Virtual Sonia Kovalevsky Day Mathematics Outreach Events for Middle School Girls

Abstract

Sonia Kovalevsky Days (SK Days) are nationally-held outreach events that are commonly organized by local chapters of the Association for Women in Mathematics (AWM) to encourage young women to continue their study of mathematics. The AWM Student Chapter at Worcester Polytechnic Institute hosted virtual renditions of SK Day for middle school girls in Spring 2020 and 2021. This paper discusses the implementation of these events, including the virtual program logistics and five interactive online mathematics activities. Participant feedback suggests a successful transition from an in-person to online format of SK Day, with benefits to both the middle school participants and the undergraduate student volunteers. The activities and online resources described in this article have the potential to be utilized in future hybrid outreach events.

Keywords:

• Mathematics outreach
• women in mathematics
• virtual programs
• online activities
• middle school
• K–12 outreach
• STEM

1. INTRODUCTION

Named in honor of the first woman mathematician to earn a doctorate, Sonia Kovalevsky Days (SK Days) are nationally-held outreach events commonly organized by local chapters of the Association for Women in Mathematics (AWM) to encourage young women to continue their study of mathematics [2, 21]. As women remain under-represented in mathematics-intensive fields and graduate programs [3, 7, 11, 17], targeted outreach events aim to help in broadening the participation of young women in the mathematical sciences. Since Spring 2019, the AWM Student Chapter at Worcester Polytechnic Institute (WPI) has held annual SK Days with the goal of inspiring middle school girls who love math.

SK Days at WPI are designed to engage sixth, seventh, and eighth grade girls in the New England area. Studies show that middle school is a particularly vital time to foster girls' interest in mathematics as they transition into high school and future studies [1, 4, 9–11, 13, 19, 26]. SK Days at WPI seek to bolster the girls' continued enthusiasm for mathematics by providing a welcoming environment in which the girls can engage in fun, interactive math activities while meeting other girls in the region who share similar interests.

To this end, our 1-day programs feature remarks from women leaders in STEM at WPI, math activities led by WPI student and faculty volunteers, and keynote talks given by women mathematicians. The activities are meant to be enjoyable while also helping the girls to build continued confidence in their mathematical skills. The keynote talks serve a dual purpose of introducing the girls to high-level mathematics research conveyed in their language while meeting successful women with careers in the mathematical sciences. The girls also have the opportunity to meet women majoring in mathematical sciences and related disciplines at WPI, who can share their reasons for studying mathematics. The importance of interacting with women role models has been identified as a key factor in helping to maintain middle school girls' interest in math and science in other outreach programs for this age group [6, 15, 19].

While we hosted our inaugural SK Day 2019 in person on WPI's campus, we successfully transitioned SK Day 2020 to an online format in light of COVID-19 and maintained a similar format for SK Day 2021. In developing the virtual programs, our primary goal was to retain the key features of the in-person event while using an online platform. In particular, the virtual SK Days provided an interactive online experience for program participants to engage in math activities, hear keynote talks and remarks from women leaders in STEM, and learn about influential women in the history of mathematics.

This paper describes our virtual implementations of SK Day, including the program logistics and math activities utilized during the events. The Program Director (the author) and a team of dedicated volunteers at WPI worked to organize the virtual events each year. While the volunteers included both graduate and undergraduate students, as well as several department faculty and staff members, the undergraduate students took on significant leadership roles in planning and running the interactive online activities. As this paper will discuss, our virtual SK Day programs provided benefits not only to the middle school girls participating, but also to the undergraduate students volunteering. The paper is organized as follows: Section 2 gives an overview of the virtual program logistics, including registration and the main components of the schedule. Section 3 provides a description of five interactive online math activities and how they were implemented for these events. Section 4 reports participant feedback on the virtual SK Days, highlighting the participants' responses to the math activities as evidence of a successful transition to an online platform. Section 5 describes some of the benefits to and experiences of the undergraduate students via feedback from a volunteer survey. Section 6 provides a discussion of the virtual SK Days and potential ways to incorporate aspects of the online activities into future in-person or hybrid outreach events.

2. VIRTUAL PROGRAM LOGISTICS

This section describes the primary logistical aspects of the virtual SK Day programs, including event registration and the components of the schedule. We used the online video conferencing platform Zoom (https://zoom.us/) to host the events, and both virtual SK Days were free to participants. All volunteers completed the required trainings and forms for programs involving minors, per university guidelines.

