Colleges are reporting more suicides and eating disorders – they need better support now, writes Richard Caulfield
Over a year ago we published our mental health survey, with stark results. Now, all the feedback we have from the first term of 2021-22 is that the challenge is increasing. It’s driven by more learners presenting with mental health problems and the complexity of the issues they are facing.
Anecdotally we are hearing from a number of colleges that more students are attempting suicide, and that eating disorders are on the rise. The NHS is now struggling to meet demand for eating disorder services.
With over 190 colleges signed up to the AoC mental health charter there is strong commitment within the sector to support the mental health and wellbeing of learners and staff.
But there is a limit to the resource that colleges can allocate to deal with the volume of issues, and a limit to employing enough staff with the expertise to support the most complex needs.
Colleges such as South Thames College group have been quick to praise the partnership and support from the trailblazer. But this support will only reach 35 per cent of schools and colleges under the current plans. What does this mean for the 65 per cent of settings who miss out?
We need to ensure all settings have access to these additional resources.
Other areas have focused on further education too. In Greater Manchester, where health monies are devolved, there has been a significant investment in mental health over the past three years, allowing colleges to develop services to test new ideas.
In the first year of the project, Hopwood Hall and Bolton College both set about becoming trauma-informed colleges. Another six have now started to implement a trauma-informed approach, including the specialist college, Bridge College. The feedback has been hugely positive.
Other work has included a successful partnership with the British Association of Counselling and Psychotherapists (BACP) to develop a programme of training in supervision skills. This is so that staff dealing with the growing number of safeguarding issues can be supported appropriately.
What about the 65% of settings missing out?
Of course, prevention is better than cure and colleges are increasingly looking for support that can help students and staff to manage their own mental health and wellbeing too, as well as support services.
I am looking forward to seeing what we can learn from tools such as the Fika app (which supports student mental fitness) that many colleges, supported by NCFE, have been implementing this year. Like other initiatives, it will not be a golden bullet, rather another tool in the box for colleges to utilise.
We are also seeing a growing interest in social prescribing, which is where individuals are referred to social support in the community, rather than, or alongside, medical intervention. The Office for Students has recently funded a social prescribing project in Merseyside and Lancashire, and several other colleges are going down this route with local partners.
There is also synergy with this approach with Good For Me, Good For FE, the volunteering projectled by London South East Colleges, Loughborough College and East Coast College, aiming to boost mental health. This has huge potential if we can increase engagement from NHS-funded link workers with colleges.
Capacity remains the biggest challenge. Through AoC, we can help colleges access lots of support from the Charlie Waller Trust and elsewhere. However, many of the initiatives I’ve mentioned cannot be implemented without the capacity.
As we begin 2022, and government and policymakers plan the next phases of education recovery, mental health support must be at the heart of any post-16 strategy. Colleges must be funded to provide the support students and staff deserve and need.
Researchers have called for more tailored support for students with BTECs at university as a new study finds that they are almost twice as likely to drop out than undergraduates with A-levels.
The study, published on Wednesday, also found that while 60 per cent of graduating BTEC students complete their university studies with a least a 2:1, they were typically 1.4 times less likely to do so than A-level students.
Funded by education charity the Nuffield Foundation, the report, titled Educational choices at 16-19 and university outcomes looked at how students’ backgrounds, entry qualifications and entry subjects impacted on their educational experience at university.
It is hoped, the Nuffield Foundation says, that a better understanding of the differences in the experiences of students with BTECs and A-levels will reduce educational disadvantages faced by students from lower socio-economic groups while at university.
Researchers found that even after accounting for a “rich set” of demographic and prior attainment data, the likelihood of a BTEC student dropping out of university was 11.4 per cent, compared to six per cent for a similar A-level student.
As well as looking at who dropped out of university, the study also looked at the entry qualifications of students who repeated their first year. While fewer students repeat than drop out (just 4.3 per cent probability overall, compared to eight per cent), researchers found a similar pattern. Student with BTECs were found to be 1.7 times more likely to repeat their first year than those with A-levels.
