Computers Math

There is now a new addition to the magnetic family: thanks to experiments at the Swiss Light Source SLS, researchers have proved the existence of altermagnetism. The experimental discovery of this new branch of magnetism is reported in Nature and signifies new fundamental physics, with major implications for spintronics.
Magnetism is a lot more than just things that stick to the fridge. This understanding came with the discovery of antiferromagnets nearly a century ago. Since then, the family of magnetic materials has been divided into two fundamental phases: the ferromagnetic branch known for several millennia and the antiferromagnetic branch. The experimental proof of a third branch of magnetism, termed altermagnetism, was made at the Swiss Light Source SLS, by an international collaboration led by the Czech Academy of Sciences together with Paul Scherrer Institute PSI.
The fundamental magnetic phases are defined by the specific spontaneous arrangements of magnetic moments — or electron spins — and of atoms that carry the moments in crystals. Ferromagnets are the type of magnets that stick to the fridge: here spins point in the same direction, giving macroscopic magnetism. In antiferromagnetic materials, spins point in alternating directions, with the result that the materials possess no macroscopic net magnetisation — and thus don’t stick to the fridge. Although other types of magnetism, such as diamagnetism and paramagnetism have been categorised, these describe specific responses to externally applied magnetic fields rather than spontaneous magnetic orderings in materials.
Altermagnets have a special combination of the arrangement of spins and crystal symmetries. The spins alternate, as in antiferromagnets, resulting in no net magnetisation. Yet, rather than simply cancelling out, the symmetries give an electronic band structure with strong spin polarization that flips in direction as you pass through the material’s energy bands — hence the name altermagnets. This results in highly useful properties more resemblant of ferromagnets, as well as some completely new properties.
A new and useful sibling
This third magnetic sibling offers distinct advantages for the developing field of next-generation magnetic memory technology, known as spintronics. Whereas electronics makes use only of the charge of the electrons, spintronics also exploits the spin-state of electrons to carry information.
Although spintronics has for some years promised to revolutionise IT, it’s still in its infancy. Typically, ferromagnets have been used for such devices, as they offer certain highly desirable strong spin-dependent physical phenomena. Yet the macroscopic net magnetisation that is useful in so many other applications poses practical limitations on the scalability of these devices as it causes crosstalk between bits — the information carrying elements in data storage.

More recently, antiferromagnets have been investigated for spintronics, as they benefit from having no net magnetisation and thus offer ultra-scalability and energy efficiency. However, the strong spin-dependent effects that are so useful in ferromagnets are lacking, again hindering their practical applicability.
Here enter altermagnets with the best of both: zero net magnetisation together with the coveted strong spin-dependent phenomena typically found in ferromagnets — merits that were regarded as principally incompatible.
“That’s the magic about altermagnets,” says Tomáš Jungwirth from the Institute of Physics of the Czech Academy of Sciences, principal investigator of the study. “Something that people believed was impossible until recent theoretical predictions is in fact possible.”
The search is on
Murmurings that a new type of magnetism was lurking began not long ago: In 2019, Jungwirth together with theoretical colleagues at the Czech Academy of Sciences and University of Mainz identified a class of magnetic materials with a spin structure that did not fit within the classic descriptions of ferromagnetism or antiferromagnetism.
In 2022, the theorists published their predictions of the existence of altermagnetism. They uncovered more than two hundred altermagnetic candidates in materials ranging from insulators and semiconductors, to metals and superconductors. Many of these materials have been well known and extensively explored in the past, without noticing their altermagnetic nature. Due to the huge research and application opportunities that altermagnetism poses, these predictions caused great excitement within the community. The search was on.