2.1. Event Registration

The Program Director sent flyers via e-mail to local K–12 schools to advertise the program, with a link to the event website and online registration. Parents/guardians filled out an online form to register each participant, with the registration period closing 2 weeks before the event, and subsequently completed a participation waiver for their student(s) before the event to gain access to the Zoom link and passcode. For SK Day 2020, the program transitioned from an in-person to online event during the registration period: Out of the 47 submitted registrations, 22 girls participated in the 2020 virtual event. For SK Day 2021, which was planned as a virtual event from the start, 36 girls participated out of 55 submitted registrations. The Program Director and departmental staff members were responsible for event registration and communication each year.

2.2. Virtual Program Components

Each virtual SK Day ran for 2.5 h on a Saturday morning in April, 10:00 AM–12:30 PM, with logon to the Zoom session beginning at 9:30 AM. The program schedule for each event included the following main components: an introduction to SK Day; opening remarks; math activities; keynote remarks; and closing remarks. Figure 1 shows the general framework for the online programs.

Figure 1. General framework for the virtual SK Day programs.

At the start of each event, the Program Director gave an introductory slide presentation welcoming the participants and providing an overview of SK Days. The slides featured an introduction to Sonia Kovalevsky and her contributions to mathematics along with motivation for the event's objectives. Women leaders in STEM at WPI gave the opening and keynote remarks each year, encouraging the girls' continued interest in mathematics while describing their own paths in STEM. SK Day 2020 included two interactive online math activities (Math Trivia and Mathematical Modeling with NetLogo), while SK Day 2021 featured three activities of shorter duration (Math Scavenger Hunt, Math Bingo, and Data Exploration); Section 3 describes these activities. At the conclusion of the activities, the Department Head of Mathematical Sciences at WPI gave closing remarks highlighting different career opportunities and application areas of mathematics.

As a gift to help commemorate the experience, program participants each received a copy of the book Women in Science: 50 Fearless Pioneers Who Changed the World by Rachel Ignotofsky; this book contains short profiles and colorful illustrations of influential women in STEM, including mathematicians such as Hypatia, Ada Lovelace, Katherine Johnson, and Maryam Mirzakhani. For SK Day 2021, participants also received an event t-shirt. In addition to the participation gifts, we held raffles in between the activities using an online spinning wheel (https://wheelofnames.com/) listing the participants' names for a total of five winners each year. Raffle winners received a small prize (i.e., a WPI keychain); winners of the Math Bingo activity during SK Day 2021 received similar prizes. Funding from a grant to the Program Director (a WIN Impact Grant from the Women's Impact Network, a philanthropic organization that supports WPI community initiatives impacting women in STEM) and from the WPI Department of Mathematical Sciences supported the purchase of the participation gifts and raffle prizes. We mailed these items to the program participants the week following the event, after confirming attendance and drawing the raffle winners.

2.3. Roles of Undergraduate Student Volunteers

While our volunteers included both graduate and undergraduate students, as well as several faculty and staff members, undergraduate students majoring in the mathematical sciences made up a majority of the volunteers each year. More specifically, undergraduate students comprised 6 of the 11 volunteers for SK Day 2020 and 11 of the 21 volunteers for SK Day 2021. Most of the student volunteers were active members of the AWM Student Chapter at WPI, which embraces both undergraduate and graduate students in leadership positions and fosters direct collaboration across grade levels in organizing chapter activities. For our virtual SK Days, several undergraduate students took on significant leadership roles in planning and executing the interactive activities. Designated as activity leaders, these students took on the primary responsibility of organizing and running their activities online during the event, working alongside a team of additional volunteers. In particular, for SK Day 2020, an undergraduate student was the activity leader for Math Trivia; for SK Day 2021, undergraduate students led both the Math Bingo and Data Exploration activities. We further detail the roles of the student volunteers with respect to each activity in the following section.

3. INTERACTIVE ONLINE ACTIVITIES

In this section, we describe the interactive online math activities used during WPI's virtual SK Days 2020 and 2021. Student volunteers played essential roles in organizing and running the activities during the online events, with undergraduate students serving as activity leaders for three out of the five activities. We provide a description of each activity and discuss its implementation during the online program.

3.1. Math Trivia

This activity involved playing a trivia game with mathematics-based multiple choice questions answered in real time by the program participants. The goal was to engage the participants in using their problem-solving skills to answer math-related questions, while also providing a mechanism for the participants to learn about prominent women in the history of mathematics.

