Author: IMC

In addition to describing biological interactions, evolutionary theory has also become a valuable tool to make sense of the dynamics of social norms. Social norms determine which behaviours should be regarded as positive, and how community members should act towards each other.

In a recent publication, published in PLOS Computational Biology, researchers from RIKEN, Japan, and the Max-Planck-Institute for Evolutionary Biology (MPI) describe a new class of social norms for cooperative interactions.

Social norms play an important role in people’s everyday lives. They govern how people should behave and how reputations are formed based on past behaviours.

In the last 25 years, there has been an effort to describe these dynamics of reputations more formally, using mathematical models borrowed from evolutionary game theory. These models describe how social norms evolve over time—how successful norms can spread in a society and how detrimental norms fade.

Most of these models assume that an individual’s reputation should only depend on what this person did in the past. However, everyday experience and experimental evidence suggest that additional external factors may as well influence a person’s reputation. People do not only earn a reputation for how they act, but also based on who they interact with, and how they are affected by those interactions.

For example, with a recent series of experiments, researchers from Harvard University have shown that victims of harmful actions are often regarded as more virtuous than they actually are. To explore such phenomena more formally, researchers at the MPI for Evolutionary Biology in Plön and RIKEN, Japan, have developed a new mathematical framework to describe social norms.

According to the new framework, when a person’s action affects the well-being of another community member, the reputations of both individuals may be updated. Using this general framework, the researchers explore which properties such norms ought have to support cooperative interactions. Surprisingly, some of these social norms indeed have the property observed in the earlier experiments: when one individual defects against another, the victim’s reputation should improve.

Moreover, the researchers also observe a fundamental trade-off. Norms that are particularly good in sustaining cooperation tend to be less robust with respect to noise (such as when reputations are shaped by third-party gossip).

Overall, this work is part of a bigger effort to understand key properties of social norms in a rigorous manner. These studies shed light on which ecological and social environments facilitate cooperation, and on the effects of social norms more generally.

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Credit of the article given to Max Planck Society

An attempt to settle a decade-long argument over a controversial proof by mathematician Shinichi Mochizuki has seen a war of words on both sides, with Mochizuki dubbing the latest effort as akin to a “hallucination” produced by ChatGPT,

An attempt to fix problems with a controversial mathematical proof has itself become mired in controversy, in the latest twist in a saga that has been running for over a decade and has seen mathematicians trading unusually pointed barbs.

The story began in 2012, when Shinichi Mochizuki at Kyoto University, Japan, published a 500-page proof of a problem called the ABC conjecture. The conjecture concerns prime numbers involved in solutions to the equation a + b = c, and despite its seemingly simple form, it provides deep insights into the nature of numbers. Mochizuki published a series of papers claiming to have proved ABC using new mathematical tools he collectively called Inter-universal Teichmüller (IUT) theory, but many mathematicians found the initial proof baffling and incomprehensible.

While a small number of mathematicians have since accepted that Mochizuki’s papers prove the conjecture, other researchers say there are holes in his argument and it needs further work, dividing the mathematical community in two and prompting a prize of up to $1 million for a resolution to the quandary.

Now, Kirti Joshi at the University of Arizona has published a proposed proof that he says fixes the problems with IUT and proves the ABC conjecture. But Mochizuki and his supporters, as well as mathematicians who critiqued Mochizuki’s original papers, remain unconvinced, with Mochizuki declaring that Joshi’s proposal doesn’t contain “any meaningful mathematical content whatsoever”.

Central to Joshi’s work is an apparent problem, previously identified by Peter Scholze at the University of Bonn, Germany, and Jakob Stix at Goethe University Frankfurt, Germany, with a part of Mochizuki’s proof called Conjecture 3.12. The conjecture involves comparing two mathematical objects, which Scholze and Stix say Mochizuki did incorrectly. Joshi claims to have found a more satisfactory way to make the comparison.

Joshi also says that his theory goes beyond Mochizuki’s and establishes a “new and radical way of thinking about arithmetic of number fields”. The paper, which hasn’t been peer-reviewed, is the culmination of several smaller papers on ABC that Joshi has published over several years, describing them as a “Rosetta Stone” for understanding Mochizuki’s impenetrable maths.