X-rays provide the proof
Obtaining direct experimental proof of altermagnetism’s existence required demonstrating the unique spin symmetry characteristics predicted in altermagnets. The proof came using spin- and angle resolved photoemission spectroscopy at the SIS (COPHEE endstation) and ADRESS beamlines of the SLS. This technique enabled the team to visualise a tell-tale feature in the electronic structure of a suspected altermagnet: the splitting of electronic bands corresponding to different spin states, known as the lifting of Kramers spin degeneracy.
The discovery was made in crystals of manganese telluride, a well-known simple two-element material. Traditionally, the material has been regarded as a classic antiferromagnet because the magnetic moments on neighbouring manganese atoms point in opposite directions, generating a vanishing net magnetisation.
However, antiferromagnets should not exhibit lifted Kramers spin degeneracy by the magnetic order, whereas ferromagnets or altermagnets should. When the scientists saw the lifting of Kramers spin degeneracy, accompanied by the vanishing net magnetisation, they knew they were looking at an altermagnet.
“Thanks to the high precision and sensitivity of our measurements, we could detect the characteristic alternating splitting of the energy levels corresponding to opposite spin states and thus demonstrate that manganese telluride is neither a conventional antiferromagnet nor a conventional ferromagnet but belongs to the new altermagnetic branch of magnetic materials,” says Juraj Krempasky, beamline scientist in the Beamline Optics Group at PSI and first author of the study.
The beamlines that enabled this discovery are now disassembled, awaiting the SLS 2.0 upgrade. After twenty years of successful science, the COPHEE endstation will be completely integrated into the new ‘QUEST’ beamline. “It was with the last photons of light at COPHEE that we made these experiments. That they gave such an important scientific breakthrough is very emotional for us,” adds Krempasky.
“Now that we have brought it to light, many people around the world will be able to work on it.”
The researchers believe that this new fundamental discovery in magnetism will enrich our understanding of condensed-matter physics, with impact across diverse areas of research and technology. As well as its advantages to the developing field of spintronics, it also offers a promising platform for exploring unconventional superconductivity, through new insights into superconducting states that can arise in different magnetic materials.
“Altermagnetism is actually not something hugely complicated. It is something entirely fundamental that was in front of our eyes for decades without noticing it,” says Jungwirth. “And it is not something that exists only in a few obscure materials. It exists in many crystals that people simply had in their drawers. In that sense, now that we have brought it to light, many people around the world will be able to work on it, giving the potential for a broad impact.” More

In the realm of quantum mechanics, the ability to observe and control quantum phenomena at room temperature has long been elusive, especially on a large or “macroscopic” scale. Traditionally, such observations have been confined to environments near absolute zero, where quantum effects are easier to detect. But the requirement for extreme cold has been a major hurdle, limiting practical applications of quantum technologies.
Now, a study led by Tobias J. Kippenberg and Nils Johan Engelsen at EPFL, redefines the boundaries of what’s possible. The pioneering work blends quantum physics and mechanical engineering to achieve control of quantum phenomena at room temperature.
“Reaching the regime of room temperature quantum optomechanics has been an open challenge since decades,” says Kippenberg. “Our work realizes effectively the Heisenberg microscope — long thought to be only a theoretical toy model.”
In their experimental setup, published in Nature, the researchers created an ultra-low noise optomechanical system — a setup where light and mechanical motion interconnect, allowing them to study and manipulate how light influences moving objects with high precision.
The main problem with room temperature is thermal noise, which perturbs delicate quantum dynamics. To minimize that, the scientists used cavity mirrors, which are specialized mirrors that bounce light back and forth inside a confined space (the cavity), effectively “trapping” it and enhancing its interaction with the mechanical elements in the system. To reduce the thermal noise, the mirrors are patterned with crystal-like periodic (“phononic crystal”) structures.
Another crucial component was a 4mm drum-like device called a mechanical oscillator, which interacts with light inside the cavity. Its relatively large size and design are key to isolating it from environmental noise, making it possible to detect subtle quantum phenomena at room temperature. “The drum we use in this experiment is the culmination of many years of effort to create mechanical oscillators that are well-isolated from the environment,” says Engelsen.
“The techniques we used to deal with notorious and complex noise sources are of high relevance and impact to the broader community of precision sensing and measurement,” says Guanhao Huang, one of the two PhD students leading the project.

The setup allowed the researchers to achieve “optical squeezing,” a quantum phenomenon where certain properties of light, like its intensity or phase, are manipulated to reduce the fluctuations in one variable at the expense of increasing fluctuations in the other, as dictated by Heisenberg’s principle.
By demonstrating optical squeezing at room temperature in their system, the researchers showed that they could effectively control and observe quantum phenomena in a macroscopic system without the need for extremely low temperatures. Top of Form
The team believes the ability to operate the system at room temperature will expand access to quantum optomechanical systems, which are established testbeds for quantum measurement and quantum mechanics at macroscopic scales.
“The system we developed might facilitate new hybrid quantum systems where the mechanical drum strongly interacts with different objects, such as trapped clouds of atoms,” adds Alberto Beccari, the other PhD student leading the study. “These systems are useful for quantum information, and help us understand how to create large, complex quantum states.” More

