One possible explanation lies in differences in how the brain selects and manages strategies for solving problems. A new study from Stanford University suggests that children with persistent math difficulties may have trouble adjusting their approach when faced with different mathematical challenges. The researchers also identified distinctive patterns of brain activity associated with these struggles.

The findings, published in JNeurosci, come from research led by Oliver Lasnick and colleagues at Stanford University. Their work focused on children with a condition that causes ongoing difficulty with mathematical problem solving (developmental dyscalculia). Although the condition has been recognized for years, scientists are still working to understand the specific thinking processes and brain mechanisms that contribute to it.

Why Some Children Struggle With Math Strategies

To investigate these challenges, the Stanford team studied 68 children between the ages of 8 and 10. They examined how the children approached math problems, how effectively they used different strategies, and how their brain activity related to their performance.

Solving a math problem often requires more than knowing numbers or remembering arithmetic facts. Children must also decide which approach will work best. For example, a child might count individual numbers to find an answer or use a more efficient method based on a familiar mathematical relationship. As problems become more difficult, the ability to recognize when a different strategy is needed can become increasingly important.

The researchers found that children with developmental dyscalculia were generally less effective at using different mathematical strategies than children without the condition. They took longer to shift from one method to another and were less responsive when the difficulty of a problem changed.

Another important difference involved learning to choose better strategies over time. While other children became more effective at selecting appropriate approaches, those with developmental dyscalculia did not show the same improvement. This suggests that their difficulties may involve not only performing calculations but also deciding how to approach a problem in the first place.

Brain Activity Reveals New Clues to Math Difficulties

The researchers also examined patterns of brain activity to better understand what might be happening behind these behavioral differences.

They discovered that activity within a particular brain system differed between children with developmental dyscalculia and those who were more skilled at selecting and using math strategies. These neural patterns were not simply unrelated differences. They could also predict how effectively children counted and how well they switched between approaches when solving problems.

The findings highlight the possible importance of several mental abilities that extend beyond mathematics itself. These include attention, memory, and cognitive flexibility, which is the ability to adjust thinking or behavior when circumstances change.

Such abilities are part of what researchers often call executive functions. These mental processes help people organize information, stay focused on a task, hold relevant details in mind, and change plans when an approach is not working. In mathematics, they can help a child keep track of numbers, compare possible solutions, and recognize when to try a different method.

The Stanford findings suggest that difficulties involving these processes may contribute to the development of dyscalculia. Differences in brain activity may also help explain why some children have persistent trouble choosing and changing problem-solving strategies.

However, the observed connections do not establish that the brain activity differences directly cause the condition. They provide new evidence about the cognitive and neural processes associated with these mathematical difficulties.

Understanding Why Math Struggles Differ Between Children

An important conclusion is that developmental dyscalculia does not appear to involve one simple problem shared by every affected child. Instead, different children may experience difficulties involving several interacting mental processes.

As Lasnick explains, “Importantly, this study also emphasizes the individual variability observed in dyscalculia, further demonstrating that the disorder reflects cognitive and neural dysfunction across multiple processes.”

By connecting children’s mathematical behavior with measurable differences in brain activity, the research offers a more detailed picture of why math can be persistently challenging for some students.

The findings also point toward the importance of looking beyond whether a child gets the correct answer. Understanding how children choose strategies, adapt to more difficult problems, and manage the mental demands of mathematics could ultimately help researchers develop better ways to identify and support those with developmental dyscalculia.

As a result, our picture of prehistoric life is filled with major gaps. Some geological periods and parts of the world have produced abundant fossils, giving scientists a detailed understanding of the life that existed there. Other periods and regions remain largely unexplored. Because fossil excavations require considerable time and resources, knowing where to search could make a major difference in uncovering new evidence of ancient life.

To help solve this problem, Thomas A. Neubauer of the Bavarian State Collections of Natural History (SNSB) and Mathias Harzhauser of the Natural History Museum in Vienna have developed a new tool for guiding fossil research. The two paleontologists analyzed the geographic distribution of fossil discoveries from animals that inhabited shallow marine environments over the past 540 million years. For the first time, they also mapped the regions of the world where fossil information is missing, providing a clearer picture of where future discoveries may be possible.

Mapping 540 Million Years of Ancient Marine Life

To build their map, the researchers examined records from the Paleobiology Database (PBDB), the world’s leading freely accessible repository of fossil information. The database contains a substantial portion of the paleontological findings published by scientists around the world.

Using these records, the team reconstructed where fossils from ancient shallow marine environments have been documented throughout Earth’s history. They also examined how fossil research has developed over decades and centuries, measuring how frequently investigations in different regions have produced new scientific information.

The researchers then compared these findings with geological information from the Macrostat database. This allowed them to assess not only where fossils have already been discovered, but also where suitable rock formations could provide opportunities to fill important gaps in the fossil record.

Where Earth’s Missing Fossils May Be Hiding

The analysis revealed a surprising imbalance in our understanding of prehistoric life. The Early Mesozoic (approx. 252 to 66 million years ago) and the Palaeozoic (approx. 539 to 252 million years ago) have already been studied extensively. According to the researchers, additional fossil discoveries from these periods are unlikely to produce a substantial increase in scientific knowledge in the near future.

The greatest opportunities for expanding the fossil record may instead lie in more recent geological history. Although scientists have already collected extensive evidence from the Cenozoic Era (beginning 66 million years ago), the analysis suggests that its shallow marine deposits still contain significant untapped potential for fossil discoveries.

To help researchers investigate this period, the team identified locations around the world where previously unknown fossil species are especially likely to be found. Crucially, these are also places where the appropriate geological layers are exposed or otherwise accessible, making actual discoveries possible.