Despite BTECs being accepted university entry qualifications for some time, and millions of pounds having been invested in widening participation, researchers report that students with BTECs have a 24.9 per cent chance at achieving a degree classification below 2:1, compared to 17.7 per cent for A-level students. That gap is larger for students at the lower socio-economic levels.
Drop-out rates are low in the UK compared to other countries, as is the number of students who repeat their first year. The report also highlights that BTECs are a highly effective route to a degree for students from lower socio-economic backgrounds.
Cohorts of students that researchers studied for this work pre-dated reformed BTECs. This means that it is not known what those performance gaps would look like for more recent generations of undergraduates, who would have experienced more external assessment as part of their BTEC.
Differences found in academic performance while at university, explored by using results of modules, are believed to be a big part of the explanation for the differences in the educational experience of university students arriving with BTECs compared to those with A-levels.
The report states “for the one university for which we have data on assessment method by first year module, we find that the performance gap between students with A-levels and BTECs is larger for modules assessed as least in part by written examination, compared with modules assessed by coursework only”.
Schools, colleges and universities should be more mindful of the differences between A-level and BTEC teaching and assessment when giving advice about post-18 options, the report argues. Further, tailoring courses to try and close these gaps, which disproportionately affect students from lower socio-economic backgrounds, rather than just focussing on recruiting them, should be integral to universities’ widening participation.
The report’s findings provide some challenge to the government’s current approach to level 3 qualifications reform, the Sixth Form Colleges Association (SFCA) has said. James Kewin, deputy chief executive at the SFCA, told FE Week: “This welcome research from the Nuffield Foundation shows that the vast majority complete their studies and most graduate with at least a 2:1. The report provides further evidence that scrapping the majority of BTEC qualifications will stop many disadvantaged young people from progressing to university in the future – a key concern of the Protect Student Choice coalition.
“If ministers are serious about making evidence-based decisions on the future of these qualifications, they should respond to the concerns set out in this report by pausing the defunding process until data on reformed BTECs is available and then look at the evidence in the round, rather than focusing exclusively on comparing outcomes between A-level and BTEC students.”
‘Conditionality’ rules are forcing people to give up their training courses, writes Peter Aldous
Like all MPs, I am regularly contacted by constituents struggling to access the training they need to secure fulfilling and meaningful work. I also speak to employers about the severe skills shortages they face in key areas across the local economy. This is replicated nationally and finding a solution is central to levelling up.
Resolving this issue is complicated and something that governments of all stripes have tried to answer.
There is one area where further education colleges play a key role ̶ supporting unemployed people to train and retrain.
Modest changes to the way the current welfare system operates provide the opportunity to make access to this support from colleges much easier and fairer. I and many other MPs support these changes.
For many, the key obstacle they face is the rigid and complex rules around studying and claiming universal credit at the same time. As those who work in colleges know all too well, recipients of universal credit considered able to work face strict requirements, known as ‘conditionality’.
Typically, they must spend up to 35 hours per week looking for work, provide evidence of their work search to their Jobcentre Plus work coach and be available to meet with them and attend interviews.
Claimants must also be prepared to give up their training course if they are offered suitable work.
This leaves many in a Catch-22 situation, where they may secure employment in the short term, but are prevented from developing skills that would allow them to get into higher quality, more stable and better-paid employment.
Claimants are left in a Catch-22 situation
The high employment rate in the 2010s should not disguise the fact that some people have moved from job to job with little chance to train or retrain for more meaningful and sustainable employment with prospects for progression.
Most claimants have a certain number of hours they can study per week and are typically limited to 12 weeks of full-time education and training (with 16 weeks for skills bootcamps), which restricts the options available. Extension to the amount of study time is at the discretion of work coaches, leaving scope for inconsistency and unfairness.
Claimants can be required to take part in Department for Work and Pensions’ courses that take them out of college courses. Otherwise, they risk sacrificing payments.