With help from a group of volunteers, the activity leader (an undergraduate student) prepared slides with multiple choice questions, each with four answer choices. Questions included math problems and logic puzzles with skill level appropriate for middle school students, as well as “Who am I?” questions introducing trivia facts about influential women mathematicians throughout history. The latter questions provided an opportunity for the participants to learn more about the lives and mathematical contributions of these women (including the event's namesake, Sonia Kovalevsky) that they may not have known before. Appendix gives an example of this question type. The slides included 20 main questions for the activity, along with an additional set of “bonus” questions (if needed to fill the allotted time).

To make the game more interactive, participants recorded their answers to the trivia questions in real time using Poll Everywhere (https://www.polleverywhere.com/), an online polling service which can be incorporated directly into slide presentations. The participants' responses were received and displayed live in the slide presentation as histograms, with individual answers remaining anonymous and shown only in aggregate. After a brief introduction with instructions for accessing Poll Everywhere, the game proceeded with the activity leader clicking through the questions one at a time, together with the full group of participants. For each question, a volunteer read the statement of the question and the answer choices out loud, then gave a few minutes for the participants to work out their answers and enter their responses via Poll Everywhere. After allowing time for participants to respond, the volunteers displayed the live polling results on the slide and revealed the correct answer, also providing a brief explanation of the solution for each question.

3.2. Mathematical Modeling with NetLogo

This activity introduced the participants to some basic concepts involved in mathematical modeling and showed how changing model parameters affects the outcome of a simulation. The participants explored these concepts by running modeling simulations in real time with NetLogo [29], an open source programmable environment for agent-based modeling, which offers a variety of models that are directly usable online via NetLogo Web (https://www.netlogoweb.org/).

With input from a group of volunteers, the activity leader (a graduate student) prepared slides to introduce the main ideas behind mathematical modeling, how modeling can be used to address real-world problems in different application areas, and the role of model parameters in the model output. The slides also gave an introduction to NetLogo and offered links to three preselected models on NetLogo Web for the participants to work on: Wolf Sheep Predation [27], Virus [28], and Rabbits Grass Weeds [30]; these models are among those available from the NetLogo Models Library (https://ccl.northwestern.edu/netlogo/models/). Preselecting the models allowed the volunteers to run simulations in advance of the event, look for over-arching themes in the results, and have suggestions ready for the participants.

The activity leader began by presenting the introductory slides and giving a live demonstration of how to use NetLogo Web. Student volunteers used the Wolf Sheep Predation model [27] as a first example to show how changing the model parameters affected the simulation results, then gave the participants time to work on the three suggested models individually. After some time, the participants came back together as a group to discuss their findings and what they noticed while running the different simulations.

3.3. Math Scavenger Hunt

This activity implemented a virtual scavenger hunt, providing an interactive environment through which the participants could work together in groups to solve mathematics-related riddles and trivia questions. As with an in-person scavenger hunt, the idea was to collect items (here virtually) by clicking on them and correctly answering the corresponding math questions. Using breakout rooms, small groups of participants explored the virtual environment and kept track of the number of questions answered correctly (i.e., the number of items “collected” in the scavenger hunt) with the help of activity volunteers.

Using questions compiled by several student volunteers, the activity leader (a graduate student) generated the scavenger hunt environment using a Google slide with clickable items each linking to a corresponding Google form with a math-related question. There are a variety of tutorials available online for creating virtual classrooms and escape rooms using Google slides; see, e.g., [25]. The volunteers used a picture taken on WPI's campus for the slide background and placed over 30 clickable items around the environment. Figure 2 shows a portion of this slide with a number of clickable items (e.g., calculator, apple, clock, etc.). Some items were easier to spot than others, and hovering over an item revealed that it was linked to a question. Questions involved math puzzles and riddles with skill level appropriate for middle school students. We also included several “Who am I?” questions with facts about influential women mathematicians throughout history, similar to those described for the Math Trivia activity in Section 3.1. When possible, the images for the items were chosen to match the content of the related question (e.g., a pair of dice linking to a question about how many different ways you can roll a certain number).

Figure 2. A portion of the interactive Google slide used during the Math Scavenger Hunt activity. The student activity leader used the Clip2Comic app [5] to modify the background image and the Bitmoji app [22] to generate the character holding the books. The environment contains a number of clickable items that link to math questions via Google forms.

