What are some key elements that should form the core of maths education and maths enrichment? Under the auspices of the UWCSEA Innovation Incubator and a small grant, our team, Project 0 Lab, initiated a pilot extracurricular programme to encourage the interdisciplinary exploration of mathematics in a research-oriented, project-based context.
Watch the session to learn more about our five projects described briefly below, but more importantly, we want to share and discuss ideas on the future of maths education - one that is more open-ended, inclusive, and fundamentally creative?
Anthony: Welcome to the UWCSEA 50th Forum, we are very glad to have you here today. My name is Anthony Shen and I am currently a G12 student at UWCSEA. Because this is a pre-recorded video, feel free to type up your questions in the chat, we are free to answer them for the entire duration of this 25 minute session. We also have an optional networking room after the session if you would like to ask further questions or connect with us.
Tippi: Hello, everyone, welcome to the first optional session for today, thank you for your interest in the potential of maths education. My name is Tippi ZHU and we are here to share our ideas and our experiment of reimagining maths education at East over the past year.
Anthony: Before we continue, I would like to emphasise that we are just two representatives of a community of maths enthusiasts at East, including our student leaders Uditi, Joonseok, Arunav, and Anvay who have supported our experiment in reimagining maths education.
Tippi: So Anthony, our student leaders have been contributing to organise, learn and lead extracurricular maths-related activities for years, what might be some inspiration for them to see the necessity to reimagine maths education?
Anthony: So when we interviewed Dr. Ayesha, who is an industry expert in AI but also heavily involved in educational initiatives in the government and as a social enterprise, she said the following, “When I grew up, there was only one answer in maths, and one answer in science. And it was only when I went to college and met students from Eastern Europe that showed me to look at science and maths as poetry, as a way to investigate the truth, approximate the truth, and as a way to experiment.” And we feel that this statement lies at the heart of why the traditional way of mathematics enrichment - a series of progressively higher stakes exam-based competitions might be lacking in some respects. Think of the progression of the high school mathematics achievement in most countries actually, for example in the United States: you have the American Mathematics Competitions, American Invitational Mathematics Competitions, then the American mathematical olympiads, followed by what is currently the most prestigious recognition of mathematical achievement as a high schooler right now, the International Mathematical Olympiad, or the IMO.
Tippi: Thank you Anthony, Although we have work collaboratively on providing maths activities outside of academic class for extra stretching of maths lovers, limitation of could line in the singularity of the format: One answer, as you mention, or multiple answers, but doesn’t change the fact that the answers are designed to be solvable. So what might be some different approaches that are worth exploring?
Anthony: So we wanted to run an experimental programme that was designed to encourage an alternative path for mathematics exploration, one that is interdisciplinary in nature to encourage students to see the intimate connections between the abstract mathematics they are learning and other subject areas, one that is student driven as to encourage more freedom organic motivation on where they wanted to take their exploration, and one that is project based, which allows for much deeper and satisfying exploration of one specific topic of interest.
Tippi: With my 8 years teaching experience here, I know that our maths department has always been interested in alternative approaches that might attract different types of learners from a diverse background. Such as integrating the UWC mission & values into our academic program. Also, I have noticed that our campus has built up the innovation@east, which has provided potential for our students to apply mathematics innovatively for investigation in science and technology. Taking the opportunity of the 50 anniversary of UWCSEA, we had the chance to apply for an innovation grant for some experimental programs. What were the goals you have presented to get the grant approved?
Anthony: So the two goals that we set for ourselves 12 months ago when we started all this brainstorming was to encourage the personal growth of students, in both their capabilities as a mathematician and as a learner in general, as well as for it to reflect our mission competencies. Linking it to UWCSEA’s educational philosophy, how can we make mathematics enrichment, which fall under the activities element of the five-element programme, to be both disciplinary and interdisciplinary, to be experiential, and to encourage the development of transferable skills.
Basically, we had boiled it down to three fundamental questions
How can we show students that mathematics is a fundamentally open-ended endeavour?
How can we make our mathematics enrichment more welcoming and inclusive?
How can we make our students realise the intricate connections between mathematics and the wider world?
