learning and teaching with a computer scanner
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Learning and teaching with a computer scanner
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2014 Phys. Educ. 49 586
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1. IntroductionAn optical scanner is a computer-operated device for taking images of paper documents. A scan-ner can also be used for taking images of other objects when they are placed appropriately. It can also be used in many exciting physics experi-ments. In this paper we not only describe a variety of experiments with a scanner, but most impor-tantly show how a teacher can use these experi-ments with supporting questions to help students develop and apply the concepts of relative motion, graphing and the Doppler effect, and learn to think like scientists. Specifically, we will use the well- established framework of the Investigative Science Learning Environment (ISLE).
2. Investigative science learning environmentISLE [1] is an educational framework that can guide the design of instruction and student learn-ing. ISLE engages students in the processes that mirror scientific practice to help them learn
physics. Specifically, students start learning a new concept by observing a few very simple experi-ments (called observational experiments). They do not make any predictions before those obser-vations. They then identify patterns, develop mul-tiple explanations for those patterns and finally, test the explanations (with the purpose of rul-ing them out). The testing involves designing a new experiment (called a testing experiment), the outcome of which they can predict using the explanation. After they conduct the experiment and compare the predictions to the outcomes of the testing experiment, they make a judgment on the explanation. If the outcome matches the pre-diction, more testing experiments are needed to gain confidence in the explanation, if there is a mismatch, then there is a need to re-examine the explanation, hidden assumptions, experimental design, etc. Finally, if a few testing experiments fail to reject the proposed explanation, students can use it (together with other established ideas) to solve new experimental problems (these are called application experiments). This sequence is
Learning and teaching with a computer scannerG Planinsic1, B Gregorcic1 and E Etkina2
1 Faculty for Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia2 Graduate School of Education, Rutgers University, New Brunswick, New Jersey, USA
E-mail: [email protected]
AbstractThis paper introduces the readers to simple inquiry-based activities (experiments with supporting questions) that one can do with a computer scanner to help students learn and apply the concepts of relative motion in 1 and 2D, vibrational motion and the Doppler effect. We also show how to use these activities to help students think like scientists. They will conduct simple experiments, construct different explanations for their observations, test their explanations in new experiments and represent their ideas in multiple ways.
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0031-9120/14/050586+10$33.00 © 2014 IOP Publishing Ltd
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called an ISLE cycle (figure 1). An ISLE cycle for a particular concept can be purely qualitative or can contain the analysis of quantitative data, developing representations for such analysis, quantitative derivations, etc. What is important here is that any cycle starts with collecting exper-imental evidence and ends by testing reasoning based on that evidence in new experiments. ISLE has been used in introductory physics courses in middle schools, high schools and colleges [2], and with teachers in professional development activities [3].
3. Using a scanner to learn physical concepts
3.1. General comments
The following simplified description of scan-ner operation is sufficient for a teacher to guide students through the activities described in this paper. A stepper motor is moving the scanner head at a constant speed along the document. During this time the optical system in the scan-ner head is projecting (or simply casting) a nar-row strip of the document on the pixel-wide light sensitive detector. Signals from the detector are sent to a computer and stored as a time sequence of line images. Line images are recorded at equal time intervals and digitally put together to make the whole image. Throughout this paper we will assume that the scanner head moves across the scanner window from left to right and that the x, y coordinate system is placed as shown in figure 2.
For each activity that the students conduct, we will first describe the goals of the activity, then pre-sent the instructions that the teacher gives them (in italics) with the explicit steps of the ISLE cycle, then describe what students might do when they engage in the activity and finally, when necessary, provide photos of the outcomes of the experiments.
Note that most of these experiments can also be done using a photocopying machine but since scanned images can be observed without wasting any paper, readers are advised to use a photocop-ier only if a scanner is not available. The activi-ties described in this paper can be used with high school students in their first physics course or with college students. The level of the students will determine how much mathematics will be used.
3.2. Understanding physics with a scanner
3.2.1. How does a computer scanner work? The goal of this cycle is to help students understand how a scanner makes an image of an object. Before stu-dents start, prepare a transparency printed with par-allel lines separated by 1 cm (we found that yellow gives the best contrast). Also, take a toy car, put some white tape on its bottom and write the word CAR.
