ARTICLE pubs.acs.org/jchemeduc
An Interactive Computer Model for Improved Student Understanding of Random Particle Motion and Osmosis Johannes Kottonau* Institute of Teacher Education, University of Zurich, Beckenhofstrasse 35, 8006 Z€urich, Switzerland
bS Supporting Information ABSTRACT: Effectively teaching the concepts of osmosis to college-level students is a major obstacle in biological education. Therefore, a novel computer model is presented that allows students to observe the random nature of particle motion simultaneously with the seemingly directed net flow of water across a semipermeable membrane during osmotic simulations. Specifically, the simulations are intended to help students understand that the membrane-crossing probability of water molecules depends solely on their concentrations on both sides of the membrane. The interactive model allows for user-controlled concentration gradients and should also help students avoid some common osmotic misconceptions including those that derive from the use of teleological or anthropomorphic explanations. The model is implemented in the multiagent NetLogo environment and is accessible as a platform-independent Java applet. KEYWORDS: Second-Year Undergraduate, Upper-Division Undergraduate, Physical Chemistry, Computer-Based Learning, Misconceptions/Discrepant Events, Bioanalytical Chemistry, Biological Cells, Equilibrium, Molecular Modeling the directedness of water flow on the macro level and the randomness of molecular motions on the micro level are not contradictory processes, a secure basis for avoiding the above misconceptions will be created. Consequently, to appreciate the compatibility of osmotic processes at the micro and macro levels, students should be provided with the opportunity to observe both the randomness of particle motion and the one-sided net accumulation of water molecules in a single application. Because of the inadequacy of macroscopic models to represent the behavior of microscopic particles, scholars investigating osmotic misconceptions have postulated that “computer simulations may help in illustrating the micro-level phenomena involved” (ref 3, p 551). Additionally, increasing evidence emphasizes that computer simulations improve student thinking about various molecular processes.8 11 Computer simulations are particularly persuasive for teaching macro behavior to students because they do not need to be preprogrammed by the teacher (as is true for animations) and because they can be interactive. While running a computer simulation model, students can directly observe the emergence of macro behavior in real time, simply by allowing the particles to move according to preset conditions. It is assumed that using traditional drawings and other textual or visual explanations to convey that randomness and semipermeability will “somehow” end up in the net movement of water is less effective in attaining the desired conceptual change for students than using interactive visual computer simulations.12 15 One
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smosis is the diffusion of a solvent, frequently water, through a semipermeable membrane.1 Because osmotic processes have important physiological roles in cells and organs, osmosis is widely taught in many biological curricula. A thorough understanding of osmosis allows students to appreciate the parallels between such diverse processes as the reabsorption of water in renal tubules, turgor pressure in plants, and water balance in aquatic organisms. Despite its key roles, osmosis is one of the most difficult topics for biology students to grasp,2 and overall student understanding of osmosis is remarkably poor.2 6 There are at least three misconceptions that teachers of osmosis should address: • Assigned Intentionality: Many students believe that molecules “want” to move from low to high solute concentration and can somehow “sense” high solute concentrations.5,6 Unfortunately, such teleological or anthropomorphic explanations are sometimes used even by teachers and introductory biology textbooks,7 for example, to teach osmotic principles.3 • Static Equilibrium: Some students believe that when osmotic equilibrium is reached, all molecules cease movement or that water molecules stop crossing the membrane.6,8 • Speed: Some students do not understand why the rate of osmosis is faster if the concentration gradient is steeper.8 It is hypothesized that an important precondition for eliminating these common misconceptions is to bring together plausibly in the mind of the student two key facts: directedness of the water “flow” (macro level) and randomness of the particle motion (micro level). If students can acquire an awareness that Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
Published: March 14, 2011 772
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Figure 1. Overview of the functional interactive elements of the osmosis simulator “cockpit” (numbered 1 to 10). The simulation is written in the NetLogo environment and provides control buttons, sliders, switches, moving elements, and monitors to display various parameters temporally using xy plots and histograms.
possible explanation for the difficulty teachers face in attaining the appropriate conceptual changes in their students might be related to the strong student misconception that randomness cannot possibly be efficient for achieving well-defined or directed chemical or biological processes.16 On the basis of these previous studies and considerations, a novel computer simulation model is designed to simultaneously unite the randomness of particle motion and the directedness of net water flow into a single interactive visual application to reveal effectively the molecular concepts of osmosis. Furthermore, it is intended that this model will efficiently prevent the common osmotic misconceptions related to static equilibrium and speed and will obviate any teleological or anthropomorphic explanations pertaining to osmosis.