Tippi: With these three goals in mind, we set out to develop Project 0, an extracurricular mathematical enrichment programme funded by the UWCSEA 50th Anniversary Innovation Incubator Grant. Unlike a traditional activity, which is very much a linear progression following a set path by either a teacher or a student leader, all of the student groups in our programme independently develop and evolve their project from start to finish.
Anthony: So what is a presentation about mathematics without some numbers? Some 93 students comprising of 27 groups in total applied to be part of Project 0, of which we selected 21 students and 5 projects. As with any selective activity, we are always at a pains when not everyone can receive the opportunity to be part, and I’m sure many other ideas would have done well. This is one of the challenges that we will elaborate on later. But working with our 6 student leaders, 11 community members comprising of industry professionals, alumni, and on-campus staff, 9 months of project work, and 103 supporting meetings from our student leaders with the project groups.
Tippi: Maybe it’s time for us to share more details of the experiment to let our guests have some concrete ideas of what we are actually doing. We have a project that is focused on the global concern of optimal social distancing during the time of pandemic. Our students have looked into the graphic design of static scenarios such as theatre and restaurant, as well as simulation of the dynamic scenario such as shopping malls and an active classroom. They are currently extending their simulation from two dimensional measure to three dimensional.
Anthony: Another of our projects groups prototypes, 3-d printed, and assembled a low cost-EEG detecting device. The mathematics involved including a Fast-Fourier transform to break down the brain waves into different frequency ranges, which they then are testing against different independent variables such as resting, reading, and watching a video. They are also now looking at a potential collaboration with our local service partner Apex Harmony Lodge to look at the effects of music on the brain activity of dementia patients
Tippi: We have a project that is looking at daily life issues such as Traffic jams before and after school hours. Which is a great direction to practice problem solving with mathematics, especially when this topic could have gone all the way to a phD level thesis.
Our candidates have done observations on the key corners around the campus. After identifying the cause of traffic jams, they looked into different AI algorithms to detect cars that were changing lanes inappropriately. Though Being in Grade 9, they have managed to detect car counts from video collected and made very insightful data analysis.
Anthony: Now don’t get misled into thinking that all of our Projects are STEM- based! This project group looks at whether group diversity as measured by personality, leadership traits, and gender, have an effect on group performance. What is to be commended about their journey is that they used several different approaches to approaching the core problem of whether more diverse teams are better teams, such as through a computerised simulation (this here is all coded by one of their members), interviews with different groups around school, as well as a randomised psychology experiment on over 200 students where they tested three different methods of group organisation.
Tippi: Our Vertical agriculture project aims to enhance sustainability with innovation. Although multiple models of vertical plants models have been done, they are often designed as a unique modulus that fits specific spaces. Our candidates have researched the advantages and disadvantages of past designs from the perspectives of life expectation, climate impacts, and energy efficiency and made a revolutionary model: to design one piece simple modules that could be scaled up to any size in any space. They have created the prototype and they will use data simulation and collection to analyse and optimise the model within our campus.
Anthony: Now throughout our project, we had encountered several challenges, particularly around the domains of the resources and talents that we had access to. We tackled these challenges by focusing on developing the potential for our students to learn and develop capabilities independently with a healthy dose of guidance from our student leaders and community experts. Our pedagogical core of project-based, student-driven, and open ended-learning meant that there was a lot of freedom for students to focus explore areas that interested them, and we found that motivating specific key mathematical concepts such as such as hypothesis testing, p-value, and mathematical optimization were much more easily done with the concrete examples which naturally lent itself through the projects that these students were conducting. Digital literacy, which comprises reading technical literature, conducting effective research, as well as developing presentation skills is a second part of the challenge comprising the skills that we wanted our students to develop. Engaging with what other people are doing, just as how the great mathematicians of the past engaged and argued with the contemporaries (think of the rivalry between Newton and Leibniz) and built on the work of giants that came before them, is a key part of mathematical maturity. Analytic tool boxes also comprised a final and key part of the skills that we wanted students to develop. Unlike perhaps a century and a half ago, where almost all of mathematics had to be done via pen, paper, slide rule, and abacus, in the modern era, we have a plethora of digital mathematical tools that we wanted students to take advantage of. Simulation, optimization, and various sorts of statistical or graphical analysis could be done with MATLAB (an education licence was one of the benefits afforded to us through the 50th grant) and other languages such as Python, and computer-aided design would be done with Fusion 360.