To begin the activity, the activity leader displayed the virtual scavenger hunt environment to the full group of participants and demonstrated how to find and select the items linking to the math questions. Participants were then split into five breakout rooms, each containing multiple volunteers (comprising undergraduate and graduate students, as well as faculty volunteers) to help lead the smaller groups and guide the activity. The volunteers in each room encouraged the participants to interact and take turns choosing the items to select. One volunteer in each room was responsible for clicking on the items, reading out the corresponding questions, and entering the group's answers into the Google forms to check for correctness. After some time, the small groups were brought back together to discuss how many items they collected and their main take-aways from the activity.

3.4. Math Bingo

This activity provided an interactive bingo game that utilized the participants' basic math skills, while also briefly introducing the participants to random number generation and scientific computing. In traditional bingo games in the United States, the caller randomly draws a number (typically integers from 1 to 75) that the players look to mark off on their cards. Instead of drawing a number, in this game the caller (i.e., the undergraduate student activity leader) provided an arithmetic expression or geometric question that the players (the middle school participants) had to solve before looking to mark off the answer on their bingo cards.

We prepared two different variations of the game: one using basic mathematical operations (e.g., the call is “$3\times 3$” so the participants look to mark off 9 on their bingo cards) and geometry (e.g., the call is “number of sides of a triangle” so the participants look to mark off 3), and another using more challenging expressions requiring order of operations (e.g., “$20\times 3-42$”) and geometry (e.g., “number of faces of a cube”). In each case, a group of student volunteers prepared a unique expression or geometric question for the numbers 1 through 75. We note that [12] also presents a math bingo activity, but with higher-level questions primarily intended for undergraduate student participants at in-person events.

For our virtual Math Bingo, each participant received a link to generate an individual online bingo card, with numbers ranging from 1 to 75. We used the website Bingo Baker (https://bingobaker.com/), which allows for free online game play where users can click on their cards to mark off the numbers. To connect the game with the concepts of random number generation and scientific computing, we introduced the activity with a live demonstration using the built-in functions rand [23] and randi [24] in MATLAB^® (The MathWorks, Inc., Natick, MA) to generate random numbers. The activity leader also hand coded a script in Python (https://www.python.org/) to randomly draw the mathematical expressions for each call and used this code to make the calls during the game.

We allowed each game to have multiple winners and encouraged the participants to announce when they completed a winning card (i.e., a card with five numbers marked off in a horizontal, vertical, or diagonal row) by saying “Bingo!” out loud or by writing it in the Zoom chat. Student volunteers checked the cards for correctness, and the first 10 participants to win received a small prize. Since it took some time for winning cards to emerge, we ended up playing just one game of the variation using basic operations and geometry until we reached 10 winners.

3.5. Data Exploration

This activity introduced the topics of data exploration and visualization and provided a hands-on experience for the program participants to interpret real data sets based on different visualizations. We made use of the online tools provided by Gapminder (https://www.gapminder.org/tools/), which allow for various data sets (e.g., world population by country) to be displayed in a variety of different ways (e.g., as bubbles of different sizes and colors on the world map). Figure 3 shows an example visualization from Gapminder of the world population data set. Students are able to interact with, explore, and change the way the data is visualized in order to find patterns and make connections between the different contributing factors.

Figure 3. Example visualization from Gapminder of the world population data set, where the size of each circle is relative to the population size of the country in the year 2020. Free material from www.gapminder.org.

In advance of the event, student volunteers identified three data sets to focus on and developed a list of questions to help guide the participants in exploring the data. The selected data sets included renewable water, population growth, and primary school completion of girls, all of which are freely available on the Gapminder website. The activity leader (an undergraduate student) began by presenting a brief overview of data visualization and an introduction to the Gapminder site. We then split the participants into three breakout rooms, each investigating a different data set; the volunteers in each room (which included undergraduate students, graduate students, and faculty volunteers) led the participants through exploration of the data using the visualization tools on Gapminder. Undergraduate students took on main roles in helping to guide the conversation in two of the three breakout rooms, while a graduate student led the third. The volunteers asked the participants questions relating to what was observed in the smaller group sessions, then everyone gathered back together to discuss the main take-aways as a full group.