Neither Joshi nor Mochizuki responded to a request for comment on this article, and, indeed, the two seem reluctant to communicate directly with each other. In his paper, Joshi says Mochizuki hasn’t responded to his emails, calling the situation “truly unfortunate”. And yet, several days after the paper was posted online, Mochizuki published a 10-page response, saying that Joshi’s work was “mathematically meaningless” and that it reminded him of “hallucinations produced by artificial intelligence algorithms, such as ChatGPT”.

Mathematicians who support Mochizuki’s original proof express a similar sentiment. “There is nothing to talk about, since his [Joshi’s] proof is totally flawed,” says Ivan Fesenko at Westlake University in China. “He has no expertise in IUT whatsoever. No experts in IUT, and the number is in two digits, takes his preprints seriously,” he says. “It won’t pass peer review.”

And Mochizuki’s critics also disagree with Joshi. “Unfortunately, this paper and its predecessors does not introduce any powerful mathematical technology, and falls far short of giving a proof of ABC,” says Scholze, who has emailed Joshi to discuss the work further. For now, the saga continues.

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*Credit for article given to Alex Wilkins*

Region by region projections of how climate is likely to change over the coming decades help to make the prospect of global warming more tangible and relevant.

Picturing the climate we are likely to have with unabated increases in greenhouse gas concentrations in, say, Melbourne, Sydney, or the Murray Darling, lets us weigh up the costs and benefits of actions to reduce greenhouse gas emissions.

Regional projections also let us plan how to adapt to any unavoidable changes in our climate. Planning changes to farming practices, water supply or natural ecosystem management, for example, requires some idea of what our future regional climate is likely to be.

Here in Australia we have had a long history of national climate change projections. Since 1990, CSIRO has released five updates of projected changes in temperature, rainfall, extreme events and many other key aspects of our climate system.

CSIRO’s last release was done with the Bureau of Meteorology in 2007. It provided the most detailed product available up to that time.

This release included the innovation (a world first amongst national projections at the time) of providing probabilities for the projected changes.

Why modelling?

The complexity of the climate system means that we cannot simply extrapolate past trends to forecast future conditions. Instead, we use climate models developed and utilised extensively over recent decades.

These are mathematical representations of the climate systems based on the laws of physics.

Results from all of the climate modelling centres around the world are considered in preparing Australian projections. We place greatest weight on the models that are best in representing our historical climate.

Global climate modelling has continued to develop over recent years. Most of the modelling centres are now running improved versions of their models compared to what was available in 2007.

As part of an international coordinated effort, a new database of the latest climate model output is being assembled for researchers to use ahead of the next report of the Intergovernmental Panel on Climate Change (IPCC). It is many times richer than any previously available.

Analysing this massive resource will be a focus of research of a large number of scientists in CSIRO, BoM and the universities over the next few years.

Putting the models to good use

While the science has been developing, so have the demands of users of this projection information. Policymakers at all levels of government, natural resource planners, industry, non-government organisations and individuals all are placing demands on climate projection science. These are growing in volume and complexity.

For example, researchers want regionally specific scenarios for changes in the frequency of hot days, extreme rainfall, fire, drought, cyclones, hail, evaporation, sunshine, coral bleaching temperatures, ocean acidification and sea level rise.

This type of information is particularly useful for risk assessments that can inform policy development and implementation.

For example, assessing future climate risks to infrastructure can place quite different demands on climate projection science compared to, say, assessing risks to agricultural enterprises.

Given these developments, the time is coming for the Australian climate research community to update and expand their projections. Planning has begun for a release in 2014. This will be just after the completion of the next IPCC assessment.

At that time, Australians will have the latest climate projections for the 21st century for a range of factors, including sea levels, seasonal-average temperatures and rainfall, as well as extreme weather events.

Resources permitting, these new projections will also include online services which will enable users to generate climate scenarios to suit the specific needs of many risk assessments.

Finding out more about summer rainfall

As climate scientists start to analyse these new model data, a major focus of attention will be simulated changes to summer rainfall over Australia.

Models have consistently indicated a drying trend for the winter rainfall regions in southern Australia and this is a result which also aligns with other evidence such as observed trends.