In supramolecular chemistry, the self-assembly state of molecules plays a significant role in determining their tangible properties. Controlling the self-assembled state has garnered significant attention as it can be exploited to design materials with desired properties like charge transport capability and fluorescence wavelength. For years, scientists have been trying to decipher how molecular organization impacts the properties of supramolecular assemblies that are in the nano (10 nm) and mesoscopic (10-1000 nm) scales. However, the study of structures with supramolecular polymer assemblies derived from the same monomer is often hindered by dynamic structural changes and immature control over self-assemblies.
A recent study published on January 1, 2024, in the Journal of the American Chemical Society, investigated the properties of one-dimensional mesoscale supramolecular assemblies of two different structures composed of the same luminescent molecule. It showed how two structures showed very different properties depending on whether they had their molecules arranged in a closed circular pattern or not. The study was led by Prof. Shiki Yagai from Chiba University, with Sho Takahashi, a doctoral course student at the Graduate School of Science and Engineering at Chiba University, as the first author. It also included Prof. Martin Vacha from the Department of Materials Science and Engineering at Tokyo Institute of Technology, and Dr. Hikaru Sotome from the Graduate School of Engineering Science at Osaka University as corresponding authors.
“The geometrical beauty of a circular structure, which has no termini and no corners, has fascinated people. Chemists have realized the synthesis of giant cyclic molecules using various approaches not only to create beautiful structures but also to compete in the elegance of the process of synthesizing such beautiful structures,” says Prof. Yagai, speaking of the inspiration behind this study. “The best example of nature utilizing the functional beauty of circular structures would be the light-harvesting antenna organ (LH2, LH1) of purple photosynthetic bacteria. LH2 has a beautiful circular structure due to the protein’s outstanding self-organizing ability, and it is thought that by arranging chlorophyll dyes in a circular array based on this framework, lean light collection and excitation energy transfer are achieved.”
Through the self-assembly of luminescent molecules synthesized based on their own molecular design, the team obtained a mixture of two one-dimensional π?conjugated molecular aggregates with different structures, namely terminus-free cyclic structures (toroids) and randomly coiled structures. The mixture exhibited low-energy and low-intensity luminescence.
The two structures were separated using a novel dialysis technique that exploited the difference in their kinetic stability. Post-separation, it was shown that the terminus-free closed toroidal structure led to higher energy and more efficient luminescence when compared to random coils. The team carried out ultrafast laser spectroscopy to investigate the mechanism of their topology-dependent fluorescence properties. The results indicated random coils with termini lost excitation energy due to defects generated by fluctuations in solution, unlike toroids that were not easily deformed and exhibited fluorescence without energy loss. Furthermore, it was found that in the mixed solution of toroids and random coils, the excitation energy was transferred from the toroid to the random coil due to the agglomeration of both assemblies, and only the random coil-derived luminescence was observed.
This study establishes morphological control of materials at the mesoscale as a possible new guideline for the design of functional materials. It also highlights that in the case of materials that are prone to supramolecular polymorphism, such as the toroid and random coil, it is essential to purify the assemblies before analyzing their photophysical properties. If not separated, the results obtained might only reflect biased properties instead of distinct ones due to energy transfer between different structures.
The researchers are hopeful that these insights can encourage the development of high-performance flexible devices using cyclic molecular assemblies. “We can gladly say that a correlation between structural beauty and functional beauty has been found here, even in meso-scale molecular assemblies. We believe that the insights from our study could help improve the performance of solar cell devices and light-emitting devices in the long run, thereby facilitating their widespread acceptability and enriching people’s lives along the way,” concludes Prof. Yagai. More