between 0 and 8 osm. After the setup button is pressed, the monitors (3) display the calculated initial characteristics of the solutions in the left and the right compartments. The monitors (4) on the left and the right sides of the compartments (10) show the number of simulated particles and the corresponding water concentrations expressed as mole fractions. The switch on the left of the compartments (5) can be used to arrest the membrane (red dashed line) if required. At the bottom of the figure, two xy plots (6) monitor the position of the membrane and the change in water concentration differences between the left and the right compartments. If the see_speed_histograms switch (7) is turned on, histograms displaying the speed of the water molecules and the dissolved particles can be observed during the simulation. By default, this switch is turned off because it slows down the simulation. Another option that can be shown and hidden (8) traces the paths of some water molecules and dissolved particles. The integrated “speed” of osmosis monitor (9) displays the distance the membrane has moved from its initial position after 1000 time ticks, thereby providing a measure for the average speed of osmosis. Finally, using the slider at the top of the compartments (10), the simulation speed can be adjusted to maintain smoothness of particle motion or to slow down particle movements for their effective visual tracking on certain fast computers. The applet can be run in two steps as described in more detail below. In the first step, depending on the selected osmolarities, a situation in which two compartments are separated by a semipermeable membrane is created. In the second the step, a situation that allows for movement of the particles and the membrane is created. Glucose is the chosen solute because of its relevance to students in many biological contexts. Furthermore, being a nondissociating substance, glucose is ideal for maintaining
’ THE OSMOSIS SIMULATION JAVA APPLET This osmosis simulation model was created using NetLogo, a cross-platform multiagent programmable modeling environment.17 It can be started as a stand-alone applet in any browser on any platform without the need to install the NetLogo software. This makes the application ideal for classroom use where multiple workstations exist. The only software requirements are Java 1.4.1 or higher, some preinstalled browser software, and the URL http://lsvr12.kanti-frauenfeld.ch/KOJ/Java/Osmosis_fast.html. If an Internet connection is not available, the current version of NetLogo17 and the model file (see the Supporting Information) can be predownloaded. An overview of the simulator interactive “cockpit” is provided in Figure 1. The most important controls for running the simulation are the gray setup and start/stop buttons (1). The osmolarity sliders (2) allow the student to choose glucose osmolarities 773
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osmolarities without the need to consider the formation of ions or a water mantle in the simulation.
’ STEP 1: CHOOSING THE INITIAL OSMOLARITIES AND SETTING UP THE COMPARTMENTS The black square area (Figure 1) opens the view to a threedimensional space separated by a semipermeable membrane (red dashed line). The two separated subspaces can be thought of as two adjacent biological cells, thus, affording an extremely large view of their cytoplasms. These subspaces are also referred to below as compartments that contain a specified number of water molecules (blue) and solute molecules (brown). The plasma osmolarities can be selected using the sliders. The default values are 6.0 osm for the left compartment and 2.0 osm for the right compartment. To make the simulated processes as conspicuous as possible, these default presets are rather high but are still realistic considering the high solubility of glucose. At simulation setup, the characteristics of the initial solutions are calculated with respect to the slider values. The osmolarities directly translate into the grams of glucose that will be contained in 1 L of each solution (based on the molar mass of glucose of 180 g/mol). Then, an algorithm calculates the amount of water that would have to be added to the glucose to achieve exactly 1 L of solution. This algorithm incorporates empirical data from available density tables published in the CRC Handbook of Chemistry and Physics,18 for example. Next, starting from the mass of glucose and the mass of water contained in 1 L of each solution, the respective numbers of glucose and water molecules are calculated in moles per liter for each solution. Finally, the ratio of the number of solute to solvent molecules is calculated for each solution. These ratios are now graphically implemented by displaying the solutions in the compartments. Initially, each compartment is filled by 5 times the corresponding osmolarity value (e.g., 30 particles if the osmolarity to display is 6.0). A number of five is selected to correspond to the current computational power of most personal computers (PCs). A larger factor would result in the simulation of more particles and more collisions, which would slow down the simulation speed and diminish the conspicuousness of the simulated dynamics. In the final step, depending on the calculated ratio of glucose to water molecules in each compartment, water molecules are added on each side. This procedure results in the display of the two glucose solutions with their preset osmolarities. The spatial effect of different osmolarities is now immediately visible. It is important to note that for a realistic setup of the compartments, the only relevant criteria are that the ratio of the displayed solute particles meets the ratio of the preset osmolarities and that a corresponding number of water molecules are calculated by the algorithm in each compartment. The actual volume of the simulated compartments is not important. In an educational setting, this correspondence to reality is one of the most valuable characteristics of this simulation model. Teachers or students can first perform the real experiment and then switch to the simulation using the osmolarities from the experiment. ’ STEP 2: PRESSING THE START/STOP BUTTON TO INITIATE PARTICLE MOVEMENTS As long as the simulation is running, water molecules will randomly move and bounce within the total volume defined by the two compartments, thus, exhibiting their characteristic Brownian motion, and the larger, solvated solute particles will