Tippi: While overcoming the challenges in the lack of resources, we realised we are also in the lack of talents. Besides our team, we need innovative volunteers who have connections with our students in different fields of studies or possibly with some industrial perspectives.
Or, I might say, we need you, you, who are attending this session today, because you care about reimagining mathematics education.
You might be an alumni who is studying in..
You might be a teacher who is…
you might be a parent who is willing to provide us with Industrial perspectives in…
Luckily, we have found some of you. We have teachers and partners working on campus to give directions when we need resources. We have 6 UWC alumni who contributed to our projects through discussion and virtual meetings with our candidates. And I am grateful that we have 5 expertise and have voluntarily supported our program by advising, and providing professional perspectives.
Anthony: Now that we are at the tail end of our year, we wanted to showcase some of our achievements, in the three areas of student growth, alumni connections, and equity and inclusion. Now, we’ve been talking a lot about what we think everyone is learning, and you might be skeptical, so in the following video, which was filmed last December, you can hear directly from some of our students reflect on their experiences in Project 0.
- Start of video -
Jason: I mean for me, what Project 0 is, it’s been a big exercise in problem solving. So it’s about how you look at it, what is this problem and how can we overcome this together towards a bigger goal. Personally, in terms of what this has allowed me to develop is that idea of, hey, we are getting stuck here, do we need another perspective? Do we need to look at this in another way? Or do we need someone else to come in and provide a fresh look on things.
Gauri: All of our ideas that we have brainstormed initially were all about enhancing and contributing towards the wellbeing of our school community. And especially, I think it kind of shows our value of community and giving back to the community and how we can use something like maths, which is something we’re all passionate about, to be able to bring back.
Asrshi: So one of the challenges that I faced, and that we sort of overcame as a group was we sort of brought nature that we started with, it was vertical agriculture. Yes, it is specific, but it requires so much thinking. So you have to be open-minded and you have to negotiate with other people, as well as being steadfast on the target and setting that target and streamlining that target was what we struggled with initially. And by researching and researching and non stop researching, we were able to develop those skills and that is really important.
Sky: I would say that in the beginning we were kind of, on augments and we didn’t really have a clear focus, like first we started out with a concussion and stuff like that. So it’s kind of been difficult to manage what we focus on, what we’re focusing on research on, and I know personally I’ve had to like, basically restart my research, as we switched up our focus. So I think that’s been challenging but as of now, we are getting positive results and we have a clear direction and focus.
Alexander: It’s like we chose this topic because we each had some interests or something we wanted to pursue. The important thing is to try and see how each of the things we want to pursue in this topic, connects together.
- End of video -
Anthony: Again, I want to relate it to our fundamental questions that we asked ourselves in the beginning - that mathematics is a fundamentally open-ended endeavour with intricate links to the outside world. We hope that you see in our students reflection how they are developing not only the mathematical skills, but also skills of collaboration, communication, and critical thinking and creativity which are also essential to being a good mathematician, and whatever field of study they pursue in the future
Tippi: Another achievement that we have accounted for is the solid, valuable and productive connection between our candidates and our alumni.
Anthony: These past couple of years have reminded us of the central importance of Equity and Inclusion in whatever we do, and in the spirit of this goal, we decided to use mathematics to analyse our mathematics community at UWCSEA East.
Just to properly contextualise the data that you are about to see, this is only pertaining to the for mathematics-related extracurricular activities at East, of which there are currently four, SEAMC Junior, which is aimed at Grade 9 and 10 students, SEAMC Senior, which is aimed at Grade 10 to Grade 12 students, and the Competitions maths club, which is aimed at all all high school grades, and of course, Project 0 Lab.
SEAMC Junior and Senior as well as the competitions maths club can be considered as a traditional mathematics activity, because they focus on preparing members for representing the school at various mathematics competitions, such as the American and UK Mathematics Competitions. The difference is that SEAMC Junior and Senior are selective activities, which in the past has involved both a written paper and interview during the selection process.