Chiral skyrmions are a special type of spin textures in magnetic materials with asymmetric exchange interactions. They can be treated as quasi-particles and carry integer topological charges. Scientists from Waseda University have recently studied the random walk-behaviors of chiral skyrmions by simulating their dynamics within a ferromagnetic layer surrounded by chiral flower-like obstacles. The simulations reveal that the system behaves like a topological sorting device, indicating its use in information processing and computing devices.
In nature, the collective motion of some birds and fish, such as flocks of starlings and shoals of sardines, respectively, can generate impressive dynamic phenomena. Their study constitutes active matter science, which has been a topic of great interest for the past three decades. The unique collective dynamics of active matter are governed by the motion of each individual entity, the interactions among them, as well as their interaction with the environment. Recent studies show that some self-propelling molecules and bacteria show circular motion with a fixed chirality (the property of an object where it cannot be superimposed upon its mirror image through any number of rotations or translations), which can enable the selection of molecules and bacteria with specific chirality based on their dynamics. However, there is a lack of research on active matter-like objects in non-biological magnetic and ferroelectric materials for electronic device applications.
In this regard, chiral skyrmions are promising. They are a special type of spin textures in magnetic materials with asymmetric exchange interactions, which can be treated as quasi-particles. They carry integer topological charges and have a fixed chirality of either +1 or -1.
Recently, a group of scientists, led by Professor Masahito Mochizuki from the Department of Applied Physics at Waseda University and including Dr. Xichao Zhang from Waseda University and Professor Xiaoxi Liu from Shinshu University, has extensively studied the active matter behaviors of chiral skyrmions. Their paper was made available online on December 6, 2023, and published in Volume 23, Issue 24 of the journal Nano Letters on December 27, 2023.
In this study, the scientists placed chiral skyrmions within chiral nanostructure obstacles in the shape of a simple chiral flower. They then studied the random-walk dynamics of the thermally activated skyrmion interacting with the chiral flower-like obstacle in a ferromagnetic layer, which could create topology-dependent outcomes. “Our research demonstrates for the first time that magnetic chiral skyrmions exhibit active matter-like behaviors even though they are of non-biological origin and even merely intangible spatial patterns,” says Prof. Mochizuki, highlighting the novelty of their study.
The skyrmion with chirality -1 has the potential to leave a left chiral flower, and the skyrmion with a chirality of +1 has the potential to leave a right chiral flower. The researchers conducted a series of simulations to observe how skyrmions would behave in both cases at different temperatures: 100 K, 150 K, 180 K, and 200 K. They set the simulation time as 500 ns, with a time step of 0.5 ns. The team found that depending on the combination of variables, the skyrmion either remains within the obstacle or escapes it. Since the motion of the skyrmion is due to temperature-dependent Brownian motion, which is disorderly in nature, this is an interesting case of getting an orderly result through disordered motion. Notably, this system can be used to develop a topological sorting device.
When asked about the long-term implications of their work, Prof. Liu remarks: “Our research results may be useful for building future information processing and computing devices with high storage density and low power consumption.”
“In the long term, they may provide guidelines for the design and development of non-conventional electronic and spintronic hardware, where the information is carried by topological spin textures in nanostructures. This achievement is expected to improve people’s lives as they would be able to process information in an energy-efficient manner, leading to a greener society,” concludes Dr. Zhang. More

As you scroll through any social media feed, you are likely to be prompted to follow or friend another person, expanding your personal network and contributing to the growth of the app itself. The person suggested to you is a result of link prediction: a widespread machine learning (ML) task that evaluates the links in a network — your friends and everyone else’s — and tries to predict what the next links will be.
Beyond being the engine that drives social media expansion, link prediction is also used in a wide range of scientific research, such as predicting the interaction between genes and proteins, and is used by researchers as a benchmark for testing the performance of new ML algorithms.
New research from UC Santa Cruz Professor of Computer Science and Engineering C. “Sesh” Seshadhri published in the journal Proceedings of the National Academy of Sciences establishes that the metric used to measure link prediction performance is missing crucial information, and link prediction tasks are performing significantly worse than popular literature indicates.
Seshadhri and his coauthor Nicolas Menand, who is a former UCSC undergraduate and masters student and a current Ph.D. candidate at the University of Pennsylvania, recommend that ML researchers stop using the standard practice metric for measuring link prediction, known as AUC, and introduce a new, more comprehensive metric for this problem. The research has implications for trustworthiness around decisionmaking in ML.
AUC’s ineffectiveness
Seshadhri, who works in the fields of theoretical computer science and data mining and is currently an Amazon scholar, has done previous research on ML algorithms for networks. In this previous work he found certain mathematical limitations that were negatively impacting algorithm performance, and in an effort to better understand the mathematical limitations in context, dove deeper into link prediction due to its importance as a testbed problem for ML algorithms.
‘”The reason why we got interested is because link prediction is one of these really important scientific tasks which is used to benchmark a lot of machine learning algorithms,” Seshadhri said. “What we were seeing was that the performance seemed to be really good… but we had an inkling that there seemed to be something off with this measurement. It feels like if you measured things in a different way, maybe you wouldn’t see such great results.”
Link prediction is based on the ML algorithm’s ability to carry out low dimensional vector embeddings, the process by which the algorithm represents the people within a network as a mathematical vector in space. All of the machine learning occurs as mathematical manipulations to those vectors.