I welcome the steps the government has taken to address the disjointed education and welfare policies in recent years, including skills bootcamps. But unfortunately these are too temporary, creating instability and complexity in the system. This is challenging for people, some of whom already have educational disadvantages, and for colleges to navigate.
At the meeting of the All-Party Parliamentary Group (APPG) on further education and lifelong learning last summer, we heard about the important role that colleges play in supporting unemployed people into work through working with the local Jobcentre Plus (as captured in the Association of Colleges’ Let Them Learn report).
To empower colleges to do even more, the report called for the government to reform universal credit rules, removing existing barriers. I wrote to the-then skills minister Gillian Keegan, alongside a cross-party group of parliamentarians, encouraging her to take action.
The Skills Bill currently progressing through parliament is a unique opportunity for the government to commit to reviewing conditionality rules.
A review would enable a better understanding of the barriers to training that claimants are facing. It could show where flexibilities are needed in pursuit of a benefits system that encourages, not prohibits, education and training.
I intend to bring forward an amendment to the bill that would bring about this review with support from MPs across the House. While it may not make it on to the face of the bill, I’m confident that a constructive dialogue with government has been established and positive steps forward can be made.
The cost of taking no action will ultimately be fewer people in stable and meaningful employment, slower economic growth and bigger tax burdens.
College staff absences have spiked since the start of term, but despite the shortages, there appears to have been no major disruption to January exams.
Where challenges have arisen, staff are working extra hours, with managers stepping in to help invigilate vocational and technical qualifications (VTQs) this month.
Some colleges believe there should be an additional exam series in March to help those learners having to defer tests until the summer due to catching Covid.
The Department for Education’s latest attendance survey data estimates that one in 25, or four per cent, of FE college teachers and leaders were off on January 6 because of Covid. The figure for support and other staff sat at 3.4 per cent.
This is up from 1.6 per cent of teachers and leaders and 1.2 per cent of other staff on December 15, increases of 150 per cent and 183 per cent respectively.
Geoff Barton, leader of the Association of School and College Leaders, said “any hope” the Christmas holidays would act as a firebreak for schools and colleges “have evaporated”.
“The challenges posed by having so many staff absent will continue to put schools and colleges under severe pressure.”
It comes as about 300,000 learners sit exams each January, with exam boards having flexibility to bring in adaptations this year because of Covid disruption.
FE Week approached ten of the largest colleges to ask whether they had faced problems and how they worked to overcome them. Of those who responded, four said plans were going smoothly.
However, Stuart Rimmer, chief executive at East Coast College, said their usual bank of invigilators had shrunk for the 1,500 VTQ exams they’re putting on this month. This was in part due to current Covid rates, but also because of staff retiring or taking extra precautions against infection.
He said: “The staff have been absolutely amazing, whether that’s short-term cover work or doing extra hours or working on days they wouldn’t normally or stepping in to invigilate. We’ve had to deploy teachers and managers to invigilate some of these exams.”
Earlier this week, nearly 40 out of 550 staff (seven per cent) were absent, with 25 of these testing positive for Covid, Rimmer added.
Ofqual’s framework this year allows exam boards to make adaptations to take into account the disruption students have faced. But it’s up to each awarding organisation to make its own choice.
Pearson, for example, has extended the assessment window and delayed the start of the series by a week, to allow more time for teaching.
HCUC, in Uxbridge, said its 4,825 January exams are a “major logistical challenge” and had created “emergency invigilation schedules” due to staff absences.
A spokesperson said this schedule extends to senior management as well as external invigilators, which has extra costs and training time implications.
The college’s usual staff absence rate at this time of year (five per cent) has risen to 18 per cent because of sickness and self-isolation. A spokesperson commended all teams for their “commitment and creativity”.
However, a spokesperson said a March 2022 re-sit series should take place before the summer to prevent potential student disadvantage if they have had to isolate this January.
A spokesperson added: “Without a March exam sitting, students will only have a June sitting and no re-sit opportunity. Many are on a one-year programme and cannot defer exam re-sits to a second year.”
