic factors and geographic location in the Central Asia. The annual air temperatures a ect precipitation regime of Tian Shan: runo , snow and ice coverage. Totally, there are 7,590 glaciers with an overall area of 13,271.45 km 2 detected in Tian Shan, which makes it one of the major water supply in Central Asia. The most prevalent glacier type is large valley glacier, which takes 82% of all glacier areas. Glaciers often occur along the crests of the mountain ranges. The largest glaciers are concentrated in central, inner part of Tian Shan. Since the Late Pleistocene Maximum, there are uctuations in Tian Shan glaciation with the maximum level corresponding to the Issyk-Kul lake transgression. The changes in the glaciation regime are still presented, which includes general trend of warming, but also some advances of small glaciers occurred recurrently, as proved by moraine sediments.

Hydrology and climate of Tian Shan

The rivers in Tian Shan have typically mountain character Since there is a signi cant di erence in elevations between the mountain ridges and the plains at their base, river streams, usually plunge down the mountain slopes through deep and narrow gorges (Fig. 2). After they ow out onto the plains, they form vast fan-shaped deposits of silt and mud. Climatic conditions of Tian Shan directly a ect hydro-energetic resources and in uence formation of glaciers and snow elds. In general, Tian Shan has typical continental climate, which is caused by Central Asian location.

However, there are some local climatic di erences formed in various geographic conditions: the most extremely cold and dry climate is in inner parts of mountains on the high plateaux, while northern and western slopes of Tien-Shan are characterized by more temperate climate. Thus, the mean summer temperature is 3.7°C at the altitude of the Equilibrium Line Altitude (ELA) in the western regions and -8.1°C in the east; the annual precipitation is 1500-2000 mm in the west and 200-400 mm in the east, respectively. The northern slopes of Tian Shan, such as Kyrgyz Alatau and Zailinsky Alatau, have major in uence of cyclonic activity. Precipitation in Tian Shan reaches its maximal level in spring and summer seasons, which coincides with the ice and snow melt. In winter the Siberian anticyclone prevents much precipitation in this area. In general, precipitation also increases with altitude. According to the moisture conditions, i.e. precipitation and evaporation, the alpine zone in Tian Shan ranges is similar to the zonal ecosystems of other mountain vegetation alpine zones in boreal and subboreal palearctic regions.

Water Usage and Supply in Tian Shan Region

Geopolitically, Tian Shan crosses borders of several Central Asian countries and western China. Approximately half of the Tian Shan mountains, the Eastern region from 80°E (eastwards from Issyk Kul Lake), is located in China, Xinjiang Uyghur Autonomous Region. Western territories are situated in Kyrgyzstan (including Issyk Kul lake depression), and northern ranges of Tian Shan are placed in Kazakhstan. Some small ranges of the Tian Shan spread to Uzbekistan and Tajikistan.

Hydro energy systems in the region

Hydropower resources are a major factor directly a ecting and in uencing sustainable development of the politician and economic systems in Central Asia. The main water resources in Central Asia are located in Tajikistan and Kyrgyzstan, which control major river basins. It is caused by the upper location on Tian Shan plateau of both of these countries. For example, on the territory of Tajikistan 64 km 3 of water ow of the Aral Sea basin is formed, which is ca 60% of the total ow towards Aral Sea basin. The particularity of Tajikistan consists in hydro-energetic sector as the most powerful and in uencing the overall economy of the country: 95% from all energetic sectors are taken by hydro-energy, while usually this part is not exceeding 10-20% in other countries. At the same time, only about 10% is used for internal purposes within republic from the total country runo . The rest of the runo goes downwards from the country where it is used e.g. for irrigation. In Kazakhstan, on the contrary, it is demonstrated that electricity demand in the country is high for all sectors: the industrial, service, and residential sectors, but the country is depending of water resources. As for Kyrgyzstan, this country is rich in hydro energetic resources, and generates ca 90% of its electricity from large-scale hydroelectric power stations, located along the cascade of the Naryn River. However, after the fall of the USSR, water resources in Kyrgyzstan have declined due to climate change issues, ine ective management and cross-border water claims among Central Asian states.

