Celeste Kidd, University of California, Berkeley

I’m in a coffee shop when a young child dumps out his mother’s bag in search of fruit snacks. The contents spill onto the table, bench and floor. It’s a chaotic – but functional – solution to the problem.

Children have a penchant for unconventional thinking that, at first glance, can look disordered. This kind of apparently chaotic behavior served as the inspiration for developmental psychologist Jean Piaget’s best-known theory: that children construct their knowledge through experience and must pass through four sequential stages, the first two of which lack the ability to use structured logic.

Piaget remains the GOAT of developmental psychology. He fundamentally and forever changed the world’s view of children by showing that kids do not enter the world with the same conceptual building blocks as adults, but must construct them through experience. No one before or since has amassed such a catalog of quirky child behaviors that researchers even today can replicate within individual children.

While Piaget was certainly correct in observing that children engage in a host of unusual behaviors, my lab recently uncovered evidence that upends some long-standing assumptions about the limits of children’s logical capabilities that originated with his work. Our new paper in the journal Nature Human Behaviour describes how young children are capable of finding systematic solutions to complex problems without any instruction. https://www.youtube.com/embed/Qb4TPj1pxzQ?wmode=transparent&start=0 Jean Piaget describes how children of different ages tackle a sorting task, with varying success.

Putting things in order

Throughout the 1960s, Piaget observed that young children rely on clunky trial-and-error methods rather than systematic strategies when attempting to order objects according to some continuous quantitative dimension, like length. For instance, a 4-year-old child asked to organize sticks from shortest to longest will move them around randomly and usually not achieve the desired final order.

Psychologists have interpreted young children’s inefficient behavior in this kind of ordering task – what we call a seriation task – as an indicator that kids can’t use systematic strategies in problem-solving until at least age 7.

Somewhat counterintuitively, my colleagues and I found that increasing the difficulty and cognitive demands of the seriation task actually prompted young children to discover and use algorithmic solutions to solve it.

Piaget’s classic study asked children to put some visible items like wooden sticks in order by height. Huiwen Alex Yang, a psychology Ph.D. candidate who works on computational models of learning in my lab, cranked up the difficulty for our version of the task. With advice from our collaborator Bill Thompson, Yang designed a computer game that required children to use feedback clues to infer the height order of items hidden behind a wall, .

The game asked children to order bunnylike creatures from shortest to tallest by clicking on their sneakers to swap their places. The creatures only changed places if they were in the wrong order; otherwise they stayed put. Because they could only see the bunnies’ shoes and not their heights, children had to rely on logical inference rather than direct observation to solve the task. Yang tested 123 children between the ages of 4 and 10. https://www.youtube.com/embed/GlsbcE6nOxk?wmode=transparent&start=0 Researcher Huiwen Alex Yang tests 8-year-old Miro on the bunny sorting task. The bunnies are hidden behind a wall with only their sneakers visible. Miro’s selections exemplify use of selection sort, a classic efficient sorting algorithm from computer science. Kidd Lab at UC Berkeley.

Figuring out a strategy

We found that children independently discovered and applied at least two well-known sorting algorithms. These strategies – called selection sort and shaker sort – are typically studied in computer science.

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More than half the children we tested demonstrated evidence of structured algorithmic thinking, and at ages as young as 4 years old. While older kids were more likely to use algorithmic strategies, our finding contrasts with Piaget’s belief that children were incapable of this kind of systematic strategizing before 7 years of age. He thought kids needed to reach what he called the concrete operational stage of development first.

Our results suggest that children are actually capable of spontaneous logical strategy discovery much earlier when circumstances require it. In our task, a trial-and-error strategy could not work because the objects to be ordered were not directly observable; children could not rely on perceptual feedback.

Explaining our results requires a more nuanced interpretation of Piaget’s original data. While children may still favor apparently less logical solutions to problems during the first two Piagetian stages, it’s not because they are incapable of doing otherwise if the situation requires it.

