Impact case study database

Penazzi has developed methods to teach mathematics experientially enabling students to become more mathematically resilient. This has led to a change in maths teaching in Benin, benefitting student attainment and improving the perception of maths. In the UK, Penazzi ran a three-day experiential residential course called Frontier Education Mathematics. It consisted of outdoor activities involving problem solving processes and the formulation of questions and strategies that are analogous to mathematical study. In the pre- and post-activity interaction, participants review and transfer their learning to the context of their maths course and their own future employment. After the course, one lecturer commented: “ There is a noticeable difference before and after the residential course”, and that they were “more lively.” Furthermore, “In a workshop environment, the students can reinforce their learning when discussing their tasks, and helping each other out. For this purpose, the attained friendships and more active “class-life” is definitely beneficial.” [A]

Penazzi led a research trip to Benin in June 2018 that included four University of Central Lancashire students involved in his research and work in schools. Penazzi made contact with a local Non-Governmental Organisation (NGO) called Servime, which supports African countries and Benin in particular to help reduce skills loss through emigration. A partnership was created with Servime and four primary schools to support the engagement of pupils with mathematics [B].

In Beninese education, pupils attend the Ecole Primaire at 6 years old, equivalent to KS1 & 2, followed by 3 years in College-1, equivalent to KS3, and 3 years in College-2, equivalent to KS4, before entering University. For College-2 they choose between four strands or ‘Series’, of which only one (Serie C) has a strong mathematical content and leads to university courses in Mathematics, Physics or Engineering. Currently only around 5% of students choose Serie C, compared to the 20% that the Benin government identifies as needed for national development. In particular, the Government has identified the need for a more widespread and equal access to technical and mathematical-based courses. The focus is to create a critical mass of trained teachers who can deliver the specific pedagogical support required to increase student access to Serie C. The years in Primary school and College-1 are pivotal in the formation of the students’ approach towards Mathematics. Addressing Mathematical Anxiety at this stage will help to equip more students with the confidence and skills needed to choose Serie C and then go on to study STEM courses at university. These activities address specific Objective 3 from the Benin Education Sector Plan Post 2015 which has the aim to provide children aged 3-15 access to a quality basic education [C].

Enhancing mathematics teaching in Benin through experiential mathematical activity

Penazzi and his students visited schools in Natitingou and neighbouring villages in the Atakora Department to form a discussion group to identify the strengths and weaknesses of Beninese teaching strategies. The teaching methods observed were extremely methodical, with students working rigidly within taught parameters without being given the personal space to explore problems. This regimented, disciplinary approach was discovered to be a cause of disengagement with Mathematics [J]. Teachers in Benin, like their counterparts in the UK, also reported experiencing Mathematical Anxiety and this was highlighted in their feedback [E1]. “A lot of teachers also didn’t like mathematics, so we had a preconceived idea, mathematics is hard, it’s hard, kids don’t work when we didn’t know how to teach [mathematics]” Leon Mpo, Principal, EPP SOS Enfants [E2].

Penazzi and Servime agreed a plan with the local Beninese authorities [D], for a year-long pilot project with four primary schools in different settings which began in 2019. During the pilot study Penazzi trained 20 primary teachers from the four schools, which served approximately 280 pupils, on delivering Experiential Mathematical Activities [I]. A resource hub was created, operated by Servime, where teachers met and co-created six Experiential Mathematical Activities tailored to the Beninese curriculum. These new teaching materials were then delivered in all four schools.

The feedback from teachers was very positive, highlighting a general increase in their confidence in teaching mathematics: “I used to have difficulty explaining certain mathematical concepts, but with the experiential mathematics it is easier to approach the topics” [E1] “With the course given by Davide Penazzi I understood that I can go via simple games to then get to satisfying results and this [made me overcome] the mathematical anxiety” [E1].