Meanwhile, independent training providers’ January exams appear to be largely unscathed, although their staff absence rates are not published by the DfE.
Simon Ashton, an assistant principal with Nacro, said it has fewer than 50 students taking exams, with only one deferral to the summer so far. But the staff absences are hitting its day-to-day operations, such as not being able to run some practical classes because there are not enough supervisors. Several of its 14 sites had staff levels of below 50 per cent over the last month.
“We’ve had to be resilient and make the best of it,” Ashton said. “We’ve had to combine classes, and managers have had to step in to help run classes to ensure learners still get a face-to-face session.
“But, for example, in motor vehicle classes, we’ve had to move to more theory-based work with the staff that we’ve got.”
There will be a focus on practical catch-up as part of the government’s 16-to-19 tuition fund, he added.
Less than half of all UK universities have confirmed they will accept T Levels for entry this year – with most Russell Group members turning their backs on the new technical qualifications.
An FE Week investigation has also found many universities still yet to decide whether to accept T Levels despite there being less than two weeks before the UCAS deadline for 2022 admissions.
The first T Level students – who study either digital, construction or education and childcare – began their two-year course in September 2020 and will be deciding their next steps now.
While T Levels were designed so that students can enter work straight after completing their course, ministers have repeatedly made clear that the courses are still a viable entry route into university.
One parent of a T Level student who spoke to FE Week slammed the “disconnect” between the government and universities after spending months scrambling to find higher education institutions that might accept her son, with no clear way of identifying them.
The Department for Education said universities are independent of government and it is for them to set entry requirements, but urged them to offer prospective students “transparent information about their entry requirements” as soon as possible.
DfE finally publishes list of unis that will accept T Levels
On December 17 – the last day of term for most colleges – the DfE published a list of higher education institutions that had confirmed T Levels were suitable for at least one of their courses.
Eighty were listed, of which 66 were traditional universities. There are 140 universities in the UK, meaning just 47 per cent currently accept students who have studied T Levels.
The new technical qualifications are equivalent to three A-levels and have UCAS tariff points allocated to them.
Ten of the 24 universities in the elite Russell Group are so far not accepting T Levels.
The University of Oxford told FE Week that T Levels alone “are unlikely to satisfy the requirements for entry, as they are technical qualifications, while all degree courses at Oxford are highly academic”. Cambridge University said the three initial T Level subjects “would not be a natural fit” with any of their degrees.
Some universities, such as Imperial College London, said they will wait until T Levels are rolled out further before determining whether students studying them are academically able to cope with their courses.
Others, including the likes of Leicester and Loughborough, told FE Week they have still not decided whether to consider T Levels as entry criteria.
Nick Hillman, director of the Higher Education Policy Institute think tank, said universities legally have autonomy over who they admit but pressed that it is vital that there is clarity about how they treat applicants. “Where universities are already clear that T Levels are unlikely to provide effective preparation for a specific course, they should make this really clear,” he said. “Otherwise, disadvantaged students in particular are likely to continue lagging behind middle-class students when it comes to entering highly selective institutions.”
Universities UK, which represents the country’s 140 universities, said it expects to see T Level acceptance increase within the sector as the number of subject areas expands “to give learners the opportunities and flexibility they deserve”.
The DfE’s list doesn’t even include details of which courses T Levels are accepted as entry criteria. Instead, it encourages students to “look at UCAS and at their preferred higher education provider’s website for more information on entry requirements”.
‘I’ve been really struggling to get a clear answer’
Annie Dorrington’s son Niall is in his second year of digital, design production and development T Level and she began helping him search for university opportunities at the start of the 2021 autumn term.
She said it was a confusing and frustrating time as most universities failed to advertise whether or not they accepted T Levels as entry criteria, while others had still not made up their mind.
Most shocking to Dorrington was that some universities said they would only accept her son if he also had an A-level in maths, despite the T Level effectively being a nine-to-five course.