4. PARTICIPANT FEEDBACK

We conducted online surveys using SurveyMonkey (https://www.surveymonkey.com/) after each virtual SK Day to obtain participant feedback. The Program Director created and administered the surveys by sending links via e-mail to the parents/guardians of the participants after the events. The emails asked the parents/guardians to complete the surveys together with their respective middle school participants. Survey responses were anonymous, and replies to all questions were optional (i.e., there were no required questions). Questions included a mix of multiple choice (i.e., select one out of a list of options), rating scale, and open-ended response. The goal of the surveys was to gauge the overall success of the events in terms of the main aims of SK Day, that is, that the participants had a fun experience, enjoyed the activities, and learned something new.

Nine out of the 22 program participants responded to the survey in 2020 and 15 out of the 36 program participants responded in 2021. Out of the 24 total respondents, 4 were in sixth grade, 10 were in seventh grade, and 10 were in eighth grade. When asked to rate the event overall (with choices of “Excellent,” “Very Good,” “Good,” “Fair,” or “Poor”), 12 responded with “Excellent,” nine with “Very Good,” two with “Good,” and one with “Fair.” There were no “Poor” ratings of the event, and 100% of the respondents indicated that they would attend SK Day again.

When asked to describe their favorite part of the event (open-ended) for SK Day 2020, four respondents mentioned listening to the speakers; one mentioned learning about different career paths in the mathematical sciences; four mentioned Math Modeling with NetLogo; and two mentioned Math Trivia. For SK Day 2021, all of the open-ended responses included at least one of the activities: nine mentioned Math Bingo; six mentioned the Math Scavenger Hunt; and four mentioned Data Exploration. One response also mentioned hearing success stories (presumably from the speakers). Replies to the specific questions listed in Table 1 indicate an overall positive response to the activities in both years, with almost all respondents agreeing that the activities were fun and a majority agreeing that they learned something new from the activities (with a lower percentage for Math Bingo).

Table 1. Participant feedback on the activities from virtual SK Days at WPI.

Statement	Agree	Disagree	Neither
Math Trivia was fun	9 (100.00%)	0 (0.00%)	0 (0.00%)
The Math Trivia questions were appropriately challenging	6 (75.00%)	2 (25.00%)	0 (0.00%)
I learned something new from Math Trivia	7 (77.78%)	2 (22.22%)	0 (0.00%)
Math Modeling with NetLogo was fun	8 (88.89%)	0 (0.00%)	1 (11.11%)
Math Modeling with NetLogo was appropriately challenging	5 (55.56%)	2 (22.22%)	2 (22.22%)
I learned something new from Math Modeling with NetLogo	7 (77.78%)	1 (11.11%)	1 (11.11%)
Math Scavenger Hunt was fun	15 (100.00%)	0 (0.00%)	0 (0.00%)
The Math Scavenger Hunt questions were appropriately challenging	11 (73.33%)	2 (13.33%)	2 (13.33%)
I learned something new from the Math Scavenger Hunt	10 (66.67%)	1 (6.67%)	4 (26.67%)
Math Bingo was fun	13 (86.67%)	0 (0.00%)	2 (13.33%)
The Math Bingo questions were appropriately challenging	5 (33.33%)	4 (26.67%)	6 (40.00%)
I learned something new from Math Bingo	5 (33.33%)	6 (40.00%)	4 (26.67%)
Data Exploration was fun	13 (86.67%)	0 (0.00%)	2 (13.33%)
Data Exploration was appropriately challenging	9 (60.00%)	0 (0.00%)	6 (40.00%)
I learned something new from Data Exploration	15 (100.00%)	0 (0.00%)	0 (0.00%)

Note: Percentages are calculated from the total number of responses to each question and rounded to two decimal places.

When asked what was the single most valuable thing they learned at SK Day in 2021 (open-ended), respondents gave a variety of answers, including learning about women in mathematics (four responses); math is fun (two responses); different application areas and careers in the mathematical sciences (three responses); and the speakers' talks (three responses). When asked if there was anything else they'd like to share, open-ended responses in both years emphasized that the respondents had fun and would participate again. One respondent in 2021 mentioned that they would have liked to have access to the Math Scavenger Hunt questions after the event to work out on their own. Another respondent commented:

SK Day is a great event for anyone to be inspired by other impactful women in the Mathematical Industry.