Teachers made changes in how they presented their material, using Penazzi’s strategy to teach the concepts of mathematics [E2]. “…we have understood the importance of bringing the students to apply to reality the formulas they learn” [E4]. Consequently , “experiential mathematics have changed the pupils’ attitudes towards maths” and “They are drawn towards mathematics much more because they have found an interest in it” [E1]. A teaching pathway was formed starting from the outdoor applied, experiential mathematics and ending with the abstraction of manipulating figures and numbers in the classroom: “The training in the methods has made my teaching easier. This training has enabled me to go from concrete to abstract mathematical ideas.” The impact of the training was to change their pupils’ attitudes towards maths. “They like the sessions much more and they are thriving.” Significantly, teachers reported better scores: “experiential maths activities have had a significant effect on the pupils’ results.” “The students’ results have really improved.” Teaching is easier too: “teaching is much easier now due to the experiences we’re able to give in order to pass on the knowledge” [E1].

These projects are addressing Benin National Specific objective 3, and thus UN Sustainable Development Goal 4: ‘Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all.’ Furthermore, with an increased number of students in STEM subjects, they are addressing Goals 8 ‘sustainable economic growth’ and Goal 9, ‘sustainable industrialization and [the fostering of] innovation’. Kevidjo Idoho, Head of the Natitingou-Toucountouna Teaching region and representative coordinator of the Ministry of Maternal and Primary Education said: “…above all the impact is to bring a little more to the clarification of the teachings of mathematics, to the learning of mathematics by our learners and […] I think it is a good thing that children can learn mathematics more easily. The fear they have about teaching, the learning of mathematics, is dispelled by the approaches you implement.” [F]

Experiential Mathematical Activities in the UK

The first application of the project in the UK was the development of the three-day residential course to support transition to HE Mathematics, called Frontier Education Mathematics. This course has run with the first year BSc Mathematics and MMath at University of Central Lancashire since 2016. The positive effects of this intervention have been studied across four years. Students who attended the Frontier Education course have gained a 14 grade higher average percentage at the end of their first year compared to students who did not attend the course [K].

Penazzi has developed and delivered experiential learning activities in UK schools, along with CPD sessions for 20 primary and secondary school teachers. All attending teachers reported that they found the training useful. Thematic analysis shows that they will start implementing Experiential Mathematical Activities (EMAs) in their practice. The teachers stated they would use the problem-solving activities and games to elicit greater interest in maths. They also comment on changing their delivery method, embedding models that will engage with the affective sphere of the students: “[The] comfort zone model will be in my mind when thinking about more able [students]” says one . “[I will spend] more time on anxiety in maths and how it can be addressed” , says another. They will also share their knowledge with their colleagues to create good practice: “[I will] encourage others in my school regarding [the] 'learning pit' and growth mind set.” Whilst another colleague comments that they will : “Develop support staff approaches in school”. [H]

The effects of Covid-19

The original plan involved a visit to the four schools in Benin in May 2020 to obtain further evidence. Due to travel restrictions, it was not possible to make that visit. Some of the evidence was obtained remotely but several items of evidence collection were not possible. We were unable to meet with pupil focus groups to hear about the effects of the pilot project on their perceptions and their engagement with mathematics. Similarly, we were unable to meet with teacher’s focus groups to discuss the effect of the pilot project on their perception of mathematics. We also wanted to create a working group to share experiences of delivering the developed activities and writing activities for the production of a booklet. Furthermore, we were going to meet with governmental bodies with the aim of securing a continuation of the project. Some interviews have been done but plans for further work have been paused for a year awaiting the pandemic to subside.

The Mathematics Research Group (MRG) primarily through Anscombe and Bowman have helped to inform a wide range of public engagement (PE) activities aimed at improving levels of awareness of, and engagement with, mathematics. These targeted activities were undertaken as part of wider multidisciplinary ventures across associated STEM (science, technology, engineering as well as mathematics) subjects, part of a strategic decision to work alongside university colleagues in the Jeremiah Horrocks Institute and beyond to maximise PE opportunities both regionally and nationally. The two main approaches are outlined below.

Inspiring young people from disadvantaged backgrounds

The Lancashire Science Festival (LSF) has been run by the University of Central Lancashire since 2011, and from 2014, MRG researchers have annually contributed to public lectures and interactive hands-on stalls. The festival is a free event and aims to make STEM and Higher Education more accessible to a variety of audiences, with particular focus on primary-age children and their families, often from disadvantaged backgrounds.