Fix the transparency on the scanner window to set the scale. Place the car on the opened scan-ner and scan it (figure 2).
(a) Observe: Observe the scanning process and the resulting image (figure 3(a)).
(b) Explain: Based on the observation propose several explanations for how the scanned image is composed.
(c) Test: Suggest an experiment to test your explanations.
In our experience most of the students suggest that the image is captured line by line (explanation 1), however some have an alternative explanation that the scanner is capturing the image from the whole window all the time while the light source is illuminating it from below (explanation 2). A possible testing experiment, which will rule out the second explanation, is to remove the car from the scanner when the scanner head is at about the middle of the car. The prediction based on expla-nation 1 is that the image will show only half of the car and the prediction based on explanation 2 is that there will be a whole car on the image, but some parts of the image will be less bright than
Figure 1. The elements and the flow of the ISLE cycle.
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others. When the students perform the experiment they see that the outcome is in agreement with the prediction based on the first explanation (see figure 3(b)), so we can reject explanation 2.
It is important that at the end of this step stu-dents understand that the scanned image is cap-tured line by line and that during capturing the scanner head moves with constant speed vs (if time permits you can ask them to test this experimen-tally). You may stimulate a discussion through which students realize that measuring the distance between x coordinates of two points on the scanned image and knowing the speed of the scanner head, one can calculate how much time passed between taking the image of the first and the second point.
3.2.2. Linear motion in the direction of scanning (simple cases). Here the students will continue to observe and explain the scanning they started in part 3.2.1. As a result of the activity students construct the concept of relative motion.
(a) Observe: Place the car on the scanner window with the front part pointing in the direction of scanning. During the scanning move the car in the same direction as the scanner head, at a constant speed that is smaller than the speed of the scanner head (vc < vs), so that the scanner head passes the car in motion. Record your observations (figure 3(c)).
(b) Explain: Why is the scanned image of the car in this case longer than the image of the stationary car that we obtained in part 3.2.1? Draw a sketch of the image. Make sure you
draw all the details including the letters that are painted on the bottom of the car.
(c) Test: Predict the outcome of the following experiment using your explanation of the elongated image of the car that is moving in the same direction as the scanner head. The car starts in the middle of the scanner window (front of the car still pointing in the direction of scanning) and during scanning moves with constant speed towards the scanner head (i.e. car moves backwards). What can you say about the shape of the image that will appear? After you have made the prediction (the best way is to draw what you will see), conduct the experiment and compare the result to the prediction. Do you need to revise your reasoning? The result is shown in figure 3(d).
For part (b) students should reason in the fol-lowing way. Since the car is moving in the same direction as the scanner head it takes more time for the scanner head to travel between the back and the front of the car than for the stationary car. Therefore, the length of the car on the image appears longer than on the original image. By coming up with this explanation, the students will construct the concept of relative motion–the length of the car as ‘seen’ by the scanner head is larger than the length of the car as seen by the observer in the laboratory reference frame. The next step is to help students construct the idea of relative velocity by asking them how the speed of the car and the speed of the scanner head affect
Figure 2. The basic equipment: a computer scanner (with opened cover), transparency with 1 cm lines and the toy car.
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the length of the scanned image. Once students come up with the idea of relative velocity, they can test it by using it to predict the outcome of a new experiment. The result is shown in figure 3(d).
3.2.3. Representing motion graphically. Here the students analyze graphically both experiments that we described in 3.2.2. The goal is to help stu-dents learn not only to represent motion graphi-cally but also to connect graphical representations to the real physical phenomena.
Try to represent the motion of the scanner head and the car (as seen by the observer in the laboratory reference frame) on one graph. Suggest the type of the graph that will also allow you to predict the length of the scanned image of
the car. Draw two separate graphs, one for the observational experiment (the outcome of which is shown in figure 3(c)) and one for your testing experiment (the outcome of which is shown in figure 3(d))
Students will need some time (at least 10 min) to construct the first graph. Some students may first suggest velocity–time graphs but when they realize that such graphs do not contain informa-tion on the length of the car they quickly agree that those graphs are not productive. Students might also treat the car as a point object (they rep-resent its motion with a single line) while drawing a position versus time graph but they will quickly realized that they need to follow two points on the car (front and back) in order to determine the length of the scanned image and therefore they cannot simplify the car as a point object.
