Activity Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
pubs.acs.org/jchemeduc
Introducing Electron Probability Density to High School Students Using a Spiral Drawing Toy Mikhail Kurushkin* and Chantal Tracey Chemistry Education Research and Practice Group, SCAMT Laboratory, ITMO University, 9 Lomonosova Str., Saint Petersburg 191002, Russian Federation
Downloaded via UNIV OF GOTHENBURG on January 23, 2019 at 06:23:54 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: A difficult topic to impart to students is the location of an electron within an atom. One possible way of introducing the concept of the electron probability density in an elementary classroom is by use of a Spirograph geometric ruler. Upon scrutinizing the generated patterns, it can be seen that they have areas that are notably dense and others that are almost bare. This probability density can be likened to that of the electron. The suggested activity was carried out with a group of 14-year-old students that had no prior knowledge of atomic structure. The gaps in the pattern and its color intensity gradient were commented on by the students. The students (N = 86) were given a post-test to evaluate their understanding. As the results show, 83% of the students’ grades were satisfactory. The present research suggests that the Spirograph activity is suitable for the primary introduction of the concept of probability density in an elementary classroom. KEYWORDS: Elementary/Middle School Science, Physical Chemistry, Analogies/Transfer, Collaborative/Cooperative Learning, Hands-On Learning/Manipulatives, Inquiry-Based/Discovery Learning, Atomic Properties/Structure, Student-Centered Learning
■
INTRODUCTION
conclusion that it is best to introduce orbitals from the get go.12 One possible way of doing so is by use of a Spirograph geometric ruler. The Spirograph geometric ruler is a toy composed of several gears and outer rings that, depending on how they are combined, produce various patterns known as rosettes. The Spirograph geometric ruler has previously been used in science to depict probability patterns. One example is the visualization of ecological networks13 which occur in nature. Upon scrutinizing the generated patterns, it can be seen that they have areas that are notably dense and others that are almost bare. This probability density can be likened to that of an electron.
Actively engaging students in the learning process is an effective way to ensure cognitive permanence.1 As children learn by doing, hands-on learning is a powerful technique oftentimes employed where possible. The use of toys in the classroom is nothing foreign and is not only constructive but also provides a good source of entertainmentencouraging avid interest in students,2 particularly in science, technology, engineering, and mathematics.3,4 Introducing new scientific concepts to children in an entertaining way is challenging. As misconceptions can easily occur,5 it is imperative that new topics are taught simply and accurately the first time around. Toys have been used in the classroom to assist in teaching students some of the more difficult aspects of science.6 Examples include the utilization of a Hoberman Switch Pitch to teach transition state theory,7 an Etch-a-Sketch to depict Clapeyron’s equation,8 Legos to teach the visually impaired different trends observed in the periodic table,9 and Neo Magnets to demonstrate carbon catenation.10 Another difficult topic to impart is the location of an electron within an atom. The often used approach is the introduction of the Bohr model, where students initially learn that electrons are confined to shells that surround the nucleus.11 Students then later have to be disabused of the notion that electrons orbit the nucleus and instead are highly likely to be found in certain places near the nucleus known as orbitals. Many students find it taxing to go from the classical orbits to the quantum mechanical orbitals, leading to the © XXXX American Chemical Society and Division of Chemical Education, Inc.
■
HOW TO ORGANIZE
Instructions
Although the Spirograph geometric ruler is a readily available and highly affordable toy from any local store, it is recommended that the teacher has a number of them on hand instead of having the students source them for themselves. This allows for consistency in the model used, ensuring that the students obtain the same pattern when following the given instructions. It is recommended that the classic Spirograph geometric ruler be used. The classic Received: May 24, 2018 Revised: December 3, 2018
A
DOI: 10.1021/acs.jchemed.8b00391 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Activity
gently steering questions. The teacher should then explain the similarities between the rosette and the electron probability density of a typical s orbital. It should be stressed that the darker the area, the more likely it is that the electron would be found there. Therefore, the very dark areas represent where the electron is most likely to be. The lighter the area, the less likely it is that the electron will appear there at any given moment in time. The generated rosette has some noticeable gaps within it. The teacher should highlight that these gaps illustrate where within an orbital the electron will never be found, as certain areas are inaccessible to it. The most obvious gap is at the center of the pattern. The center of the rosette can be compared to the nucleus of the atom. The instructor should emphasize that the electron is never found in the nucleus but instead moves around it.
Spirograph geometric ruler (Figure 1) comprises three gears and two outer rings (with the smaller one having 96 teeth and the bigger one having 105 teeth).
Figure 1. Typical Spirograph geometric ruler. Dashed lines represent gear toothed holes, and solid lines represent smooth holes.
■
Depending on the class size and the number of Spirograph geometric rulers available, this can be either an individual or a group activity. Regardless, the instructions remain the same. Use the first hole of the largest gear and the smaller outer ring to produce the desired pattern (Figure 2).
EDUCATIONAL GOALS
The Results and Discussion
The suggested activity was carried out with a group of 14-yearold students that had no prior knowledge of atomic structure. The task was conducted as a group activity with students being placed in groups of four or five. The Spirograph geometric ruler was passed among them. Accounting for all of this, the students took a maximum of 10 min to complete the activity. The process of creating the rosettes is shown in Figure 3. A collaborative learning technique was applied.
Figure 2. Rosette.
Students should play with the Spirograph geometric ruler for 5−10 min. If it is a group activity, ensure that the Spirograph geometric ruler is rotated among the students so that each child gets a turn. Students should have a pattern similar to that depicted above.
Figure 3. Students drawing the rosettes cooperatively.
