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Using Internet of Things (IOT) and Virtual Lab Activities to Enhance Learning in Online Chemistry Labs hosted in Google Classroom
A particularly challenging aspect of the rapid move to online instruction necessitated by the COVID-19 pandemic was that of providing students with laboratory-based instruction. This presentation will provide a summary of UALR's experience with IOT- enhanced online labs hosted in Google Classroom and LibreText. These were initially used in an accelerated 5 week General Chemistry class offered in the summer of 2020. The lab materials were then restructured in the LibreText OER to enable use by other faculty. The resources include collaborative online activities involving hands-on experiments, virtual labs and simulations from ChemCollective and PhET. In addition, students used both IOT enabled data streams and virtual labs to design actual laboratory experiments, gather data and analyze the results. Students worked in Zoom breakout rooms using Google Docs and Sheets, within Google Classroom, to collaborate and report their results. We will also discuss the topic of safety in online lab environments, and how we used that to engage students.
We will start with an introduction of ongoing Internet of Chemistry Things (IOCT) courses co-developed at UHSP and UALR, that allowed us to develop the IOT-enhanced general chemistry labs. In these courses students learn to use $35 Raspberry Pi microcomputers to stream data from a variety of sensors (pressure, temperature, pH,...) to web services such as Google Sheets. This includes building basic circuits and writing Python programs to operate and stream data from the sensors. The instructional material for these courses are posted on LibreTexts in the interdisciplinary course, the "Internet of Science Things" (IOST).
The final aspect of this work will deal with our broader efforts to advance IOT in chemistry education. We created a site devoted to the Internet of Chemistry Things (ioct.tech) and a Google Group on this topic (IOSTEd), that anyone can join. We wish to organize a future intercollegiate OLCC course on IOCT that would allow instructors with no prior experience with Raspberry Pis or programming to offer this course on their campus. Our hope is to offer such an IOCT OLCC in the spring of 2022, and we are seeking interested faculty who would like to participate.
Introduction
The Internet of Things (IOT) allows students to easily gather and share chemical data from physical and chemical sensors connected to digital networks. The growing availability of low-cost, easily-customized, distributed IOT laboratory components has the potential to improve instruction across the chemistry curriculum. This paper examines application of IOT in two courses.
The first course is a chemistry elective dedicated to IOT, in which students learn how to program microcomputers and microcontrollers, build circuits to obtain data from physical and chemical sensors, and connect them to digital networks. This course uses IOT as a makerspace for chemical experimentation, providing students with a learning environment that promotes creativity, provides opportunities for development of trouble-shooting and problem-solving skills, and promotes development of collaborative skills essential to success in a professional workplace. The course also develops technical skills, such as programming and interfacing to chemical instruments, that better prepare students for the modern chemical workforce.
The second course is a general chemistry course, in which students use IOT in conjunction with collaborative web technologies. The IOT tools, including some developed in the above IOT course, enable students to collaboratively gather and analyze data as part of their general chemistry laboratory instruction. This support for remote and collaborative experimentation became especially useful during the COVID pandemic.
To help other instructors incorporate IOT into their teaching, we have developed all of our instruction as Open Educational Resources (OER). We also recognize the challenges associated with introducing a new elective into a chemistry program. We close by describing our plans for an intercollegiate Online Chemistry Course (OLCC), the Internet of Chemistry Things, which allows instructors new to IOT to collaboratively teach an IOT elective course across institutions[1].
IOT Courses in the Chemistry Curriculum
This work started with an IOT course offered at the University of Health Sciences and Pharmacy in St. Louis that targeted problem solving abilities. The course is organized around projects[2] that use IOT as a makerspace, promoting active learning[3] that applies the chemical principles students learned in their prerequisite chemistry courses to the design and implementation of experiments[4]. Students interface $35 Raspberry Pi microcomputers (figure 1) [5,6,7] to simple circuits on breadboards, and create code in Python to control these IOT devices.
Figure 1: Raspberry Pi computer (📷: Belford/Lisitsyna, cc0)
Because many of these students have little coding or electronics experience, modules were developed to support both of these aspects of IOT. The python programming modules were adapted from CS-POGIL[9] content [10]. The electronics modules also use a Learning Cycle Method[8] , in which students are guided in constructing simple circuits, gathering data and examining it for patterns, and modifying the circuits to achieve meaningful goals. The video in Figure 2 is from an OER we developed that explains how to connect a breadboard to a Raspberry Pi.