There are high levels of deprivation across Preston and the North West; according to the English Indices of Deprivation 2019, approximately 18% of the city’s population live in the most deprived 10% of local authority areas in the country. Since 2014, 65,055 people have attended the Festival [A1], and an audience analysis conducted by the UK Science Festival Network in 2017 and 2018 showed that attendees with limited budgets or living in rented accommodation were overrepresented at the LSF when compared to national averages [D]. Low socioeconomic status, such as those seen in Preston and the surrounding region, has an established link with poor educational attainment. Research on the LSF found that 70% of parents attending the Festival reported a positive impact on their perception of STEM with this proportion increasing among parents from more deprived areas [B]. The MRG plays an important role in the festival offering and we would highlight the following two activities:

Experiment Packs

As part of the 2019 Festival activites, Anscombe contributed to an ‘Experiment Pack’ which was available for free to children from disadvantaged backgrounds who attended the festival with their schools or their families. Informed by her research, Anscombe developed a series of engaging logic puzzles suitable for primary school children. In total, 755 packs were sent to nineteen schools in the surrounding region. Positive feedback from teachers noted that the packs would “Allow the parents to see what they can do [to] support their child's learning” and “Inspire them and show them how accessible science is to do at home” [E].

Rocket to the Moon

As part of a series of celebratory events centred around the 50^th anniversary of the Moon landings, Bowman developed and delivered ‘Rocket to the Moon’, a PE cinematic experience which broke down the mathematical challenges faced and solved in the effort to land humans on the moon. The political, economic, ground breaking engineering and hitherto unexplored scientific challenges faced by the Apollo missions all involved the solving of related mathematical problems.

Presented at the Lancashire Science Festival as well as at the Harris Museum, Preston, and World Museum, Liverpool, the events were attended by over 500 members of the public, ranging from primary school children experiencing the story for the first time to adults reliving their memories of the momentous occasion [C1]. The event was praised for how it engaged members of the public with the mathematical science involved, with many commenting how inspiring and informative the talk was. One, initially reluctant, attendee commented “I will confess that I was almost dragged there, like a reluctant teenager, with just the promise of lunch afterwards as a way to keep me looking forward. I have to say that within seconds you had me hooked. From the warm up screen presence of the TV and film related space characters to you finishing to both canned and in-house cheering I was intrigued and I learned so much.” Another attendee praised the use of mathematics to provide context: “I liked the maths calculations to explain things more in context, even though I am not a Maths person.”[C2]

Engaging audiences with Mathematics through thrills, movies and superheroes

From the perspective of a lay audience, mathematics and other related science subjects are intimidating topics that are often difficult to grasp. However, placing them in the context of something more familiar and relatable can break down pre-conceived barriers and anxieties to learning, enhancing the appreciation of how vital yet enjoyable mathematics can be.

In this context, Bowman regularly delivers popular maths-focused talks at festivals and public venues designed to engage the younger audience members. His session ‘Maths, Disney and Pixar’ and subsequent sequels showed the audience how mathematics plays an integral role in the design and production of our most beloved animated characters. Other related sessions target how maths is employed in the construction of rollercoasters and in robotic design. Using these appealing themes, Bowman introduced attendees not just to the basic mathematics of gravity and speed but also those of shapes integral to the creation of thrill rides as well as use in animation techniques. Over 700 people attended the public talks in 2018 and 2019, with 90% of feedback respondents praising the presentations and its application of mathematics in an unusal yet accessible manner [A2]. The feedback for these events has highlighted the successes that have been achieved in engaging with audiences. One attendee commented on Twitter “Dr. Kevin Bowman Maths, Disney and Pixar lecture -best I've ever seen.” [A3]

In a similar fashion, Anscombe was part of a transdisciplinary project that built on the surging popularity of the superhero genre. Unmasked: The Science of Superheroes is a popular science book (ISBN 978-1912979080) authored by seven UCLan researchers to explore the scientific realities behind famous comic book legends and blockbusting movie icons. Launched on World Book Day in February 2020, the book draws on Mathematics alongside Computing, Engineering, Physics, Biology and Psychology to examine how real-world research can be just as wondrous and intriguing as the explosive events presented on our cinema screens. As part of the project, each of the authors were spectacularly turned into superheroes themselves across the pages of the book, with each character reflecting different types of superpowers and their scientific basis. Anscombe played a central role in the project team including writing a book chapter on “Superhero Mathematics”. As of end of 2020, 191 books had been sold online via the usual booksellers with a rating of 4.7/5 on Amazon [H1, H2].