She criticised the government for not publishing a list of universities that would accept T Levels sooner, explaining that it was released after the timeframe for university open days. “It seems to me that the DfE thought it was enough to give T Levels UCAS points and leave it at that,” she told FE Week.
“I work at a university and know my way around the admissions process but even I’ve been really struggling to get a clear answer in most cases.”
Dorrington, who described the T Level course as “fantastic”, said she knew from the get-go that there would be some universities who would not be interested in students with T Levels but did not expect the process to be so difficult: “I was expecting there to be a list of universities accepting T Levels much earlier. The college didn’t have that, nor did the government.”
Around 1,300 students studied the first three T Levels in 2020 and a further 5,450 signed up in 2021, with a total of ten subjects now on offer at over 100 colleges and schools.
A DfE spokesperson said the government expects the number of universities offering T Levels “to grow in the coming weeks”.
The boss of a defunct training provider has declared bankruptcy as the government seeks to reclaim over £20 million from his firm following a subcontracting scandal.
SCL Security Ltd, founded and run by Andrew Merritt, went insolvent in October 2020 after the Education and Skills Funding Agency kicked the company out of the apprenticeship market.
The decision followed an audit, prompted by several FE Week investigations, which found apprenticeship funding was being used to pay the wages for the 16-to-18-year-olds, which is strictly against the funding rules.
A liquidators’ statement for SCL Security was published this week and revealed its debts have ballooned seven-fold over the past year, from an initial £3.85 million to £26.3 million.
The uplift in claims “predominantly relates to claims arising as a result of the ESFA review in respect of monies paid by a number of colleges and agencies”, the report said.
Brooklands College subcontracted out more than £20 million to SCL Security over a three-year period and had faced having to repay a similar sum to the ESFA following the agency’s investigation into SCL Security, as it was the prime provider responsible for the funding.
It is not clear whether the agency has now agreed to pass the repayment on to SCL Security, or whether it is seeking similar clawback from both providers.
The ESFA refused to comment on the investigation.
Christine Ricketts, principal of Brooklands College, said she could not comment on the clawback or SCL Security investigation but told FE Week her college “continues as a going concern” and has benefited from a “recent increase in recruitment and improved financial performance”.
The college is “well advanced in discussions to resolve outstanding issues” and expects to publish its much-delayed accounts for 2019 and 2020 before the end of this financial year, Ricketts added.
Merritt, who took a director’s loan of over £8 million from SCL Security, “decided he had no alternative” but to file for bankruptcy, which was granted in July 2021, the liquidators’ statement states.
His main asset was a property owned jointly between him and SCL Security’s other director, Kym Rowe. The property is currently on the market and any proposal for repayment would be funded by way of the sales proceeds.
The joint liquidators, Phil Deyes and Anthony Milnes from Leonard Curtis Business Rescue and Recovery, have submitted a claim in the bankruptcy to recoup the overdrawn loan account.
Their report states that although there are currently no funds available to “enable a distribution” to unsecured creditors, it is “considered likely that there will be sufficient funds available to enable a distribution to creditors in part from asset realisations in the future”.
However, the liquidators have “not formally agreed” to any claim as yet from the ESFA. They have “spent a considerable amount of time” reviewing the agency’s claim in order to understand the impact on their investigation “both in terms of the liquidators’ statutory duties and assessment if these could lead to any other realisations”.
Over the past year the liquidators have also received claims from “a college” and another “agency” identified in the ESFA investigation, according to the report.
“Again, time has been spent reviewing the supporting documentation provided in respect of these claims together with the information brought to the joint liquidators attention as a result of the ESFA investigation,” it said.
“Due to the quantum and nature of the claims received the joint liquidators instructed lawyers from Andrew Jackson solicitors to provide legal advice in relation to these claims.”
The liquidators warn that if these investigations determine there are further monetary claims against SCL Security’s directors, it is “uncertain whether these would ultimately affect the overall recovery from this source”.
Awarding giant Pearson has been contracted to develop the legal services T Level, the Institute for Apprenticeships and Technical Education announced today.