A Treasure Map for Future Fossil Discoveries

By highlighting regions where important evidence may still be waiting, the new approach could help paleontologists plan more productive expeditions and make better use of limited research resources. Rather than concentrating on areas that have already been explored extensively, scientists can focus on locations with the greatest potential to reveal something new about Earth’s prehistoric ecosystems.

“The fact that many regions of the Earth remain unexplored offers hope for valuable new discoveries,” says SNSB paleobiologist Neubauer.

“But precisely because expanding the fossil record is quite challenging and progresses only slowly, our work can help researchers worldwide to focus their research specifically on these still largely unexplored areas. We provide a valuable guide for planning future projects and excavation campaigns. The same applies to the examination of existing museum collections awaiting scientific analysis. Through sensible prioritization, we can fill gaps in the fossil record strategically.”

The study identified a connection between estrogen receptor-negative, or ER-negative, breast cancer and two widely encountered chemicals: perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic acid (PFOS). Women with greater concentrations of these substances in their blood were more likely to develop this type of cancer. However, researchers found no clear link between either chemical and breast cancer risk overall.

Both substances belong to a large family of per- and polyfluoroalkyl substances, commonly called PFAS. These chemicals have been used in numerous everyday consumer products and are often described as “forever chemicals” because they resist breaking down in the environment. They can also accumulate in the human body and remain there for years.

“Women deserve clear answers about how chemicals in their environment may affect their health,” said HHS Secretary Robert F. Kennedy, Jr. “This NIH study links two forever chemicals to a higher risk of ER-negative breast cancer and demands further investigation. Under President Trump’s leadership, we will pursue the evidence, confront environmental health risks, and give women the information they need to protect their health.”

Why This Aggressive Breast Cancer Is Concerning

ER-negative breast cancer differs from more common forms of the disease because its tumor cells lack the receptors that allow estrogen to stimulate cancer growth. These cancers are often more aggressive and generally have poorer outcomes than tumors that respond to estrogen.

Despite their severity, researchers still have relatively little information about what makes someone more likely to develop ER-negative breast cancer. The new findings suggest that exposure to certain persistent environmental chemicals could be one contributing factor.

“Our findings, which we confirmed using a meta-analysis of prior research, indicate that certain legacy PFAS, including PFOA and PFOS, are associated with a higher risk of ER-negative breast cancer, a more aggressive tumor type with few known risk factors,” explained NIH Stadtman Investigator Alexandra White, Ph.D., who led the study.

The findings were published in the Journal of Clinical Oncology.

Higher Forever Chemical Levels Linked to Greater Cancer Risk

To investigate the possible connection, NIH scientists and their collaborators examined blood samples that had been collected years before participants received a cancer diagnosis. The researchers measured concentrations of 17 different PFAS chemicals, allowing them to compare earlier exposure levels with subsequent breast cancer outcomes.

The results revealed substantial differences for two chemicals. Women in the highest PFOA exposure group had a 67% higher rate of ER-negative breast cancer than women in the lowest group. The association was even stronger for PFOS, with the highest exposure group showing a 93% higher rate, nearly twice that of the lowest group.

These percentages represent relative differences between groups rather than the absolute probability that an individual woman will develop breast cancer. The findings also establish an association, not proof that the chemicals directly cause the disease.

The analysis used data from the Sister Study, a major research project conducted by NIH’s National Institute of Environmental Health Sciences (NIEHS). Between 2003 and 2009, the study enrolled 50,884 women ages 35-74 from across the United States and Puerto Rico.

All participants were free of breast cancer when they enrolled, although each had a full or half-sister who had already been diagnosed with the disease. For the PFAS investigation, researchers analyzed information from 1,609 women who subsequently developed breast cancer and a comparison group of 2,269 women.

Could Reducing PFAS Exposure Lower Cancer Risk?

Although PFAS can remain in the environment and the body for long periods, researchers emphasize that exposure is not necessarily unavoidable. The findings could eventually help identify new ways to reduce the risk of aggressive breast cancer.

“These findings matter for women’s health broadly,” said first author, Che-Jung Chang, Ph.D., who previously worked as an NIH research fellow and is now a researcher at DLH, a scientific research organization. “Although PFAS are persistent in the environment and in our bodies, exposure to them is still potentially modifiable, meaning people can take steps to reduce their exposure, and these findings could open new avenues for prevention.”

The researchers are also interested in understanding how these chemicals might influence cancer development. Because the strongest associations appeared in tumors that lack estrogen receptors, the findings suggest that PFAS could act through biological processes unrelated to hormonal signaling.

Potential explanations include changes in gene activity or alterations in the immune system. However, the study did not directly investigate these mechanisms, so their involvement remains uncertain.

Newer Forever Chemicals Raise Unanswered Questions

Although PFOA and PFOS have largely been phased out and replaced with other PFAS compounds, measurable amounts of both substances are still present in most people’s bodies. Their persistence means that exposure to these older chemicals remains a potential public health concern.

The researchers say additional investigations should focus on populations with greater PFAS exposure, as well as groups that experience higher rates of ER-negative breast cancer. Such research could help clarify the strength of the observed associations and identify whether certain populations face greater risks.

Scientists also need to determine whether the newer chemicals introduced as replacements for PFOA and PFOS carry similar health concerns.

“More research is needed, particularly evaluating the risk of breast cancer associated with newer replacement PFAS chemicals,” White said.

The findings add to growing questions about the long-term health effects of forever chemicals and highlight the importance of understanding how environmental exposures may contribute to aggressive forms of breast cancer.

The research received support from NIEHS grants Z01ES044005; Z1AES103332; and R01ES032831.