During 2020, a series of schools outreach events was planned to coincide with the publication in addition to an extensive engagement programme at science, literary and comic festivals across the UK. This included author talks with demos, reading sessions, panel discussions and interactive stands; however, the COVID-19 pandemic halted all this activity. Instead the authors sought other possible avenues for engagement. In particular, the Science and Technology Facilities Council Public Engagement Team saw the opportunity for a unique approach to interdisciplinary outreach provided by the book and the UCLan team; so much so that STFC invested almost GBP23,000 in the printing of 12,000 copies to be used for their national activites.[G]

Unforunately once again, the rolling national lockdowns prevented any STFC school and science centre engagements from taking place. However, it was possible (i) to create an “Unmasked Science” website [H3] containing national curriculum lesson plans on elements from each book chapter as well as some online games (”Density Matters” and “Super Maths” respectively for mathematics); and (ii) in conjunction with the Reading Agency, distribute approximately 5,200 copies of the book to libraries right across the UK.

Debbie Hicks, Creative Director at The Reading Agency, commented, “Research and experience show that children learn by incorporating reading into play. Developing science knowledge through superheroes is a brilliant way to get children interested and engaged in STEM subjects. We know children and families will love unmasking the astounding world of science and superheroes by borrowing the book from their local library." [G] Similarly, Carol Stump, Chief Librarian at Kirklees Council and President of Libraries Connected, stated: " The book will definitely engage children with STEM, using superheroes and the comic book legends to explore and understand science. A brilliant concept and way of getting children interested in STEM subjects through reading!" [G]

The team also worked with the STFC on sending copies of the book to a number of targeted groups or organisations. In particular, Anscombe led on the engagement with STEAM Packs, a small local charity based in Kent. Knowing from their own experience that life in hospital can sometimes be “boring, painful and a little scary”, STEAM Packs create and distribute educational science, technology, engineering, art and maths packs to chronically sick children in hospital. As well as planning the production of additional mathematical puzzle sheets for these packs, in late November 2020 over 600 books were sent to specialist play teams in Darent Valley Hospital, Kent and the Royal National Orthopaedic Hospital, Middlesex as well as three specialist children’s cancer wards with support from the Chartwell Children’s Cancer Trust (Croydon University Hospital; Kings College Hospital, London; Queen Elizabeth Hospital, Woolwich). The books, which were given to both paediatric patients and their siblings, helped the children feel “…valued and cared for” and gave the staff “…a positive boost” [F].

Also in collaboration with the Public Engagement Team at the STFC Daresbury Laboratory in Warrington, 100 books were received by the specialist play team at Liverpool's Alder Hey Children's Hospital. Hayley Thomas, Head of Corporate Fundraising at Alder Hey Children's Charity, commented: " Thank you for generously donating the Unmasked: The Science of Superheroes books for our patients. Our Play Team was delighted to receive them. New books are a great way to entertain patients during their hospital stay so your donation is really appreciated."[I]

Follow-up contacts with all the aforementioned organisations will take place from early 2021 onwards.

Effect of COVID-19

Due to the COVID-19 restrictions a considerable number of impact activities have been adversely affected. The 2020 Lancashire Science Festival and a wide range of associated regional school engagement activities were cancelled; hence no PE maths lectures have taken place. In particular, the launch of the “ Unmasked: the Science of Superheroes” book just four weeks before the first lockdown resulted in a loss of critical time and severely inhibited the plans for promotion of the book in schools. Major events where the book had been due to be promoted were cancelled including for example, the Northern Young Adult Literary Festival and the Blue Dot Festival, Manchester. Although in collaboration with STFC and the Reading Agency, copies of the book have reached the vast majority of libraries across the UK, all in-library activites (eg. author readings, science clubs) cannot be undertaken. Visits to support the STEM activity in children’s wards was just not possible. Combined, this had a significant impact on the uptake and engagement possible for the use of the superhero book.