Many of the toughest decisions faced by cancer patients involve knowing how to use numbers -- calculating risks, evaluating treatment options and figuring odds of medication side effects.

But for patients who aren't good at math, decision science research can offer evidence-based advice on how to assess numeric information and ask the right questions to make informed choices.

"The ability to understand numbers is associated with all kinds of positive health outcomes, including for cancer patients," said Ellen Peters, professor of psychology at The Ohio State University.

"The problem is that too many people aren't good with numbers or are afraid of math. But we're starting to figure out the best ways to help these patients so they aren't at a disadvantage when it comes to their treatment."

Peters, who is director of the Decision Sciences Collaborative at Ohio State, presented research on cancer patients' health and numeracy -- the ability to understand and use numbers -- Feb. 20 in Boston at the annual meeting of the American Association for the Advancement of Science.

Numerous studies have shown that people who are less numerate experience worse health outcomes. Peters says these are examples of the "tyranny of numbers." For example, diabetics with lower numeracy scores have higher blood sugar levels. And children with diabetes have higher blood sugar levels if their parents are less numerate.

A 2010 study by Peters shows how skill with numbers can affect breast cancer patients. In this research, women who had surgery for breast cancer were presented with options for further treatment, including hormonal treatment, chemotherapy, combined treatment or no treatment. The patients were given information, based on their characteristics, on how likely they were to survive 10 years for each possible treatment plan.

The patients were then asked to estimate, based on this information, what their own chances of survival were for 10 years with each treatment.

The patients who scored higher in numeracy were more pessimistic than the data suggested they should be. But their estimates of their own survival did vary based on the numbers they were given.

"For those who were less numerate, their survival estimates were pessimistic, but remained the same no matter what numbers they were presented. It was as if they didn't read the numbers at all," Peters said.

"This is critical. We were giving them information that should help them choose the best treatment, but they were ignoring it."

Other research shows that less numerate people "rely more on their emotions" to make health-related decisions. They are also more swayed by how information is presented to them rather than by the information itself, she said.

If a patient recognizes that he or she is not good with numbers, how can he or she cope? Peters said research suggests four strategies:

Ask for the numbers. This may seem counter-intuitive, but research backs it up. In one study, less numerate people were asked to estimate their risk of side effects from a medication. Some were given numeric information about the risks of a particular side effect, while others were told only that there was a risk. When they weren't given the numbers, 70 percent of less numerate people overestimated their risk, but only 17 percent did when given the numbers. They didn't do as well at evaluating risk as more numerate people when given the numbers, but they still did much better than when they didn't have them at all.

Ask what the numbers mean. Along with the numbers, doctors should be able to tell you what the numbers mean in practical terms. "If 80 percent of people are helped by this particular drug, is that good or bad? Ask your doctor to say if this is above or below average, if it is a fair, good or excellent treatment compared to other options," she said.

Ask for absolute risk. Saying that a particular drug doubles your risk of a dangerous side effect sounds scary. But this is what is called a relative risk. The absolute risk is more important. "If you're doubling your risk from 0.01 percent to 0.02 percent, that is much less threatening than if you are doubling from 10 percent to 20 percent," Peters said.

Cut down the choices. If you're given a bewildering list of choices for treatment, ask your doctor to choose the best two options to consider. "It is absolutely OK to tell the doctor that this is too complicated. You don't need to have doctors make a treatment decision for you, but they should be able to identify the most critical information for you to consider."

Health care providers should do a better job in presenting critical information to patients, Peters said. But when they don't, patients should ask for help.

"Numbers are important, whether you like them or not. And nowhere are they more important than when it comes to your health," she said.

Cognitive neuroscience researcher Joonkoo Park at the University of Massachusetts Amherst, who recently received a five-year, $751,000 faculty early career development (CAREER) grant from the National Science Foundation (NSF) to address basic research questions about how our brains process number and magnitude and how such processes give rise to more complex mathematical thinking, has co-authored a paper that reports this week where in the brain numerical quantity evaluation is processed.

In a series of experiments, Park and colleagues at Carnegie Mellon University used a psychophysical method that allowed them to "explore the extent to which the adult human subcortex contributes to number processing," in particular to distinguish between cortical and subcortical involvement. Details appear in the current online edition of Proceedings of the National Academy of Sciences.

As Park explains, people can tell at a quick glance the difference between 8 and 10 apples without counting them. "It's called number sense, and it's evolutionarily ancient," he notes. "That is, we share this ability with other primates, mammals, birds and fish. Even babies can discriminate between 10 and 20 dots well before they learn to count."

In the recent study led by Marlene Behrmann at Carnegie Mellon, Park and colleagues measured college students' performance in making numerical judgments on two dot array images presented very briefly one after another. Sometimes these two images were presented to a single eye (monocular presentation), and other times these two images were presented to different eyes (dichoptic presentation).

Under the monocular, but not the dichoptic, presentation, the visual information reaches the same subcortical structure. So, if participants do better in the monocular condition compared to the binocular condition, one can conclude that the subcortex is involved in numerical judgment. Indeed, the researchers found that participants performed better under monocular presentation when making the numerical judgment, especially when they discriminated two dot arrays with large ratios (4:1 or 3:1).

