Previous research has shown that interventions grounded in behavioral science that target student motivation have been effective at increasing math scores, suggesting that taking a similar “behaviorally informed” approach with teachers might have a comparable effect.

Now, a collaborative study published in the Proceedings of the National Academy of Sciences, and led by researchers at the Behavior Change for Good Initiative (BCFG) at the University of Pennsylvania has found that behaviorally informed email messages slightly improved students’ math progress compared to control messages.

“Our results showed that simple, low-cost nudges can help teachers support student progress in math,” says Angela Duckworth, Rosa Lee and Egbert Chang Professor in Penn’s School of Arts & Sciences and the Wharton School, who led the study and co-directs BCFG. “These nudges worked across different school contexts, with effects persisting eight weeks after teachers stopped receiving the nudges.”

The key to this megastudy was the partnership with Zearn Math, a nonprofit educational platform. “Large-scale studies on teacher-focused interventions have been rare due to the high cost and logistical challenges involved. Thanks to our partnership with Zearn Math, we were able to overcome these challenges,” says co-author Dena Gromet, executive director of BCFG.

A megastudy is “a large-scale experiment in which multiple interventions are tested simultaneously on the same outcome, a tournament approach, if you will,” says co-author Katy Milkman, James G. Dinan Endowed Professor and professor of operations, information and decisions at the Wharton School and co-director of BCFG. “Because all interventions run concurrently and are compared to a common control group, this method allows for direct comparisons of their effectiveness.”

In one of the largest studies of its kind — involving more than 140,000 teachers and nearly 3 million elementary students — the researchers compared the impact of 15 different interventions to a reminder-only message.

“These messages were behaviorally informed, meaning they were based on prior insights from behavioral science. For instance, one intervention asked teachers to make a specific plan for how they would use Zearn Math that week, an approach backed by research showing that people are more likely to follow through when they make detailed plans. Another intervention appealed to teachers’ empathy for their students, which previous research has demonstrated is supportive of student success,” Duckworth says.

Co-authors Katy Milkman (left) and Angela Duckworth are committed to dig deeper into what makes these kinds of interventions work and how to make them even more effective over time.

Specifically, the research team found that, compared to standard email reminders, behaviorally informed email messages improved students’ math progress during the four-week intervention period by 1.89%. The most effective intervention, which increased student math progress by about 5.06%, encouraged teachers to log into Zearn Math weekly for an updated, personalized report on their students’ progress.

“One especially promising takeaway is that personalized nudges — those that referenced progress updates about a teacher’s own students — were more effective than nonpersonalized ones,” Duckworth says.

The researchers note that though they are promising, the effects were small. “These results suggest the need for more intensive support than the light-touch email nudges we tested,” Milkman says. “And they underscore how hard it is to change human behavior.”

These findings, Milkman says, suggest several additional valuable avenues for future research, including “more random-assignment field experiments to confirm the causal benefits of teacher-targeted nudges and studies to probe the longer-term effects of behaviorally-informed interventions.”

Additional research is also needed, Duckworth says, “to confirm and explain the benefits of referencing personalized data when nudging teachers. It may be that capitalizing on teachers’ intrinsic motivation to help their students is a distinct and potentially cost-effective approach that can complement other interventions, such as offering performance bonuses and other extrinsic incentives.”

Next steps for researchers are to dig deeper into what makes these kinds of interventions work and how to make them even more effective over time. Future studies are needed to look into the long-term effects of nudges and explore why some interventions are more effective than others.

“The better we understand why something works, the more powerfully we can use it to create positive change,” Duckworth says. “Ultimately, this line of research could help shape smarter, more effective education policies.”

Angela L. Duckworth is the Rosa Lee and Egbert Chang Professor in the Department of Psychology in the School of Arts & Sciences and in the Department of Operations, Information, and Decisions in the Wharton School at the University of Pennsylvania and faculty co-director of the Penn-Wharton Behavior Change for Good Initiative.

Katherine L. Milkman is the James G. Dinan Endowed Professor in the Department of Operations, Information, and Decisions in the Wharton School of the University of Pennsylvania and faculty co-director of the Penn-Wharton Behavior Change for Good Initiative.

Dena M. Gromet is the Executive Director of the Behavior Change for Good Initiative at the University of Pennsylvania.