Figure 2: YOUTUBE video from IOT module 1.4: GPIO Outputs- First Circuit (https://youtu.be/Ljd3dpfa1JQ)
In 2018 this material was posted to an OER on the Internet of Chemistry Things, (www.ioct.tech/edu/) and subsequently modified in 2020 and posted to an Internet of Science Things course on the LibreText OER. Figure 3 is a screenshot of the modules available through the IOST class.
Figure 3: List of modules for the Spring 2020 IOST class posted in LibreText OER. (📷: cc0)
Student Projects
Depending on the course, after instruction on some basic electronic and computational principles, students are expected to define a problem and, throughout the remainder of the semester, work to implement solutions. Therefore, these courses ensure students are actively engaged in both the theoretical and practical domains. Figure one is a collage of student projects. More information on select projects is available in the appendix.
Figure 3: Collage of student projects (A) Imager for gels obtained in biochemistry labs which allows students to print and email pictures of gels (B) Melting point apparatus that monitors when melting starts, stops, and saves and sends images via email (C) Student experiments on multiple temperature sensors and different Raspberry Pis. (D) data from an aquarium being streamed to a Google sheet, (E) particulate data being streamed to a Google Sheet (not shown) and (F) Citizen science gas cell using multiple sensors to identify VOCs. (📷: Belford/Bucholtz cc0)
IOT Enhanced labs
This work integrated three IOT-enhanced labs into a general chemistry course, to complement the use of kitchen chemistry, ChemCollective virtual labs, and PhET simulations. An online integrated lab-lecture experience was created by building the instruction into a LibreTextbook developed by the instructor, supplemented with Carnegie Mellon's General Chemistry I OLI adaptive learning platform. Figure 5 describes the general schema for the IOT-enhanced labs. In all of the labs used in the course, students interact in the cloud through Zoom Breakout rooms and shared Google Docs and Sheets. The IOT-enhanced labs extend this to include a Raspberry Pi that is connected to physical and chemical sensors, and that transmits data to Google Sheets that students can access in real time.
Figure 5: Outline of IOT general chemistry labs. The instructor streamed data to a Google sheet in real time (see figure 5) and students worked up reports in Google Docs and Sheets while communicating in Zoom breakout rooms. (📷: Belford/Lisitsyna cc0)
We developed 3 IOT experiments for use in general chemistry courses. For these, an instructor carries out experiments using IOT connected sensors and streams the data in real time to students for analysis (Fig. 5). Students do a small online prelab and then work in small groups to design the experiment. The class then meets as whole, to combine the designs from the individual groups into one experimental protocol. The instructor then carries out the experiment live and the data is streamed to a google spreadsheet. The students then return to their small groups and analyze the data, within a separate copy of the original google sheet. We have been working on a second paradigm, in which students are provided with lab kits containing Raspberry Pis and appropriate sensors, where students perform the experiments in online groups and stream their data to a Google sheet acting as a classroom dashboard.
The first IOT-enhanced lab was a Molar Heat of Neutralization experiment in which an IOT sensor is used to gather temperature as a function of time. The video in figure 6 shows how the data was streamed in real time. Although the lab was run in Google Classroom we have made it available in LibreText Experiment 5: Calorimetry.
Figure 6: YouTube demonstrating real time temporal streaming of calorimetry data to a Google Sheet that all students could copy and work up. https://youtu.be/HqzL2k7eRSQ
Then next two IOT-enhanced labs involved gas law data, and these have been posted to LibreText Experiment 8: Gases. In the Boyle's Law experiment, students gather data to determine the ideal gas constant (fig.7). The experimental design component of this lab was very challenging, especially figuring out what the volume of the gas was when the syringe read zero.
Figure 7: Data and apparatus for Boyle's Law experiment.
The third IOT-enhanced lab was the determination of Absolute Zero using Gay-Lussac (PT) data. Here, the volume is held constant while the syringe is inserted into water at varying temperatures (Fig. 8).
Figure 8: Apparatus and data for Gay Lussac's Law and the calculation of absolute zero. Note the syringe is taped and so can not move.
These IOT experiments have the advantage of integrating smoothly into existing courses and utilizing standard collaboration tools such as Zoom and Google Classroom.