On the other hand, models give inconsistent projections for summer rainfall change, ranging from large increase to large decrease. Researchers will be hoping to reduce this key uncertainty as they begin to analyse the results.

However, when it comes to projecting our future climate, there will always be some uncertainty to deal with.

Dealing with uncertainty

Climate projection scientists have to clearly convey the uncertainties while not letting these overwhelm the robust findings about regional climate change that the science provides.

Climate projection uncertainties can be presented in many different ways, such as through ranges of plausible change, as probabilistic estimates, or as alternative scenarios.

We shouldn’t necessarily be most interested in the most likely future. In some cases, it may be more prudent to plan for less likely, but higher risk, future climates.

It can be difficult to make a complex message as relevant as possible to a wide range of decision-makers. CSIRO climate scientists are tackling this by working with social scientists to help develop new and more effective communication methods. These should be ready in time for the next projections release.

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*Credit for article given to Penny Whetton*

Malawi introduced free primary education in 1994. This has significantly improved access to schooling. However, the country—which is one of the poorest in the world—still faces a high learning poverty rate of 87%. Learning poverty is a measure of a child’s inability to meet minimum proficiency in reading, numeracy and other skills at the primary school level. Malawi’s rate means that 87% of children in standard 4, at age 10, are unable to read. Only 19% of children aged between 7 and 14 have foundational reading skills and 13% have foundational numeracy skills. This leads to social and financial dependency. It also limits the extent to which individuals can actively participate in society. Children become especially vulnerable to pernicious social issues such as forced marriage, female genital mutilation, and child labor.

The primary education sector also has many challenges. These include overcrowded classrooms, limited learning materials, and a shortage of trained teachers.

There is a pressing need for innovative, transformative approaches to providing foundational education to meet the goals envisioned in Malawi 2063, the country’s long-term national plan. To accomplish this, the government of Malawi is using scientific evidence to enable meaningful and effective learning happen at scale.

This evidence has been generated in parallel by researchers from the University of Nottingham in the UK and the NGO Imagine Worldwide in the US and Africa. We have been testing the efficacy of an interactive educational technology (EdTech) developed by UK-based non-profit onebillion to raise foundational education by different groups of learners in Malawi.

The EdTech delivers personalized, adaptive software that enables each child to learn reading, writing and numeracy at the right level. Children work on tablets through a carefully structured course made up of thousands of engaging activities, games and stories. Over the past 11 years, we have built a complementary and robust evidence base focusing on different aspects of the software and program.

In 2013, I conducted the first pupil-level randomized control trial at a state primary school in Malawi’s capital city, Lilongwe. Randomized controlled trials are prospective studies that measure the effectiveness of a new intervention compared to standard practice. They are considered the gold standard in effectiveness research. We wanted to test whether the EdTech could raise young children’s numeracy skills. The study showed that after eight weeks of using the EdTech for 30 minutes a day, learners in grades 1–3 (aged 6 to 9) made significant improvements in basic numeracy compared to standard classroom practice. Teachers were also able to put the EdTech to use with ease.

Now, after many studies, Malawi’s government, in collaboration with Imagine Worldwide, is embedding the EdTech program in all state primary schools nationwide. This will serve 3.8 million children per year in grades 1–4 across all 6,000 state primary schools in Malawi.

Rigorous testing

After our initial 2013 study, we kept testing the EdTech through rigorous studies. Oneshowed that the EdTech program significantly raised foundational numeracy and literacy skills of early grade learners. Our results showed similar learning gains for girls and boys with the EdTech. This equalizes foundational education across gender.

Another study showed that children with special educational needs and disabilities could interact and learn with the EdTech, albeit at a slower pace than mainstream peers.

The EdTech wasn’t just tested in Malawi. We wanted to see if it could address learning poverty in different contexts, thus equalizing all children’s opportunities, no matter where they live.

Research in the UK demonstrated that the same EdTech raised the basic numeracy skills of children in the early years of primary schools compared to standard classroom instruction. It was also found to support numeracy acquisition by developmentally young children, including those with Down syndrome.

It was also shown to be effective in a bilingual setting. Brazilian children’s basic numeracy skills improved compared to standard practice after instruction with the EdTech delivered in either English, their language of instruction, or their home language, Brazilian-Portuguese.