Other authors of the new study are Ron Berman, Eugen Dimant, Ahra Ko, Joseph S. Kay, Youngwoo Jung, Madeline K. Paxson, Ramon A. Silvera Zumaran, and Christophe Van den Bulte of the University of Pennsylvania; Aden Halpern of the University of Pennsylvania and the University of Pittsburgh; Nina Mazar of Boston University; Colin F. Camerer and Marcos N. Gallo of the California Institute of Technology; Amy Lyon of Colby-Sawyer College; Mary C. Murphy of Indiana University; Kathryn M. Kroeper of Sacred Heart University; Benjamin S. Manning of the Massachusetts Institute of Technology; Ilana Brody, Hengchen Dai, and Hal E. Hershfield of the University of Los Angeles; Ariel Kalil, Michelle Michelini, and Susan E. Mayer of the University of Chicago; Matthew D. Hilchey, Philip Oreopoulos, Renante Rondina, and Dilip Soman of the University of Toronto; Elizabeth Canning of Washington State University; and Sharon E. Parker of Philadelphia.

Research reported in this article was supported in part by an anonymous donor to Zearn Math. Support for this research was also provided in part by the AKO Foundation, J. Alexander, M. J. Leder, W. G. Lichtenstein, and A. Schiffman and J. Schiffman.

In the shallow waters of the Lighthouse Reef Atoll, located 80 kilometers off the coast of the small Central American country of Belize, the seabed suddenly drops steeply. Resembling a dark blue eye surrounded by coral reefs, the “Great Blue Hole” is a 125-meter-deep underwater cave with a diameter of 300 meters, which originated thousands of years ago from a karst cave located on a limestone island. During the last ice age, the cave’s roof collapsed. As ice sheets melted and global sea level started to rise, the cave was subsequently flooded.

In the summer of 2022, a team of scientists — led by Prof. Eberhard Gischler, head of the Biosedimentology Research Group at Goethe University Frankfurt, and funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) — transported a drilling platform over the open sea to the “Great Blue Hole.” They then proceeded to extract a 30-meter sediment core from the underwater cave, which has been accumulating sediment for approximately 20,000 years. The core was subsequently analyzed by a research team from the universities of Frankfurt, Cologne, Göttingen, Hamburg, and Bern.

Coarse layers are a testimony to tropical storms

Some 7,200 years ago, the former limestone island of what is now Lighthouse Reef was inundated by the sea. The layered sediments at the bottom of the “Great Blue Hole” serve as archive for extreme weather events of the past 5,700 years, including tropical storms and hurricanes. Dr. Dominik Schmitt, a researcher in the Biosedimentology Research Group and the study’s lead author, explains: “Due to the unique environmental conditions — including oxygen-free bottom water and several stratified water layers — fine marine sediments could settle largely undisturbed in the ‘Great Blue Hole.’ Inside the sediment core, they look a bit like tree rings, with the annual layers alternating in color between gray-green and light green depending on organic content.” Storm waves and storm surges transported coarse particles from the atoll’s eastern reef edge into the “Great Blue Hole,” forming distinct sedimentary event layers (tempestites) at the bottom. “The tempestites stand out from the fair-weather gray-green sediments in terms of grain size, composition, and color, which ranges from beige to white,” says Schmitt.

The research team identified and precisely dated a total of 574 storm events over the past 5,700 years, offering unprecedented insights into climate fluctuations and hurricane cycles in the southwestern Caribbean. Instrumental data and human records available to date had only covered the past 175 years.

Rising incidence of storms in the southwestern Caribbean

The distribution of storm event layers in the sediment core reveals that the frequency of tropical storms and hurricanes in the southwestern Caribbean has steadily increased over the past six millennia. Schmitt explains: “A key factor has been the southward shift of the equatorial low-pressure zone. Known as the Intertropical Convergence Zone, this zone influences the location of major storm formation areas in the Atlantic and determines how tropical storms and hurricanes move and where they make landfall in the Caribbean.”

The research team was also able to correlate higher sea-surface temperatures with increased storm activity. Schmitt states: “These shorter-term fluctuations align with five distinct warm and cold climate periods, which also impacted water temperatures in the tropical Atlantic.”

Climate change results in greater storm activity

Over the past six millennia, between four and sixteen tropical storms and hurricanes passed over the “Great Blue Hole” per century. However, the nine storm layers from the past 20 years indicate that extreme weather events will be significantly more frequent in this region in the 21^st century. Gischler warns: “Our results suggest that some 45 tropical storms and hurricanes could pass over this region in our century alone. This would far exceed the natural variability of the past millennia.” Natural climate fluctuations cannot account for this increase, the researchers emphasize, pointing instead to the ongoing warming during the Industrial Age, which results in rising ocean temperatures and stronger global La Niña events, thereby creating optimal conditions for frequent storm formation and their rapid intensification.

MIT instructor Karol Bacik and his colleagues studied the flow of human crowds and developed a first-of-its-kind way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.

In a paper appearing in the Proceedings of the National Academy of Sciences, the researchers consider a common scenario in which pedestrians navigate a busy crosswalk. The team analyzed the scenario through mathematical analysis and simulations, considering the many angles at which individuals may cross and the dodging maneuvers they may make as they attempt to reach their destinations while avoiding bumping into other pedestrians along the way.