While it has been well established that humans share such a primitive numerical ability with other animals and even invertebrates, the brain basis of such an ability has been largely unknown, Park explains. This is because many other animals known to possess such a numerical ability have very limited computational power provided by the cortex. This new finding suggests that the coarse, primitive numerical ability shared across many species stems from the subcortex, an evolutionarily older brain structure.

With his CAREER grant, Park plans to study further questions that remain about the nature of this skill. Understanding mathematical ability is not only of interest to basic neuroscience but to educators who want to improve math education, he says. Similar to language development, the creation and use of mathematics is uniquely human, yet little is understood about the cognitive and neural processes that support it.

The neuroscientist points out that some research suggests that the sense of magnitude, which allow us to judge which is more and which is less without counting or using numerical symbols, provides a rudimentary foundation for mathematical thinking. But the picture is far from complete.

He says, "My research interest revolves around the neural basis of numerical cognition, its development, and individual differences, such as who is good at learning numbers and math, who is not, and why."

One controversy Park is particularly interested to investigate is whether "number sense" involves judgment about numbers or is derived from judgment about mass/size. "It's a technical distinction," he says, "but actually quite important from a theoretical point of view. It goes back at least to Kant, who argued that we have an innate sense of number, space and time. We and other creatures may have been born with this ability but how the sense of number emerges is still an open question."

Using a series of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) studies, Park plans to go beyond naming the brain region where magnitude processing takes place to identify the anatomy and function of neural pathways involved in magnitude processing and reveal neural mechanisms that support mathematical thinking. He says the EEG and fMRI techniques "counter each other's weaknesses" in pathway analysis.

In addition, Park plans to pursue practical applications. By relating results to individual differences in more complex mathematical ability, he hopes to provide new insights into the factors that underlie successful math education. "This is meaningful because a lot of recent studies have shown that young children's number sense is a reasonable predictor of their math skills. We'll study to what extent the brain's representation of magnitude is directly related to different aspects of more complex math ability such as geometry or arithmetic."

Park also plans to create a new course in cognitive neuroscience methods for undergraduates at UMass Amherst and will engage pre-college high school students in his research over summer. He hopes to engage underrepresented minority students, children and families from diverse backgrounds in the scientific research.

Researchers have developed a mathematical formula based on the rhythmic movement of a sperm's head and tail, which significantly reduces the complexities of understanding and predicting how sperm make the difficult journey towards fertilizing an egg.

Researchers at the Universities of York, Birmingham, Oxford and Kyoto University, Japan, found that the sperm's tail creates a characteristic rhythm that pushes the sperm forward, but also pulls the head backwards and sideways in a coordinated fashion.

Successful fertility relies on how a sperm moves through fluid, but capturing details of this movement is a complicated issue.

The team aim to use these new findings to understand how larger groups of sperm behave and interact, a task that would be impossible using modern observational techniques. The work could provide new insights into treating male infertility.

Dr Hermes Gadêlha, from the University of York's Department of Mathematics, said: "In order to observe, at the microscale, how a sperm achieves forward propulsion through fluid, sophisticated microscopic high precision techniques are currently employed.

"Measurements of the beat of the sperm's tail are fed into a computer model, which then helps to understand the fluid flow patterns that result from this movement.

"Numerical simulations are used to identify the flow around the sperm, but as the structures of the fluid are so complex, the data is particularly challenging to understand and use. Around 55 million spermatozoa are found in a given sample, so it is understandably very difficult to model how they move simultaneously.

"We wanted to create a mathematical formula that would simplify how we address this problem and make it easier to predict how large numbers of sperm swim. This would help us understand why some sperm succeed and others fail."

By analysing the head and tail movements of the sperm, researchers have now shown that the sperm moves the fluid in a coordinated rhythmic way, which can be captured to form a relatively simple mathematical formula. This means complex and expensive computer simulations are no longer needed to understand how the fluid moves as the sperm swim.

The research demonstrated that the sperm has to make multiple contradictory movements, such as moving backwards, in order to propel it forward towards the egg.

The whip-like tail of the sperm has a particular rhythm that pulls the head backwards and sideways to create a jerky fluid flow, countering some of the intense friction that is created due to their diminutive sizes.

Dr Gadêlha said: "It is true when scientists say how miraculous it is that a sperm ever reaches an egg, but the human body has a very sophisticated system of making sure the right cells come together.

"You would assume that the jerky movements of the sperm would have a very random impact on the fluid flow around it, making it even more difficult for competing sperm cells to navigate through it, but in fact you see well defined patterns forming in the fluid around the sperm.

"This suggests that to achieve sperm stirs the fluid around in a very coordinated way locomotion, not too dissimilar to the way in which magnetic fields are formed around magnets. So although the fluid drag makes it very difficult for the sperm to make forward motion, it does coordinate with its rhythmic movements to ensure that only a few selected ones achieve forward propulsion."

Now that the team has a mathematical formula that can predict the fluid movement of one sperm, the next step is to use the model for predictions on larger numbers of cells. They also believe that it will have implications for new innovations in infertility treatment.