AUC, which stands for “area under curve” and is the most common metric for measuring link prediction, gives ML algorithms a score from zero to one based on the algorithm’s performance.
In their research, the authors discovered that there are fundamental mathematical limitations to using low dimensional embeddings for link predictions, and that AUC can not measure these limitations. The inability to measure these limitations caused the authors to conclude that AUC does not accurately measure link prediction performance.
Seshadhri said these results call into question the widespread use of low dimensional vector embeddings in the ML field, considering the mathematical limitations that his research has surfaced on their performance.
Leading methods fall short
The discovery of AUC’s shortcomings led the researchers to create a new metric to better capture the limitations, which they call VCMPR. They used VCMPR to measure 12 ML algorithms chosen to be representative of the field, including algorithms such as DeepWalk, Node2vec, NetMF, GraphSage, and graph benchmark leader HOP-Rec, and found that the link prediction performance was worse using VCMPR as the metric rather than AUC.
“When we look at the VCMPR scores, we see that the scores of most of the leading methods out there are really poor,” Seshadhri said. “It looks like they’re actually not doing a good job when you measure things a different way.”
The results also showed that not only was performance lower across the board, some of the algorithms that performed worse than other algorithms when measured with AUC in turn performed better than the cohort with VCMPR, and vice versa.

Trustworthiness in machine learning
Seshadhri suggests that ML researchers use VCMPR to benchmark the link prediction performance of their algorithms, or at the very least stop using AUC as their measure. As metrics are so tightly connected to decision making in ML, using a flawed system to measure performance could lead to flawed decision making about which algorithms to employ in real world ML applications.
“Metrics are so closely tied to what we decide to deploy in the real world — people need to have some trust in that. If you have the wrong way of measuring, how can you trust the results?” Seshadri said. “This paper is in some sense cautionary: we have to be more careful about how we do our machine learning experiments, and we need to come up with a richer set of measures.”
In academia, using an accurate metric is crucial to creating progress in the ML field.
“This is in some sense a bit of a conundrum for scientific progress. A new result has to supposedly be better than everything previously, otherwise it’s not doing anything new — but that all depends on how you measure it.”
Beyond machine learning, there are researchers across a wide range of fields who use link prediction and ML to conduct their research, often with profound potential impact. For example, some biologists use link prediction to determine which proteins are likely to interact as a part of drug discovery. These biologists and other researchers outside of ML depend on the ML experts to create trustworthy tools, as they often cannot become ML experts themselves.
While he thinks these results may not be a huge surprise to those deeply involved in the field, he hopes that the larger community of ML researchers, and particularly graduate and Ph.D. students who use the current literature to learn best practices and common wisdom about the field, will take note of these results and take caution in their work. He sees this research that presents a skeptical view to be in somewhat contrast to a dominant philosophy in ML, which tends to accept a set of metrics and focuses on “pushing the bar” when it comes to progress in the field.
“It’s important that we have the skeptical view, are trying to understand deeper, and are constantly asking ourselves ‘Are we measuring things correctly?'”
This research was funded by the National Science Foundation and the Army Research Office. More