Problem of water supply and usage: regional con icts and decisions

The reason of the hydro-energetic problems and water usage in Central Asia lies in the fact that water resources in Central Asia are unevenly distributed: Central Asian region is clearly divided into water-rich countries (Tajikistan and Kyrgyzstan) and those dependent on them (Uzbekistan, Turkmenistan and Kazakhstan). Kyrgyzstan majorly controls Syr Darya River basin, and Tajikistan -the Amu Darya river (Tab.1). The Amu Darya is the largest, longest and the most important river in Central Asia. The river is 2400 km, basin area is over 500 thousands km 2 . Syr Darya has its most drainage areas in Kyrgyzstan, where it loses water for irrigation in its lower reaches.

With the total annual hydropower resources in the country of ca 600 billion kWh, Tajikistan is the third largest in the world and second in the new independent (post-Soviet) countries after Russia. For example, the Nurek hydroelectric power station (capacity of 3 M kWh) controls about 40% of water resources needed by Uzbekistan and Turkmenistan. Additionally, Tajikistan has signi cant fresh water reserves mostly stored in glaciers (over 60% of Central Asia). The uneven distribution of water resources in Central Asia evidently leads to regional and local con icts of interest among key water providers (Tajikistan and Kyrgyzstan) and its major customers (Uzbekistan, Kazakhstan and Turkmenistan). In particular, Tajikistan and Kyrgyzstan are interested to use generate hydro power electricity both to meet their own needs and for export to third countries. They are opposed by Kazakhstan, Turkmenistan and Uzbekistan, which insist on the primarily irrigation water usage, for old built in Soviet times hydro power plants, as well as for the planned new ones. The main point of claims from Kyrgyzstan and Tajikistan to the neighboring countries consists in nancial expenses that they bear due to the hydro plants exploitation. They require that Uzbekistan, Kazakhstan and Turkmenistan increase their nancial contribution for Kyrgyzstan and Tajikistan. The main demand is to contribute equally to the expenses of hydroelectric power production. Kyrgyzstan and Uzbekistan debate over the years about prices to maintain hydro-technical infrastructure. Kyrgyzstan consider water as a commercial product and wants to introduce monetary charge for water in the future (nowadays, Kyrgyzstan receives some compensation for excess in generated electricity from Uzbekistan and Kazakhstan). But the problem in the region is that that price elasticity in the region is very low, which means that it is with di culties that countries perform a dialog about market relationships.

In view of this, a paid water usage on the commercial basis is the worst idea to be introduced in Central Asia. Possibly it can cause high risks of social and political rebels and revolutions in the countries within the region. The o cial purpose of Kyrgyzstan and Tajikistan is to receive reasonable market compensation from other central Asian countries for services that they provide with water supply. Though both these countries are trying to solve current nancial problems by increasing state wealth, but current strategy should be adjustment into a regional scenario of sustainable geopolitical development with all countries as bene ciaries and no those one in disadvantage position. Another problem within the region consists in active water usage for agricultural needs, which is in generally increasing (Tab. 2). An additional factor of hydro energetic di culties in the region is caused by an arti cially accelerated development of hydro power energetics in Tajikistan comparing to actual water usage, since the country does not have enough oil and gas reserves. Thus, as planned on the governmental level, by 2010, Tajikistan plans to become energy independent state and start electricity export to Iran, Pakistan and India. For instance, in Tajikistan it is planned to construct 14 hydroelectric power plants on the river Panj, a major tributary of the Amu Darya, and on river Rogun (Fig. 3). This project is interesting to investors from the United States and Pakisatn and China. Kyrgyzstan is also seeking foreign investors for the construction of the cascade of Kambarata hydro power plants on Syr Darya. This situation caused negative reaction of neighbor countries, because construction of new hydropower plants will involves serious changes in water delivery: huge dams will be constructed and large territories will be lled out by the water (Fig. 3), which will cause water shortage in the surrounding territories. Evidently, the non-diplomatic, one-sided energy policy of energy-rich countries can lead to the di culties in the geopolitical relationships, especially with strategic neighboring countries. The problem of water usage and delivery is a constant and important topic in the energy debates in Central Asia. Uzbekistan and Turkmenistan are countries with predominant natural gas economy, rich in hydrocarbon resources. Kazakhstan has the most signi cant oil resources and natural gas reserves, and is expected to become one of the world's top 10 oil producers within the next decade. Therefore, these hydrocarbon rich countries threaten to make pressure on Tajikistan and Kyrgyzstan, using resources of natural gas that they almost totally control (Tab.3). Lack of water in the densely populated Ferghana valley in Uzbekistan is a serious potential trigger of social revolution, which may arise in case of de cit of water. In such situation special attention should be paid to oil and natural gas resources stored in Caspian Sea basin which is potential major reservoir for energy [START_REF] Lemenkova | Current Problems of Ecology, Ecological monitoring and management of natural protection[END_REF]. However, a consensus in the energy usage should be strongly observed for all parties, since the supply in oil, gas, hydro and coal resources are distributed highly uneven in the study region (Tab.3).Local Uzbek-Kyrgyz con icts concerning water supply happen from time to time in Ferghana valley (Uzbekistan). The main claim of Uzbekistan is to provide necessary amount of water for Uzbek agriculture. However, the prices for the water resources are often a point of disagreement. The debates about new hydro plants construction arise, because it will negatively a ect sensitive environment and a mannature balance within the region. To reduce water supply con icts, water management should be based on e ective operating existing hydro power plants rather than construction of new water supply systems [START_REF] Lemenkova | Seagrass Mapping and Monitoring Along the Coasts of Crete, Greece[END_REF]. The e ective management options and decisions for economic values should be taken in an integrated manner, so that problem of water scarcity can be smoothly solved.