Future Efforts
Our goal is to work together with other instructors to expand the use of IOT in chemical education. The materials we are developing are made freely available as Open Educational Resources through the Internet of Chemistry Things (ioct.tech) site, or the Internet of Science Things course in the intercollegiate section of LibreText. We have also created a Google Group IOSTEd, Internet of Science Things: Education that anyone can join, to share and learn about resources and opportunities related to the use of IOT in science education.
We are especially excited about organizing a future intercollegiate OLCC course on IOCT. OLCC courses are a service of CHED CCCE that has been ongoing since 1996, making these some of the oldest ongoing online chemistry courses in existence. We recently ran a series of OLCC courses on cheminformatics, as described in this open access Journal of Chemical Education article [1]. The goal of the IOCT OLCC is to allow instructors, with no experience in Python programming or working with Raspberry Pis, to enroll their students in an IOCT course taught collaboratively with instructors at other institutions. Through this collaboration, instructors can gain the experience needed to offer their own IOCT course, or to build IOCT into chemistry courses throughout their curriculum. Please join the IOSTEd Google group and contact the authors of this article if you are interested in offering this course at your school.
References
(1) Kim, S.; Bucholtz, E. C.; Briney, K.; Cornell, A. P.; Cuadros, J.; Fulfer, K. D.; Gupta, T.; Hepler-Smith, E.; Johnston, D. H.; Lang, A. S. I. D.; Larsen, D.; Li, Y.; McEwen, L. R.; Morsch, L. A.; Muzyka, J. L.; Belford, R. E. Teaching Cheminformatics through a Collaborative Intercollegiate Online Chemistry Course (OLCC). J. Chem. Educ. 2020, acs.jchemed.0c01035. https://doi.org/10.1021/acs.jchemed.0c01035.
(2) Fuhrmann, T.; Mandl, R.; Shamonin, M. Analysis of Learning Improvement on Changing Lab Course from Single Experiments to Projects. International Journal of Electrical Engineering & Education 2015, 52 (4), 287–297. https://doi.org/10.1177/0020720915583863.
(3) Freeman, S.; Eddy, S. L.; McDonough, M.; Smith, M. K.; Okoroafor, N.; Jordt, H.; Wenderoth, M. P. Active Learning Increases Student Performance in Science, Engineering, and Mathematics. Proceedings of the National Academy of Sciences 2014, 111 (23), 8410–8415. https://doi.org/10.1073/pnas.1319030111.
(4) Matz, R. L.; Rothman, E. D.; Krajcik, J. S.; Banaszak Holl, M. M. Concurrent Enrollment in Lecture and Laboratory Enhances Student Performance and Retention. J. Res. Sci. Teach. 2012, 49 (5), 659–682. https://doi.org/10.1002/tea.21016.
(5) Richardson, M.; Wallace, S. P. Getting Started with Raspberry Pi, 1st ed.; Make: projects; O’Reilly Media: Sebastopol, CA, 2012.
(6) Foundation, T. R. P. Teach, Learn, and Make with Raspberry Pi https://www.raspberrypi.org/ (accessed Dec 20, 2020).
(7) Johnston, S.; Cox, S. The Raspberry Pi: A Technology Disrupter, and the Enabler of Dreams. Electronics 2017, 6 (3), 51. https://doi.org/10.3390/electronics6030051.
(8) CS-POGIL Process Oriented Gujided Inquiry Learning in Computer Science, http://cspogil.org/Home (accessed Dec. 25, 2020).
(9) CS-POGIL | Lisa Olivieri https://cspogil.org/Lisa+Olivieri (accessed Dec 20, 2020).
(10) McComas, W. F. Learning Cycle. In The Language of Science Education; McComas, W. F., Ed.; SensePublishers: Rotterdam, 2014; pp 59–60. https://doi.org/10.1007/978-94-6209-497-0_52.
Appendix: Student Projects
Example Student Projects from IOT courses
For the course itself, students are told to design a remotely monitored system that uses a chemical sensor which will be their final graded summative assessment for the course. They are required to program a computer, interface with a sensor, collect data, and show that they solved the problem.