The announcement now means that the institute has a full-house of awarding organisations to develop all 23 of the government’s flagship level 3 qualifications.
It also means that Pearson has the complete set of T Levels under the legal, finance and accounting route. A total of 35 providers are currently preparing to deliver the finance and accounting T Levels from this September. Delivery of the legal services qualification begins in September 2023.
The value of Pearson’s contract totals £3.44 million.
Pearson’s head of technical products Suzanne Hall said “We are delighted to be delivering the legal services T Level technical qualification. We look forward to using our expertise to support students as they begin their programmes of study and playing our part in developing talent in this vital industry.”
Pearson, along with NCFE, was one of the first awarding organisations to receive contracts to develop T Levels. The very first cohorts of students on its T Levels in digital production, design and development and design, surveying and planning began their studies in 2020 and are due to become some of the first T Level graduates in the country later this year.
A spokesperson for the Institute for Apprenticeships and Technical Education said the delay was because there were no successful bidders in the main procurement round for the subject which concluded in summer 2021.
But a further procurement took place in the autumn after more interest was received. The spokesperson confirmed the T Level will be delivered in the same timescales as the other contracts in wave four.
Employers and the institute have said that the legal services T Level will improve social mobility by attracting people from more diverse backgrounds into legal professions.
Cassie Williams, a barrister from Bedford Row Chambers, said: “Justice is served when lawyers and people working across legal services come from all walks of life. This T Level will provide the opportunity for this to become a reality.”
Jennifer Coupland, chief executive at the institute, said she “couldn’t wait” to see the T Level rolled out in classrooms and that it will “help open out the profession to people who may want to follow a more direct training route into work”.
This will include, Coupland added, being “an important stepping stone to degree apprenticeships and more conventional degrees.”
The government plans to encourage schools, colleges and training providers to trawl the social media of would-be employees and beef up training requirements for governors under proposed changes to safeguarding rules.
The Department for Education also wants child-on-child abuse guidance, which has been published separately since 2017, withdrawn and “incorporated throughout” its main statutory document for education providers.
A consultation was launched yesterday on changes to the statutory keeping children safe in education (KCSIE) guidance, which now applies to independent training providers as well as colleges. If approved, the changes would come into effect in September this year.
The consultation also seeks views on some changes enacted in 2021 and whether they have worked.
Many of the proposals are technical and involve moving guidance around the document itself.
But there are also several substantive changes proposed that will affect the way education settings operate. Here’s what you need to know.
1. Consider ‘online search’ on shortlisted candidates
The DfE’s new draft guidance says that as part of the shortlisting process for new staff, colleges and providers “should consider carrying out an online search (including social media) as part of their due diligence on the shortlisted candidates”.
This “may help identify any incidents or issues that have happened, and are publicly available online, which the school or college might want to explore with the applicant at interview”, the draft guidance states.
2. Ensure governors receive safeguarding training
Although the DfE said that evidence suggests the “majority of governors and trustees” already undertake “some form” of safeguarding training, they intend to make the need for it more explicit.
The new draft guidance states that governing bodies and provider proprietors “should ensure that all governors and trustees receive appropriate safeguarding and child protection training at induction”.
This training “should be regularly updated”.
The consultation document states that training is “essential to ensure new governors/trustees understand their roles and responsibilities, particular in them taking a strategic rather than an operational approach”.
3. Child-on-child abuse guidance to become statutory
The DfE said making it “incorporated throughout KCSIE” would “give the issue the prominence it deserves in statutory guidance”.
This will also “remove duplication”, as “much of the content in the standalone advice was already in part five of KCSIE”, the department said.
The guidance will also be updated to use the phrase “child-on-child abuse”, rather than “peer-on-peer abuse”, and to use the terms “victims” and “perpetrators”. The DfE said this was done for “consistency”.
4. Students ‘may not feel ready’ to speak about abuse
In a section on “what school and college staff need to know”, the DfE has added a paragraph that states “all staff should be aware that children may not feel ready or know how to tell someone that they are being abused, exploited, or neglected, and/or they may not recognise their experiences as harmful”.