Conclusion and Discussion

The Central Asian region is one of the most complex regions of the world, due to the di cult geopolitical situation, complex boundaries pattern and concentration of the densely populated countries with huge demand for water resources. At the same time, after the fall of the USSR the nancial situation of Central Asian countries became difcult. Lack of development investments leads to the outdated style of economy and agrarian system (e.g. ine ective, water-consuming irrigation). The situation is aggravated by natural factors (fundamental climate issues and glacier melt). Since the independence of Central Asian countries after the disintegration of the USSR, there were serious tensions n the point of sharing water resources. The main reason for these con icts is caused by uneven distribution of the resources and geospatial location of the involved countries: Uzbekistan, Turkmenistan and Kazakhstan, located in the lower reaches of Tian Shan region, have lack of the resources though demand huge amount of water for various needs, while Tajikistan and Kyrgyzstan, typically mountain countries, are rich in water resources and control almost all hydro-energetic resources, supply and delivery within the region. The paradox in this situation consists in the overall availability of the water resources in the Tian Shan region. In general, there are more than enough water resources in Central Asia. The most problems are caused by ine ective resource management. Thus, excessive loss of water use in Central Asia is mostly caused old irrigation system, which is still traditionally used in agriculture, when water consumption exceeds 3-10 times the world standards. The transition towards modern agricultural system and sustainable water management will save considerable amounts of the water resources in the region. Another problem is that the modernization of the Central Asian agriculture and introduction of modern city management require serious internal support and external nancial investments. That being said, the optimal decision of the sustainable water usage in Central Asia, should be based on well-balanced and politically wise decisions, which consider interests of all countries. This should be taken as a major, general direction for further development of hydro energetic system in Central Asia. Thus, the decisions taken at governmental level should be well discussed and agreed by all parties, with strictly coordinated actions at local, regional and national levels of water and hydro-energy management. Furthermore, the decisions should be exact and concrete. Finally, the inter-governmental contradictions between the states controlling water resources and those consuming them, should be regulated. Advisable can also be involvement of the independent third governmental party with no interest in local con ict, which could assist in solving dubious questions of water energy usage and supply. Current paper performed critical analysis of the geopolitical situation caused by uneven distribution of hydro energetic resources within Central Asia, as well as discussion and an overview of some of the current local con icts and tensions caused by ine ective management of water resources. Besides, a geospatial analysis of the current environmental problems within the study area, caused by the climatic and anthropogenic factors, is made.

Figure 2 :

 2 Figure 2: A typical mountain river in Tain Shan. Source: Web

Figure 3 :

 3 Figure 3: Rogun dam for planned hydro power plants of Vakhsh River (under construction), Tajikistan. Source: Web