Alongside the research from the University of Nottingham, Imagine Worldwide undertook a series of studies in Malawi and other countries to investigate how this EdTech could raise foundational skills over longer periods of time and in different languages and contexts, including refugee camps.

Imagine Worldwide conducted six randomized control trials, including two of the longest over eight months and two years. They showed robust learning gains in literacy and numeracy. They also found that children’s excitement about school, their attendance, and their confidence as learners improved.

The EdTech program also mitigated against learning loss during school closures. During Imagine’s 2-year randomized control trial in Malawi, program delivery was interrupted for seven months by COVID-related closures. Yet, results showed that children who had participated in the EdTech program prior to schools closing returned to school with higher achievement levels than their peers who had received standard instruction only.

Applying the evidence to policy

Malawi’s government was pleased with the early results and the program was expanded to about 150 schools, with the help of UK non-profit Voluntary Service Overseas. A national steering committee was established by Malawi’s government to monitor the program and review additional emerging research. In 2022 the Education Ministry formally launched the program through which the EdTech will be rolled out; it was introduced in 500 new schools at the start of the 2023/2024 school year, in September 2023.

To achieve the promise of the early research, ongoing implementation research and monitoring is helping to ensure program quality and impacts are sustained as it rolls out nationwide.

Strong evidence

Basic literacy and numeracy are the keys to unlocking a child’s potential—improving their health, wealth and social outcomes. Our combined research has shown that child-directed EdTech can deliver high-quality education for millions of marginalized children worldwide. The evidence is strong, diverse and replicable. Now governments need to follow the lead of Malawi to abolish learning poverty and make foundational education a reality for all children, everywhere.

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Credit of the article given to Nicola Pitchford and Dr. Karen Levesque, The Conversation

Tens of thousands of handwritten pages by one of the 20th century’s greatest mathematicians, Alexander Grothendieck, many of which the eccentric genius penned while living as a hermit, were unveiled in France on Friday.

The unpublished manuscripts, which veer from math to metaphysics, autobiography and even long musings on Satan, offer a unique insight into the enigmatic mind of the French mathematician, according to experts at the Paris library where they were donated.

Grothendieck, who died aged 86 in 2014, is considered by some to have revolutionized the field of mathematics in the way that Einstein did for physics. His work on algebraic geometry earned him the 1966 Fields Medal, known as the Nobel prize of the math world.

At that time Grothendieck was already a radical environmentalist and pacifist. But he withdrew from the world almost entirely in the early 1990s, in part to focus on what he referred to as his “scribblings”.

While living as a hermit in the southern French village of Lasserre he frantically wrote “Reflections on Life and the Cosmos,” one of the two main works added to the collection of the National Library of France (BnF) on Friday.

The massive tome includes 30,000 pages across 41 different volumes covering science, philosophy and psychology—all densely scribbled with a fountain pen.

The second work, “The Key to Dreams or Dialogue with the Good Lord,” is a typed manuscript in which he explores the interpretation of dreams.

These pages, which have previously circulated online, were written between 1987-1988.

‘Completely cut ties’

At that time, Grothendieck remained a professor at the University of Montpellier but had largely withdrawn from the mathematical community.

He became a recluse when he moved to Lasserre.

“He completely cut ties with his family, we could no longer communicate with him,” his daughter Johanna Grothendieck told AFP.

“When we sent him a letter, it was returned to sender,” said Johanna, a 64-year-old ceramic artist who traveled from southwest France to attend the ceremony at the library.

“Writing was his main activity,” she added.

Towards the end of Grothendieck’s life, a neighbour told his family that his health was deteriorating.

Johanna and one of her brothers were finally able to visit their father. It was than that they discovered “Reflections on Life and the Cosmos,” which was meticulously catalogued in his library.

In his 1997 will, Grothendieck left the early sections of the tome to the BnF. Now his children have donated the rest.

“It was an extremely important work in his eyes. He even wanted to create a foundation to look after it,” Johanna Grothendieck said.

‘Ghosts of his past’

Jocelyn Monchamp, a curator an the BnF, said the manuscripts were unique because they covered so many subjects at the same time yet formed a whole with “undeniable literary qualities”.

This is particularly the case for the autobiographical volume “Harvest and Sowing”, which depicts the author “in a metaphysical retreat,” she said.