Mathematical modeling refers to the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight. There is a distinction between applying a formula and the actual creation of a mathematical relationship. Some graphical illustrations of the modeling process can be seen on this one-page flyer.
Real-world, messy problems can be approached with mathematics, resulting in a range of possible solutions to help guide decision making. Students and teachers are sometimes uncomfortable with the notion of math modeling because it is so open-ended. So much unknown information seems prohibitive. And how do you decide which factors are most relevant? But it is this open-ended nature of real-world problems that leads to building and applying problem solving skills, creativity, and innovation in mathematics.
Math modeling obliterates the question “Why do I need math?” by demonstrating the value and importance of math in approaching big problems found in our communities, regions, and world. Identifying the important variables and quantifying them—even with assumptions and incomplete information—can lead students to insights and understanding that have reason and structure.
It’s a Process
Mathematical modeling can be thought of as an iterative process made up of the following components. (Note that the word “steps” is intentionally avoided: there is no prescribed ordering—some may occur simultaneously, and some may be repeated.)
Identify the Problem—Be specific in defining what you want to find out.
Make Assumptions and Identify Variables—It is impossible to account for all the important factors in a given situation; you must make choices about what to incorporate in your representation of the real world. Making assumptions helps reveal the variables to be considered and reduces their number by deciding not to include everything. Relationships between variables will emerge based on observations, physical laws, or simplifications.
Do the Math—Eventually, a relationship between input and output will allow for a solution to be found.
Analyze and Assess the Solution—Consider the results and insights gained from the model. Does the answer make sense?
Iterate—Usually the model can be refined, and the process can be repeated to improve performance.
Implement the Model and Report Results—Make the model understandable to others.
Pitfalls to Avoid
The biggest pitfall in developing a reasonable model is often time management. When modeling is new to students, it is easy for them to become overwhelmed, and they may spend too much time “in the weeds.” To define a succinct problem statement, students need to brainstorm, and they should be encouraged not to get rid of any ideas. However, there are times when students may get caught up in trying to include variables or relationships in their model that are not tractable or where data is unavailable. If this happens, students should assume and move on, making sure they come back to those assumptions after they have gone through the entire modeling process. Having said that, sometimes students include unneeded assumptions in their documentation that are never explicitly used in the modeling process. This can cause them to lose valuable time and could detract from the presentation of the solution. Students must try not to get off track while creating models, particularly by making choices or assumptions that undermine the quality of the solution.
When students are in a time crunch, apprehension may lead to mathematical relationships that are removed from reality being introduced, even to the point of being nonsense! For example, students may form an additive relationship between the key variables they identified but the units are meaningless (for example, adding dollars to time to get a model for resources). Coefficients are often used in models that also do not reflect units properly or there is no justification as to why they were chosen. Other times, students may have a sound idea for a mathematical relationship, but they overcomplicate it to make the mathematics look more sophisticated than it is (for example, introducing a triple integral when really addition is appropriate). This is another reason leaving time for reflection is critical, so that students can read over their entire solution and ask themselves “Does this make sense?”.
Dealing with data can also be overwhelming. Students may have a brilliant idea for a model but cannot find the data they need to move it forward (again, at this point they should make an assumption and stop wasting time looking). Other times, datasets may be prohibitively large, and students are not equipped with the tools to interpret key trends. Linear regression or high-degree polynomials are often used to fit data without any sound reason and then used as predictors. The connection to the underlying physical problem that instigated the data fitting can get lost, or the quality of the fit is ignored completely due to relief at having done something that seemed to work.
All the above pitfalls (which are by no means an exhaustive list) can be amended if the team reflects on the quality of their work. If an assumption seemed way off base, students could report out the identified weaknesses of their approach and point the way toward improvements, even if they do not have the means or access to the information to do so. Even better, a sensitivity analysis can help a student assess the robustness of their model and make comments on its applicability. Much of this goes back to time management.