A systematic approach to life

Algorithmic thinking is crucial not only in high-level math classes, but also in everyday life. Imagine that you need to bake two dozen cookies, but your go-to recipe yields only one. You could go through all the steps of making the recipe twice, washing the bowl in between, but you’d never do that because you know that would be inefficient. Instead, you’d double the ingredients and perform each step only once. Algorithmic thinking allows you to identify a systematic way of approaching the need for twice as many cookies that improves the efficiency of your baking.

Algorithmic thinking is an important capacity that’s useful to children as they learn to move and operate in the world – and we now know they have access to these abilities far earlier than psychologists had believed.

That children can engage with algorithmic thinking before formal instruction has important implications for STEM – science, technology, engineering and math –education. Caregivers and educators now need to reconsider when and how they give children the opportunity to tackle more abstract problems and concepts. Knowing that children’s minds are ready for structured problems as early as preschool means we can nurture these abilities earlier in support of stronger math and computational skills.

And have some patience next time you encounter children interacting with the world in ways that are perhaps not super convenient. As you pick up your belongings from a café floor, remember that it’s all part of how children construct their knowledge. Those seemingly chaotic kids are on their way to more obviously logical behavior soon.

Celeste Kidd, Professor of Psychology, University of California, Berkeley

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Valley Metro is officially shifting gears on high-capacity transit planning in west Phoenix following a Phoenix City Council vote earlier this year.

In a message to the public, Valley Metro said that after the Jan. 27, 2026 City Council decision to re-evaluate high-capacity transit options and prioritize a proposed West Phoenix corridor along Indian School Road, the agency will exit project development and the Federal Transit Administration Capital Investment Grant (CIG) process for the Capitol Extension (CAPEX) project.

What the City Council voted to do

According to Valley Metro, the Phoenix City Council voted to take another look at high-capacity transit options for west Phoenix and to prioritize studying a new corridor alignment along Indian School Road.

What Valley Metro is doing next

Valley Metro emphasized it still supports expanding high-capacity transit in west Phoenix, citing demand and mobility needs in the corridor. But the agency says it will now pivot away from CAPEX and toward the new study effort.

Key next steps Valley Metro outlined include:

• Exiting the CAPEX project development process and the federal CIG pipeline
• Advancing planning for the West Phoenix study along Indian School Road
• Centering comprehensive community engagement, including outreach to residents, business owners, and stakeholders along the corridor
• Working closely with the City of Phoenix on project development
• Coordinating with the Federal Transit Administration to explore funding opportunities

How to stay engaged

Valley Metro is encouraging residents to sign up for updates as the next phase moves forward at valleymetro.org/notices.

Dive into “The Knowledge,” where curiosity meets clarity. This playlist, in collaboration with STMDailyNews.com, is designed for viewers who value historical accuracy and insightful learning. Our short videos, ranging from 30 seconds to a minute and a half, make complex subjects easy to grasp in no time. Covering everything from historical events to contemporary processes and entertainment, “The Knowledge” bridges the past with the present. In a world where information is abundant yet often misused, our series aims to guide you through the noise, preserving vital knowledge and truths that shape our lives today. Perfect for curious minds eager to discover the ‘why’ and ‘how’ of everything around us. Subscribe and join in as we explore the facts that matter.  https://stmdailynews.com/the-knowledge/

Thomas Robertson, Macalester College

On April 9, 1940, Nazi tanks stormed into Denmark. A month later, they blitzed into Belgium, Holland and France. As Americans grew increasingly rattled by the spreading threat, a surprising place became crucial to U.S. national security: the vast, ice-capped island of Greenland.

The island, a colony of Denmark’s at the time, was rich in mineral resources. The Nazi invasions left it and several other European colonies as international orphans.

Greenland was essential for air bases as U.S. planes flew to Europe, and also for strategic minerals. Greenland’s Ivittuut (formerly Ivigtut) mine contained the world’s only reliable supply of the most important material you’ve probably never heard of: cryolite, a frosty white mineral that the U.S. and Canadian industries relied upon to refine bauxite into aluminum, and thus essential to assembling a modern air force.