Monchamp has spent a month poring over the writing, trying to decipher the dense fountain pen text.

“I became used to it,” she said, adding that at least Grothendieck methodically wrote the numbers and dates on all the pages.

In one of the sections, “Structures of the Psyche,” enigmatic diagrams translate psychology into the language of algebra.

In another, “The Problem of Evil,” Grothendieck muses over 15,000 pages on metaphysics and Satan.

One gets the feeling of a man “overtaken by the ghosts of his past,” Johanna Grothendieck said.

The mathematician’s father fled Germany during World War II, only to be handed by the Vichy France government to the Nazis and die at the Auschwitz concentration camp. Experts expect it will take some time to fully understand Grothendieck’s writing. On Friday, the collection joined the manuscript department of the BnF, where it will only be accessible to researchers.

During the donation ceremony, one of the volumes was placed in a glass case next to a manuscript by ancient Greek mathematician Euclid, considered the father of geometry.

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Credit of the article given to Juliette Collen

Calculus is the study of change. Calculus teaching methods, however, have changed little in recent decades. Now, FIU research shows a new model could improve calculus instruction nationwide.

A study published in Science shows a reimagined, innovative active learning approach to calculus instruction benefits all students. The model, developed at FIU, focuses on mastering different ways of thinking and solving problems—skills that are important beyond the classroom.

Rote memorization and large lecture halls have been replaced by active learning classrooms where students work collaboratively to solve problems. The result is greater learning outcomes and an understanding of calculus concepts, as well as better grades than their peers in traditional, lecture-based classes, according to the research.

“This large-scale study shows us what we’ve been seeing at FIU: If you put students in an interactive, active learning environment, they can and do learn significantly more, developing the ‘habits of mind’ they’ll use for a long time and throughout their careers,” said Laird Kramer, the study’s lead author and founding director of FIU’s STEM Transformation Institute.

Kramer and a team from the STEM Transformation Institute followed 811 FIU undergraduates enrolled in different sections of the same Calculus I course with two very different teaching methods—half of the sections were traditional lecture-based classes and the other half employed the evidence-based active learning model developed at FIU.

To see which group retained more information and better understood calculus concepts, the students were tested at the end of the course. Active learning classes had a higher average pass rate of 11%. Apply that to the roughly 300,000 students taking calculus each year in the U.S. and it could mean an additional 33,000 students passing calculus and getting closer to a STEM degree and career.

The active learning group’s learning gains cut across majors and academic paths and included underrepresented groups in STEM. This finding is significant since less than half of students entering universities as STEM majors actually graduate with a STEM degree. Failing calculus is a major reason.

“Calculus remains a critical step on the pathway to numerous STEM careers in engineering and the sciences,” said Michael J. Ferrara, Program Director at NSF Directorate of STEM Education. “This study makes a rigorous and compelling argument that active, student-centered calculus courses result in significantly greater learning and success outcomes when compared to more traditional approaches.

“These benefits are particularly profound for students from populations that have traditionally been underrepresented in the STEM workforce, which underscores how a more modern approach to teaching mathematics is critical as we look to nurture the full spectrum of STEM talent across the nation.”

Improving teaching methods in calculus means students are more likely to stay on track and stick with a STEM program. That, in turn, helps graduate more STEM professionals.

“Student success is FIU’s priority, as demonstrated by the development and successful implementation of active learning strategies in our calculus courses,” FIU Executive Vice President and Provost Elizabeth M. Béjar said. “This research builds on years of studying the positive impacts of active learning in the classroom to ensure students have the knowledge and skills they need to move through their STEM courses with confidence.”

FIU has led collaborative initiatives through its nationally recognized STEM Transformation Institute to improve learning. Research has informed the development and introduction of innovative instructional strategies for calculus, mathematics and other sciences and engineering. That’s led to significant increases in four-year graduation rates for STEM majors at FIU.

FIU’s active learning model is just as challenging and rigorous as a traditional lecture style, but more effective for the often incredibly complex process of learning and provides opportunities for different parts of the brain to engage and store information. Students learn by doing. Class time is collaboration time. In small groups, students work face-to-face developing and testing hypotheses. The goal is to learn to ask the right questions and look at problems in new ways—meaning, they think and act like mathematicians, engineers, scientists, doctors.