Gel imager (UHSP)
A group of students in Fall 2016 were co-enrolled in a biochemistry course and defined a project to take and save quality images of protein gels. Initially they set up a IoT system with three buttons attached to a breadboard to control taking pictures (preview and save) and emailing the resultant image using a Raspberry Pi computer. A prototype hood to place over a lightbox was constructed using foam core board. Throughout the remainder of the semester, the group explored using TKinter for graphical user interfaces (which was never discussed in the course) and connected a printer to the system for students to print out images to paste in lab notebooks. They also learned how to design and 3D print a replacement hood that would stand up to liquids over time. This imager has been in use in the biochemistry lab since Fall 2017. Students in Spring 2017 explored this project further using a UV lamp for imaging thin layer chromatography plates in organic chemistry labs.
Figure A.1: Gel Imager
Automated melting point apparatus (UHSP)
The goal for this student group was to modify an older Mel-Temp apparatus using less than $100 of IoT parts compared to purchasing a new unit for $3000. The modification should determine when melting starts and ends, collects temperature data and images, turns off and email complete data (temperature and images) when complete. Students were able to identify start and end points of crystal melting via counting pixel change using the Raspberry Pi camera and Python programming, and turn on and off the heating of the unit using a relay. The apparatus was linked to temperature measurement of a high temperature thermocouple. Melting data can be emailed. While the heating apparatus can be controlled to run on and off, computer controlled heating (1 deg C/ minute) has not been successful.
Figure A.2: Automated melting point apparatus
Calibration of DB18B20 one-wire temperature sensors (UHSP)
A commonly used temperature sensor in IoT projects is the inexpensive DB18B20. This sensor is easily connected to projects using one-wire protocols in the Raspberry Pi system setup. A student group wanted to explore the precision and accuracy of these sensors, and determine if there would be any differences between sensors if switched out in projects (e.g. a sensor fails over time, or connected to a different computer). Manufacturers data sheets indicate the DB18B20 has a usable temperature range of -10 to 85 ℃ with precision of 0.5 ℃. Students created an ice bath to measure 0 ℃ and boiling water baths to measure 100 ℃. While they were only able to explore three sensors in the time allotted, they did confirm that boiling water was outside the range of accuracy of the sensors, but more importantly a sensor could result in different values depending on which Raspberry Pi it was connected to.
Figure A.3: Calibration of DB18B20 1-wire Temp Sensor
Air Quality Monitoring (UALR)
The first student project (Neal, 2018 class) involved connecting metal oxide gas and particulate sensors to a breadboard and streaming them to a Google Sheet, which now has 4,876,688 cells of data and is operating at Heifer International. This morphed into a citizen science gas cell project (figure A.4), which in the 2020 class another student (Tiner, 2020 class) extended to see if we could use machine learning/artificial intelligence to identify volatile organic compounds based on the behavior of multiple cheap metal oxide probes. This is ongoing work and has morphed into a Master's thesis.
Figure A.4: Citizen Science Gas Cell
These are very cheap sensors (9 for $18.99) and every one of them picks up a signal for both acetone and cyclohexane. Figure A.5 is a "melt" of 50 data points from the eight sensors in figure A.4 collected after a signal for acetone or cyclohexane was detected (4 pts before and 45 after, collected every 5 minutes) where points 0,50,100,150,...300,350 are the same point in time but a different sensor. The question we are asking is can we identify gasses by the patterns across multiple sensors, and can machine learning be used to do that? That is, can we develop a "feature space" that ML/AI algorithms can use to predict the identity of an unknown?
Figure A.5: Data from 8 sensors in Citizen Science Gas Cell
One of the students (Tiner) has been working with R to try and develop this approach. The apparatus was set up in the hood and in addition to times he would add VOCs, other "events" would occur by them selves. The file name defines the parameters we use to generate an event, so if MQ2 has a normalized jump between two datapoints of 3% we collected 50 data points from all 8 sensors and "melted" them as in figure A5. Figure A6 shows preliminary applications of k-Means unsupervised clustering and Naive Bayes supervised learning. Note, the Naive Bayes data is from a training set and not validated, but our first attempt at applying this algorithm to our data. There were 11 samples of ethanol and 11 of acetone in this run, and it correctly identified the ethanol, but once it identified acetone as ethanol.