Once the students construct graphs encour-age them to identify the following important fea-tures on their graphs (figure 4): xf—front part of the car, xb—back part of the car, vs—speed of the scanner head (slope), vc—speed of the car (slope), ts—time needed for scanner head to pass the car, a—length of the car and b—length of the scanned image of the car. Let them work in groups. Some of the students will probably need help to realize which distance on the graph represents the length of the scanned image of the car. If needed, give them a hint by pointing that this is the distance passed by the scanner head during ts. The graphs for the two experiments described above are shown in figures 4(a) and (b).
3.2.4. Representing motion mathematically. In this section students will connect the graphical representations to the mathematical representa-tion of the same motion by analysing the same experiments from a different perspective. We assume that they are familiar with the mathe-matical description of the motion with constant velocity.
Prepare two scanned images of a car: the first one (figure 3(a)) with a stationary car (vc = 0) and the second one (figure 3(c)) with the same car moving slower than the scanner head (vc < vs) in the direction of the scanning.
Based on the scanned images calculate the speed of the car as measured in the laboratory ref-erence frame (vc) and the speed of the car relative to the scanner head (vc rel to s) (i.e. the speed of the car
Figure 3. Scanned images of a car: (a) stationary, (b) car removed in the middle of scanning (the testing experiment), (c) car starting in front of the scanner head and moving in the same direction as scanner head (vc < vs), (d) car moving towards the scanner head and (e) car starting behind the scanner head and moving in the same direction as scanner head (vc > vs). Note that in all cases the front of the car (close to letter R is) is pointing to the right.
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as measured in the reference frame that is moving together with the scanner head). Assume the speed of the scanner head was equal to vs = 8 cm s−1 in all experiments. Show your calculations and use the same symbols as you did on the graphs. (Hint: you can get ideas for the mathematical expressions of the speed of the car from the graph that you con-structed in the previous activity.)
Based on the graph (figure 4(a)) students may realize that the speed of the car in the labora-tory reference frame can be expressed as
= −v
b a
tc
s (1)
and that the scanning time ts is the time needed for the scanner head to pass a distance equal to the length of the scanned car b
=tb
v.s
s (2)
Combining these two equations one can express the speed of the car in the laboratory ref-erence system in terms of the speed of the scanner head and the lengths a and b:
= −v
b a
bv .c s (3)
Students intuitively know that the speed of the car relative to the scanner head is smaller than rela-tive to the laboratory reference frame. You can guide them to the mathematical expression for the speed of the car relative to the scanner head (vc rel to s)
− = −=v v va
bv .c rel to s c s s (4)
Discuss with students the meaning of the negative sign of vc rel to s (for the observer on the scanner head the car seems to move in the nega-tive x direction) and the limiting case when speed of the car is approaching the speed of the scan-ner head (vc approaches vs is consistent with b approaching infinity and vc rel to s approaching zero; see equations (3) and (4)).
3.2.5. Linear motion in the direction of scanning (complex case). In this activity students are challenged to predict the image produced by the scanner for a more complex motion. The graphs that students learned to make in part 3.2.3. are very helpful here. Now that students have a firm idea of how a scanner works, they are not test-ing this idea anymore, they are applying it to solve more complex problems, thus this activity belongs to the application part of the cycle (see figure 1).
Imagine that you place the car on the left edge of the scanner, outside the glass, as shown in figure 5 and start the scanning process. During scanning you move the car with constant speed larger than the speed of the scanner head (vc > vs) and in the same direction as the head, so that the car will catch up and pass the scanner head before the head reaches the right side of the window.
Figure 4. Graphs of (a) the car moving in the same direction as the scanner head (vc < vs) and (b) the car moving towards the scanner head. Both graphs describe motion as seen by the observer in the laboratory reference frame.