An Opportunity for Students to Engage in Math Modeling
MathWorks Math Modeling Challenge (M3 Challenge) is an annual free online contest in which high school juniors and seniors and sixth form students work in teams of 3-5 to solve an open-ended problem about a real-world issue in 14 continuous hours over Challenge weekend. The Challenge problem is completely unknown until teams download it during Challenge weekend. The use of online collaboration tools and resources is encouraged.
Scholarships totaling £75,000+ (will be awarded in 2022. Extra credit awards are available for teams who choose to write or employ outstanding code as part of their solution. The competition has given $1.65 million+ to date.
A program of Society for Industrial and Applied Mathematics (SIAM) that is funded by leading technical computing software developer MathWorks, M3 Challenge motivates students to study and pursue careers in applied mathematics, computational science, data science, and technical computing. It has been a virtual competition since its inception in 2006. Past competition topics include issues such as the transition of trucking from diesel to electric, universal internet access, substance abuse, food insecurity, plastic recycling, and car sharing.
From Judges, Coaches, and Past Participants
Submissions are judged by an international panel of 150 primarily Ph.D.-level mathematicians, and almost every team receives specific feedback on their submission from the judges who read their papers during rigorous assessments. “The questions can be approached in a variety of ways depending on students’ skills and experiences,” says problem development committee member and judge Dr. Katie Kavanagh of Clarkson University in Potsdam, New York. “For example, participants may use simulation and programming, probability and statistics, or even algebra and basic math to model aspects of the open-ended problem. We are always eager to see how the students approach the issue,” says Kavanagh. “They offer unique perspectives on what factors are important to consider, particularly at that critical, transitional time in their own lives and influenced by their unique circumstances.”
Joy Qu, a member of a 2021 finalist team from Adlai Stevenson High School in Lincolnshire Illinois, was asked about the secret to the team’s success. “We always give a line of reasoning behind our equations and how we derive them. So I think reasoning is really important because if you can support your model, it increases the validity of your model.”
David Stein is a teacher at Montgomery Blair High School in Silver Spring, Maryland who has coached multiple finalist teams in M3 Challenge. He believes that teachers can influence students to study and pursue STEM careers and can demonstrate the interdisciplinary nature of the sciences by basing rigorous lessons on real-world issues and problems, focusing students’ attention on communication and writing, and providing opportunities like M3 Challenge for them to showcase their work.
M3 Challenge has had a profound impact on many of its participants, including Dr. Chris Musco, a 2008 M3 Challenge finalist who is now head of the competition’s technical computing judging and a member of the problem development committee. “Being involved in this program as a judge and using my experience and perspective to help shape the problem the students will work on is really exciting,” says Musco, assistant professor in the Tandon School of Engineering at New York University. “M3 Challenge changed the trajectory of my college major and career, and it’s great to play a part in doing that for the students who are participating now.”
“For M3 Challenge, students work together and put forward ideas and models—some teams even include computer code – toward a solution or an approach to the problem presented. Every year we are blown away by the work produced by teams in just 14 hours,” said Dr. Suzanne Weekes, executive director at SIAM. “Problem topics are relevant and meaningful – for example the 2021 topic of reliable access to the internet for all, which became so prominent and important during the pandemic. Students are solving real problems by asking questions, digging for information, making assumptions to get started, getting creative in their approaches, and then providing insight about the issue that can be used to make decisions going forward.”
“Every year without fail, we hear from students who refer to their participation in M3 Challenge as a transformative experience that helped open their eyes to how important, useful, and valuable the application of mathematics can be,” said Michelle Montgomery, M3 Challenge program director at SIAM. “I am confident that this year’s Challenge will do the same.”
Challenge weekend (Friday through Monday): February 25-28, 2022
*Much of the content for this article was written by Katie Kavanagh and Ben Galluzzo of Clarkson University, and is based on ideas presented in GAIMME: Guidelines for Assessment and Instruction in Mathematical Modeling Education, Second Edition, Sol Garfunkel and Michelle Montgomery, editors, COMAP and SIAM, Philadelphia, 2019.