The researchers also carried out controlled crowd experiments and studied how real participants walked through a crowd to reach certain locations. Through their mathematical and experimental work, the team identified a key measure that determines whether pedestrian traffic is ordered, such that clear lanes form in the flow, or disordered, in which there are no discernible paths through the crowd. Called “angular spread,” this parameter describes the number of people walking in different directions.

If a crowd has a relatively small angular spread, this means that most pedestrians walk in opposite directions and meet the oncoming traffic head-on, such as in a crosswalk. In this case, more orderly, lane-like traffic is likely. If, however, a crowd has a larger angular spread, such as in a concourse, it means there are many more directions that pedestrians can take to cross, with more chance for disorder.

In fact, the researchers calculated the point at which a moving crowd can transition from order to disorder. That point, they found, was an angular spread of around 13 degrees, meaning that if pedestrians don’t walk straight across, but instead an average pedestrian veers off at an angle larger than 13 degrees, this can tip a crowd into disordered flow.

“This all is very commonsense,” says Bacik, who is a instructor of applied mathematics at MIT. “The question is whether we can tackle it precisely and mathematically, and where the transition is. Now we have a way to quantify when to expect lanes — this spontaneous, organized, safe flow — versus disordered, less efficient, potentially more dangerous flow.”

The study’s co-authors include Grzegorz Sobota and Bogdan Bacik of the Academy of Physical Education in Katowice, Poland, and Tim Rogers at the University of Bath in the United Kingdom.

Right, left, center

Bacik, who is trained in fluid dynamics and granular flow, came to study pedestrian flow during 2021, when he and his collaborators looked into the impacts of social distancing, and ways in which people might walk among each other while maintaining safe distances. That work inspired them to look more generally into the dynamics of crowd flow.

In 2023, he and his collaborators explored “lane formation,” a phenomenon by which particles, grains, and, yes, people have been observed to spontaneously form lanes, moving in single-file when forced to cross a region from two opposite directions. In that work, the team identified the mechanism by which such lanes form, which Bacik sums up as “an imbalance of turning left versus right.” Essentially, they found that as soon as something in a crowd starts to look like a lane, individuals around that fledgling lane either join up, or are forced to either side of it, walking parallel to the original lane, which others can follow. In this way, a crowd can spontaneously organize into regular, structured lanes.

“Now we’re asking, how robust is this mechanism?” Bacik says. “Does it only work in this very idealized situation, or can lane formation tolerate some imperfections, such as some people not going perfectly straight, as they might do in a crowd?”

Lane change

For their new study, the team looked to identify a key transition in crowd flow: When do pedestrians switch from orderly, lane-like traffic, to less organized, messy flow? The researchers first probed the question mathematically, with an equation that is typically used to describe fluid flow, in terms of the average motion of many individual molecules.

“If you think about the whole crowd flowing, rather than individuals, you can use fluid-like descriptions,” Bacik explains. “It’s this art of averaging, where, even if some people may cross more assertively than others, these effects are likely to average out in a sufficiently large crowd. If you only care about the global characteristics like, are there lanes or not, then you can make predictions without detailed knowledge of everyone in the crowd.”

Bacik and his colleagues used equations of fluid flow, and applied them to the scenario of pedestrians flowing across a crosswalk. The team tweaked certain parameters in the equation, such as the width of the fluid channel (in this case, the crosswalk), and the angle at which molecules (or people) flowed across, along with various directions that people can “dodge,” or move around each other to avoid colliding.

Based on these calculations, the researchers found that pedestrians in a crosswalk are more likely to form lanes, when they walk relatively straight across, from opposite directions. This order largely holds until people start veering across at more extreme angles. Then, the equation predicts that the pedestrian flow is likely to be disordered, with few to no lanes forming.

The researchers were curious to see whether the math bears out in reality. For this, they carried out experiments in a gymnasium, where they recorded the movements of pedestrians using an overhead camera. Each volunteer wore a paper hat, depicting a unique barcode that the overhead camera could track.

In their experiments, the team assigned volunteers various start and end positions along opposite sides of a simulated crosswalk, and tasked them with simultaneously walking across the crosswalk to their target location without bumping into anyone. They repeated the experiment many times, each time having volunteers assume different start and end positions. In the end, the researchers were able to gather visual data of multiple crowd flows, with pedestrians taking many different crossing angles.

When they analyzed the data and noted when lanes spontaneously formed, and when they did not, the team found that, much like the equation predicted, the angular spread mattered. Their experiments confirmed that the transition from ordered to disordered flow occurred somewhere around the theoretically predicted 13 degrees. That is, if an average person veered more than 13 degrees away from straight ahead, the pedestrian flow could tip into disorder, with little lane formation. What’s more, they found that the more disorder there is in a crowd, the less efficiently it moves.