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Represent the motion of the car and the scan-ner head using the same type of graph that you developed in part 3.2.3. Based on the graph make a prediction of how the scanned image of the car in this case will compare to the image of the sta-tionary car that you obtained in part 3.2.1. Draw a sketch of the anticipated image. Make sure you draw all the details including the letters that are painted on the bottom of the car. Then perform the experiment and observe the scanned image (fig-ure 3(e)). Compare the scanned image with your prediction and discuss any details that you did not account for.
Since the students became familiar with drawing graphs in activity 3.2.3, it should not be a problem for them to draw the graph for this situ-ation (figure 6). However, they might have some difficulty to predict how the letters on the bot-tom of the car will look on the scanned image. Analysis of the graph helps a lot, but some stu-dents may need hints even in this case. Some students may suggest that letters on the scanned image will appear in the reverse order (RAC). Tell them to focus on the scanning of the letter R first and draw the anticipated image.
As the car passes the scanner head, the head meets the front of the car first, then the middle part of the car, and finally the rear part of the car. However the computer still puts together the line scans from left to right in the order of their appear-ance. The result is a mirrored (or flipped) image of the bottom of the car. Note that the scanned image cannot be obtained by a rotation of the word CAR. Many students think that in this case
the length of the scanned image is always shorter than the length of the car because the speed of the car is larger than the speed of the scanner head. Remind them that the length of the scanned image depends on the time needed for the scanner head to pass the car and point to the limiting case when the speed of the car is just slightly larger than the speed of the scanner head.
3.2.6. Linear motion in the direction perpendicu-lar to the scanning direction. The goal of this section is to help students to analyze relative motion in 2D by applying their knowledge of the scanning process. So we can call the below experiment an application experiment, the same as in section 3.2.5.
Part 1. Predict the scanning result. Imagine you move a thin rod with constant speed across the scanner window in the direction perpendicular to the scanning direction (the rod remains parallel to the x axis and moves with constant speed in the negative y direction). Use your knowledge of how the scanner works to predict how the scanned image will look. Draw a sketch and if necessary add a description in words. Try to account for as many details as possible.
Perform the experiment and observe the scanned image (figure 7). Compare the scanned image with your prediction and discuss any details that you did not account for.
Several students will correctly predict that the image will resemble a tilted line, but they will need some time to come up with a quantitative analy-sis of the image. There are two key points in this
Figure 5. Starting position of the car for the case when vc > vs and the car moves in the same direction as the scanner head.
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activity that students need to realize: (1) because the scanner produces non-distorted images, the horizontal scale (in cm) applies also for the verti-cal direction, and (2) by measuring the difference between x coordinates of two points on the rod trace one can calculate the time interval needed for the rod to pass this distance (assuming the speed of the scanner head is known). Combining these two findings students can find out that the slope of the trace on the image equals the ratio vr/vs, where vr is the speed of the rod (note that the rod is moving in the y direction only). Once students successfully solve this activity they are
ready for the next one in which they need to apply the acquired knowledge.
Part 2. Use the scanning result to describe motion: image jeopardy. Based on what you have learned so far determine as much information as possible (qualitative and quantitative) about the motion of the thin rod from the following scanned image (see figure 8). (Note: the scanner head was moving from left to right with a constant speed 8 cm s−1; the distance between adjacent vertical lines is 1 cm).
Based on the image students can determine the speed and the direction of the motion of the rod during each of the six time intervals. One interesting point to discuss here is why the thick-ness of the rod trace appears different in differ-ent parts of the image. Remind the students that the scanner captures vertical line images and let them realized that the vertical measure of the rod is constant throughout the image.
3.2.7. Rolling down the incline. The goal of this section is to help students see applications of the equations to motion at constant acceleration. It is good to do them as application experiments after the students have learned the mathematics of this motion.
Rolling a round object. Put a book under a longer side of the scanner to tilt it in the y direc-tion a few degrees. Take a thin metal rod with a circular cross-section and let it roll down from
Figure 6. Position versus time graph for the car moving in the same direction as the scanner head (vc > vs). Note that the car’s initial position is at negative x (outside the scanner window).
Figure 7. Scanned image of a thin metal rod that was parallel to the x axis and moved with approximately constant velocity in the negative y direction.