At the end of the activity, the expected rosette was projected by the teacher (see the Supporting Information to download an HD version of the rosette). The students were encouraged to state any observations on the drawings they had made. They were able to point out that there was nothing at the center of the rosette and the lessening color gradient as one moved away from the center. They were also able to comment on those areas within the rosette that appeared to be gaps. The symmetry of the rosette was also commented on. Their observations were then related to a typical s orbital of an atom. Using the explanation guide given above, a comparison between the highlighted gaps and the light and dark areas of the rosette and the electron probability density of an s orbital was drawn.
Explanation Guide
The electron is a particle that is in constant motion. The motion of the electron is observed from moment to moment in time. Although its movement may at first seem random, if it is observed over an extended period and its path plotted, an obvious pattern emerges.14,15 This path is reminiscent of the pattern the students just drew using the Spirograph geometric ruler. Before beginning their explanation, the teacher should ask the students to comment on the appearance of the rosette before them. Close inspection shows that some areas are darker than others and discernible gaps are observed and the students should be able to point this out on their own or with B
DOI: 10.1021/acs.jchemed.8b00391 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
■
Post-test
Figure 4. Results of the post-test (N = 86). The maximum possible score at the moment of the educational experiment was 15.
A bar graph with the scores of the 86 students was drawn and its accompanying polynomial plotted as seen in Figure 4; 83% of the students tested satisfactorily.
■
CONCLUDING REMARKS During the course of the activity, the students seemed engaged and interested. When asked if they enjoyed it, they answered in the affirmative. Not only was it an enjoyable experience for them but also a learning one, as evidenced by the fact that the pass rate was 83%. ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b00391. Distributable post-test (PDF) Post-test answer key (PDF) HD version of the rosette (PDF, TIF)
■
REFERENCES
(1) Bovill, C.; Felten, P.; Cook-Sather, A. Engaging Students as Partners in Learning and Teaching: Practical Guidance for Academic Staff and Academic Developers; Wiley: Hoboken, NJ, 2014. (2) Liebermann Van Hoorn, J. Play at the Center of the Curriculum; Pearson: London, 2015. (3) Quang, L.; Hoang, L.; Chuan, V.; Nam, N.; Anh, N.; Nhung, V. Integrated Science, Technology, Engineering and Mathematics (STEM) Education through Active Experience of Designing Technical Toys in Vietnamese Schools. Br. J. Educ. Soc. Behav. Sci. 2015, 11 (2), 1−12. (4) Kim, S. Gamification in Learning and Education Enjoy Learning Like Gaming; Springer International Publishing: New York, 2018. (5) Doran, R. L. Misconceptions of Selected Science Concepts Held by Elementary School Students. J. Res. Sci. Teach. 1972, 9 (2), 127− 137. (6) Ince, E.; Acar, Y.; Temur, S. Physics Toys Effectiveness Of Undergraduates’ Understanding Physics Principles. Eur. J. Phys. Educ. 2016, 6 (4), 39−51. (7) Fieberg, J. E. Visualizing Reaction Progress and the Geometry and Instability of the Transition State. J. Chem. Educ. 2012, 89 (9), 1174−1177. (8) Darvesh, K. V. Exploring the Clapeyron Equation and the Phase Rule Using a Mechanical Drawing Toy. J. Chem. Educ. 2013, 90 (11), 1472−1475. (9) Melaku, S.; Schreck, J. O.; Griffin, K.; Dabke, R. B. Interlocking Toy Building Blocks as Hands-On Learning Modules for Blind and Visually Impaired Chemistry Students. J. Chem. Educ. 2016, 93 (6), 1049−1055. (10) Kao, J. Y.; Yang, M.-H.; Lee, C.-Y. From Desktop Toy to Educational Aid: Neo Magnets as an Alternative to Ball-and-Stick Models in Representing Carbon Fullerenes. J. Chem. Educ. 2015, 92 (11), 1871−1875. (11) McKagan, S. B.; Perkins, K. K.; Wieman, C. E. Why We Should Teach the Bohr Model and How To Teach It Effectively. Phys. Rev. Spec. Top. - Phys. Educ. Res. 2008, 4 (1), 010103. (12) Müller, R.; Wiesner, H. Teaching Quantum Mechanics on an Introductory Level. Am. J. Phys. 2002, 70 (3), 200−209. (13) Etemad, K.; Carpendale, S.; Samavati, F. Spirograph Inspired Visualization of Ecological Networks. Proceedings of the Workshop on Computational Aesthetics; Expressive ‘14, The Joint Symposium on Computational Aesthetics and Sketch Based Interfaces and Modeling and Non-Photorealistic Animation and Rendering; Vancouver, Canada, August 8−10,2014; pp 81−91. (14) Feynman, R. P.; Hibbs, A. R.; Styer, D. F. Quantum Mechanics and Path Integrals, amended ed.; Dover Publications: Mineola, 2014. (15) Dirac, P. A. M. The Quantum Theory of the Electron. Proc. R. Soc. London, Ser. A 1928, 118, 351.
The students (N = 86) were given a post-test with 15 questions to evaluate their understanding (see the Supporting Information to print out the distributable post-test and the post-test answer key). The post-test lasted for 15 min. The results are given in Figure 4.
■
Activity
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Mikhail Kurushkin: 0000-0001-9031-8247 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS We acknowledge Simon Koltsov for proposing an appropriate rosette with which to carry out the activity. Also, our wholehearted thanks to School 77 and School 309 (St. Petersburg, Russia) for allowing us to introduce the activity to the students. C
DOI: 10.1021/acs.jchemed.8b00391 J. Chem. Educ. XXXX, XXX, XXX−XXX