A month after the Nazis seized Denmark, five American Coast Guard cutters set sail for Greenland, in part to protect the Ivittuut mine from the Nazis.

People sometimes forget that World War II was a dog-eat-dog struggle for resources – oil and uranium but also dozens of other materials, everything from rubber to copper. Without these strategic materials, no modern military could produce crucial new weapons such as tanks and airplanes. The resource struggle often started before actual fighting.

Foreign materials fueled American global power, but also raised tricky questions about access to resources and about sovereignty, just as the old European imperial order was being rethought. As in 2026, U.S. presidents had to skillfully balance force and diplomacy.

As a historian at Macalester College, I research how Americans shape environments around the world through their purchasing and national security needs, and how foreign landscapes enable and constrain American actions. Today, control of Greenland’s natural resources is again on an American president’s radar as demand for critical minerals rises and supply tightens.

During the spring of 1940, America and its European allies mapped out patterns of resource use and ideas of global interconnection that would shape the international order for decades. Greenland helped give birth to this new order.

Rethinking American vulnerability

On May 16, 1940, President Franklin Roosevelt addressed a joint session of Congress, including many “American first” isolationists wary of European entanglements. Roosevelt implored Americans to wake up to new threats in the world – to, in his words, “recast their thinking about national protection.”

New weapons, he warned, had shrunk the world, and oceans could no longer shield the United States. The nation’s fate was inextricably tied to Europe’s. Nothing showed this better than Greenland: “From the fiords of Greenland,” FDR warned, “it is four hours by air to Newfoundland; five hours to Nova Scotia, New Brunswick and to the province of Quebec; and only six hours to New England.”

But Greenland set off alarm bells for another reason. To protect itself in a dangerous world, Roosevelt famously called for the U.S. to hammer out 50,000 planes a year. But in 1938, America had produced only 1,800 planes.

To meet this ambitious goal, Roosevelt and his advisers knew that little could be done without Greenland. No Greenland, no cryolite. No cryolite, no massive American air force. Without cryolite, making 50,000 planes would be infinitely more difficult.

The age of alloys

Americans, National Geographic explained in 1942, lived in an “age of alloys.” Without aluminum alloys and other metallic mixtures, assembly lines churning out modern tanks, trucks and airplanes would grind to a halt. “More than any other struggle in history, this is a war of many metals, and the lack of a single one may be a blow far worse than the loss of a battle.”

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Few materials mattered more than aluminum. Light yet strong, aluminum formed 60% of a heavy bomber’s engines, 90% of its wings and fuselage, and all of its propellers.

But there was a problem: Refining aluminum from bauxite ore required working with dangerously hot metallic mixtures, over 2,000 degrees Fahrenheit (1,100 degrees Celsius). Cryolite solved the problem by reducing the temperature to a more manageable 900 F (480 C).

The Nazis’ chemical industry had found a substitute for cryolite using fluorspar, but the U.S. preferred the more resource-efficient cryolite and wanted to prevent the Germans from having it.

After the Nazis seized Denmark

Just days after German tanks rolled into Denmark in April 1940, Allied officials huddled to devise ways to protect Ivittuut’s magical mineral. On May 3, Danish Ambassador to the U.S. Henrik de Kauffmann, risking trial for treason, requested American assistance. On May 10, the U.S. Coast Guard Cutter Comanche departed New England for Ivittuut. Four others soon followed, one with guns for the mine’s defenders.

That very week in Washington, at a meeting of the Pan American Union, Roosevelt and his advisers spoke with hundreds of geologists and other representatives from Latin America — a resource-rich region that the U.S. saw as an answer to its strategic materials shortages.

Nervous about the history of U.S. imperial high-handedness in the region, some Latin Americans thought that their countries should seal off their resources to outside control, as Mexico had in nationalizing U.S. and European oil holdings in 1938.