Figure A.6: Application of supervised and unsupervised machine learning to the data from the Citizen Science Gas Cell
The above data is preliminary and we are not publishing it, but showing how IOT classes can give chemistry students the chance to engage in cloud based data science. The real goal of Tiner's work is to see if we can develop a smart bug zapper in the lines of AIOT (Artificial Intelligence of Things). Figure A.7 shows a modified glove box with a high voltage grid from a SolaRid Photovoltaic driven bugzapper where we are trying to see if we can detect gases as insects get electrocuted, using the algorithms developed for the identification of VOCs, and then turn the sytem off when beneficial insects like honey bees are swarming, but on when pestulant insects are swarming. One of the nice things about IOT is it is on the frontier of industrial research and provides opportunities for students to work with local industries.
Figure A.7: gas sensors in glove box using code developed in VOC determination to see if it can find patterns of zapped insect emissions.
Water Quality Monitoring (UALR)
An ongoing project involving several students is the development of an IOT monitoring system for Heifer International's aquaponics unit. Students did the development work in an aquarium Heifer donated and will be moving the probes to Heifer's unit, but were delayed due to UALR going to remote instruction and Heifer closing down to the public over COVID 19 (the course was being taught during the spring of 2020). One student (Lisitsyna) has continued on with the project during the Fall of 2020.
Figure A8: Raspberry Pi with probes hardwired in three ways.
Aquaponics development unit Raspberry Pi set up on an aquarium showing three ways sensors have been wired. Vernier probes are through the USB port, 1-wire temperature probes are through the breadboard and Total Dissolved Solids and air quality data are through ports on a grove HAT (Hardware on Top). Note, both the breadboard and HAT can have separate AD converters that can opperate at different digitizer frequencies.
Figure A9: Wireless (WiFi) connected probes
Here we see a pH probe (left) and two one-wire temperature probes (right) connected to ESP32 WiFi enabled microcontroller development board that can directly stream data to the web or a Pi operating as a hotspot. Thus there are 4 ways signals can be communicated to the Pis.
Figure A10: Google Dashboard showing data being streamed by sensors over 4 different ways
There are also lots of small projects that students developed, like an indoor air quality monitor using a $20 BME 680 sensor that sent an email when there was a problem, or a soil mosture sensor that would alert you when your plants needed watering.
Comments
Quick Survey
Hi All,
We created a very quick survey on IOT/Raspberry Pi awareness and are hoping you could take 30 seconds or so to fill it out.
We would be very appreciative of your input.
With Cheers and Thanks,
Bob
Survey Link
Hi All,
I guess a link would help,
https://forms.gle/Aw1HiYmE7knkU1326
Hopefully that works,
Cheers,
Bob
Safety aspects of this work
I notice that the abstract for your paper mentions:
"We will also discuss the topic of safety in online lab environments, and how we used that to engage students."
I wonder which safety aspects of these environments you addressed in this work? Chemical safety, IT risks, field work safety all seem like they could be included in these discussions with the students. I would be interested in how you prioritized these various opportunities.
Safety in Online Environments
Hi Ralph and all,
The draft of this paper reached 34 pages at one point and we had to cut everything that was not related to IOT. There were essentially four goals for the safety module, and please review the safety section of LibreText, a lot of work was put into it, but we even introduced students the the University CHP.
OK, there was also a bit of smoke and mirrors going on, as we had 2 weeks from the end of the spring semester to the start of the summer to develop the lab, which was not enough time to get University Legal Consul to give us clearance for remote use of chemicals. So, for example, on the water of hydration lab we took pictures (out of order) from the TAs home and had the students repost those to the worksheet in the correct order to get the data (all of those are available if you log into LibreText).
Item 4 is not really about safety in-and-of-itself, but using safety to make the students feel like they were in a real lab, and working with real partners, and I am going to focus on that. That is, we were trying to get students to think about safety, and the importance of protecting each other during the lab, even when they were physically separated, and that led to very effective group work. Here is an excerpt from the omitted text, but we used safety to build up teamwork, and I think there is a synergism between safety and teamwork.
"One of the challenges with Zoom breakout rooms is to get students to turn on their cameras, and the very first assignment "Group Form," was where students created groups and learned how to collaboratively author Google Docs, and follow each other's edits through the history. This assignment was done as part of the Safety Lab and we required students to provide a personal phone number and an "emergency contact name and number". This was given right after they watched the ACS video "Working Alone in the Lab", where we emphasized that because we were doing the labs online and not at UALR, they had to have their cameras on during the breakout sessions, as they were responsible for each other's safety. This led to very effective team development and we had 95 to 100% video participation during the breakout sessions (only one student had consistent issues with his camera)."