move less rapidly than water molecules alone. Water molecules will cross the membrane coming from both the left and right compartments, but as the initial water concentration in the left compartment is lower than that in the right compartment (using the default settings), more water molecules will move from the right to the left than from the left to the right compartment per unit time. Thus, there is a net movement of water molecules from the right to the left compartment by simple diffusion. Note that only water molecules and not solute molecules can pass (diffuse) through the “semipermeable” membrane between the two compartments. Because they produce the initial difference in the water concentrations on both sides of the membrane, it is, however, the solute molecules along with random particle motion that cause the net movement of water. As soon as the number of water molecules starts increasing in the left compartment (and decreasing in the right compartment), the total kinetic energy will increase in the left compartment and correspondingly decrease in the right compartment. Given that the compartment volumes are identical at startup, any change in the number of water molecules from the startup conditions will result in a pressure difference between the two compartments. But because the membrane is moveable, the pressure difference will move the membrane until it comes to rest at the equal-pressure position. The new membrane position is supposed to release fully the pressure difference in each simulation cycle. To be clear, the pressure difference that causes the advancement of the membrane is neither explicitly calculated nor monitored in the simulation cockpit. Rather, to keep the simulation fast, the movements of the membrane are directly calculated from the actual water concentration difference. Students will not be aware of this implementational workaround, but it is still correct to instruct them that the movements of the membrane release the pressure differences in each simulation cycle. During the entire simulation run, the position of the membrane establishes the volumes of each compartment. In the long run, after hundreds of simulation cycles, the left compartment (“cell”) will “swell”, and the right compartment (“cell”) will “shrink” (which is reminiscent of the mechanism by which leaf stomata open and close). In the end, water concentrations will be balanced, and the process of osmosis stops. The concentrations of all particles in both compartments will have reached the state of dynamic equilibrium, and the membrane will forever vacillate around its expected position.
’ ADDRESSING THE MISCONCEPTIONS USING THE OSMOSIS SIMULATOR In a series of experiments, students can detect possible explicit and implicit misconceptions and adjust their conceptions about the underlying processes of osmosis. Experiment A addresses the misconception of assigned intentionality. This simulation uses the show/hide traces button (8) to emphasize the randomness of particle motion. Students can start and stop the simulation using the start/stop button (1) and detect particles that are currently moving in the “wrong” direction relative to that of the concentration gradient. Experiment B addresses the misconception of static equilibrium. Once the membrane position stabilizes at dynamic equilibrium, the students can immediately observe that all particles are still moving. Students can be asked to discuss the apparent contradiction between dynamic equilibrium and the observation that water molecules still exchange freely between the two compartments. Students should come to appreciate that when 774
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Journal of Chemical Education the concentration of water is higher on one side of the membrane than on the other side, the higher proportion of water molecules close to the membrane on one side means that an individual water molecule on that side has a statistically higher probability of crossing the membrane during a given period of time. When the difference in water concentrations between the two sides vanishes, the respective numbers of water molecules relatively close to the membrane on each side are equal, and their probabilities of crossing the membrane are equal as well. Thus, when the crossing probabilities are equal, the water movements from right to left and from left to right across the membrane will be equal. Therefore, the net water movement is zero at dynamic equilibrium. Experiment C addresses the misconception of speed. In the model, the speed of osmosis (or technically speaking, the decreasing net flux of water molecules across the membrane) can be traced by watching the moving speed of the membrane. An integral measure for the speed of osmosis during an arbitrarily defined time window of the first 1000 time ticks is the distance the membrane has moved during this interval. Students can change the initial concentration gradient and predict how the speed of the membrane will change, as displayed by the integrated “speed” of osmosis monitor (9). A more systematic experiment is to let all students in parallel calculate the distances for a particular osmolarity gradient such as 8:8, 8:7, 8:6, and continuing down to 8:0 (left:right compartment), for example, and then to plot for each gradient the average distance the membrane moved during 1000 time ticks against the ratio of the osmolarities. The students should acquire an understanding that the probability with which some water molecules leaves the left compartment is always the same, whereas their probability of leaving the right compartment is initially the same at the 8:8 condition but then steadily increases as the osmolarity gradient decreases. The greater the initial osmolarity difference, the faster the net water movement, the larger the pressure increase, and the faster the membrane moves. One of the most interesting predictions that can be asked of the students is about the membrane movement in the 8:0 gradient condition (this model is prevented from crashing by holding the membrane if it gets too close to the far right side). As an important side feature, students learn that the speed of osmosis can increase solely because of the increasing concentration gradient (and not by increasing temperature!). Teachers should also point out that in the experiment above the particles do not move more quickly or more slowly if the concentration gradient is changed. In the case of water molecules, their local concentrations simply provide them with different probabilities for crossing the semipermeable membrane.