Tippi: In the selective SEAMC activity that aims to form teams for maths competitions, the average gender percentages have become more split from junior to senior. This might indicate that the format of selective maths competition might not fit in the comfort zone of all types of learners. Although it is less split in the non-selective maths club where students have no pressure on registering specific maths competitions, it is still a significant gender imbalance. Before project 0, we were not quite sure whether it’s because the approaches of the activities are less attractive to some types of learners or if it’s the fact that some activities are more selective than the others. However, we realised that althong project 0 is a very selective activity that requires a long process of application, the approach of the programme has attracted more diverse types of students.
Anthony: Now, this second chart shows a box and whisker plot of the gender distribution among our applicants, and those who were successful. The horizontal line in the middle marks the median percentage, while the cross marks the mean percentage. A total of 27 groups applied to us, and the distribution of the group’s gender composition is displayed in 1. The distribution of successful groups is displayed in 2. In 3 and 4 you can see the overall gender composition of the applicants and those which were successful. It is interesting to note that while we didn’t intentionally select for gender in any part of our screening process, and this is true for all the other activities, all the other mathematics activities at East. our final groups and Project 0 at least, were more balanced than the original applicant group.
Tippi: So looking at our journey in reimagining mathematics education, what can you take away from it?
Anthony: I think it emphasises the flipped model of the learning cycle. In a traditional model, the teacher is the one who is driving the learning. While now, we have a student driving the learning process, demonstration agency and leadership, and the teacher plays the role to give support, prompting the student to reflect and consolidate their learning.
Tippi: My take away as a teacher is that this learning cycle seems to be for both sides. It will challenge our educators to make innovative applications of mathematics rather than giving out one answer, to make into this binary connection rather than just maths formulas, and to provide spontaneous support rather than standard unit plans.
Anthony: That means as soon as this process has much more freedom of what they’ve learned, and because Project 0 is by nature, an extracurricular activity meant to supplement maths classes, there is much more space to explore concepts in depth without the looming worry of a terminal examination.
So just to sum up, we started very simply from an idea, an idea that mathematical enrichment done right is a key and essential part of reimagining maths education as a whole. An idea that turned into a project, a project that we received an innovation grant to explore, and that took us on an experimental journey over the past year to where we are right now.
I think this reminds me of another quote that Dr. Khanna mentioned in her interview with us that as we reimagine mathematics, we should always go right back to how the great mathematicians of the world thought about things, as interesting puzzles to be tackled. Each of our students in our project groups were driven primarily by their intrinsic motivation to find out something more that interests them, that challenges them, and allows them to stretch their skills in both mathematics and other areas. And I think this should be the guiding north star of whatever type of enrichment that we see in mathematics and even other subjects that we are going to reimagine in the future.
Tippi: So in the past 9 months, our experiment has reimagined mathematical education in the context of extra curricular, and transformed it from the traditional “ONE answer” model into a journey of exploration. An opportunity to work in groups to present innovative projects that requires research and analysis so as to solve problems using technology.
Anthony: Inspiringly, our academic programmes are also reimagining mathematics education by providing a new option of UWCSEA curriculum in mathematics as an alternative option of IGCSE and IB. The diversity in the new curriculum also overlaps with our journey in Project 0.
Looking at the extracurricular program, there has also been an increased emphasis on innovation, such as the creation of the innovation east department last year and addition of a data science lead and computing lead to guide and mentor students the coming year.
Tippi: As the Data Science Lead at East in the coming year, I am looking forward to working with our student leaders, alumni, and volunteers for another cycle of reimaging mathematical education. We are blending our activities with project based, in a laboratory environment. We will have a Maths lab, a Data Science Lab and an Initiatives lab to include more diverse types of learners. We as the community of Diverse Mathematics will play a more active role in organising theme lectures, workshops, and maybe a pie day conference to showcase our achievement in the journey ahead.
Anthony: Now we wanted to thank you for listening to our presentation. Twenty-five minutes is quite a long time to sit through, but if you want to join our networking session immediately after, you can ask us some more questions about our work. You can also connect with us on Instagram and at Project 0 lab, and also explore our website at www.projectzerolab.com if you want to find out more about the projects our students are working on. You can also explore the innovation at East website which are supported by at the following address.
So, whether you are a student like me or a teacher in the audience, or just someone who’s interested in education, we wanted to ask you the question “So, how do you reimagine maths education?”.
Tippi: We invite you to come to our Networking session immediately after, to discuss your thoughts face-to-face.