“This research began as an experiment to see if we could identify new ways of teaching coursework and give students an alternative way of learning the rigorous content in calculus,” said Mike Heithaus, executive dean of the College of Arts, Sciences & Education. “Based on prior research, we felt confident the active learning method would be effective. But even we were surprised at how much better students did in the active learning sections versus the traditional. As soon as we got these results, we began implementing these methods throughout our entire math curriculum.”

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Credit of the article given to Angela Nicoletti, Florida International University

It could be argued that the square is the ‘nicest’ rhombus, but the rhombus with angles of 60 and 120 degrees seems nicer still. One of the nice things about the 60/120 rhomb are the plane tilings that can be constructed from it. One of these tilings is the ‘tumbling blocks’ tiling shown at the top of the post, in which at some points you see ‘cubes’ (around the degree 3 vertices), while at others you see ‘flowers’ (around the degree 6 vertices). Because of the two different types of vertices, this is known as a quasi-regular rhombic tiling. (Another tiling that uses the 60/120 rhomb is this one.)

If you want to build a polyhedron that resembles the tumbling block tiling, one method is to reduce the number of petals in your flowers to 5, and then stretch your 60/120 rhombs until they are have angles of 63.435 and 116.565 degrees. Thirty of these rhombs arranged around vertices of degree 3 and 5 produces a quasi-regular polygon known as the rhombic triacontahedron.

The image above is of a model that was built using rhombic units printed onto card stock.

Despite the apparent ugliness of the 63.435 and 116.565 degree angle-measurements, our nice 60/120 rhomb has been, arguably, stretched into an even nicer one – a ‘golden rhombus,’ so called because the ratio of the diagonals is equal to the golden ratio.

The dual of the rhombic triacontahedron is the archemedian polyhedron known as the icosidodecahedron.

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*Credit for article given to dan.mackinnon*

Children’s interest in, and competence perceptions of, mathematics are generally quite positive as they begin school, but turn less positive during the first three years. Changes in interest and self-concept are also associated with each other. In other words, if a child’s interest fades, so does their competence perception, and vice versa.

This is shown by a recent study from Finland published in the British Journal of Educational Psychology that explores the development of children’s motivation for mathematics during the early school years and how that development is associated with their mathematics competence. The researchers followed nearly 300 children for three years.

“A significant observation was that both school beginners’ higher initial motivation, and less decline in motivation during the follow-up, predicted better competence in the third grade, after accounting for initial differences in competence,” says Professor Markku Niemivirta of the University of Eastern Finland.

There were no gender differences in school beginners’ motivation and competence, but at the end of the follow-up, girls’ motivation had, on average, declined more than that of boys.

Gendered development is starting to show

The study shows that children are able to assess their motivation for mathematics rather accurately already when beginning school. In addition, children’s assessments of their interest and competence are already differentiated, despite being closely related.

“It is only natural that children are more interested in things they feel good at. And vice versa, they may do better in something they’re interested in.”

On average however, school beginners’ positive motivation starts to decline during the early school years, and the scale of this decline is associated with later differences in competence. Although there are no gender differences in competence, girls’ more negative change in motivation on average reflects an unfortunate gendered development, the traces of which remain visible until much later.

Practices for maintaining interest and having experiences of success

Although the negative change observed in the study may partly reflect children’s more realistic self-assessment over time, the researchers suspect that a role is also played by mathematics gradually getting more difficult, and an emphasis being placed on performance.

“The observed association between a change in motivation and competence shows, however, the added value of positive interest and self-concept. It would be important to develop and apply teaching practices that support and maintain children’s interest in mathematics and strengthen their experiences of success,” Niemivirta says.

In the three-year study conducted by the Motivation, Learning and Well-being research collective, MoLeWe, children assessed their interest in, and competence perceptions of, mathematics annually. Mathematics competence was assessed by tests and teacher evaluations.

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Credit of the article to be given University of Eastern Finland

Intelligent tutoring systems for math problems helped pupils remain or even increase their performance during the pandemic. This is the conclusion of a new study led by the Martin Luther University Halle-Wittenberg (MLU) and Loughborough University in the U.K.