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Future empirical studies are clearly required to determine the contribution of this new model toward effective teaching of Brownian motion and the colligative property of osmosis.
’ ASSOCIATED CONTENT
bS
Supporting Information The model file. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The author thanks Hans-Ueli Ehrensperger, Markus M€uller, Constantin Kappel, and Helmuth Eirainer for testing the model in classroom settings and providing valuable suggestions for improvement. ’ REFERENCES (1) Haynie, D. T., Biological Thermodynamics; Cambridge University Press: Cambridge, 2001. (2) Johnstone, A. H.; Mahmoud, N. A. J. Biol. Educ. 1980, 14 (2), 163–166. (3) Friedler, Y.; Amir, R.; Tamir, P. Int. J. Sci. Educ. 1987, 9 (5), 541–551. (4) Odom, A. L. Am. Biol. Teach. 1995, 57 (7), 409–415. (5) Odom, A. L.; Barrow, L. H. J. Res. Sci. Teach. 1995, 32 (1), 45–61. (6) Zuckerman, J. T. Am. Biol. Teach. 1994, 56 (1), 22–25. (7) Freeman, S., Biological Science; Prentice Hall: NJ, 2002. (8) Meir, E.; Perry, J.; Stal, D.; Maruca, S.; Klopfer, E. Cell Biol. Educ. 2005, 4, 235–248. (9) Sanger, M. J.; Brecheisen, D. M.; Hynek, B. M. Am. Biol. Teach. 2001, 63 (2), 104–109. (10) Williamson, V. M.; Abraham, M. R. J. Res. Sci. Teach. 1995, 32 (5), 521–534. (11) Wu, H.; Shah, P. Sci. Educ. 2004, 88 (3), 465–492. (12) Chi, M. T. H. J. Learn. Sci. 2005, 14 (2), 161–199. (13) Jacobson, M. J.; Wilensky, U. J. Learn. Sci. 2006, 15 (1), 11–34. (14) Levy, S. T.; Wilensky, U. Cognition Instruct. 2008, 26 (1), 1–47. (15) Penner, D. E. J. Res. Sci. Teach. 2000, 37 (8), 784–806. (16) Garvin-Doxas, K.; Klymkowsky, M. W. Life Sci. Educ. 2008, 7, 227–233. (17) Wilensky, U. NetLogo; http://ccl.northwestern.edu/netlogo; Northwestern University: Evanston, IL, 1999 (accessed Feb 2011). (18) CRC Handbook of Chemistry and Physics; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2010.
’ FIRST EXPERIENCES WITH THE MODEL The effect of teaching osmosis using the osmosis simulator has not yet been empirically tested. There is, however, feedback from various teachers (14 biology or chemistry classes with a total of 277 students have used the model so far). Generally, students using the model appear to show a deeper understanding of the compatibility of random particle motion and the directed nature of osmosis. Most teachers are particularly positive about the tracing function, which provides easy visibility of random particle motion (Figure 1). Because probabilistic thinking is one of the most difficult issues in science teaching in general,16 considerable uncertainty remains as to how completely the students will understand the relationship between water concentrations and membrane crossing probabilities, even after exposure to this simulation program. 775
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