I believe this is a bigger deal than many people may realize, that is, with COVID19 social distancing and mask mandates, students are not getting the kind of social interaction they normally would, and we used safety in the lab as a way to connect students to each other, which I think is one of the biggest challenges with online classes. Please forgive me, but here is another part of the omitted text:
"One of the biggest challenges for online education is connecting students to the University experience. Many of the students in general chemistry are freshmen, who are living in dorms and are away from their parents for the first time in their life, and part of the university experience is a sort of growth into adulthood, where students ultimately take on responsibility for their own lives and decisions. Part of this growth involves social interaction with peers under the stress of academic environments like the chemistry lab, and COVID-19 pandemic social distancing requirements and on-campus mask mandates were denying both online and off campus students this valuable experience. Part of the goal of our online lab program was to engage the students and make them feel they were part of the university experience, the initial modules were designed to engage students and the successful implementation of these modules was crucial to the success of the class. It started with safety."
I believe safety must be central to the design and implementation of an online lab, even if there are no wet experiments, and it was a consideration the students had to write up about on every lab they designed. I could also go on about my thoughts on digital literacy, but don't want to give you a 34 page response.
Thanks for your question.
Bob
RE: Bob Belford: Safety in Online Environments
>I think there is a synergism between
safety and teamwork.
I am very pleased to see the use you made of the ACS working alone video that I helped develop. Home labs were not what we had in mind when we produced this video, but you make a very important point that zoom monitoring of work at home is both builds community and provide some oversight of lab practices at home. The metaphor we used in the video addresses both of those aspects, I think.
questions about class size, student plus policies
Hello Bob,
Thank you for sharing your experiences. It seems that distance learning can be better than what the news articles say. I taught chemistry online for 15 years of my 51 years of teaching lab and lecture classes. I have a large number of questions about your work. Here are a few.
How many students participated in the course?
Were students told the course structure before they registered?
Were class activities scheduled for specific times just like an typical campus lab session?
Was the course conducted for a full semester?
Was there a difference between the completion rate for students in a traditional class and the home lab class?
Was the grading policy used for the at home laboratory class different from the one for the traditional course?
Does a typical on campus lab class involve the same level of group work?
I enjoyed reading your paper. I liked your comment about providing students experience that would help them get a job.
reply to questions
Hi Walt,
We had 1 lab section, which is normally 24 students, but I tried to keep it to 20 as I was concerned about being able to navigate breakout rooms, and I think we started with 21 and ended with 18.
All instruction had moved online so they knew that up front, and before the summer started I sent several emails to the class list alerting them that they would need a computer with internet connection, but that was after they had registered, so no, they did not know what we were doing before they registered.
Yes, it was a synchronous class meeting every M-F from 8:40-11:50 AM. I now realize that if a class is truly online, you can do lecture and lab concurrently, as you do not have to worry about scheduling lab space. It was team taught with one instructor and one TA, and we both participated the entire duration (lab and lecture), although we were only paid for either the lab or the lecture.
We did this on the fly, and only had two weeks between the end of the Spring and the start of the summer. The person who did the Fall class I believe had 5 sections and 3 TAs, and only did one of the IOT enhanced labs. I believe they also omitted the safety module, which I think was a big mistake, and my understanding was the TAs had a harder time getting students in breakout rooms to keep their cameras on, and I attribute that to the synergistic effect of combining group work with safety responsibilities. That is, in the summer they were introduced to group work in the context of the safety module, and that module was omitted in the fall. The Fall person used clickers, I did not.
For the Spring and Summer sessions the university faculty senate instigated a credit/no credit option, which required me to have two grade policies; one for credit/no credit, and one for letter grade. Because of this, we can not compare with the traditional class. We also used Honorlock on the exams.
As for group work, our prior gen chem 1 labs did not have group work (I normally do not teach that class), and part of the reason I took it up the challenge of teaching the accelerated summer class was that the chair told me I could restructure the lab as I felt best. That was, because we were offering it online, I had liberty to adjust the syllabus, and I would say we actually covered more material than we normally did. The students knew we were trying something new and they really engaged, it was one of the most enjoyable classes I have ever taught.
Thanks for your questions,
Bob