With European empires crumbling, Roosevelt faced a delicate diplomatic dance with Greenland. He wanted to maintain the appearance of neutrality, keep skeptical isolationists in Congress from revolting and give no provocations to Latin American anti-imperialists to cut off resources. Crucially, he also needed to avoid giving the resource-starved Japanese a legal justification to seize the oil-rich Dutch East Indies, now Indonesia – another European colony orphaned by the Nazi invasion.

Roosevelt’s solution: enlist Coast Guard “volunteers” to guard Ivittuut. By the end of the summer, long before the U.S. officially entered the war, 15 sailors resigned from their ships and took up residence near the mine.

Seeing Greenland as crucial to US security

Roosevelt also got creative with geography.

In an April 12, 1940, press conference, just days after the Nazi invasion, he began to emphasize Greenland as part of the Western Hemisphere, more American than European, and thus falling under Monroe Doctrine protections. To calm fears in Latin America, U.S. officials recast the doctrine as development-oriented hemispheric solidarity.

Maj. William S. Culbertson, a former U.S. trade official speaking before the Army Industrial College in fall 1940, noted how the scramble for resources pulled the U.S. into a form of nonmilitary warfare: “We are engaged at the present time in economic warfare with the totalitarian powers. Publicly, our politicians don’t state it quite as bluntly as that, but it is a fact.” For the rest of the century, the front line was just as likely a far-off mine as an actual battlefield.

On April 9, 1941, exactly a year after the Nazis seized Denmark, Kauffmann met with U.S. Secretary of State Cordell Hull to sign an agreement “on behalf of the King of Denmark” placing Greenland and its mines under the U.S. security blanket. At Narsarsuaq, on the island’s southern tip, the U.S. began constructing an airbase named “Bluie West One.”

During the rest of World War II and throughout the Cold War, Greenland would house several important U.S. military installations, including some that forced Inuit families to relocate.

Critical minerals today

What transpired in Greenland in the 18 months before Pearl Harbor fit into a larger emerging pattern.

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As the U.S. ascended to global leadership and realized that it couldn’t maintain military dominance without wide access to foreign materials, it began to redesign the global system of resource flows and the rules for this new international order.

It rejected the Axis’ “might makes right” territorial conquest for resources, but found other ways to guarantee American access to critical resources, including loosening trade restrictions in European colonies.

The U.S. provided a lifeline to the British with the destroyers-for-bases deal in September 1940 and the Lend-Lease Act in March 1941, but it also gained strategic military bases around the world. It used aid as leverage to also pry open the British Empire’s markets.

The result was a postwar world interconnected by trade and low tariffs, but also a global network of U.S. bases and alliances of sometimes questionable legitimacy designed in part to protect U.S. access to strategic resources.

During the Cold War, these global resources helped defeat the Soviet Union. However, these security imperatives also gave the U.S. license for support of authoritarian regimes in places like Iran, Congo and Indonesia.

America’s voracious appetite for resources also often displaced local populations and Indigenous communities, justified by the old claim that they misused the resources around them. It left environmental damage from the Arctic to the Amazon.

Strategic resources have been at the center of the American-led global system for decades. But U.S. actions today are different. The cryolite mine was a working mine, rarer than today’s proposed critical mineral mines in Greenland, and the Nazi threat was imminent. Most important, Roosevelt knew how to gain what the U.S. needed without a “damn-what-the world-thinks” military takeover.

Thomas Robertson, Visiting Associate Professor of Environmental Studies, Macalester College

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Dive into “The Knowledge,” where curiosity meets clarity. This playlist, in collaboration with STMDailyNews.com, is designed for viewers who value historical accuracy and insightful learning. Our short videos, ranging from 30 seconds to a minute and a half, make complex subjects easy to grasp in no time. Covering everything from historical events to contemporary processes and entertainment, “The Knowledge” bridges the past with the present. In a world where information is abundant yet often misused, our series aims to guide you through the noise, preserving vital knowledge and truths that shape our lives today. Perfect for curious minds eager to discover the ‘why’ and ‘how’ of everything around us. Subscribe and join in as we explore the facts that matter.  https://stmdailynews.com/the-knowledge/

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