5. UNDERGRADUATE STUDENT BENEFITS AND EXPERIENCES

In response to a recent survey, nine undergraduate students provided feedback on their experiences volunteering for the virtual SK Day programs. Out of these respondents, one volunteered for the event only in 2020, five volunteered for the event only in 2021, and three volunteered for both events; six majored in Mathematical Sciences, one in Actuarial Mathematics, one in Management Engineering, and one in Data Science; and the students ranged from first-year (freshman) to fourth-year (senior) grade level at the time of volunteering. Eight of these students identified as AWM Student Chapter members, and all learned about the event through AWM Student Chapter communications.

Regarding their motivation for volunteering, several respondents mentioned wanting to help out with an event that they wish they could have attended in middle school:

I first heard about the virtual SK Day during meetings and email communications with AWM. Learning more about math through games and activities, what it's like being a woman in STEM and partaking in the event with college students is something I would have been a part of as a middle school student. Being a part of an event that gives this opportunity to students is something I knew I wanted to partake in, especially during an unprecedented time where connecting with others was important.

I had always wanted something exactly like this when I was younger; that is, an event for young girls interested in math, not just STEM in general, because I went to 3+ STEM events like this and…none of them ever had any math sessions or activities.

When asked how they had benefited from working with the middle school girls who participated in the program, the undergraduate students mentioned that it helped them gain teaching experience and leadership skills, understand a different perspective on learning math, and that it was rewarding to see the girls enjoying the activities. The following are some of the replies directly addressing this question:

It helped resurge some of the passion I have for what I do, being able to see the girls understand the math and get excited over it. It also was nice to still be able to give the girls this experience even during the pandemic.

I definitely learned a lot about myself when it came to showing these younger girls all the fun and cool things you can do with math. I was almost jealous that I did not have this type of program growing up. It was such a rewarding feeling to watch them have fun and be interested in the different ways they could use math.

Working with the middle school girls helped me improve my ways of interacting with any student in general. Definitely gave me the exposure of how important learning is for anyone and inspired me to be a future leader.

Before SK Day, most of my math-related conversations were with peers or professors. Through working with the middle school girls who participated in the program, I was able to gain valuable experience in talking/teaching to a younger audience as well as solidify a better understanding of what math means to me.

When asked how volunteering for the virtual SK Day(s) benefited their undergraduate educational experience as a whole, the respondents emphasized that it helped them to become more adaptable, provided hands-on experience in planning virtual programs and activities, and gave them an opportunity to contribute positively to the community. Some specific responses to this question include:

I think it is really a good skill set to be able to explain what you've learned in a high-level way that anyone can understand. Simplifying things such as mathematical modeling to explain to a middle schooler is not super easy, but super beneficial when done right.

It taught me how to be more adaptable since we had to shift planning to the virtual event in a short turn around the first year. I learned how to become more comfortable utilizing online tools which was definitely helpful. I also just really enjoyed the program and it was something I looked forward to every year. It is a great reminder that having this event could be what shapes one of the young girls to want to pursue a degree in mathematics or any STEM field.

Volunteering for the virtual SK Days allowed me to get the feeling of what it is like doing things remotely, especially when it comes to planning and implementing activities in general. It gave me the chance to develop and implement my learning skills to students who would soon be stepping into my place.

It empowered me to see these young girls pursuing their love for math and in a way re-inspired my own love for math and why I major in Actuarial Mathematics.

It reminded me of how exciting math can be for younger girls and how important it is to introduce STEM topics at a young age.

Last year was the first time I volunteered for SK Day, and I was also only a freshman at the time. Given that the learning environment and social atmosphere at WPI was predominantly through Zoom and in many cases for me asynchronous, being able to plan an event with other like-minded WPI students and connect with the local community greatly improved my spring semester.

6. DISCUSSION AND CONCLUSIONS

This paper describes the implementation of two virtual SK Day outreach events for middle school girls, hosted by the AWM Student Chapter at WPI in Spring 2020 and 2021. Participant feedback suggests a successful transition from an in-person to online format that maintained the key features of SK Days at WPI, with benefits to both the middle school participants and undergraduate student volunteers.

Compared to our on-campus SK Day in 2019, one consideration we made when transitioning to the virtual event in 2020 was how the level of interaction might differ between in-person activities and those done online. The activities implemented for the online events were chosen specifically to encourage interaction and hands-on learning by the participants in the remote setting. We also aimed to introduce the participants to online resources (such as NetLogo and Gapminder) that they could continue to explore on their own afterwards. It is encouraging to note that the participants were engaged during both virtual SK Days, contributed to discussions, asked questions, and seemed comfortable with the online platform.