Soft robotics is the study of creating robots from soft materials, which has the advantage of flexibility and safety in human interactions. These robots are well-suited for applications ranging from medical devices to enhancing efficiency in various tasks. Additionally, using different forms of robotic movement may also serve us well in exploring the ocean or space, or doing certain jobs in those environments.
To broaden our understanding of locomotion, Richard Desatnik, who works in the labs of Philip LeDuc and Carmel Majidi at Carnegie Mellon University and collaborates with paleontologists from Europe, turns to the past. The team creates robots with the movement of ancient animals such as pleurocystitids, a sea creature that lived around 500 million years ago. Desatnik will present their findings from the process of building a soft robot based on pleurocystitids at the 68th Biophysical Society Annual Meeting, to be held February 10 — 14, 2024 in Philadelphia, Pennsylvania.
“We’ve learned a lot from modern creatures, but that’s only 1% of the animals that have existed during our planet’s history, and we want to see if there is something we can learn from the other 99% of creatures that once roamed the earth,” Desatnik said. He added, “there are animals that were very successful for millions of years and the reason they died out wasn’t from a lack of success from their biology — there may have been a massive environmental change or extinction event.”
Desatnik and colleagues started off with fossils of pleurocystitids, which are related to present-day sea stars and sea urchins but that had a muscular stem — a kind of tail — to move. They used CT scans to get a better idea of the 3D shape. Computer simulations suggested the ways it may have propelled itself through the water. Based on these data, they built a soft robot that mimics the prehistoric creature.
Their work suggests that a sweeping motion of the stem could have helped these animals glide along the ocean floor. They also found that a longer stem — which the fossil record suggests pleurocystitids developed over generations — could have made them faster without requiring much more energy.
These underwater soft robots may help in the future, “whether it’s geologic surveying, or fixing all the machinery that we have underwater,” Desatnik points out.
The researchers’ approach of using extinct animals to inform soft robotic design, which they call paleobionics, has the potential to further our understanding of evolution, biomechanics, and soft robot movements. More

With a brain the size of a pinhead, insects perform fantastic navigational feats. They avoid obstacles and move through small openings. How do they do this, with their limited brain power? Understanding the inner workings of an insect’s brain can help us in our search towards energy-efficient computing, physicist Elisabetta Chicca of the University of Groningen demonstrates with her most recent result: a robot that acts like an insect.
It’s not easy to make use of the images that come in through your eyes, when deciding what your feet or wings should do. A key aspect here is the apparent motion of things as you move. ‘Like when you’re on a train’, Chicca explains. ‘The trees nearby appear to move faster than the houses far away. Insects use this information to infer how far away things are. This works well when moving in a straight line, but reality is not that simple.
Moving in curves makes the problem too complex for insects. To keep things manageable for their limited brainpower, they adjust their behaviour: they fly in a straight line, make a turn, then make another straight line. Chicca explains: ‘What we learn from this is: if you don’t have enough resources, you can simplify the problem with your behaviour.’
Brains on wheels
In search of the neural mechanism that drives insect behaviour, PhD student Thorben Schoepe developed a model of its neuronal activity and a small robot that uses this model to navigate. All this was done under Chicca’s supervision, and in close collaboration with neurobiologist Martin Egelhaaf of Bielefeld University, who helped to identify the insects’ computational principles.
Schoepe’s model is based on one main principle: always steer towards the area with the least apparent motion. He had his robot drive through a long ‘corridor’ — consisting of two walls with a random print on it — and the robot centred in the middle of the corridor, as insects tend to do.
In other (virtual) environments, such as a space with obstacles or small openings, Schoepe’s model also showed similar behaviour to insects. ‘The model is so good’, Chicca concludes, ‘that once you set it up, it will perform in all kinds of environments. That’s the beauty of this result.’

Hardwired instead of learned
The fact that a robot can navigate in a realistic environment is not new. Rather, the model gives insight into how insects do the job, and how they manage to do things so efficiently. Chicca explains: ‘Much of Robotics is not concerned with efficiency. We humans tend to learn new tasks as we grow up and within Robotics, this is reflected in the current trend of machine learning. But insects are able to fly immediately from birth. An efficient way of doing that is hardwired in their brains.’
In a similar way, you could make computers more efficient. Chicca shows a chip that her research group has previously developed: a strip with a surface area that is smaller than a key on your keyboard. In the future, she hopes to incorporate this specific insect behaviour in a chip as well. She comments: ‘Instead of using a general-purpose computer with all its possibilities, you can build specific hardware; a tiny chip that does the job, keeping things much smaller and energy-efficient.’
Elisabetta Chicca is part of the Groningen Cognitive Systems and Materials Center (CogniGron). Its mission is to develop materials-centred systems paradigms for cognitive computing based on modelling and learning at all levels: from materials that can learn to devices, circuits, and algorithms. More

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 exploring 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 three hundred 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 points out.
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. More