Figure 8. The scanned image of a thin rod. The rod started from rest at y = 0, moved with constant speed in the +y direction, stopped for a while, moved with constant speed in the –y direction, stopped again and finally moved in the +y direction with approximately constant speed.
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the elevated side of the scanner widow so that the scanner head is perpendicular to the stick during scanning.
Explain the shape of the image. Based on the scanned image (figure 9(a)) determine as much information as possible (qualitative and quan-titative) about the motion of the rod. List your assumptions.
Most students will probably remember that motion down the incline is uniformly accelerated or they will get the hint noting the parabolic shape of the stick trace. However, the quantitative analysis of the image will reveal how good their understand-ing of these concepts is. Ask them to determine the acceleration of the rod from the image and discuss energy conversions for the motion that is captured in the image. The acceleration of the rod a can be determined from the slope of the graph y versus x2 for the points where the rod trace crosses vertical
lines (the slope is equal to a
v2 s2).
Rolling a pencil. Take an ordinary (hexago-nal) pencil and let it roll down the scanner win-dow the same way as you rolled the metal stick in the previous experiment. Obtain the scanned image of a rolling pencil (figure 9(b)). Explain the shape of the image. Based on the image deter-mine as much information as possible (qualitative and quantitative) about the motion of the pencil. List your assumptions.
Students will notice that the pencil rolls down the incline with approximately constant speed and they will determine this speed of the pencil in the same way as in the first activity in this sec-tion. With some help from a teacher students may suggest the following qualitative explanation that addresses the energy aspect of the problem: a hex-agonal pencil soon reaches a constant terminal
speed because at each collision some fraction of a pencil’s kinetic energy is transformed into inter-nal energy. Quantitative analysis of this problem is beyond the introductory physics level, but it can be a good project for undergraduate physics majors (for more details see [4]).
3.2.8. Vibrational motion. Activities in this sub-section can be used at the beginning of the unit on vibrational motion to help students learn the nature of simple harmonic motion.
Studying a new type of motion. Tie two strings to the ends of a metal rod and hang it horizontally above the scanner window. Push the rod to make it oscillate in the direction perpendicular to the scanning direction.
(a) Observe: Record the image of the vibrating rod with the scanner (figure 10).
(b) Explain: Use your knowledge of how scanner works to explain as many details of the scanned image as possible.
Figure 9. Experiments on the scanner which is titled in the y direction; (a) scanned image of a thin metal rod and (b) of a pencil with hexagonal cross-section. Both rolled down the tilted scanner window.
Figure 10. Scanned image of a thin metal rod oscillating in the y direction above the scanner window.
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Students will see the periodic nature of the motion—you can introduce the physical quantities of the period of oscillations and the amplitude and the students can determine the values of both from the image. Most importantly, by using the knowl-edge from the previous activity they can qualita-tively describe the changes in the motion of the rod, and figure out that it stops at the ends of the swing and moves fastest when the rod is at the lowest point and that the speed does not change linearly.
3.2.9. Discovering the Doppler effect. A moving scanner head can be treated as a moving detector and thus used to help students devise the concept of a Doppler effect. If such a detector is moving toward or away from the waves, a Doppler change of frequency may be observed. Ideal waves in our case are water waves, such as those produced in a ripple tank. One can make a simple and cheap ripple tank from a transparent plastic box cover (we found the box of Ferrero Rocher sweets to be ideal for this purpose; see figure 11(a)). We glued a stripe of plastic foam on each side to reduce the reflection of waves and consequently standing waves. The experiment can serve as an observa-tional experiment that helps students discover the Doppler effect.
(a) Observe: Place a transparent plastic tray on the scanner window and pour in water to about 5 mm depth. Hold flat a piece of plastic board vertically above the middle of
the tank and start moving the board up and down periodically with constant frequency (figure 11(a)). You will observe two waves propagating in opposite directions from the board toward the sides of the tray. Start scan-ning and keep making the waves. Observe the scanned image and describe any pattern that you can see on the image.
(b) Explain: Try to explain the pattern using what you have learned in the activities in section 3.2.2.