As part of their work, the researchers analysed data from 5 million exercises done by about 2,700 pupilsin Germany over a period of five years. The study found that particularly lower-performing children benefit if they use the software regularly. The paper was published in the journal Computers and Education Open.

Intelligent tutoring systems are digital learning platforms that children can use to complete math problems. “The advantage of those rapid learning aids is that pupils receive immediate feedback after they submit their solution. If a solution is incorrect, the system will provide further information about the pupil’s mistake.

“If certain errors are repeated, the system recognizes a deficit and provides further problem sets that address the issue,” explains Assistant Professor Dr. Markus Spitzer, a psychologist at MLU. Teachers could also use the software to discover possible knowledge gaps in their classes and adapt their lessons accordingly.

For the new study, Spitzer and his colleague Professor Korbinian Moeller from Loughborough University used data from “Bettermarks,” a large commercial provider of such tutoring systems in Germany. The team analysed the performance of pupils before, during and after the first two coronavirus lockdowns.

Their analysis included data from about 2,700 children who solved more than 5 million problems. The data was collected between January 2017 and the end of May 2021. “This longer timeframe allowed us to observe the pupils’ performance trajectories over several years and analyse them in a wider context,” says Spitzer.

The students’ performance was shown to remain constant throughout the period. “The fact that their performance didn’t drop during the lockdowns is a win in and of itself. But our analysis also shows that lower-performing children even managed to narrow the gap between themselves and higher achieving pupils,” Spitzer concludes.

According to the psychologist, intelligent tutoring systems are a useful addition to conventional math lessons. “The use of tutoring systems varies greatly from state to state. However, our study suggests that their use should be expanded across the board,” explains Spitzer. The systems could also help during future school closures, for example in the event of extreme weather conditions, transport strikes or similar events.

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Credit of the article to be given Tom Leonhardt, Martin Luther University Halle-Wittenberg

People love to complain about the weather – and especially about weather forecasters. But real, accurate forecasting beyond five to seven days is immensely complicated, due to the sheer volume of atmospheric processes and factors. Fortunately for us, advances in computing are making it possible for mathematicians, atmospheric scientists and statisticians to create “models of everything,” which may lead to accurate long-range weather forecasts.

NC State mathematician John Harlim is working on one such “model of everything,” specifically for longer-range weather and climate prediction. He’s part of a five-year project led by NYU’s Andrew Majda that is creating simpler, less expensive stochastic models (a model that includes random variables) for extended range weather and climate prediction.

One major stumbling block to extending and improving weather predictions beyond seven-day forecasts is a lack of understanding of the tropical weather dynamics that drive global weather patterns. The mix of factors in these patterns is amazingly complex. According to Harlim, “The dynamics in the tropics involve hierarchies of processes on both huge scales – like, 10,000 km – and much smaller scales over many months.  Physical processes in individual clouds can affect these larger processes in the long run.

“In terms of a model, then, you would have to resolve the entire globe in one-kilometer chunks, look at every possible weather pattern that could possibly occur over every moment given all sorts of variables, and then scale it up,” Harlim adds. Since this approach is very expensive, computationally speaking, Harlim and his colleagues hope to develop simpler, cheaper models that can capture tropical dynamics and understand their interactions with extratropical weather patterns.

Says Harlim, “Understanding tropical dynamics is the Holy Grail of atmospheric modeling, and if we’re successful, you’ll be able to get accurate weather forecasting for months, not just days, in advance.”

Atmospheric scientist Sukanta Basu is part of a team working on a “model of everything” for atmospheric turbulence by studying airflow over complex terrain, including islands. The team wants to understand how atmospheric turbulence affects laser propagations, but their work could have other applications as well – such as predicting microbursts for aircraft safety or estimating evaporation rates for water management in agriculture. And just like Harlim’s, Basu’s model will have to take a huge number of factors into account.

“We’ll be looking at 10-meter terrain maps, finding out every spatial location and time and what the atmospheric field may look like,” Basu says. “The amount of computational power needed is huge – one simulation can fill up a terabyte disk – so we’re looking at petascale computing, which can do a quadrillion operations per second. We didn’t have computing on this scale ten years ago, so projects like this were impossible.”

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Credit of the article given to Tracey Peake, North Carolina State University