The team plans to test their predictions on real-world crowds and pedestrian thoroughfares.

“We would like to analyze footage and compare that with our theory,” Bacik says. “And we can imagine that, for anyone designing a public space, if they want to have a safe and efficient pedestrian flow, our work could provide a simpler guideline, or some rules of thumb.”

This work is supported, in part, by the Engineering and Physical Sciences Research Council of UK Research and Innovation.

The peer-reviewed study found that electricity serving primary needs, such as heating or lighting, ultimately costs three times more than electricity for tertiary needs such as long-distance mobility — mostly due to taxation policies.

Further highlighting the ongoing social inequalities of fuel and related policies, the findings also demonstrate within the European Union (EU), the wealthiest 1% of all its population is responsible for 66% of the distance currently travelled by air. In fact, air travel is almost non-existent for 50%, and even quite limited for 90% of EU citizens the paper shows.

This 90% of people, therefore, emit less than 0.1 ton of CO₂ equivalent emissions per person, per year. Meanwhile the top 1% emit more than 22 tons per person/year.

Dr Jean-Baptiste Jarin, from the TREE laboratory (Energy and Environment Transitions) at the University of Pau and Pays de l’Adour, who carried out the research, used France as an example of current and future electricity use as a basis for similar countries worldwide — especially across Europe. And although based on EU regulations applied to France, the methodology and conclusions of this study can be transposed to other countries, and to other energy carriers based on electricity, such as hydrogen.

To evaluate the impacts of these electricity tax schemes and final prices, he collected data on electricity consumption for primary (household), secondary (electric vehicle local mobility) and tertiary (e-fuel long distance mobility) needs, and then compared electricity prices, before and after taxation.

Results demonstrate:

• Electricity serving household and local mobility needs cost 194 €/Mwh (euros per megawatt-hour). This was three times more than e-fuel (synthetic sustainable aviation fuels, that are renewable jet fuels produced from fossil-free electricity and recycled carbon dioxide) for aviation — 65.5 €/Mwh.
• Tax policies accounted for 120 €/Mwh of this cost in the case of household and local mobility fuel needs but only 11.2 €/Mwh in the case of aviation.
• Electro-intensive facilities that produce aviation e-fuel benefit from little or no taxation, and jet fuel is also untaxed.
• A round trip by air between Paris and New York for one person, when using this low carbon (which is designed to be more eco-friendly) e-fuel, still requires 7,300 kWh — exceeding the total annual primary and secondary needs (5,000 kWh) of an individual.

The European Union recently introduced the obligation to incorporate e-fuels for aviation as soon as 2030. In the UK, this obligation is as soon as 2028; in-line with its Renewable Transport Fuel Obligations Order 2024.

Dr Jarin has 25 years of experience in the aviation industry, prior to his career in academia. He recommends to key policymakers that ahead of any transformational policies and strategies, aimed at achieving low emissions in aviation, provisions should be made to “not interfere with energy justice.”

Additionally, he indicates that future taxation rates should become proportional to the final purpose of the energy, and this principle should be a “pillar of energy justice.”

Commenting, Dr Jarin says: “As e-fuel, along with other energy carriers based on electricity, is still within its infancy, it’s time for policy-makers to address the potential social injustices which may arise when formulating e-fuel policies.

“Electricity for basic needs such as heating or cooking benefits everyone but using it for air mobility mostly benefits the upper classes. Taxation rates should be proportional to the final purpose of the energy, and policies should drive not only production but also consumption, within a distributive justice perspective.”

Dr Jarin adds: “And that is what I find most worrying about the findings from within my paper, that, essentially, low carbon policies could foster energy injustice to people across society.

“Sadly, a massive production of e-fuel — especially when dedicated to aviation — could mean that tax inequalities, along with volume inequalities, spread the gap between the very wealthiest and the rest. That is why policy makers need to pay close attention.

“I feel that most people perhaps do not yet understand that energy, and therefore electricity, especially when low carbon, is not gifted!

“In the Global South, but also within the EU, during winters of 2022 and 2023, electricity bills were so high in most EU countries that people had to — and even were asked to by some — reduce heating and other appliances consumptions.”

Limitations of the paper include that while all EU countries follow the same tax directive on energies, the focus is limited to France and since electricity prices in Europe vary for each country, the results, when expressed in €/MWh, could be slightly different.

Also, carbon tax and redistribution mechanisms are not addressed in this study, and “where to tax within the value chain remains an important issue,” Dr Jarin adds.

“This,” Dr Jarin says, “is a particularly important issue as low carbon electricity with high load factor is a must to produce e-fuel.

“As such, the EU has significant assets to become a potential producer, rather than a potential importer.”