Students will observe that the distance between the adjacent lines (that correspond to the wave crests in the water) on the scanned image is different on each side of the board (figure 11(b)). The lines that resulted from waves moving toward the scanner head seem to be closer together and the lines that resulted from waves moving with the scanner head seem to be further apart. Students who already know about the Doppler effect may mistakenly think that the image shows a change in wavelengths while in fact it shows the change in the time needed for the scanner head to pass suc-cessive wave crests. Using a theory similar to that in section 3.2.4., one can express the length of the scanned distance between two lines (b) in terms of the original distance between the wave crests (a) for a general case
=−
b av
v u.s
s (5)
Figure 11. Using the scanner to discover the Doppler effect: (a) setup for the experiment: scanner, transparent plastic container with water, plastic board, 1 cm scale; (b) a scanned image of the water waves (the scanner head was moving from the top to the bottom of the image).
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From here one can express the time interval during which the scanner head passes distance b in terms of the time needed for waves to pass dis-tance a
′ = =−
tb
vt
1
1,
v
us
0s (6)
where u is the speed of the water waves, and
=ta
u.0 Note that in our case u is negative on one
side of the plastic board and positive on the other. In the experiment photographed in figure 11 we produced waves with a frequency of about 5 Hz which propagated with a speed of about 20 cm s−1 and had a wavelength of about 4 cm. The speed of the scanner head was 6.7 cm s−1. From the scanned image in figure 11(b) one can estimate length b in the upper part of the tank (1 cm) and in the lower part of the tank (2 cm). The readers can check for themselves that the calculated values obtained from equation (5) agree very well with the measured values.
4. SummaryIn this paper we wanted not only to share simple but exciting experiments that one can do with a scanner in an introductory physics classroom, but also to show how you can use the scanner to help your students construct the concepts that are part of the high school physics curriculum. Most importantly we wished to provide support for those who plan to engage their students in an authentic inquiry process using the scanner and to show how one can combine experimental investigations with reasoning using multiple representations.
The scanner offers additional challenging opportunities that can be used in teaching and learn-ing at university level. A paper on using a scanner to study relative motion that combines translation and rotation was published recently by Gregorcic and Planinsic in this journal [5]. We also believe that the activities described in section 3.2.2 can serve as a preparation for studying special relativity.
AcknowledgmentAuthors wish to thank Laurence Viennot and late Elena Sassi for valuable suggestions during the initial development of scanner-related activities.
References[1] Etkina E and Van Heuvelen A 2007 Investigative
science learning environment—a science process approach to learning physics Research Based Reform of University Physics ed E F Redish and P Cooney http://per-central.org/per_reviews/media/volume1/ISLE-2007.pdf
[2] Etkina E, Gentile M and Van Heuvelen A 2013 College Physics (San Francisco, CA: Pearson)
Etkina E, Gentile M and Van Heuvelen A 2013 The Physics Active Learning Guide 2nd edn (San Francisco, CA: Pearson)
[3] Etkina E, Planinsic G and Vollmer M 2013 A simple optics experiment to engage students in scientific inquiry Am. J. Phys. 81 815–22
[4] Rezaeezadeh A 2009 Motion of a hexagonal pencil on an inclined plane Am. J. Phys. 77 401–6
[5] Gregorcic B and Planinsic G 2012 Why do photo finish images look weird? Phys. Educ. 47 530–6
Received 1 February 2014, accepted for publication 19 March 2014doi:10.1088/0031-9120/49/5/586
Gorazd Planinsic is a professor of physics in the Faculty of Mathematics and Physics, University of Ljubljana, Slovenia. He also works at the Ljubljana House of Experiments. He leads a physics education program for future high school physics teachers and a continuing education program for in-service physics teachers in Slovenia. His main interest is in development and educational applications of simple experiments.
Bor Gregorcic graduated from the Faculty for Mathematics and Physics in Ljubljana, where he now works as a researcher in physics education. He is writing his PhD on the topic of computer-supported collaborative learning and the use of interactive whiteboards in high school physics instruction.
Eugenia Etkina is a professor of science education at Rutgers University, GSE (USA). She works with pre- and in-service high school physics teachers and develops physics curriculum materials. She is one of the creators of the Investigative Science Learning Environment (ISLE) and a co-author of the recently published College Physics textbook. Her research is in helping students develop‚ ‘scientific habits of mind’.