Still, some avenues for interpersonal interaction were lost in the virtual setting, mainly due to the shorter duration of the online events (e.g., there was no free time in the schedule for the girls to talk informally, as they may have done at lunch or in between activities in person). The shorter event duration also posed a challenge in terms of timing for the activities and talks, but this was alleviated by building flexibility into the schedule while planning for the event (e.g., in preparing extra questions for Math Trivia in case they were needed, and in designing activities like the Math Scavenger Hunt and Data Exploration to potentially run for a shorter or longer duration depending on the timing situation).

At the time of writing, the literature on virtual STEM outreach programs is limited, specifically with respect to mathematics-focused programs for girls. A few recently published articles describe virtual implementations of an engineering summer camp for high school girls [8], a multi-day community science festival [14], a STEM outreach event for fourth through sixth grade girls [18], and a math circle for fourth through ninth grade girls [20]. Similarly to our experience with SK Day, in the transition to online programming, several of these articles acknowledge shortened timing or a change in format to prevent screen fatigue and fewer opportunities for connection among participants due to the remote environment. However, the articles also similarly report an overall positive response to the virtual programs, noting that the online events met outreach objectives and had some advantages in flexibility as well as the potential to reach a broader audience with remote participation.

With the prospect of returning to in-person programming for future SK Days, we note that all of the math activities described in this paper could be modified for in-person outreach events, allowing for a more hybrid approach. For example, in our return to in-person programming for SK Day 2022, we developed a hands-on coding activity using NetLogo that led the participants through an interactive example while working together in a computer lab. We also played a game of Math Bingo using the same hand-coded Python script to randomly generate the calls, but this time we gave the participants printed bingo cards that they could mark with stickers. We plan to incorporate additional elements of the virtual programming (e.g., using Poll Everywhere for real-time feedback) into future SK Days at WPI.

ACKNOWLEDGMENTS

Many thanks to the wonderful WPI student and faculty volunteers who dedicated their time to helping make our virtual SK Days a great success: Francesca Bernardi, Jane Bouchard, Madhusree Chowdhury, Liz Cole, Elizabeth Euwart, Kayla Fabry, Allyson Floria, Dane Johnson, Leah Mitchell, Justine Moy, Olivia Pineiro, Xavier Ramos Olive, Ally Salvino, Bella Speer, Natalie Tierney, Alix Wagner, Duncan Wright, and Bauyrzhan Yerghizit. Special thanks to our WPI AWM Student Chapter officers and Virtual SK Day activity leaders for their outstanding contributions: Sara Amato, Cyra Katoch, Mona Ma, Dayna Mercadante, Lynne Moore, Elisa Negrini, and Laura Staugler. Our sincere thanks to Laurie Leshin, Jean King, Luca Capogna, Sarah Olson, Suzanne Weekes, Mike Malone, and Rhonda Podell for their much-appreciated support of these events, as well as to the reviewers and editors for their valuable feedback on this manuscript.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Virtual SK Days 2020 and 2021 at WPI were supported by a grant from the Women's Impact Network (to Andrea Arnold) and by the WPI Department of Mathematical Sciences.

Notes on contributors

Andrea Arnold

Andrea Arnold is an applied mathematician with research interests in computational inverse problems and uncertainty quantification. She received her Ph.D. in Applied Mathematics from Case Western Reserve University and her B.S. in Mathematics from Duquesne University. Before joining the faculty at Worcester Polytechnic Institute (WPI), she completed her postdoctoral research in Mathematical Biology at North Carolina State University. She is the faculty advisor of the Association for Women in Mathematics (AWM) Student Chapter at WPI. She serves as a program director for Sonia Kovalevsky Days at WPI, with events held annually since Spring 2019.

APPENDIX. “WHO AM I?” QUESTION EXAMPLE

The following is an example of the “Who am I?”-type questions used in the Math Trivia and Math Scavenger Hunt activities, with the goal of providing historical facts about influential women mathematicians. For biographical information, see, e.g., [16] and the references therein.

Sample Question:

Who am I?

• I was born in Russia in 1850.

• I was not permitted to attend classes at the university, but I was taught privately by Karl Weierstrass for many years and was granted my doctorate in 1874.

• I was the first woman mathematician to earn a doctorate.

• I was the first woman mathematician to be appointed to a full professorship at a university.

Answer: Sonia Kovalevsky